Brochantite, Cu4SO4(OH)6: OD character, polytypism and crystal structures
9
Introduction Brochantite, Cu 4 SO 4 (OH) 6 , is a widespread alteration phase, known in hundreds of mineralogical localities, typi- cally deriving from the alteration of copper sulphides. Woods & Garrels (1986) discussed the formation and the stability of the most common basic copper salts, such as azurite, malachite, atacamite and brochantite, also in rela- tion to various waters typically occurring at the Earth’s surface. They remarked that the above mentioned minerals react on the time-scale of days to the changing chemical environment and are therefore possibly useful as environ- mental indicators. Apart from its wide occurrence in natural environments, brochantite is a common constituent of the green patinas formed during the deterioration of copper and bronze manufacts (Gettens, 1970; Mattsson & Holm, 1982). Regarding this latter aspect, Mattsson & Holm (1982) remarked that brochantite is the most common alteration product in the urban/industrial environ- ment. The monoclinic symmetry of brochantite, P2 1 /a, a = 13.05 Å, b = 9.83, c = 5.85, b = 103°22’, was determined by Palache (1939), using X-ray and morphological studies on crystals from Tsumeb. Lauro (1939, 1941) performed rotating crystal studies, that confirmed Palache’s (1939) data for the Tsumeb crystals, and reported the cell parame- ters a = 12.75 Å, b = 9.82, c = 5.94 for brochantite from Sa Duchessa mine, Sardinia. The crystal structure of brochantite was firstly investi- gated, using the Tsumeb material, by Cocco & Mazzi (1959), who confirmed the space group P2 1 /a and found the unit cell parameters a = 13.08 Å, b = 9.85, c = 6.02, b = 103.4°. In agreement with the previous studies, they noticed a constant (100) twinning, giving rise to a diffrac- tion pattern which displayed orthorhombic symmetry and could be referred to a B centred pseudo-rhombic cell with A = 2a+c, B = b, C = c. Moreover, they made the following interesting observations on some peculiarities of the diffraction pattern: - While all the spots with l = 2n are sharp, the spots with l = 2n+1 appear to be diffuse in a well defined direction, so that they fade out in the [201] (axis A) direction. - Looking at the 0KL reflections (indices given on the basis of the pseudo-rhombic cell), one can observe that, besides the “normal” space group absences, all reflec- tions with K odd are absent (“non space-group absences”). Examining specimens of brochantite from Capo Calamita (Elba island, Tuscany, Italy), we observe that, whereas the reflections with l = 2n closely match the corresponding reflections of specimens from Tsumeb, the reflections with l = 2n+1 have different intensities Eur. J. Mineral. 2003, 15, 267-275 Dedicated to the memory of Luciano Ungaretti Brochantite, Cu 4 SO 4 (OH) 6 : OD character, polytypism and crystal structures STEFANO MERLINO * , NATALE PERCHIAZZI ** and DAVID FRANCO Dipartimento di Scienze della Terra, Via S.Maria 53, I-56126 Pisa, Italy Abstract: Single-crystal X-ray diffraction studies of brochantite demonstrate its Order-Disorder (OD) character. The OD struc- tures of the brochantite family can be described as built up by equivalent OD layers with symmetry Pn2 1 m. Two MDO polytypes are possible in this family, and both have been identified in specimens of brochantite from various localities. The MDO 1 polytype corresponds to “normal” brochantite P12 1 /a1, a = 13.140(2) Å, b = 9.863(2), c = 6.024(1), b = 103.16(3)°, whereas the newly discovered MDO 2 polytype is monoclinic, P2 1 /n11, a = 12.776(2) Å, b = 9.869(2), c = 6.026(1), a = 90.15(3)°. Given their polytypic relationships, the two MDO 1 and MDO 2 polytypes can be designated as brochantite-2M 1 and brochantite-2M 2 , respectively. The refined structure (R 1 = 0.049) of brochantite-2M 1 substantially agrees with the model of Cocco & Mazzi (1959) and confirms the assignment of the OH bands due to Schmidt & Lutz (1993). On the basis of the OD relationships between the two polytypes, a structural model for the newly discovered 2M 2 polytype was derived and subsequently refined up to R 1 = 0.062. Key-words: brochantite, OD structures, 2M 1 and 2M 2 polytypes, structure refinement. 0935-1221/03/0015-0267 $ 4.05 © 2003 E. Schweizerbart’sche Verlagsbuchhandlung. D-70176 Stuttgart DOI: 10.1127/0935-1221/2003/0015-0267 *Email: [email protected] **corresponding author: [email protected]
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Transcript of Brochantite, Cu4SO4(OH)6: OD character, polytypism and crystal structures
Introduction
Brochantite Cu4SO4(OH)6 is a widespread alterationphase known in hundreds of mineralogical localities typi-cally deriving from the alteration of copper sulphidesWoods amp Garrels (1986) discussed the formation and thestability of the most common basic copper salts such asazurite malachite atacamite and brochantite also in rela-tion to various waters typically occurring at the Earthrsquossurface They remarked that the above mentioned mineralsreact on the time-scale of days to the changing chemicalenvironment and are therefore possibly useful as environ-mental indicators Apart from its wide occurrence innatural environments brochantite is a common constituentof the green patinas formed during the deterioration ofcopper and bronze manufacts (Gettens 1970 Mattsson ampHolm 1982) Regarding this latter aspect Mattsson ampHolm (1982) remarked that brochantite is the mostcommon alteration product in the urbanindustrial environ-ment
The monoclinic symmetry of brochantite P21a a =1305 Aring b = 983 c = 585 b = 103deg22rsquo was determinedby Palache (1939) using X-ray and morphological studieson crystals from Tsumeb Lauro (1939 1941) performedrotating crystal studies that confirmed Palachersquos (1939)data for the Tsumeb crystals and reported the cell parame-
ters a = 1275 Aring b = 982 c = 594 for brochantite from SaDuchessa mine Sardinia
The crystal structure of brochantite was firstly investi-gated using the Tsumeb material by Cocco amp Mazzi(1959) who confirmed the space group P21a and foundthe unit cell parameters a = 1308 Aring b = 985 c = 602b = 1034deg In agreement with the previous studies theynoticed a constant (100) twinning giving rise to a diffrac-tion pattern which displayed orthorhombic symmetry andcould be referred to a B centred pseudo-rhombic cell withA = 2a+c B = b C = c Moreover they made the followinginteresting observations on some peculiarities of thediffraction pattern- While all the spots with l = 2n are sharp the spots with
l = 2n+1 appear to be diffuse in a well defined directionso that they fade out in the [201] (axis A) direction
- Looking at the 0KL reflections (indices given on thebasis of the pseudo-rhombic cell) one can observe thatbesides the ldquonormalrdquo space group absences all reflec-tions with K odd are absent (ldquonon space-groupabsencesrdquo)Examining specimens of brochantite from Capo
Calamita (Elba island Tuscany Italy) we observe thatwhereas the reflections with l = 2n closely match thecorresponding reflections of specimens from Tsumebthe reflections with l = 2n+1 have different intensities
Eur J Mineral2003 15 267-275
Dedicated to the memoryof Luciano Ungaretti
Brochantite Cu4SO4(OH)6 OD character polytypism and crystalstructures
STEFANO MERLINO NATALE PERCHIAZZI and DAVID FRANCO
Dipartimento di Scienze della Terra Via SMaria 53 I-56126 Pisa Italy
Abstract Single-crystal X-ray diffraction studies of brochantite demonstrate its Order-Disorder (OD) character The OD struc-tures of the brochantite family can be described as built up by equivalent OD layers with symmetry Pn21m Two MDO polytypesare possible in this family and both have been identified in specimens of brochantite from various localities
The MDO1 polytype corresponds to ldquonormalrdquo brochantite P121a1 a = 13140(2) Aring b = 9863(2) c = 6024(1) b =10316(3)deg whereas the newly discovered MDO2 polytype is monoclinic P21n11 a = 12776(2) Aring b = 9869(2) c = 6026(1)a = 9015(3)deg Given their polytypic relationships the two MDO1 and MDO2 polytypes can be designated as brochantite-2M1 andbrochantite-2M2 respectively
The refined structure (R1 = 0049) of brochantite-2M1 substantially agrees with the model of Cocco amp Mazzi (1959) andconfirms the assignment of the OH bands due to Schmidt amp Lutz (1993) On the basis of the OD relationships between the twopolytypes a structural model for the newly discovered 2M2 polytype was derived and subsequently refined up to R1 = 0062
Key-words brochantite OD structures 2M1 and 2M2 polytypes structure refinement
0935-1221030015-0267 $ 405copy 2003 E Schweizerbartrsquosche Verlagsbuchhandlung D-70176 StuttgartDOI 1011270935-122120030015-0267
Email merlinodstunipiit corresponding author nataledstunipiit
S Merlino N Perchiazzi D Franco
and positions in reciprocal space indicating a distinctpolytype with cell parameters very close to thosereported by Lauro (1939) for the Sa Duchessa brochan-tite
All the above mentioned peculiarities namely the ubiq-uitous twinning the disorder along a definite direction nonspace-group absences and polytypism clearly suggest theOD nature of the mineral A preliminary account of the ODfeatures of brochantite has already been given (Merlino1997) The aim of the present paper is to present a compre-hensive study of brochantite including its OD nature aswell as a definition of the main polytypes and details oftheir structural arrangements
OD nature of brochantite
As it is explained in the following brochantite displaysdiffraction features characteristic of OD structures(Dornberger-Schiff 1956 1964 Egrave urovi 1997) consistingof equivalent layers In such structures neighbouring layerscan be arranged in two or more geometrically and there-fore energetically equivalent ways different ways ofstacking neighbouring layers allow the existence of a seriesof both disordered and ordered (polytypes) sequences allof them constituting a family of OD structures Thesymmetry properties common to all the members of an ODfamily are described by the lsquoOD groupoid familyrsquo symbolwhich reports the partial symmetry operations (POs) thattransform each layer into itself (l operations) or into anadjacent layer (s operations) Considering the infinitenumber of ordered and disordered members of an ODfamily OD theory pays special attention to the so-calledMDO (Maximum Degree of Order) polytypes In suchpolytypes there are not only pairs of layers but possiblyalso tripleshellip n-tuples of layers that are geometricallyequivalent MDO polytypes are the simplest of the possibleordered sequences and usually correspond to the mostfrequently occurring polytypes in the family
The crystal structure of brochantite determined byCocco amp Mazzi (1959) can be described in terms of struc-tural layers (Fig 1) with basic vectors b c (translationvectors of the layer with b = 985 Aring c = 602) and ao[ao = (asin b)2 = 636 Aring] and layer group symmetryP(n)21m (the parentheses in the first position indicate thatthe basic vector a0 is not a translation vector)
Adjacent layers are related by screw axes along a0 thedirection of missing periodicity with translational compo-nent a0 (22 operations) by glide planes normal to b withtranslational component a0+c4 (n122 operators) and screwaxes parallel to c with translational component -c4 (2-12operators)
Therefore the OD groupoid family symbol forbrochantite is
P (n) 21 m
[ (22) n122 2-12 ] 1
It is just the presence of a mirror plane in the singlebuilding layer that make it possible for adjacent layers tobe related through n122 (and through 2-12 too) as well asthrough n-122 (and through 212 too) operations the pairsof layers obtained in both ways are geometrically equiva-lent
Two MDO polytypes are possible namely MDO1 corre-sponding to a regular sequence of n122 n122 n122operations (or 2-12 2-12 2-12) and MDO2 with regularalternation of n-122 n122 n-122 n122 operations (or
268
Fig 1 A pair of adjacent layers and their l-POs and s-POs as seenalong b White tetrahedra indicate sulphate groups The twodistinct copper atoms are represented in square coordination(chains of edge-sharing squares running along c) and lsquosqueezedrsquotetrahedral coordination (chains of corner-sharing lsquosqueezedrsquotetra-hedra running along c)
1It may be useful to recall that the symbols of the partial operations are in keeping with the symbols used for normal space group opera-tions Therefore 22 in the first position is the symbol for a twofold rotation with translational component a0 whereas n122 in the secondposition is the symbol for a glide normal to b with translational component c4+a0 and 2-12 in the third position is the symbol for atwofold rotation with translational component ndashc4
212 2-12 212 2-12) Their dimensions and symmetrydepend on the dimensions and symmetry of the singlelayer as well as on the specific sequence of operationsgiving rise to them
In MDO1 (Fig 2a) the partial s-operation n122 (withtranslational component a0+c4) is constantly applied andbecomes a true glide valid for the whole structure whichhas a translation vector a1 = 2a0+c2 (the other translationvectors are b1 = b c1 = -c where a0 b c are the basicvectors of the single layer) Similarly the l operation 21and the s-operation ndash1 are total operations valid for thewhole structure The resulting space group for MDO1 isP121a1 with cell parameters a1 1307 Aring b1 985c1 602 b1 1033deg corresponding to the polytypestudied by Cocco amp Mazzi (1959) The sequence n-122n-122 n-122 (or 212 212 212) corresponds to thesame structural arrangement (MDO1rsquo) in (100) twinningrelationships
In MDO2 (Fig 2b) due to the relative position of thelayers the l operation n normal to a0 becomes a total oper-ation and the 22 s-operation is continued through the wholesequence of layers becoming a 21 total operation in a struc-ture with a2 = 2a0 (the other translation vectors are b2 = bc2 = -c) space group symmetry P21n11 and cell parame-ters a2 1272 Aring b2 985 c2 602 a2 90deg
According to the nomenclature established by Guinieret al (1984) the MDO1 and MDO2 polytypes should bedenoted as brochantite-2M1 and brochantite-2M2 respec-tively both presenting two layers within the unit a transla-tion Distinction can be made between the two polytypesthrough their diffraction pattern in which we found asusual in OD structures two distinct classes of reflectionsnamely the family and the characteristic reflections Thefamily reflections which in the present family have evenl indices are independent from the stacking of the layersand remain sharp and unchanged in all the ordered anddisordered structures of the family These reflections corre-spond to the so-called lsquofamily structurersquo which is closelyrelated to the structures of the family and displays in thepresent case space group symmetry Pbnm witha = 1272 Aring b = 985 and c = 301
The characteristic (non-family) reflections (those withodd l indices) depend both in position and intensity on thestacking of layers and consequently are typical of eachsequence They may be more or less diffuse sometimesappearing as continuous streaks
A detailed discussion of the diffractional effects in thewhole brochantite family is presented in Appendix Theresults obtained in Appendix were helpful for distin-guishing the polytypes occurring in the examined speci-mens as discussed in the following section
Experimental
A systematic X-ray diffraction study of brochantitecrystals from specimens preserved in the mineralogicalcollection of the Natural History Museum of PisaUniversity was carried out using the Weissenberg tech-nique All the examined crystals showed the presence of
variable degrees of structural disorder and the MDO1 poly-type was found in the majority of the specimens On theother hand apart from the Capo Calamita crystalsevidence for the existence of MDO2 polytype was found inthe diffraction patterns of crystals from the Italian localitiesof Trentin mine (Veneto) Sa Duchessa mine (Sardinia)and Val Fucinaia (Tuscany) These patterns correspond tothe overlapping of the reciprocal lattices of the MDO1MDO1rsquo and MDO2 polytypes and point to the co-existenceof the two distinct MDO polytypes in those specimens
Intensity data were collected with a Siemens P4 four-circle diffractometer from crystals previously tested usingWeissenberg photographs and made up of almost pureMDO1 (Val Fucinaia) and MDO2 (Capo Calamita) poly-types experimental details and crystallographic data forboth structural studies are given in Table 1
In the structure refinement of MDO1 polytype we usedas a starting model the results of the study by Cocco amp
OD character of brochantite 269
Fig 2 The crystal structures of MDO1 (a) and MDO2 (b) poly-types as seen along b In both cases the sequences of 212 and 2-
12 s-operations are indicated The other indicated l- ands-operations are just those which become total symmetry opera-tions in both polytypes
S Merlino N Perchiazzi D Franco270
Table 1 Crystal data and refinement details for MDO1 and MDO2 brochantite polytypes
Wavelength 071073 Aring MDO1 polytype MDO2 polytypeLocality Val Fucinaia Capo CalamitaMonoclinic P 1 21a 1 P 21n 1 1Unit cell dimensions a = 13140(2) Aring 12776(2) Aring
b = 9863(2) Aring 9869(2) Aringc = 6024(1) Aring 6026(1) Aringb = 10316(3) deg a = 9015(3) deg
Crystal size 014 014 003 mm 009 008 004 mmq range for data collection 4 to 5128 deg 4 to 50 degIndex ranges -7 pound h pound 7 -11 pound k pound 1 -1 pound l pound 15 -1 pound h pound 11 -1 pound k pound 15 -7 pound l pound 7Reflections collected unique 1643 1239 [Rint = 00415] 1821 1334 [Rint = 00638]Absorption correction y-scan on 14 reflections on 12 reflectionsRefinement method Full-matrix least-squares on F2
Final R1 indexa [Fo gt4s( Fo)] R1 = 00488 (831 refl) R1 = 00619 (607 refl) Data restraints parameters 1239 6 137 1334 0 86Goodness-of-fita (all data) 1071 0893wR2 a (all data) 01481 02084Largest diff peak and hole 119 and -128 e Aring-3 257 and ndash112 e Aring-3
Note a Goodness-of-fit = [S [w(Fo2-Fc
2)2](N-P)]12 where N P are the numbers of observations and parametersrespectively R1 = S Fo Fc S Fo w R2 = [S[w(Fo
2-Fc2)2 ] S[ w(Fo
2)2]]12 w = 1 [s 2 (Fo2) +
(00243Q)2 + 057Q] where Q = [MAX(Fo20) + 2Fc
2] 3
Table 2 a) Final positional and displacement parameters (Aring2) for MDO1 polytype b) calculated positional coordinates and final posi-tional and displacement parameters (Aring2) for MDO2 polytype
a) MDO1 polytype
x y z Ueq
Cu1 02061(1) 09911(2) 04799(3) 00207(4)Cu2 02023(1) 09908(3) -00237(3) 00244(5)Cu3 01181(1) 02614(2) 01819(3) 00185(4)Cu4 01199(1) 02571(2) 06848(3) 00197(4)S 03877(2) 01989(4) 03167(5) 00233(7)O1 00936(6) 01325(9) 0417(1) 0022(2)O2 00827(6) 01345(9) -0082(1) 0022(2)O3 01590(6) 03823(9) 0454(1) 0021(2)O4 01556(6) 03826(9) -0052(1) 0020(2)O5 02559(6) 00936(9) 0758(1) 0022(2)O6 01428(6) 08991(9) 0198(1) 0023(2)O7 02797(6) 0145(1) 0260(1) 0027(2)O8 03822(7) 0351(1) 0312(2) 0028(2)O9 04435(6) 0149(1) 0142(1) 0029(2)O10 04415(6) 0152(1) 0547(1) 0026(3)
b) MDO2 polytype
x y z x y z Ueq or Uiso
Cu1 02061 09911 03768 Cu1 02066(2) 09902(3) 03770(5) 00118(7)Cu2 02023 09908 -01248 Cu2 02019(2) 09906(3) -01249(5) 00135(7)Cu3 01181 02608 01228 Cu3 01183(2) 02608(3) 01261(4) 00111(6)Cu4 01199 02571 06249 Cu4 01205(2) 02569(3) 06258(4) 00109(7)S 03877 01989 01229 S 03881(4) 01991(5) 01226(9) 0015(1)O1 00936 01325 03704 O1 0091(1) 0130(2) 0374(2) 0016(4)O2 00827 01345 -01229 O2 0084(1) 0136(1) -0125(2) 0009(3)O3 01590 03823 03759 O3 0158(1) 0381(2) 0374(2) 0014(4)O4 01556 03826 -01298 O4 0158(1) 0385(2) -0122(2) 0012(3)O5 02559 00936 06300 O5 0258(1) 0094(2) 0628(3) 0023(4)O6 01428 08991 01264 O6 0142(1) 0897(2) 0124(2) 0019(3)O7 02797 01451 01205 O7 0275(1) 0141(2) 0126(3) 0023(4)O8 03822 03510 01208 O8 0383(1) 0352(2) 0125(2) 0016(3)O9 04435 01488 -00799 O9 0442(1) 0147(2) -0084(3) 0023(4)O10 04415 01523 03267 O10 0443(1) 0150(2) 0329(3) 0020(3)
Mazzi (1959) After some isotropic refinement cyclesanisotropic displacement factors were introduced for all theatoms Refinement readily converged to R1 = 0049 Finalpositional coordinates and displacement isotropic equiva-lent Ueq parameters for MDO1 are reported in Table 2a
The starting atomic coordinates for MDO2 polytypewere derived through OD considerations from the finalpositional coordinates of the MDO1 polytype (matrix trans-formation for coordinates [100010-1201]) The non-stan-dard space group P21n11 was chosen for MDO2 polytypeto allow an easier comparison between the two polytypes
After some isotropic refinement cycles anisotropicdisplacement factors were introduced only for Cu and SThe refinement converged to R1 = 0062 for MDO2
The calculated coordinates are closely similar to thoseobtained from the structural refinement indicating that theOD layers are remarkably similar in the two polytypesThere is also a clear indication that the atomic positionsconform to the symmetry of the single layer Cu3 O6 O7O8 and S are located on the mirror plane at z = 0125(l operation of the single layer) Cu4 and O5 are located onthe mirror plane at z = 0625 while O2 O4 and Cu2 aresymmetrically related to O1 O3 and Cu1 respectively onboth sides of the mirror plane at z = 0125 Clearly thelsquoidealrsquo symmetry of the single layer is not perfectly main-tained in the real structures of the two polytypes whichactually present a slight lsquodesymmetrizationrsquo (Egrave urovi 1979)
OD character of brochantite 271
Table 3 Bond distances (Aring) and angles (deg) in the coordination polyhedra of MDO1 (a) and MDO2 (b) polytypes
a) Brochantite-2M1
Cu1 Cu2 Cu3 Cu4 SO6 194(1) O5iii 192(1) O1 198(1) O4v 198(1) O7 148(1)O5i 194(1) O6 192(1) O4 199(1) O1 199(1) O10 148(1)O1i 201(1) O2i 209(1) O2 199(1) O2v 200(1) O9 150(1)O3ii 203(1) O4iv 211(1) O3 201(1) O3 201(1) O8 150(1)O8ii 234(1) O8iv 230(1) O7 236(1) O5 237(1)O7i 236(1) O7i 234(1) O9v 242(1) O10vi 247(1)
O1i-Cu1-O3ii 1677(3) O2i-Cu2-O4iv1676(3) O1-Cu3-O2 969(3) O1-Cu4-O2v 998(3) O7-S-O8 1084(6)O1i-Cu1-O5i 836(3) O2i-Cu2-O5iii 846(3) O1-Cu3-O3 814(3) O1-Cu4-O3 812(3) O7-S-O9 1085(5)O1i-Cu1-O6 905(3) O2i-Cu2-O6 915(3) O1-Cu3-O4 1747(3) O1-Cu4-O4v 1763(3) O7-S-O10 1094(5)O3ii-Cu1-O5i 901(3) O4iv -Cu2-O5iii 883(3) O2-Cu3-O3 1771(3) O2v-Cu4-O3 1789(3) O8-S-O9 1102(6)O3ii-Cu1-O6 959(3) O4iv -Cu2-O6 953(3) O2-Cu3-O4 822(3) O2v-Cu4-O4v 823(3) O8-S-O10 1097(6)O5i-Cu1-O6 1740(3) O5iii-Cu2-O6 1758(4) O3-Cu3-O4 993(3) O3-Cu4-O4v 967(3) O9-S-O10 1106(5)
Symmetry transformations used to generate equivalent atoms in MDO1 polytypei atom at x 1+y zii 12-x 12 +y 1-ziii x 1+y z-1iv 12 -x 12 +y -zv x y z+1vi x-12 12-y z
b) Brochantite-2M2
Cu1 Cu2 Cu3 Cu4 SO6 196(1) O6 192(1) O3 197(1) O2vi 198(1) O10 151(1)O5i 194(2) O5iii 194(2) O2 200(1) O1 200(1) O10 151(2)O1i 202(1) O2i 208(1) O4 200(1) O3 201(1) O8 151(1)O4ii 202(1) O3iv 209(1) O1 201(1) O4vi 203(1) O7 155(2)O7i 230(1) O8iv 230(1) O7 233(1) O5 238(1)O8ii 233(1) O7i 231(2) O10 242(1) O9v 248(2)
O1i-Cu1-O4ii 1679(6) O2i-Cu2-O3iv 1676(6) O1-Cu3-O2 974(6) O1-Cu4-O2vi 988(6) O7-S-O8 1092(9)O1i-Cu1-O5i 840(6) O2i-Cu2-O5iii 845(6) O1-Cu3-O3 824(6) O1-Cu4-O3 816(6) O7-S-O9 1081(9)O1i-Cu1-O6 903(6) O2i-Cu2-O6 926(6) O1-Cu3-O4 1751(7) O1-Cu4-O4vi 1772(6) O7-S-O10 1076(9)O4ii-Cu1-O5i 887(6) O3iv-Cu2-O5iii 873(6) O2-Cu3-O3 1776(6) O2vi-Cu4-O3 1796(6) O8-S-O9 1116(9)O4ii-Cu1-O6 970(6) O3iv-Cu2-O6 953(6) O2-Cu3-O4 823(6) O2vi-Cu4-O4vi 821(6) O8-S-O10 1095(9)O5i-Cu1-O6 1743(6) O5iii-Cu1-O6 1769(6) O3-Cu3-O4 977(6) O3-Cu4-O4vi 975(6) O9-S-O10 1108(8)
Symmetry transformations used to generate equivalent atoms in MDO2 polytypei atom at x 1+y zii 12-x 12+y 12+ziii x1+y z-1iv 12-x 12+y z-12v x-12 12-Y 12-zvi x y z+1
S Merlino N Perchiazzi D Franco
The table of anisotropic displacement parameters andthe lists of the FoFc data for both polytypes are availablefrom the authors upon request (or through the EJMEditorial Office Paris)
Structure description
The results of the present structural study are given inTables 3 and 4 The main features of the crystal structure ofbrochantite were already outlined by Cocco amp Mazzi(1959) More accurate data were subsequently obtained byHelliwell amp Smith (1997) on a very tiny (015x005x001mm) untwinned crystal from Socorro County NewMexico USA using data collected with a rotating anodediffractometer (MoKa radiation)
As regards the Cu and S coordination polyhedra boththe data of Helliwell amp Smith (1997) and our resultssubstantially agree with Cocco amp Mazzirsquos (1959) modelAs expected from their polytypic nature the coordinationpolyhedra and their linking are essentially the same inMDO1 and MDO2 polytypes (Table 3) so in the followingstructure description we refer only to the data obtained forthe MDO1 polytype The sulphate tetrahedron is veryregular in the MDO1 structure whereas it is slightly largerand a little more distorted in the MDO2 structure As shownin Table 3 Cu octahedra due to the Jahn-Teller effect arestrongly distorted towards an elongated tetragonal bipyra-midal coordination Four hydroxyls with Cu-OH distancesclose to 2 Aring are arranged in a nearly planar square coordi-nation with two additional longer bonds about 23 Aring inlength to complete the sixfold coordination
In Fig 1 and 2 the structures are represented assumingfourfold coordination around the copper atoms Cu3 andCu4 exhibit a nearly square planar coordination with fourCu-O distances between 198 and 201 Aring whereas Cu1 andCu2 exhibit two shorter (192 to 194 Aring) and two longer(201 and 203 Aring in Cu1 209 and 211 Aring in Cu2 coordi-
nation) distances Moreover the oxygen atoms around Cu1and Cu2 slightly deviate from a square-planar coordina-tion which explains the different representation of the twofourfold coordinations in Fig 1 and 2
In these Figures the Cu3- and Cu4-squares are inter-connected through common edges to build infinite planarchains running along c The Cu1- and Cu2-squares repre-sented as strongly squeezed tetrahedra are interconnectedby sharing vertices (O5 and O6 hydroxyl groups) to buildlsquozig-zagrsquo chains running along c Both chains areconnected one to the other by shared vertices to build infi-nite layers parallel to (100) [Cocco amp Mazzi (1959 Fig 8in their paper] The layers are seen along b in Fig 1 and 2where they appear distincly separated from each otherwhich indicates that in the present case the OD layerscorrespond to crystal chemically significant layers whichis not generally the case in OD structures
If we complete the octahedral coordination around eachcopper atom as represented in Fig 3 we can observe thatsubsequent layers are actually connected through thesulphate groups Accordingly in their presentation of astructural hierarchy for sulphate minerals Hawthorne et al(2000) placed brochantite among the structures with infi-nite frameworks as being built up of double chains ofcopper octahedra that are cross-linked by SO4 tetrahedra toform frameworks Sabelli amp Trosti-Ferroni (1985)presented a different kind of structural classification ofsulphate minerals based on the lsquomode of linking of thepolyhedra of the metals present in the mineralsrsquo assigningsulphate minerals to four structural type (insular chainsheet and framework) and 22 sub-types Within their clas-sification brochantite belongs to sub-type 14 in the sheettype as characterized by single undulating layers of copperoctahedra parallel to (100) (Fig 3)
The connection between these layers is ensured not onlyby sulphate tetrahedra but also by hydrogen bondsHelliwell amp Smith (1997) presented a hydrogen bondingsystem on the basis of the hydrogen positions determined
272
Table 4 Bond valence (vu) in brochantite-2M1 (MDO1 polytype)
O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 Sav
Cu1 0409 0387 0494 0494 0154 0168 1952Cu2 0329 0312 0521 0507 0168 0182 2019Cu3 0443 0420 0420 0431 0159 0135 2008Cu4 0431 0420 0409 0443 0154 0115 1972S 1476 1436 1436 1436 5784Scv 1283 1169 1216 1186 1169 1001 1957 1786 1571 1551Srsquocv 1061 1008 1078 1043 0922 1162 1957 2008 1842 181
Scv is the sum of bond strengths reaching the anions Srsquocv after correction for hydrogen bonds
O1-O8iii 271(1) 0222 O5-O9i 302(1) 0126O3-O10iv 296(1) 0138 O5-O10 305(1) 0121O4-O9ii 293(2) 0145 O2-O6v 287(1) 0161
OmiddotmiddotmiddotO distances (Aring) and hydrogen bond strengths (vu) Ineach pair of hydrogen bonded oxygen atoms the first one isthe donor the second one is the acceptor Atom at i x y z+1 ii 12ndashx 12+y -z iii x-12 12-y ziv 12-x 12+y 1-z v x y-1 z
through difference Fourier syntheses Looking at Table 2 ofHelliwell amp Smith (1997) we can see that the D-HAangles are far from ideal and that the O3-H3O9 distancesinvolve two oxygen atoms belonging to the same polyhe-dron
Our hydrogen bonding scheme was derived by lookingat the distances shorter than 31 Aring between oxygen atomsand not belonging to the same polyhedron These distancesare reported in Table 4 together with the bond valencebalance The Scv row shows the sums of bond strengthscalculated following Brese amp OrsquoKeeffe (1991) whereas inthe Srsquocv row these sums are corrected for hydrogen bondcontributions evaluated according to Ferraris amp Ivaldi(1988) The balance can be considered as quite satisfac-tory Among the oxygen atoms of the sulphate group (withthe exception of O7 which is linked to three Cu atoms) O8O9 and O10 are all taken up as acceptors O9 anionreceives two contributions from O4 and O5 hydroxylsthis latter forming a bifurcated bond with O9 and O10anions belonging to different sulphate groups Our datatherefore validate the assignment of the OH bands madeby Schmidt amp Lutz (1993) on the basis of infrared andRaman spectra all the hydrogen bonds shown in Table 4are consistent with those indicated by Schmidt amp Lutz(1993) moreover there is a close inverse relation betweenOO bond lengths given in our Table 4 and the stretchingfrequences reported by Schmidt amp Lutz (1993) Thehighest stretching frequency given in their Table 3 corre-sponds to a bifurcated hydrogen bond of O6 with O9 andO10 not included in our Table 4 For this bond we foundOO distances of 324 Aring (0097 vu) and 321 Aring (vu0100) respectively If we correspondingly correct thebond valence sums for O6 O9 and O10 we obtain sumscloser to the ideal values
Conclusions
In the X-ray diffraction patterns of brochantite weobserve typical features of OD structures These compriseubiquitous twinning disorder along a definite directionnon space-group absences and the presence of distinctdiffraction classes namely family and characteristic reflec-tions Accordingly we show that the crystal structure ofbrochantite may be conveniently described as built up ofOD layers with layer group symmetry P(n)21m moreoverwe derive the two MDO polytypes in the OD family ofbrochantite The X-ray single-crystal study of specimensfrom various Italian localities allows us to define a newpolytype brochantite-2M2 (corresponding to one MDOstructure) in addition to the ldquonormalrdquo brochantite-2M1(corresponding to another MDO structure) This new poly-type is found in specimens from four distinct mineralogicallocalities The crystal structure of this new polytype isoutlined on the basis of OD considerations and successfullyrefined It is possible that more complex polytypes exist atleast as small domains embodied within larger domains ofthe two main polytypes Their presence could be reliablydetermined only through electron diffraction and HRTEMstudies
Whereas our study was carried out on relativelylsquogoodrsquo brochantite crystals it would be interesting toinvestigate brochantite occurring as decay products in theurbanindustrial environment more specif ically as aconstituent of the green patinas formed in the deteriora-tion of copper and bronze manufacts In these patinasbrochantite is commonly found as massive or dustyencrustations not suitable for X-ray single-crystal studyOn the other hand an unambiguous distinction betweenthe brochantite polytypes cannot be made on the basis ofpowder data only as all polytypes exhibit commonlsquofamily reflectionsrsquo with intensities largely dominatingover the characteristic reflections Electron diffractionand HRTEM studies appear necessary to distinguishbetween the two main polytypes and would also be usefulin indicating the presence of other more complex poly-types
Acknowledgement This work was supported by theUniversity of Pisa and MIUR (Ministero dellrsquoUniversitagrave edella Ricerca Scientifica) through grants to the projectlsquoTransformations reactions ordering in mineralsrsquo
Appendix
Discussion of the diffraction pattern on the basis of the OD character of brochantite
It is useful to discuss the common features of all poly-types (and also of the disordered sequences) in the wholeOD family as well as the distinctive features of thedifferent polytypes In particular it is relevant to indicatethe diffractions which characterize the two most importantpolytypes MDO1 and MDO2 It is correct in this respect torefer to the orthogonal cell with AO = 4ao = 2546 AringBO = b = 985 Aring CO = c = 602 Aring In fact this cell is thecommon cell of both polytypes being a B centred cell for
OD character of brochantite 273
Fig 3 The crystal structure of brochantite-2M1 as seen along cshowing the interconnection of the undulating layers of copperoctahedra parallel to (100) with the sulphate groups
S Merlino N Perchiazzi D Franco
the polytype MDO1 and doubly primitive for the polytypeMDO2 (Fig 4)
The single structural layer has symmetry P(n)21m andis repeated by the operation n122 (normal to b with trans-lational component ao+c4) The Fourier transform of thewhole structure (structure factor F) may be obtained bysumming the contributions of the successive layers takingaccount of their relative positions
We shall indicate fo(hkl) as the contribution of the layerL0 The indices k and l are integers and correspond to the band c translations of the layer whereas h is a continuousvariable corresponding to axis A the direction of missingperiodicity The next layer gives a contribution
f1(hkl) = fo(hndashkl) exp[2pi(h4+k2plusmnl4)]
as for every atom at xjyjzj in the layer L0 there is an equalatom at xj+14 12-yj zjplusmn14 in the layer L1 It can be seenthat all the even layers L2p and all the odd layers L2p+1 aretranslationally equivalent to the layers L0 and L1 respec-tively according to the same translation vector
T2p = pA2 + a2pc2 with a2p = 0 1
The Fourier transform of the whole structure may beexpressed as
F(hkl) = fo(hkl) + fo(hndashkl) exp[2pi(h4+k2plusmnl4)] S(hkl) (1)
S(hkl) = 1(2M) Sp exp[2pi(ph2+a2p l2)] (2)
For l = 2L the expression is independent of the param-eter a2p and therefore of the degree of disorder For largevalues of M the expression tends to zero except whenh = h = 2H with integer H Therefore the reflections witheven l (and even h) are common to the whole OD familyand are always sharp (family reflections)
Moreover we observe that for k = 0 (and consideringonly the family reflections namely for even l and h) thefirst factor in expression (1) gives
F(H0L) = fo(H0L) [1 + exp[2pi(H2plusmnL2)]
This factor becomes zero for H+L = 2n+1 The diffrac-tion pattern of the two main polytypes differs only in theodd l reflections In the case of MDO1 (and MDO1rsquo) thevalue of the parameter a2p in the general expression (2) is1 Therefore for l = 2L+1 (the case of l = 2L is alreadyconsidered in a general way)
S(hkl) = (12M) Sp exp[2pi(ph2+(2L+1)2)]
For large values of M this expression tends to zeroexcept when h = h = 2H+1
In the case of MDO2 the value of the parameter a2p is0 therefore for l = 2L+1
S(hkl) = (12M) Sp exp[2pi(ph2]
For large values of M this expression tends to zeroexcept for even integer values of h ie for h = h = 2HFigure 5 presents the diffraction pattern of a crystalpresenting both main polytypes indicating the familyreflections and the characteristic reflections of both MDOstructures Three subsequent planes of the reciprocal latticeare shown with k = 0 1 and 2 As indicated in the Figure0kl reflections are present for odd l values (non-familyreflections) only at k odd values due to the symmetry ofthe single layer
References
Brese NE amp OrsquoKeeffe M (1991) Bond-valence parameters forsolids Acta Cryst B47 192-197
Cocco G amp Mazzi F (1959) La struttura della brochantitePeriod Mineral 28 121-149
274
Fig 4 Relationships between the common orthogonal cell and thecells of the two polytypes MDO1 and MDO2
Fig 5 Diffraction pattern of a brochantite crystal presenting bothmain polytypes The non-family reflections (odd l values) are repre-sented with short (for MDO2 reflections) and long (for MDO1 +MDO1rsquo reflections) dashes
Dornberger-Schiff K (1956) On the order disorder structures(OD-structures) Acta Cryst 9 593-601
mdash (1964) Grundzuumlge einer Theorie von OD-Strukturen ausSchichten Abh Dtsch Akad Wiss Berlin Kl Chem GeolBiol 3 1-107
Egrave urovi S (1979) Desymmetrization of OD structures Krystallund Technik 14 1047-1053
mdash (1997) Fundamentals of the OD theory In Merlino (ed)ldquoModular aspects of mineralsrdquo EMU Notes in Mineralogy 13-28
Ferraris G amp Ivaldi G (1988) Bond valence vs bond length inOmiddotmiddotmiddotO hydrogen bonds Acta Cryst B44 341-344
Gettens RJ (1970) Patina noble and vile In ldquoArt andTechnology A Symposium on Classic Bronzesrdquo (eds SDoeringer DG Mitten and A Steinberg) pp 57-72 The MITpress Boston MA
Guinier A Bokij G B Boll-Dornberger K Cowley J MEgrave urovi S Jagodzinski H Krishna P de Wolff P MZvyagin B B Cox D E Goodman P Hahn Th KuchitsuK Abrahams S C (1984) Nomenclature of polytype struc-tures Report of the International Union of Crystallography ad-hoc Committee on the Nomenclature of Disordered Modulatedand Polytype Structures Acta Cryst A40 399-404
Hawthorne FC Krivovichev SV Burns PC (2000) The crystalchemistry of sulphate minerals In Alpers C N Jambor J Lamp Nordstrom B K (eds) ldquoSulfate mineralsrdquo Reviews inMineralogy amp Geochemistry 40 1-112
Helliwell M amp Smith JV (1997) Brochantite Acta Cryst C531369-1371
Lauro C (1939) Brochantite della miniera di ldquoSa Duchessardquo(Sardegna) Period Mineral 3 327-341
mdash (1941) Sulle costanti reticolari della brochantite PeriodMineral 3 419-427
Mattsson E amp Holm R (1982) Atmospheric corrosion of copperand its alloys In ldquoAtmospheric Corrosionrdquo (ed W H Ailor)Chap 24 pp 365-381 John Wiley New York
Merlino S (1997) OD approach in minerals examples and appli-cations In Merlino (ed) ldquoModular aspects of mineralsrdquo EMUNotes in Mineralogy 1 29-54
Palache C (1939) Brochantite Am Mineral 8 463-481Sabelli C amp Trosti-Ferroni R (1985) A structural classification
of sulphate minerals Period Mineral 54 1-46Schmidt M amp Lutz HD (1993) Hydrogen bonding in basic
copper salts a spectroscopic study of malachite Cu2(OH)2CO3and brochantite Cu4(OH)6SO4 Phys Chem Mineral 2027-32
Woods TL amp Garrels RM (1986) Use of oxidized copperminerals as environmental indicators Appl Geochem 1181-187
Received 8 January 2002Modified version received 29 July 2002Accepted 12 November 2002
OD character of brochantite 275
S Merlino N Perchiazzi D Franco
and positions in reciprocal space indicating a distinctpolytype with cell parameters very close to thosereported by Lauro (1939) for the Sa Duchessa brochan-tite
All the above mentioned peculiarities namely the ubiq-uitous twinning the disorder along a definite direction nonspace-group absences and polytypism clearly suggest theOD nature of the mineral A preliminary account of the ODfeatures of brochantite has already been given (Merlino1997) The aim of the present paper is to present a compre-hensive study of brochantite including its OD nature aswell as a definition of the main polytypes and details oftheir structural arrangements
OD nature of brochantite
As it is explained in the following brochantite displaysdiffraction features characteristic of OD structures(Dornberger-Schiff 1956 1964 Egrave urovi 1997) consistingof equivalent layers In such structures neighbouring layerscan be arranged in two or more geometrically and there-fore energetically equivalent ways different ways ofstacking neighbouring layers allow the existence of a seriesof both disordered and ordered (polytypes) sequences allof them constituting a family of OD structures Thesymmetry properties common to all the members of an ODfamily are described by the lsquoOD groupoid familyrsquo symbolwhich reports the partial symmetry operations (POs) thattransform each layer into itself (l operations) or into anadjacent layer (s operations) Considering the infinitenumber of ordered and disordered members of an ODfamily OD theory pays special attention to the so-calledMDO (Maximum Degree of Order) polytypes In suchpolytypes there are not only pairs of layers but possiblyalso tripleshellip n-tuples of layers that are geometricallyequivalent MDO polytypes are the simplest of the possibleordered sequences and usually correspond to the mostfrequently occurring polytypes in the family
The crystal structure of brochantite determined byCocco amp Mazzi (1959) can be described in terms of struc-tural layers (Fig 1) with basic vectors b c (translationvectors of the layer with b = 985 Aring c = 602) and ao[ao = (asin b)2 = 636 Aring] and layer group symmetryP(n)21m (the parentheses in the first position indicate thatthe basic vector a0 is not a translation vector)
Adjacent layers are related by screw axes along a0 thedirection of missing periodicity with translational compo-nent a0 (22 operations) by glide planes normal to b withtranslational component a0+c4 (n122 operators) and screwaxes parallel to c with translational component -c4 (2-12operators)
Therefore the OD groupoid family symbol forbrochantite is
P (n) 21 m
[ (22) n122 2-12 ] 1
It is just the presence of a mirror plane in the singlebuilding layer that make it possible for adjacent layers tobe related through n122 (and through 2-12 too) as well asthrough n-122 (and through 212 too) operations the pairsof layers obtained in both ways are geometrically equiva-lent
Two MDO polytypes are possible namely MDO1 corre-sponding to a regular sequence of n122 n122 n122operations (or 2-12 2-12 2-12) and MDO2 with regularalternation of n-122 n122 n-122 n122 operations (or
268
Fig 1 A pair of adjacent layers and their l-POs and s-POs as seenalong b White tetrahedra indicate sulphate groups The twodistinct copper atoms are represented in square coordination(chains of edge-sharing squares running along c) and lsquosqueezedrsquotetrahedral coordination (chains of corner-sharing lsquosqueezedrsquotetra-hedra running along c)
1It may be useful to recall that the symbols of the partial operations are in keeping with the symbols used for normal space group opera-tions Therefore 22 in the first position is the symbol for a twofold rotation with translational component a0 whereas n122 in the secondposition is the symbol for a glide normal to b with translational component c4+a0 and 2-12 in the third position is the symbol for atwofold rotation with translational component ndashc4
212 2-12 212 2-12) Their dimensions and symmetrydepend on the dimensions and symmetry of the singlelayer as well as on the specific sequence of operationsgiving rise to them
In MDO1 (Fig 2a) the partial s-operation n122 (withtranslational component a0+c4) is constantly applied andbecomes a true glide valid for the whole structure whichhas a translation vector a1 = 2a0+c2 (the other translationvectors are b1 = b c1 = -c where a0 b c are the basicvectors of the single layer) Similarly the l operation 21and the s-operation ndash1 are total operations valid for thewhole structure The resulting space group for MDO1 isP121a1 with cell parameters a1 1307 Aring b1 985c1 602 b1 1033deg corresponding to the polytypestudied by Cocco amp Mazzi (1959) The sequence n-122n-122 n-122 (or 212 212 212) corresponds to thesame structural arrangement (MDO1rsquo) in (100) twinningrelationships
In MDO2 (Fig 2b) due to the relative position of thelayers the l operation n normal to a0 becomes a total oper-ation and the 22 s-operation is continued through the wholesequence of layers becoming a 21 total operation in a struc-ture with a2 = 2a0 (the other translation vectors are b2 = bc2 = -c) space group symmetry P21n11 and cell parame-ters a2 1272 Aring b2 985 c2 602 a2 90deg
According to the nomenclature established by Guinieret al (1984) the MDO1 and MDO2 polytypes should bedenoted as brochantite-2M1 and brochantite-2M2 respec-tively both presenting two layers within the unit a transla-tion Distinction can be made between the two polytypesthrough their diffraction pattern in which we found asusual in OD structures two distinct classes of reflectionsnamely the family and the characteristic reflections Thefamily reflections which in the present family have evenl indices are independent from the stacking of the layersand remain sharp and unchanged in all the ordered anddisordered structures of the family These reflections corre-spond to the so-called lsquofamily structurersquo which is closelyrelated to the structures of the family and displays in thepresent case space group symmetry Pbnm witha = 1272 Aring b = 985 and c = 301
The characteristic (non-family) reflections (those withodd l indices) depend both in position and intensity on thestacking of layers and consequently are typical of eachsequence They may be more or less diffuse sometimesappearing as continuous streaks
A detailed discussion of the diffractional effects in thewhole brochantite family is presented in Appendix Theresults obtained in Appendix were helpful for distin-guishing the polytypes occurring in the examined speci-mens as discussed in the following section
Experimental
A systematic X-ray diffraction study of brochantitecrystals from specimens preserved in the mineralogicalcollection of the Natural History Museum of PisaUniversity was carried out using the Weissenberg tech-nique All the examined crystals showed the presence of
variable degrees of structural disorder and the MDO1 poly-type was found in the majority of the specimens On theother hand apart from the Capo Calamita crystalsevidence for the existence of MDO2 polytype was found inthe diffraction patterns of crystals from the Italian localitiesof Trentin mine (Veneto) Sa Duchessa mine (Sardinia)and Val Fucinaia (Tuscany) These patterns correspond tothe overlapping of the reciprocal lattices of the MDO1MDO1rsquo and MDO2 polytypes and point to the co-existenceof the two distinct MDO polytypes in those specimens
Intensity data were collected with a Siemens P4 four-circle diffractometer from crystals previously tested usingWeissenberg photographs and made up of almost pureMDO1 (Val Fucinaia) and MDO2 (Capo Calamita) poly-types experimental details and crystallographic data forboth structural studies are given in Table 1
In the structure refinement of MDO1 polytype we usedas a starting model the results of the study by Cocco amp
OD character of brochantite 269
Fig 2 The crystal structures of MDO1 (a) and MDO2 (b) poly-types as seen along b In both cases the sequences of 212 and 2-
12 s-operations are indicated The other indicated l- ands-operations are just those which become total symmetry opera-tions in both polytypes
S Merlino N Perchiazzi D Franco270
Table 1 Crystal data and refinement details for MDO1 and MDO2 brochantite polytypes
Wavelength 071073 Aring MDO1 polytype MDO2 polytypeLocality Val Fucinaia Capo CalamitaMonoclinic P 1 21a 1 P 21n 1 1Unit cell dimensions a = 13140(2) Aring 12776(2) Aring
b = 9863(2) Aring 9869(2) Aringc = 6024(1) Aring 6026(1) Aringb = 10316(3) deg a = 9015(3) deg
Crystal size 014 014 003 mm 009 008 004 mmq range for data collection 4 to 5128 deg 4 to 50 degIndex ranges -7 pound h pound 7 -11 pound k pound 1 -1 pound l pound 15 -1 pound h pound 11 -1 pound k pound 15 -7 pound l pound 7Reflections collected unique 1643 1239 [Rint = 00415] 1821 1334 [Rint = 00638]Absorption correction y-scan on 14 reflections on 12 reflectionsRefinement method Full-matrix least-squares on F2
Final R1 indexa [Fo gt4s( Fo)] R1 = 00488 (831 refl) R1 = 00619 (607 refl) Data restraints parameters 1239 6 137 1334 0 86Goodness-of-fita (all data) 1071 0893wR2 a (all data) 01481 02084Largest diff peak and hole 119 and -128 e Aring-3 257 and ndash112 e Aring-3
Note a Goodness-of-fit = [S [w(Fo2-Fc
2)2](N-P)]12 where N P are the numbers of observations and parametersrespectively R1 = S Fo Fc S Fo w R2 = [S[w(Fo
2-Fc2)2 ] S[ w(Fo
2)2]]12 w = 1 [s 2 (Fo2) +
(00243Q)2 + 057Q] where Q = [MAX(Fo20) + 2Fc
2] 3
Table 2 a) Final positional and displacement parameters (Aring2) for MDO1 polytype b) calculated positional coordinates and final posi-tional and displacement parameters (Aring2) for MDO2 polytype
a) MDO1 polytype
x y z Ueq
Cu1 02061(1) 09911(2) 04799(3) 00207(4)Cu2 02023(1) 09908(3) -00237(3) 00244(5)Cu3 01181(1) 02614(2) 01819(3) 00185(4)Cu4 01199(1) 02571(2) 06848(3) 00197(4)S 03877(2) 01989(4) 03167(5) 00233(7)O1 00936(6) 01325(9) 0417(1) 0022(2)O2 00827(6) 01345(9) -0082(1) 0022(2)O3 01590(6) 03823(9) 0454(1) 0021(2)O4 01556(6) 03826(9) -0052(1) 0020(2)O5 02559(6) 00936(9) 0758(1) 0022(2)O6 01428(6) 08991(9) 0198(1) 0023(2)O7 02797(6) 0145(1) 0260(1) 0027(2)O8 03822(7) 0351(1) 0312(2) 0028(2)O9 04435(6) 0149(1) 0142(1) 0029(2)O10 04415(6) 0152(1) 0547(1) 0026(3)
b) MDO2 polytype
x y z x y z Ueq or Uiso
Cu1 02061 09911 03768 Cu1 02066(2) 09902(3) 03770(5) 00118(7)Cu2 02023 09908 -01248 Cu2 02019(2) 09906(3) -01249(5) 00135(7)Cu3 01181 02608 01228 Cu3 01183(2) 02608(3) 01261(4) 00111(6)Cu4 01199 02571 06249 Cu4 01205(2) 02569(3) 06258(4) 00109(7)S 03877 01989 01229 S 03881(4) 01991(5) 01226(9) 0015(1)O1 00936 01325 03704 O1 0091(1) 0130(2) 0374(2) 0016(4)O2 00827 01345 -01229 O2 0084(1) 0136(1) -0125(2) 0009(3)O3 01590 03823 03759 O3 0158(1) 0381(2) 0374(2) 0014(4)O4 01556 03826 -01298 O4 0158(1) 0385(2) -0122(2) 0012(3)O5 02559 00936 06300 O5 0258(1) 0094(2) 0628(3) 0023(4)O6 01428 08991 01264 O6 0142(1) 0897(2) 0124(2) 0019(3)O7 02797 01451 01205 O7 0275(1) 0141(2) 0126(3) 0023(4)O8 03822 03510 01208 O8 0383(1) 0352(2) 0125(2) 0016(3)O9 04435 01488 -00799 O9 0442(1) 0147(2) -0084(3) 0023(4)O10 04415 01523 03267 O10 0443(1) 0150(2) 0329(3) 0020(3)
Mazzi (1959) After some isotropic refinement cyclesanisotropic displacement factors were introduced for all theatoms Refinement readily converged to R1 = 0049 Finalpositional coordinates and displacement isotropic equiva-lent Ueq parameters for MDO1 are reported in Table 2a
The starting atomic coordinates for MDO2 polytypewere derived through OD considerations from the finalpositional coordinates of the MDO1 polytype (matrix trans-formation for coordinates [100010-1201]) The non-stan-dard space group P21n11 was chosen for MDO2 polytypeto allow an easier comparison between the two polytypes
After some isotropic refinement cycles anisotropicdisplacement factors were introduced only for Cu and SThe refinement converged to R1 = 0062 for MDO2
The calculated coordinates are closely similar to thoseobtained from the structural refinement indicating that theOD layers are remarkably similar in the two polytypesThere is also a clear indication that the atomic positionsconform to the symmetry of the single layer Cu3 O6 O7O8 and S are located on the mirror plane at z = 0125(l operation of the single layer) Cu4 and O5 are located onthe mirror plane at z = 0625 while O2 O4 and Cu2 aresymmetrically related to O1 O3 and Cu1 respectively onboth sides of the mirror plane at z = 0125 Clearly thelsquoidealrsquo symmetry of the single layer is not perfectly main-tained in the real structures of the two polytypes whichactually present a slight lsquodesymmetrizationrsquo (Egrave urovi 1979)
OD character of brochantite 271
Table 3 Bond distances (Aring) and angles (deg) in the coordination polyhedra of MDO1 (a) and MDO2 (b) polytypes
a) Brochantite-2M1
Cu1 Cu2 Cu3 Cu4 SO6 194(1) O5iii 192(1) O1 198(1) O4v 198(1) O7 148(1)O5i 194(1) O6 192(1) O4 199(1) O1 199(1) O10 148(1)O1i 201(1) O2i 209(1) O2 199(1) O2v 200(1) O9 150(1)O3ii 203(1) O4iv 211(1) O3 201(1) O3 201(1) O8 150(1)O8ii 234(1) O8iv 230(1) O7 236(1) O5 237(1)O7i 236(1) O7i 234(1) O9v 242(1) O10vi 247(1)
O1i-Cu1-O3ii 1677(3) O2i-Cu2-O4iv1676(3) O1-Cu3-O2 969(3) O1-Cu4-O2v 998(3) O7-S-O8 1084(6)O1i-Cu1-O5i 836(3) O2i-Cu2-O5iii 846(3) O1-Cu3-O3 814(3) O1-Cu4-O3 812(3) O7-S-O9 1085(5)O1i-Cu1-O6 905(3) O2i-Cu2-O6 915(3) O1-Cu3-O4 1747(3) O1-Cu4-O4v 1763(3) O7-S-O10 1094(5)O3ii-Cu1-O5i 901(3) O4iv -Cu2-O5iii 883(3) O2-Cu3-O3 1771(3) O2v-Cu4-O3 1789(3) O8-S-O9 1102(6)O3ii-Cu1-O6 959(3) O4iv -Cu2-O6 953(3) O2-Cu3-O4 822(3) O2v-Cu4-O4v 823(3) O8-S-O10 1097(6)O5i-Cu1-O6 1740(3) O5iii-Cu2-O6 1758(4) O3-Cu3-O4 993(3) O3-Cu4-O4v 967(3) O9-S-O10 1106(5)
Symmetry transformations used to generate equivalent atoms in MDO1 polytypei atom at x 1+y zii 12-x 12 +y 1-ziii x 1+y z-1iv 12 -x 12 +y -zv x y z+1vi x-12 12-y z
b) Brochantite-2M2
Cu1 Cu2 Cu3 Cu4 SO6 196(1) O6 192(1) O3 197(1) O2vi 198(1) O10 151(1)O5i 194(2) O5iii 194(2) O2 200(1) O1 200(1) O10 151(2)O1i 202(1) O2i 208(1) O4 200(1) O3 201(1) O8 151(1)O4ii 202(1) O3iv 209(1) O1 201(1) O4vi 203(1) O7 155(2)O7i 230(1) O8iv 230(1) O7 233(1) O5 238(1)O8ii 233(1) O7i 231(2) O10 242(1) O9v 248(2)
O1i-Cu1-O4ii 1679(6) O2i-Cu2-O3iv 1676(6) O1-Cu3-O2 974(6) O1-Cu4-O2vi 988(6) O7-S-O8 1092(9)O1i-Cu1-O5i 840(6) O2i-Cu2-O5iii 845(6) O1-Cu3-O3 824(6) O1-Cu4-O3 816(6) O7-S-O9 1081(9)O1i-Cu1-O6 903(6) O2i-Cu2-O6 926(6) O1-Cu3-O4 1751(7) O1-Cu4-O4vi 1772(6) O7-S-O10 1076(9)O4ii-Cu1-O5i 887(6) O3iv-Cu2-O5iii 873(6) O2-Cu3-O3 1776(6) O2vi-Cu4-O3 1796(6) O8-S-O9 1116(9)O4ii-Cu1-O6 970(6) O3iv-Cu2-O6 953(6) O2-Cu3-O4 823(6) O2vi-Cu4-O4vi 821(6) O8-S-O10 1095(9)O5i-Cu1-O6 1743(6) O5iii-Cu1-O6 1769(6) O3-Cu3-O4 977(6) O3-Cu4-O4vi 975(6) O9-S-O10 1108(8)
Symmetry transformations used to generate equivalent atoms in MDO2 polytypei atom at x 1+y zii 12-x 12+y 12+ziii x1+y z-1iv 12-x 12+y z-12v x-12 12-Y 12-zvi x y z+1
S Merlino N Perchiazzi D Franco
The table of anisotropic displacement parameters andthe lists of the FoFc data for both polytypes are availablefrom the authors upon request (or through the EJMEditorial Office Paris)
Structure description
The results of the present structural study are given inTables 3 and 4 The main features of the crystal structure ofbrochantite were already outlined by Cocco amp Mazzi(1959) More accurate data were subsequently obtained byHelliwell amp Smith (1997) on a very tiny (015x005x001mm) untwinned crystal from Socorro County NewMexico USA using data collected with a rotating anodediffractometer (MoKa radiation)
As regards the Cu and S coordination polyhedra boththe data of Helliwell amp Smith (1997) and our resultssubstantially agree with Cocco amp Mazzirsquos (1959) modelAs expected from their polytypic nature the coordinationpolyhedra and their linking are essentially the same inMDO1 and MDO2 polytypes (Table 3) so in the followingstructure description we refer only to the data obtained forthe MDO1 polytype The sulphate tetrahedron is veryregular in the MDO1 structure whereas it is slightly largerand a little more distorted in the MDO2 structure As shownin Table 3 Cu octahedra due to the Jahn-Teller effect arestrongly distorted towards an elongated tetragonal bipyra-midal coordination Four hydroxyls with Cu-OH distancesclose to 2 Aring are arranged in a nearly planar square coordi-nation with two additional longer bonds about 23 Aring inlength to complete the sixfold coordination
In Fig 1 and 2 the structures are represented assumingfourfold coordination around the copper atoms Cu3 andCu4 exhibit a nearly square planar coordination with fourCu-O distances between 198 and 201 Aring whereas Cu1 andCu2 exhibit two shorter (192 to 194 Aring) and two longer(201 and 203 Aring in Cu1 209 and 211 Aring in Cu2 coordi-
nation) distances Moreover the oxygen atoms around Cu1and Cu2 slightly deviate from a square-planar coordina-tion which explains the different representation of the twofourfold coordinations in Fig 1 and 2
In these Figures the Cu3- and Cu4-squares are inter-connected through common edges to build infinite planarchains running along c The Cu1- and Cu2-squares repre-sented as strongly squeezed tetrahedra are interconnectedby sharing vertices (O5 and O6 hydroxyl groups) to buildlsquozig-zagrsquo chains running along c Both chains areconnected one to the other by shared vertices to build infi-nite layers parallel to (100) [Cocco amp Mazzi (1959 Fig 8in their paper] The layers are seen along b in Fig 1 and 2where they appear distincly separated from each otherwhich indicates that in the present case the OD layerscorrespond to crystal chemically significant layers whichis not generally the case in OD structures
If we complete the octahedral coordination around eachcopper atom as represented in Fig 3 we can observe thatsubsequent layers are actually connected through thesulphate groups Accordingly in their presentation of astructural hierarchy for sulphate minerals Hawthorne et al(2000) placed brochantite among the structures with infi-nite frameworks as being built up of double chains ofcopper octahedra that are cross-linked by SO4 tetrahedra toform frameworks Sabelli amp Trosti-Ferroni (1985)presented a different kind of structural classification ofsulphate minerals based on the lsquomode of linking of thepolyhedra of the metals present in the mineralsrsquo assigningsulphate minerals to four structural type (insular chainsheet and framework) and 22 sub-types Within their clas-sification brochantite belongs to sub-type 14 in the sheettype as characterized by single undulating layers of copperoctahedra parallel to (100) (Fig 3)
The connection between these layers is ensured not onlyby sulphate tetrahedra but also by hydrogen bondsHelliwell amp Smith (1997) presented a hydrogen bondingsystem on the basis of the hydrogen positions determined
272
Table 4 Bond valence (vu) in brochantite-2M1 (MDO1 polytype)
O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 Sav
Cu1 0409 0387 0494 0494 0154 0168 1952Cu2 0329 0312 0521 0507 0168 0182 2019Cu3 0443 0420 0420 0431 0159 0135 2008Cu4 0431 0420 0409 0443 0154 0115 1972S 1476 1436 1436 1436 5784Scv 1283 1169 1216 1186 1169 1001 1957 1786 1571 1551Srsquocv 1061 1008 1078 1043 0922 1162 1957 2008 1842 181
Scv is the sum of bond strengths reaching the anions Srsquocv after correction for hydrogen bonds
O1-O8iii 271(1) 0222 O5-O9i 302(1) 0126O3-O10iv 296(1) 0138 O5-O10 305(1) 0121O4-O9ii 293(2) 0145 O2-O6v 287(1) 0161
OmiddotmiddotmiddotO distances (Aring) and hydrogen bond strengths (vu) Ineach pair of hydrogen bonded oxygen atoms the first one isthe donor the second one is the acceptor Atom at i x y z+1 ii 12ndashx 12+y -z iii x-12 12-y ziv 12-x 12+y 1-z v x y-1 z
through difference Fourier syntheses Looking at Table 2 ofHelliwell amp Smith (1997) we can see that the D-HAangles are far from ideal and that the O3-H3O9 distancesinvolve two oxygen atoms belonging to the same polyhe-dron
Our hydrogen bonding scheme was derived by lookingat the distances shorter than 31 Aring between oxygen atomsand not belonging to the same polyhedron These distancesare reported in Table 4 together with the bond valencebalance The Scv row shows the sums of bond strengthscalculated following Brese amp OrsquoKeeffe (1991) whereas inthe Srsquocv row these sums are corrected for hydrogen bondcontributions evaluated according to Ferraris amp Ivaldi(1988) The balance can be considered as quite satisfac-tory Among the oxygen atoms of the sulphate group (withthe exception of O7 which is linked to three Cu atoms) O8O9 and O10 are all taken up as acceptors O9 anionreceives two contributions from O4 and O5 hydroxylsthis latter forming a bifurcated bond with O9 and O10anions belonging to different sulphate groups Our datatherefore validate the assignment of the OH bands madeby Schmidt amp Lutz (1993) on the basis of infrared andRaman spectra all the hydrogen bonds shown in Table 4are consistent with those indicated by Schmidt amp Lutz(1993) moreover there is a close inverse relation betweenOO bond lengths given in our Table 4 and the stretchingfrequences reported by Schmidt amp Lutz (1993) Thehighest stretching frequency given in their Table 3 corre-sponds to a bifurcated hydrogen bond of O6 with O9 andO10 not included in our Table 4 For this bond we foundOO distances of 324 Aring (0097 vu) and 321 Aring (vu0100) respectively If we correspondingly correct thebond valence sums for O6 O9 and O10 we obtain sumscloser to the ideal values
Conclusions
In the X-ray diffraction patterns of brochantite weobserve typical features of OD structures These compriseubiquitous twinning disorder along a definite directionnon space-group absences and the presence of distinctdiffraction classes namely family and characteristic reflec-tions Accordingly we show that the crystal structure ofbrochantite may be conveniently described as built up ofOD layers with layer group symmetry P(n)21m moreoverwe derive the two MDO polytypes in the OD family ofbrochantite The X-ray single-crystal study of specimensfrom various Italian localities allows us to define a newpolytype brochantite-2M2 (corresponding to one MDOstructure) in addition to the ldquonormalrdquo brochantite-2M1(corresponding to another MDO structure) This new poly-type is found in specimens from four distinct mineralogicallocalities The crystal structure of this new polytype isoutlined on the basis of OD considerations and successfullyrefined It is possible that more complex polytypes exist atleast as small domains embodied within larger domains ofthe two main polytypes Their presence could be reliablydetermined only through electron diffraction and HRTEMstudies
Whereas our study was carried out on relativelylsquogoodrsquo brochantite crystals it would be interesting toinvestigate brochantite occurring as decay products in theurbanindustrial environment more specif ically as aconstituent of the green patinas formed in the deteriora-tion of copper and bronze manufacts In these patinasbrochantite is commonly found as massive or dustyencrustations not suitable for X-ray single-crystal studyOn the other hand an unambiguous distinction betweenthe brochantite polytypes cannot be made on the basis ofpowder data only as all polytypes exhibit commonlsquofamily reflectionsrsquo with intensities largely dominatingover the characteristic reflections Electron diffractionand HRTEM studies appear necessary to distinguishbetween the two main polytypes and would also be usefulin indicating the presence of other more complex poly-types
Acknowledgement This work was supported by theUniversity of Pisa and MIUR (Ministero dellrsquoUniversitagrave edella Ricerca Scientifica) through grants to the projectlsquoTransformations reactions ordering in mineralsrsquo
Appendix
Discussion of the diffraction pattern on the basis of the OD character of brochantite
It is useful to discuss the common features of all poly-types (and also of the disordered sequences) in the wholeOD family as well as the distinctive features of thedifferent polytypes In particular it is relevant to indicatethe diffractions which characterize the two most importantpolytypes MDO1 and MDO2 It is correct in this respect torefer to the orthogonal cell with AO = 4ao = 2546 AringBO = b = 985 Aring CO = c = 602 Aring In fact this cell is thecommon cell of both polytypes being a B centred cell for
OD character of brochantite 273
Fig 3 The crystal structure of brochantite-2M1 as seen along cshowing the interconnection of the undulating layers of copperoctahedra parallel to (100) with the sulphate groups
S Merlino N Perchiazzi D Franco
the polytype MDO1 and doubly primitive for the polytypeMDO2 (Fig 4)
The single structural layer has symmetry P(n)21m andis repeated by the operation n122 (normal to b with trans-lational component ao+c4) The Fourier transform of thewhole structure (structure factor F) may be obtained bysumming the contributions of the successive layers takingaccount of their relative positions
We shall indicate fo(hkl) as the contribution of the layerL0 The indices k and l are integers and correspond to the band c translations of the layer whereas h is a continuousvariable corresponding to axis A the direction of missingperiodicity The next layer gives a contribution
f1(hkl) = fo(hndashkl) exp[2pi(h4+k2plusmnl4)]
as for every atom at xjyjzj in the layer L0 there is an equalatom at xj+14 12-yj zjplusmn14 in the layer L1 It can be seenthat all the even layers L2p and all the odd layers L2p+1 aretranslationally equivalent to the layers L0 and L1 respec-tively according to the same translation vector
T2p = pA2 + a2pc2 with a2p = 0 1
The Fourier transform of the whole structure may beexpressed as
F(hkl) = fo(hkl) + fo(hndashkl) exp[2pi(h4+k2plusmnl4)] S(hkl) (1)
S(hkl) = 1(2M) Sp exp[2pi(ph2+a2p l2)] (2)
For l = 2L the expression is independent of the param-eter a2p and therefore of the degree of disorder For largevalues of M the expression tends to zero except whenh = h = 2H with integer H Therefore the reflections witheven l (and even h) are common to the whole OD familyand are always sharp (family reflections)
Moreover we observe that for k = 0 (and consideringonly the family reflections namely for even l and h) thefirst factor in expression (1) gives
F(H0L) = fo(H0L) [1 + exp[2pi(H2plusmnL2)]
This factor becomes zero for H+L = 2n+1 The diffrac-tion pattern of the two main polytypes differs only in theodd l reflections In the case of MDO1 (and MDO1rsquo) thevalue of the parameter a2p in the general expression (2) is1 Therefore for l = 2L+1 (the case of l = 2L is alreadyconsidered in a general way)
S(hkl) = (12M) Sp exp[2pi(ph2+(2L+1)2)]
For large values of M this expression tends to zeroexcept when h = h = 2H+1
In the case of MDO2 the value of the parameter a2p is0 therefore for l = 2L+1
S(hkl) = (12M) Sp exp[2pi(ph2]
For large values of M this expression tends to zeroexcept for even integer values of h ie for h = h = 2HFigure 5 presents the diffraction pattern of a crystalpresenting both main polytypes indicating the familyreflections and the characteristic reflections of both MDOstructures Three subsequent planes of the reciprocal latticeare shown with k = 0 1 and 2 As indicated in the Figure0kl reflections are present for odd l values (non-familyreflections) only at k odd values due to the symmetry ofthe single layer
References
Brese NE amp OrsquoKeeffe M (1991) Bond-valence parameters forsolids Acta Cryst B47 192-197
Cocco G amp Mazzi F (1959) La struttura della brochantitePeriod Mineral 28 121-149
274
Fig 4 Relationships between the common orthogonal cell and thecells of the two polytypes MDO1 and MDO2
Fig 5 Diffraction pattern of a brochantite crystal presenting bothmain polytypes The non-family reflections (odd l values) are repre-sented with short (for MDO2 reflections) and long (for MDO1 +MDO1rsquo reflections) dashes
Dornberger-Schiff K (1956) On the order disorder structures(OD-structures) Acta Cryst 9 593-601
mdash (1964) Grundzuumlge einer Theorie von OD-Strukturen ausSchichten Abh Dtsch Akad Wiss Berlin Kl Chem GeolBiol 3 1-107
Egrave urovi S (1979) Desymmetrization of OD structures Krystallund Technik 14 1047-1053
mdash (1997) Fundamentals of the OD theory In Merlino (ed)ldquoModular aspects of mineralsrdquo EMU Notes in Mineralogy 13-28
Ferraris G amp Ivaldi G (1988) Bond valence vs bond length inOmiddotmiddotmiddotO hydrogen bonds Acta Cryst B44 341-344
Gettens RJ (1970) Patina noble and vile In ldquoArt andTechnology A Symposium on Classic Bronzesrdquo (eds SDoeringer DG Mitten and A Steinberg) pp 57-72 The MITpress Boston MA
Guinier A Bokij G B Boll-Dornberger K Cowley J MEgrave urovi S Jagodzinski H Krishna P de Wolff P MZvyagin B B Cox D E Goodman P Hahn Th KuchitsuK Abrahams S C (1984) Nomenclature of polytype struc-tures Report of the International Union of Crystallography ad-hoc Committee on the Nomenclature of Disordered Modulatedand Polytype Structures Acta Cryst A40 399-404
Hawthorne FC Krivovichev SV Burns PC (2000) The crystalchemistry of sulphate minerals In Alpers C N Jambor J Lamp Nordstrom B K (eds) ldquoSulfate mineralsrdquo Reviews inMineralogy amp Geochemistry 40 1-112
Helliwell M amp Smith JV (1997) Brochantite Acta Cryst C531369-1371
Lauro C (1939) Brochantite della miniera di ldquoSa Duchessardquo(Sardegna) Period Mineral 3 327-341
mdash (1941) Sulle costanti reticolari della brochantite PeriodMineral 3 419-427
Mattsson E amp Holm R (1982) Atmospheric corrosion of copperand its alloys In ldquoAtmospheric Corrosionrdquo (ed W H Ailor)Chap 24 pp 365-381 John Wiley New York
Merlino S (1997) OD approach in minerals examples and appli-cations In Merlino (ed) ldquoModular aspects of mineralsrdquo EMUNotes in Mineralogy 1 29-54
Palache C (1939) Brochantite Am Mineral 8 463-481Sabelli C amp Trosti-Ferroni R (1985) A structural classification
of sulphate minerals Period Mineral 54 1-46Schmidt M amp Lutz HD (1993) Hydrogen bonding in basic
copper salts a spectroscopic study of malachite Cu2(OH)2CO3and brochantite Cu4(OH)6SO4 Phys Chem Mineral 2027-32
Woods TL amp Garrels RM (1986) Use of oxidized copperminerals as environmental indicators Appl Geochem 1181-187
Received 8 January 2002Modified version received 29 July 2002Accepted 12 November 2002
OD character of brochantite 275
212 2-12 212 2-12) Their dimensions and symmetrydepend on the dimensions and symmetry of the singlelayer as well as on the specific sequence of operationsgiving rise to them
In MDO1 (Fig 2a) the partial s-operation n122 (withtranslational component a0+c4) is constantly applied andbecomes a true glide valid for the whole structure whichhas a translation vector a1 = 2a0+c2 (the other translationvectors are b1 = b c1 = -c where a0 b c are the basicvectors of the single layer) Similarly the l operation 21and the s-operation ndash1 are total operations valid for thewhole structure The resulting space group for MDO1 isP121a1 with cell parameters a1 1307 Aring b1 985c1 602 b1 1033deg corresponding to the polytypestudied by Cocco amp Mazzi (1959) The sequence n-122n-122 n-122 (or 212 212 212) corresponds to thesame structural arrangement (MDO1rsquo) in (100) twinningrelationships
In MDO2 (Fig 2b) due to the relative position of thelayers the l operation n normal to a0 becomes a total oper-ation and the 22 s-operation is continued through the wholesequence of layers becoming a 21 total operation in a struc-ture with a2 = 2a0 (the other translation vectors are b2 = bc2 = -c) space group symmetry P21n11 and cell parame-ters a2 1272 Aring b2 985 c2 602 a2 90deg
According to the nomenclature established by Guinieret al (1984) the MDO1 and MDO2 polytypes should bedenoted as brochantite-2M1 and brochantite-2M2 respec-tively both presenting two layers within the unit a transla-tion Distinction can be made between the two polytypesthrough their diffraction pattern in which we found asusual in OD structures two distinct classes of reflectionsnamely the family and the characteristic reflections Thefamily reflections which in the present family have evenl indices are independent from the stacking of the layersand remain sharp and unchanged in all the ordered anddisordered structures of the family These reflections corre-spond to the so-called lsquofamily structurersquo which is closelyrelated to the structures of the family and displays in thepresent case space group symmetry Pbnm witha = 1272 Aring b = 985 and c = 301
The characteristic (non-family) reflections (those withodd l indices) depend both in position and intensity on thestacking of layers and consequently are typical of eachsequence They may be more or less diffuse sometimesappearing as continuous streaks
A detailed discussion of the diffractional effects in thewhole brochantite family is presented in Appendix Theresults obtained in Appendix were helpful for distin-guishing the polytypes occurring in the examined speci-mens as discussed in the following section
Experimental
A systematic X-ray diffraction study of brochantitecrystals from specimens preserved in the mineralogicalcollection of the Natural History Museum of PisaUniversity was carried out using the Weissenberg tech-nique All the examined crystals showed the presence of
variable degrees of structural disorder and the MDO1 poly-type was found in the majority of the specimens On theother hand apart from the Capo Calamita crystalsevidence for the existence of MDO2 polytype was found inthe diffraction patterns of crystals from the Italian localitiesof Trentin mine (Veneto) Sa Duchessa mine (Sardinia)and Val Fucinaia (Tuscany) These patterns correspond tothe overlapping of the reciprocal lattices of the MDO1MDO1rsquo and MDO2 polytypes and point to the co-existenceof the two distinct MDO polytypes in those specimens
Intensity data were collected with a Siemens P4 four-circle diffractometer from crystals previously tested usingWeissenberg photographs and made up of almost pureMDO1 (Val Fucinaia) and MDO2 (Capo Calamita) poly-types experimental details and crystallographic data forboth structural studies are given in Table 1
In the structure refinement of MDO1 polytype we usedas a starting model the results of the study by Cocco amp
OD character of brochantite 269
Fig 2 The crystal structures of MDO1 (a) and MDO2 (b) poly-types as seen along b In both cases the sequences of 212 and 2-
12 s-operations are indicated The other indicated l- ands-operations are just those which become total symmetry opera-tions in both polytypes
S Merlino N Perchiazzi D Franco270
Table 1 Crystal data and refinement details for MDO1 and MDO2 brochantite polytypes
Wavelength 071073 Aring MDO1 polytype MDO2 polytypeLocality Val Fucinaia Capo CalamitaMonoclinic P 1 21a 1 P 21n 1 1Unit cell dimensions a = 13140(2) Aring 12776(2) Aring
b = 9863(2) Aring 9869(2) Aringc = 6024(1) Aring 6026(1) Aringb = 10316(3) deg a = 9015(3) deg
Crystal size 014 014 003 mm 009 008 004 mmq range for data collection 4 to 5128 deg 4 to 50 degIndex ranges -7 pound h pound 7 -11 pound k pound 1 -1 pound l pound 15 -1 pound h pound 11 -1 pound k pound 15 -7 pound l pound 7Reflections collected unique 1643 1239 [Rint = 00415] 1821 1334 [Rint = 00638]Absorption correction y-scan on 14 reflections on 12 reflectionsRefinement method Full-matrix least-squares on F2
Final R1 indexa [Fo gt4s( Fo)] R1 = 00488 (831 refl) R1 = 00619 (607 refl) Data restraints parameters 1239 6 137 1334 0 86Goodness-of-fita (all data) 1071 0893wR2 a (all data) 01481 02084Largest diff peak and hole 119 and -128 e Aring-3 257 and ndash112 e Aring-3
Note a Goodness-of-fit = [S [w(Fo2-Fc
2)2](N-P)]12 where N P are the numbers of observations and parametersrespectively R1 = S Fo Fc S Fo w R2 = [S[w(Fo
2-Fc2)2 ] S[ w(Fo
2)2]]12 w = 1 [s 2 (Fo2) +
(00243Q)2 + 057Q] where Q = [MAX(Fo20) + 2Fc
2] 3
Table 2 a) Final positional and displacement parameters (Aring2) for MDO1 polytype b) calculated positional coordinates and final posi-tional and displacement parameters (Aring2) for MDO2 polytype
a) MDO1 polytype
x y z Ueq
Cu1 02061(1) 09911(2) 04799(3) 00207(4)Cu2 02023(1) 09908(3) -00237(3) 00244(5)Cu3 01181(1) 02614(2) 01819(3) 00185(4)Cu4 01199(1) 02571(2) 06848(3) 00197(4)S 03877(2) 01989(4) 03167(5) 00233(7)O1 00936(6) 01325(9) 0417(1) 0022(2)O2 00827(6) 01345(9) -0082(1) 0022(2)O3 01590(6) 03823(9) 0454(1) 0021(2)O4 01556(6) 03826(9) -0052(1) 0020(2)O5 02559(6) 00936(9) 0758(1) 0022(2)O6 01428(6) 08991(9) 0198(1) 0023(2)O7 02797(6) 0145(1) 0260(1) 0027(2)O8 03822(7) 0351(1) 0312(2) 0028(2)O9 04435(6) 0149(1) 0142(1) 0029(2)O10 04415(6) 0152(1) 0547(1) 0026(3)
b) MDO2 polytype
x y z x y z Ueq or Uiso
Cu1 02061 09911 03768 Cu1 02066(2) 09902(3) 03770(5) 00118(7)Cu2 02023 09908 -01248 Cu2 02019(2) 09906(3) -01249(5) 00135(7)Cu3 01181 02608 01228 Cu3 01183(2) 02608(3) 01261(4) 00111(6)Cu4 01199 02571 06249 Cu4 01205(2) 02569(3) 06258(4) 00109(7)S 03877 01989 01229 S 03881(4) 01991(5) 01226(9) 0015(1)O1 00936 01325 03704 O1 0091(1) 0130(2) 0374(2) 0016(4)O2 00827 01345 -01229 O2 0084(1) 0136(1) -0125(2) 0009(3)O3 01590 03823 03759 O3 0158(1) 0381(2) 0374(2) 0014(4)O4 01556 03826 -01298 O4 0158(1) 0385(2) -0122(2) 0012(3)O5 02559 00936 06300 O5 0258(1) 0094(2) 0628(3) 0023(4)O6 01428 08991 01264 O6 0142(1) 0897(2) 0124(2) 0019(3)O7 02797 01451 01205 O7 0275(1) 0141(2) 0126(3) 0023(4)O8 03822 03510 01208 O8 0383(1) 0352(2) 0125(2) 0016(3)O9 04435 01488 -00799 O9 0442(1) 0147(2) -0084(3) 0023(4)O10 04415 01523 03267 O10 0443(1) 0150(2) 0329(3) 0020(3)
Mazzi (1959) After some isotropic refinement cyclesanisotropic displacement factors were introduced for all theatoms Refinement readily converged to R1 = 0049 Finalpositional coordinates and displacement isotropic equiva-lent Ueq parameters for MDO1 are reported in Table 2a
The starting atomic coordinates for MDO2 polytypewere derived through OD considerations from the finalpositional coordinates of the MDO1 polytype (matrix trans-formation for coordinates [100010-1201]) The non-stan-dard space group P21n11 was chosen for MDO2 polytypeto allow an easier comparison between the two polytypes
After some isotropic refinement cycles anisotropicdisplacement factors were introduced only for Cu and SThe refinement converged to R1 = 0062 for MDO2
The calculated coordinates are closely similar to thoseobtained from the structural refinement indicating that theOD layers are remarkably similar in the two polytypesThere is also a clear indication that the atomic positionsconform to the symmetry of the single layer Cu3 O6 O7O8 and S are located on the mirror plane at z = 0125(l operation of the single layer) Cu4 and O5 are located onthe mirror plane at z = 0625 while O2 O4 and Cu2 aresymmetrically related to O1 O3 and Cu1 respectively onboth sides of the mirror plane at z = 0125 Clearly thelsquoidealrsquo symmetry of the single layer is not perfectly main-tained in the real structures of the two polytypes whichactually present a slight lsquodesymmetrizationrsquo (Egrave urovi 1979)
OD character of brochantite 271
Table 3 Bond distances (Aring) and angles (deg) in the coordination polyhedra of MDO1 (a) and MDO2 (b) polytypes
a) Brochantite-2M1
Cu1 Cu2 Cu3 Cu4 SO6 194(1) O5iii 192(1) O1 198(1) O4v 198(1) O7 148(1)O5i 194(1) O6 192(1) O4 199(1) O1 199(1) O10 148(1)O1i 201(1) O2i 209(1) O2 199(1) O2v 200(1) O9 150(1)O3ii 203(1) O4iv 211(1) O3 201(1) O3 201(1) O8 150(1)O8ii 234(1) O8iv 230(1) O7 236(1) O5 237(1)O7i 236(1) O7i 234(1) O9v 242(1) O10vi 247(1)
O1i-Cu1-O3ii 1677(3) O2i-Cu2-O4iv1676(3) O1-Cu3-O2 969(3) O1-Cu4-O2v 998(3) O7-S-O8 1084(6)O1i-Cu1-O5i 836(3) O2i-Cu2-O5iii 846(3) O1-Cu3-O3 814(3) O1-Cu4-O3 812(3) O7-S-O9 1085(5)O1i-Cu1-O6 905(3) O2i-Cu2-O6 915(3) O1-Cu3-O4 1747(3) O1-Cu4-O4v 1763(3) O7-S-O10 1094(5)O3ii-Cu1-O5i 901(3) O4iv -Cu2-O5iii 883(3) O2-Cu3-O3 1771(3) O2v-Cu4-O3 1789(3) O8-S-O9 1102(6)O3ii-Cu1-O6 959(3) O4iv -Cu2-O6 953(3) O2-Cu3-O4 822(3) O2v-Cu4-O4v 823(3) O8-S-O10 1097(6)O5i-Cu1-O6 1740(3) O5iii-Cu2-O6 1758(4) O3-Cu3-O4 993(3) O3-Cu4-O4v 967(3) O9-S-O10 1106(5)
Symmetry transformations used to generate equivalent atoms in MDO1 polytypei atom at x 1+y zii 12-x 12 +y 1-ziii x 1+y z-1iv 12 -x 12 +y -zv x y z+1vi x-12 12-y z
b) Brochantite-2M2
Cu1 Cu2 Cu3 Cu4 SO6 196(1) O6 192(1) O3 197(1) O2vi 198(1) O10 151(1)O5i 194(2) O5iii 194(2) O2 200(1) O1 200(1) O10 151(2)O1i 202(1) O2i 208(1) O4 200(1) O3 201(1) O8 151(1)O4ii 202(1) O3iv 209(1) O1 201(1) O4vi 203(1) O7 155(2)O7i 230(1) O8iv 230(1) O7 233(1) O5 238(1)O8ii 233(1) O7i 231(2) O10 242(1) O9v 248(2)
O1i-Cu1-O4ii 1679(6) O2i-Cu2-O3iv 1676(6) O1-Cu3-O2 974(6) O1-Cu4-O2vi 988(6) O7-S-O8 1092(9)O1i-Cu1-O5i 840(6) O2i-Cu2-O5iii 845(6) O1-Cu3-O3 824(6) O1-Cu4-O3 816(6) O7-S-O9 1081(9)O1i-Cu1-O6 903(6) O2i-Cu2-O6 926(6) O1-Cu3-O4 1751(7) O1-Cu4-O4vi 1772(6) O7-S-O10 1076(9)O4ii-Cu1-O5i 887(6) O3iv-Cu2-O5iii 873(6) O2-Cu3-O3 1776(6) O2vi-Cu4-O3 1796(6) O8-S-O9 1116(9)O4ii-Cu1-O6 970(6) O3iv-Cu2-O6 953(6) O2-Cu3-O4 823(6) O2vi-Cu4-O4vi 821(6) O8-S-O10 1095(9)O5i-Cu1-O6 1743(6) O5iii-Cu1-O6 1769(6) O3-Cu3-O4 977(6) O3-Cu4-O4vi 975(6) O9-S-O10 1108(8)
Symmetry transformations used to generate equivalent atoms in MDO2 polytypei atom at x 1+y zii 12-x 12+y 12+ziii x1+y z-1iv 12-x 12+y z-12v x-12 12-Y 12-zvi x y z+1
S Merlino N Perchiazzi D Franco
The table of anisotropic displacement parameters andthe lists of the FoFc data for both polytypes are availablefrom the authors upon request (or through the EJMEditorial Office Paris)
Structure description
The results of the present structural study are given inTables 3 and 4 The main features of the crystal structure ofbrochantite were already outlined by Cocco amp Mazzi(1959) More accurate data were subsequently obtained byHelliwell amp Smith (1997) on a very tiny (015x005x001mm) untwinned crystal from Socorro County NewMexico USA using data collected with a rotating anodediffractometer (MoKa radiation)
As regards the Cu and S coordination polyhedra boththe data of Helliwell amp Smith (1997) and our resultssubstantially agree with Cocco amp Mazzirsquos (1959) modelAs expected from their polytypic nature the coordinationpolyhedra and their linking are essentially the same inMDO1 and MDO2 polytypes (Table 3) so in the followingstructure description we refer only to the data obtained forthe MDO1 polytype The sulphate tetrahedron is veryregular in the MDO1 structure whereas it is slightly largerand a little more distorted in the MDO2 structure As shownin Table 3 Cu octahedra due to the Jahn-Teller effect arestrongly distorted towards an elongated tetragonal bipyra-midal coordination Four hydroxyls with Cu-OH distancesclose to 2 Aring are arranged in a nearly planar square coordi-nation with two additional longer bonds about 23 Aring inlength to complete the sixfold coordination
In Fig 1 and 2 the structures are represented assumingfourfold coordination around the copper atoms Cu3 andCu4 exhibit a nearly square planar coordination with fourCu-O distances between 198 and 201 Aring whereas Cu1 andCu2 exhibit two shorter (192 to 194 Aring) and two longer(201 and 203 Aring in Cu1 209 and 211 Aring in Cu2 coordi-
nation) distances Moreover the oxygen atoms around Cu1and Cu2 slightly deviate from a square-planar coordina-tion which explains the different representation of the twofourfold coordinations in Fig 1 and 2
In these Figures the Cu3- and Cu4-squares are inter-connected through common edges to build infinite planarchains running along c The Cu1- and Cu2-squares repre-sented as strongly squeezed tetrahedra are interconnectedby sharing vertices (O5 and O6 hydroxyl groups) to buildlsquozig-zagrsquo chains running along c Both chains areconnected one to the other by shared vertices to build infi-nite layers parallel to (100) [Cocco amp Mazzi (1959 Fig 8in their paper] The layers are seen along b in Fig 1 and 2where they appear distincly separated from each otherwhich indicates that in the present case the OD layerscorrespond to crystal chemically significant layers whichis not generally the case in OD structures
If we complete the octahedral coordination around eachcopper atom as represented in Fig 3 we can observe thatsubsequent layers are actually connected through thesulphate groups Accordingly in their presentation of astructural hierarchy for sulphate minerals Hawthorne et al(2000) placed brochantite among the structures with infi-nite frameworks as being built up of double chains ofcopper octahedra that are cross-linked by SO4 tetrahedra toform frameworks Sabelli amp Trosti-Ferroni (1985)presented a different kind of structural classification ofsulphate minerals based on the lsquomode of linking of thepolyhedra of the metals present in the mineralsrsquo assigningsulphate minerals to four structural type (insular chainsheet and framework) and 22 sub-types Within their clas-sification brochantite belongs to sub-type 14 in the sheettype as characterized by single undulating layers of copperoctahedra parallel to (100) (Fig 3)
The connection between these layers is ensured not onlyby sulphate tetrahedra but also by hydrogen bondsHelliwell amp Smith (1997) presented a hydrogen bondingsystem on the basis of the hydrogen positions determined
272
Table 4 Bond valence (vu) in brochantite-2M1 (MDO1 polytype)
O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 Sav
Cu1 0409 0387 0494 0494 0154 0168 1952Cu2 0329 0312 0521 0507 0168 0182 2019Cu3 0443 0420 0420 0431 0159 0135 2008Cu4 0431 0420 0409 0443 0154 0115 1972S 1476 1436 1436 1436 5784Scv 1283 1169 1216 1186 1169 1001 1957 1786 1571 1551Srsquocv 1061 1008 1078 1043 0922 1162 1957 2008 1842 181
Scv is the sum of bond strengths reaching the anions Srsquocv after correction for hydrogen bonds
O1-O8iii 271(1) 0222 O5-O9i 302(1) 0126O3-O10iv 296(1) 0138 O5-O10 305(1) 0121O4-O9ii 293(2) 0145 O2-O6v 287(1) 0161
OmiddotmiddotmiddotO distances (Aring) and hydrogen bond strengths (vu) Ineach pair of hydrogen bonded oxygen atoms the first one isthe donor the second one is the acceptor Atom at i x y z+1 ii 12ndashx 12+y -z iii x-12 12-y ziv 12-x 12+y 1-z v x y-1 z
through difference Fourier syntheses Looking at Table 2 ofHelliwell amp Smith (1997) we can see that the D-HAangles are far from ideal and that the O3-H3O9 distancesinvolve two oxygen atoms belonging to the same polyhe-dron
Our hydrogen bonding scheme was derived by lookingat the distances shorter than 31 Aring between oxygen atomsand not belonging to the same polyhedron These distancesare reported in Table 4 together with the bond valencebalance The Scv row shows the sums of bond strengthscalculated following Brese amp OrsquoKeeffe (1991) whereas inthe Srsquocv row these sums are corrected for hydrogen bondcontributions evaluated according to Ferraris amp Ivaldi(1988) The balance can be considered as quite satisfac-tory Among the oxygen atoms of the sulphate group (withthe exception of O7 which is linked to three Cu atoms) O8O9 and O10 are all taken up as acceptors O9 anionreceives two contributions from O4 and O5 hydroxylsthis latter forming a bifurcated bond with O9 and O10anions belonging to different sulphate groups Our datatherefore validate the assignment of the OH bands madeby Schmidt amp Lutz (1993) on the basis of infrared andRaman spectra all the hydrogen bonds shown in Table 4are consistent with those indicated by Schmidt amp Lutz(1993) moreover there is a close inverse relation betweenOO bond lengths given in our Table 4 and the stretchingfrequences reported by Schmidt amp Lutz (1993) Thehighest stretching frequency given in their Table 3 corre-sponds to a bifurcated hydrogen bond of O6 with O9 andO10 not included in our Table 4 For this bond we foundOO distances of 324 Aring (0097 vu) and 321 Aring (vu0100) respectively If we correspondingly correct thebond valence sums for O6 O9 and O10 we obtain sumscloser to the ideal values
Conclusions
In the X-ray diffraction patterns of brochantite weobserve typical features of OD structures These compriseubiquitous twinning disorder along a definite directionnon space-group absences and the presence of distinctdiffraction classes namely family and characteristic reflec-tions Accordingly we show that the crystal structure ofbrochantite may be conveniently described as built up ofOD layers with layer group symmetry P(n)21m moreoverwe derive the two MDO polytypes in the OD family ofbrochantite The X-ray single-crystal study of specimensfrom various Italian localities allows us to define a newpolytype brochantite-2M2 (corresponding to one MDOstructure) in addition to the ldquonormalrdquo brochantite-2M1(corresponding to another MDO structure) This new poly-type is found in specimens from four distinct mineralogicallocalities The crystal structure of this new polytype isoutlined on the basis of OD considerations and successfullyrefined It is possible that more complex polytypes exist atleast as small domains embodied within larger domains ofthe two main polytypes Their presence could be reliablydetermined only through electron diffraction and HRTEMstudies
Whereas our study was carried out on relativelylsquogoodrsquo brochantite crystals it would be interesting toinvestigate brochantite occurring as decay products in theurbanindustrial environment more specif ically as aconstituent of the green patinas formed in the deteriora-tion of copper and bronze manufacts In these patinasbrochantite is commonly found as massive or dustyencrustations not suitable for X-ray single-crystal studyOn the other hand an unambiguous distinction betweenthe brochantite polytypes cannot be made on the basis ofpowder data only as all polytypes exhibit commonlsquofamily reflectionsrsquo with intensities largely dominatingover the characteristic reflections Electron diffractionand HRTEM studies appear necessary to distinguishbetween the two main polytypes and would also be usefulin indicating the presence of other more complex poly-types
Acknowledgement This work was supported by theUniversity of Pisa and MIUR (Ministero dellrsquoUniversitagrave edella Ricerca Scientifica) through grants to the projectlsquoTransformations reactions ordering in mineralsrsquo
Appendix
Discussion of the diffraction pattern on the basis of the OD character of brochantite
It is useful to discuss the common features of all poly-types (and also of the disordered sequences) in the wholeOD family as well as the distinctive features of thedifferent polytypes In particular it is relevant to indicatethe diffractions which characterize the two most importantpolytypes MDO1 and MDO2 It is correct in this respect torefer to the orthogonal cell with AO = 4ao = 2546 AringBO = b = 985 Aring CO = c = 602 Aring In fact this cell is thecommon cell of both polytypes being a B centred cell for
OD character of brochantite 273
Fig 3 The crystal structure of brochantite-2M1 as seen along cshowing the interconnection of the undulating layers of copperoctahedra parallel to (100) with the sulphate groups
S Merlino N Perchiazzi D Franco
the polytype MDO1 and doubly primitive for the polytypeMDO2 (Fig 4)
The single structural layer has symmetry P(n)21m andis repeated by the operation n122 (normal to b with trans-lational component ao+c4) The Fourier transform of thewhole structure (structure factor F) may be obtained bysumming the contributions of the successive layers takingaccount of their relative positions
We shall indicate fo(hkl) as the contribution of the layerL0 The indices k and l are integers and correspond to the band c translations of the layer whereas h is a continuousvariable corresponding to axis A the direction of missingperiodicity The next layer gives a contribution
f1(hkl) = fo(hndashkl) exp[2pi(h4+k2plusmnl4)]
as for every atom at xjyjzj in the layer L0 there is an equalatom at xj+14 12-yj zjplusmn14 in the layer L1 It can be seenthat all the even layers L2p and all the odd layers L2p+1 aretranslationally equivalent to the layers L0 and L1 respec-tively according to the same translation vector
T2p = pA2 + a2pc2 with a2p = 0 1
The Fourier transform of the whole structure may beexpressed as
F(hkl) = fo(hkl) + fo(hndashkl) exp[2pi(h4+k2plusmnl4)] S(hkl) (1)
S(hkl) = 1(2M) Sp exp[2pi(ph2+a2p l2)] (2)
For l = 2L the expression is independent of the param-eter a2p and therefore of the degree of disorder For largevalues of M the expression tends to zero except whenh = h = 2H with integer H Therefore the reflections witheven l (and even h) are common to the whole OD familyand are always sharp (family reflections)
Moreover we observe that for k = 0 (and consideringonly the family reflections namely for even l and h) thefirst factor in expression (1) gives
F(H0L) = fo(H0L) [1 + exp[2pi(H2plusmnL2)]
This factor becomes zero for H+L = 2n+1 The diffrac-tion pattern of the two main polytypes differs only in theodd l reflections In the case of MDO1 (and MDO1rsquo) thevalue of the parameter a2p in the general expression (2) is1 Therefore for l = 2L+1 (the case of l = 2L is alreadyconsidered in a general way)
S(hkl) = (12M) Sp exp[2pi(ph2+(2L+1)2)]
For large values of M this expression tends to zeroexcept when h = h = 2H+1
In the case of MDO2 the value of the parameter a2p is0 therefore for l = 2L+1
S(hkl) = (12M) Sp exp[2pi(ph2]
For large values of M this expression tends to zeroexcept for even integer values of h ie for h = h = 2HFigure 5 presents the diffraction pattern of a crystalpresenting both main polytypes indicating the familyreflections and the characteristic reflections of both MDOstructures Three subsequent planes of the reciprocal latticeare shown with k = 0 1 and 2 As indicated in the Figure0kl reflections are present for odd l values (non-familyreflections) only at k odd values due to the symmetry ofthe single layer
References
Brese NE amp OrsquoKeeffe M (1991) Bond-valence parameters forsolids Acta Cryst B47 192-197
Cocco G amp Mazzi F (1959) La struttura della brochantitePeriod Mineral 28 121-149
274
Fig 4 Relationships between the common orthogonal cell and thecells of the two polytypes MDO1 and MDO2
Fig 5 Diffraction pattern of a brochantite crystal presenting bothmain polytypes The non-family reflections (odd l values) are repre-sented with short (for MDO2 reflections) and long (for MDO1 +MDO1rsquo reflections) dashes
Dornberger-Schiff K (1956) On the order disorder structures(OD-structures) Acta Cryst 9 593-601
mdash (1964) Grundzuumlge einer Theorie von OD-Strukturen ausSchichten Abh Dtsch Akad Wiss Berlin Kl Chem GeolBiol 3 1-107
Egrave urovi S (1979) Desymmetrization of OD structures Krystallund Technik 14 1047-1053
mdash (1997) Fundamentals of the OD theory In Merlino (ed)ldquoModular aspects of mineralsrdquo EMU Notes in Mineralogy 13-28
Ferraris G amp Ivaldi G (1988) Bond valence vs bond length inOmiddotmiddotmiddotO hydrogen bonds Acta Cryst B44 341-344
Gettens RJ (1970) Patina noble and vile In ldquoArt andTechnology A Symposium on Classic Bronzesrdquo (eds SDoeringer DG Mitten and A Steinberg) pp 57-72 The MITpress Boston MA
Guinier A Bokij G B Boll-Dornberger K Cowley J MEgrave urovi S Jagodzinski H Krishna P de Wolff P MZvyagin B B Cox D E Goodman P Hahn Th KuchitsuK Abrahams S C (1984) Nomenclature of polytype struc-tures Report of the International Union of Crystallography ad-hoc Committee on the Nomenclature of Disordered Modulatedand Polytype Structures Acta Cryst A40 399-404
Hawthorne FC Krivovichev SV Burns PC (2000) The crystalchemistry of sulphate minerals In Alpers C N Jambor J Lamp Nordstrom B K (eds) ldquoSulfate mineralsrdquo Reviews inMineralogy amp Geochemistry 40 1-112
Helliwell M amp Smith JV (1997) Brochantite Acta Cryst C531369-1371
Lauro C (1939) Brochantite della miniera di ldquoSa Duchessardquo(Sardegna) Period Mineral 3 327-341
mdash (1941) Sulle costanti reticolari della brochantite PeriodMineral 3 419-427
Mattsson E amp Holm R (1982) Atmospheric corrosion of copperand its alloys In ldquoAtmospheric Corrosionrdquo (ed W H Ailor)Chap 24 pp 365-381 John Wiley New York
Merlino S (1997) OD approach in minerals examples and appli-cations In Merlino (ed) ldquoModular aspects of mineralsrdquo EMUNotes in Mineralogy 1 29-54
Palache C (1939) Brochantite Am Mineral 8 463-481Sabelli C amp Trosti-Ferroni R (1985) A structural classification
of sulphate minerals Period Mineral 54 1-46Schmidt M amp Lutz HD (1993) Hydrogen bonding in basic
copper salts a spectroscopic study of malachite Cu2(OH)2CO3and brochantite Cu4(OH)6SO4 Phys Chem Mineral 2027-32
Woods TL amp Garrels RM (1986) Use of oxidized copperminerals as environmental indicators Appl Geochem 1181-187
Received 8 January 2002Modified version received 29 July 2002Accepted 12 November 2002
OD character of brochantite 275
S Merlino N Perchiazzi D Franco270
Table 1 Crystal data and refinement details for MDO1 and MDO2 brochantite polytypes
Wavelength 071073 Aring MDO1 polytype MDO2 polytypeLocality Val Fucinaia Capo CalamitaMonoclinic P 1 21a 1 P 21n 1 1Unit cell dimensions a = 13140(2) Aring 12776(2) Aring
b = 9863(2) Aring 9869(2) Aringc = 6024(1) Aring 6026(1) Aringb = 10316(3) deg a = 9015(3) deg
Crystal size 014 014 003 mm 009 008 004 mmq range for data collection 4 to 5128 deg 4 to 50 degIndex ranges -7 pound h pound 7 -11 pound k pound 1 -1 pound l pound 15 -1 pound h pound 11 -1 pound k pound 15 -7 pound l pound 7Reflections collected unique 1643 1239 [Rint = 00415] 1821 1334 [Rint = 00638]Absorption correction y-scan on 14 reflections on 12 reflectionsRefinement method Full-matrix least-squares on F2
Final R1 indexa [Fo gt4s( Fo)] R1 = 00488 (831 refl) R1 = 00619 (607 refl) Data restraints parameters 1239 6 137 1334 0 86Goodness-of-fita (all data) 1071 0893wR2 a (all data) 01481 02084Largest diff peak and hole 119 and -128 e Aring-3 257 and ndash112 e Aring-3
Note a Goodness-of-fit = [S [w(Fo2-Fc
2)2](N-P)]12 where N P are the numbers of observations and parametersrespectively R1 = S Fo Fc S Fo w R2 = [S[w(Fo
2-Fc2)2 ] S[ w(Fo
2)2]]12 w = 1 [s 2 (Fo2) +
(00243Q)2 + 057Q] where Q = [MAX(Fo20) + 2Fc
2] 3
Table 2 a) Final positional and displacement parameters (Aring2) for MDO1 polytype b) calculated positional coordinates and final posi-tional and displacement parameters (Aring2) for MDO2 polytype
a) MDO1 polytype
x y z Ueq
Cu1 02061(1) 09911(2) 04799(3) 00207(4)Cu2 02023(1) 09908(3) -00237(3) 00244(5)Cu3 01181(1) 02614(2) 01819(3) 00185(4)Cu4 01199(1) 02571(2) 06848(3) 00197(4)S 03877(2) 01989(4) 03167(5) 00233(7)O1 00936(6) 01325(9) 0417(1) 0022(2)O2 00827(6) 01345(9) -0082(1) 0022(2)O3 01590(6) 03823(9) 0454(1) 0021(2)O4 01556(6) 03826(9) -0052(1) 0020(2)O5 02559(6) 00936(9) 0758(1) 0022(2)O6 01428(6) 08991(9) 0198(1) 0023(2)O7 02797(6) 0145(1) 0260(1) 0027(2)O8 03822(7) 0351(1) 0312(2) 0028(2)O9 04435(6) 0149(1) 0142(1) 0029(2)O10 04415(6) 0152(1) 0547(1) 0026(3)
b) MDO2 polytype
x y z x y z Ueq or Uiso
Cu1 02061 09911 03768 Cu1 02066(2) 09902(3) 03770(5) 00118(7)Cu2 02023 09908 -01248 Cu2 02019(2) 09906(3) -01249(5) 00135(7)Cu3 01181 02608 01228 Cu3 01183(2) 02608(3) 01261(4) 00111(6)Cu4 01199 02571 06249 Cu4 01205(2) 02569(3) 06258(4) 00109(7)S 03877 01989 01229 S 03881(4) 01991(5) 01226(9) 0015(1)O1 00936 01325 03704 O1 0091(1) 0130(2) 0374(2) 0016(4)O2 00827 01345 -01229 O2 0084(1) 0136(1) -0125(2) 0009(3)O3 01590 03823 03759 O3 0158(1) 0381(2) 0374(2) 0014(4)O4 01556 03826 -01298 O4 0158(1) 0385(2) -0122(2) 0012(3)O5 02559 00936 06300 O5 0258(1) 0094(2) 0628(3) 0023(4)O6 01428 08991 01264 O6 0142(1) 0897(2) 0124(2) 0019(3)O7 02797 01451 01205 O7 0275(1) 0141(2) 0126(3) 0023(4)O8 03822 03510 01208 O8 0383(1) 0352(2) 0125(2) 0016(3)O9 04435 01488 -00799 O9 0442(1) 0147(2) -0084(3) 0023(4)O10 04415 01523 03267 O10 0443(1) 0150(2) 0329(3) 0020(3)
Mazzi (1959) After some isotropic refinement cyclesanisotropic displacement factors were introduced for all theatoms Refinement readily converged to R1 = 0049 Finalpositional coordinates and displacement isotropic equiva-lent Ueq parameters for MDO1 are reported in Table 2a
The starting atomic coordinates for MDO2 polytypewere derived through OD considerations from the finalpositional coordinates of the MDO1 polytype (matrix trans-formation for coordinates [100010-1201]) The non-stan-dard space group P21n11 was chosen for MDO2 polytypeto allow an easier comparison between the two polytypes
After some isotropic refinement cycles anisotropicdisplacement factors were introduced only for Cu and SThe refinement converged to R1 = 0062 for MDO2
The calculated coordinates are closely similar to thoseobtained from the structural refinement indicating that theOD layers are remarkably similar in the two polytypesThere is also a clear indication that the atomic positionsconform to the symmetry of the single layer Cu3 O6 O7O8 and S are located on the mirror plane at z = 0125(l operation of the single layer) Cu4 and O5 are located onthe mirror plane at z = 0625 while O2 O4 and Cu2 aresymmetrically related to O1 O3 and Cu1 respectively onboth sides of the mirror plane at z = 0125 Clearly thelsquoidealrsquo symmetry of the single layer is not perfectly main-tained in the real structures of the two polytypes whichactually present a slight lsquodesymmetrizationrsquo (Egrave urovi 1979)
OD character of brochantite 271
Table 3 Bond distances (Aring) and angles (deg) in the coordination polyhedra of MDO1 (a) and MDO2 (b) polytypes
a) Brochantite-2M1
Cu1 Cu2 Cu3 Cu4 SO6 194(1) O5iii 192(1) O1 198(1) O4v 198(1) O7 148(1)O5i 194(1) O6 192(1) O4 199(1) O1 199(1) O10 148(1)O1i 201(1) O2i 209(1) O2 199(1) O2v 200(1) O9 150(1)O3ii 203(1) O4iv 211(1) O3 201(1) O3 201(1) O8 150(1)O8ii 234(1) O8iv 230(1) O7 236(1) O5 237(1)O7i 236(1) O7i 234(1) O9v 242(1) O10vi 247(1)
O1i-Cu1-O3ii 1677(3) O2i-Cu2-O4iv1676(3) O1-Cu3-O2 969(3) O1-Cu4-O2v 998(3) O7-S-O8 1084(6)O1i-Cu1-O5i 836(3) O2i-Cu2-O5iii 846(3) O1-Cu3-O3 814(3) O1-Cu4-O3 812(3) O7-S-O9 1085(5)O1i-Cu1-O6 905(3) O2i-Cu2-O6 915(3) O1-Cu3-O4 1747(3) O1-Cu4-O4v 1763(3) O7-S-O10 1094(5)O3ii-Cu1-O5i 901(3) O4iv -Cu2-O5iii 883(3) O2-Cu3-O3 1771(3) O2v-Cu4-O3 1789(3) O8-S-O9 1102(6)O3ii-Cu1-O6 959(3) O4iv -Cu2-O6 953(3) O2-Cu3-O4 822(3) O2v-Cu4-O4v 823(3) O8-S-O10 1097(6)O5i-Cu1-O6 1740(3) O5iii-Cu2-O6 1758(4) O3-Cu3-O4 993(3) O3-Cu4-O4v 967(3) O9-S-O10 1106(5)
Symmetry transformations used to generate equivalent atoms in MDO1 polytypei atom at x 1+y zii 12-x 12 +y 1-ziii x 1+y z-1iv 12 -x 12 +y -zv x y z+1vi x-12 12-y z
b) Brochantite-2M2
Cu1 Cu2 Cu3 Cu4 SO6 196(1) O6 192(1) O3 197(1) O2vi 198(1) O10 151(1)O5i 194(2) O5iii 194(2) O2 200(1) O1 200(1) O10 151(2)O1i 202(1) O2i 208(1) O4 200(1) O3 201(1) O8 151(1)O4ii 202(1) O3iv 209(1) O1 201(1) O4vi 203(1) O7 155(2)O7i 230(1) O8iv 230(1) O7 233(1) O5 238(1)O8ii 233(1) O7i 231(2) O10 242(1) O9v 248(2)
O1i-Cu1-O4ii 1679(6) O2i-Cu2-O3iv 1676(6) O1-Cu3-O2 974(6) O1-Cu4-O2vi 988(6) O7-S-O8 1092(9)O1i-Cu1-O5i 840(6) O2i-Cu2-O5iii 845(6) O1-Cu3-O3 824(6) O1-Cu4-O3 816(6) O7-S-O9 1081(9)O1i-Cu1-O6 903(6) O2i-Cu2-O6 926(6) O1-Cu3-O4 1751(7) O1-Cu4-O4vi 1772(6) O7-S-O10 1076(9)O4ii-Cu1-O5i 887(6) O3iv-Cu2-O5iii 873(6) O2-Cu3-O3 1776(6) O2vi-Cu4-O3 1796(6) O8-S-O9 1116(9)O4ii-Cu1-O6 970(6) O3iv-Cu2-O6 953(6) O2-Cu3-O4 823(6) O2vi-Cu4-O4vi 821(6) O8-S-O10 1095(9)O5i-Cu1-O6 1743(6) O5iii-Cu1-O6 1769(6) O3-Cu3-O4 977(6) O3-Cu4-O4vi 975(6) O9-S-O10 1108(8)
Symmetry transformations used to generate equivalent atoms in MDO2 polytypei atom at x 1+y zii 12-x 12+y 12+ziii x1+y z-1iv 12-x 12+y z-12v x-12 12-Y 12-zvi x y z+1
S Merlino N Perchiazzi D Franco
The table of anisotropic displacement parameters andthe lists of the FoFc data for both polytypes are availablefrom the authors upon request (or through the EJMEditorial Office Paris)
Structure description
The results of the present structural study are given inTables 3 and 4 The main features of the crystal structure ofbrochantite were already outlined by Cocco amp Mazzi(1959) More accurate data were subsequently obtained byHelliwell amp Smith (1997) on a very tiny (015x005x001mm) untwinned crystal from Socorro County NewMexico USA using data collected with a rotating anodediffractometer (MoKa radiation)
As regards the Cu and S coordination polyhedra boththe data of Helliwell amp Smith (1997) and our resultssubstantially agree with Cocco amp Mazzirsquos (1959) modelAs expected from their polytypic nature the coordinationpolyhedra and their linking are essentially the same inMDO1 and MDO2 polytypes (Table 3) so in the followingstructure description we refer only to the data obtained forthe MDO1 polytype The sulphate tetrahedron is veryregular in the MDO1 structure whereas it is slightly largerand a little more distorted in the MDO2 structure As shownin Table 3 Cu octahedra due to the Jahn-Teller effect arestrongly distorted towards an elongated tetragonal bipyra-midal coordination Four hydroxyls with Cu-OH distancesclose to 2 Aring are arranged in a nearly planar square coordi-nation with two additional longer bonds about 23 Aring inlength to complete the sixfold coordination
In Fig 1 and 2 the structures are represented assumingfourfold coordination around the copper atoms Cu3 andCu4 exhibit a nearly square planar coordination with fourCu-O distances between 198 and 201 Aring whereas Cu1 andCu2 exhibit two shorter (192 to 194 Aring) and two longer(201 and 203 Aring in Cu1 209 and 211 Aring in Cu2 coordi-
nation) distances Moreover the oxygen atoms around Cu1and Cu2 slightly deviate from a square-planar coordina-tion which explains the different representation of the twofourfold coordinations in Fig 1 and 2
In these Figures the Cu3- and Cu4-squares are inter-connected through common edges to build infinite planarchains running along c The Cu1- and Cu2-squares repre-sented as strongly squeezed tetrahedra are interconnectedby sharing vertices (O5 and O6 hydroxyl groups) to buildlsquozig-zagrsquo chains running along c Both chains areconnected one to the other by shared vertices to build infi-nite layers parallel to (100) [Cocco amp Mazzi (1959 Fig 8in their paper] The layers are seen along b in Fig 1 and 2where they appear distincly separated from each otherwhich indicates that in the present case the OD layerscorrespond to crystal chemically significant layers whichis not generally the case in OD structures
If we complete the octahedral coordination around eachcopper atom as represented in Fig 3 we can observe thatsubsequent layers are actually connected through thesulphate groups Accordingly in their presentation of astructural hierarchy for sulphate minerals Hawthorne et al(2000) placed brochantite among the structures with infi-nite frameworks as being built up of double chains ofcopper octahedra that are cross-linked by SO4 tetrahedra toform frameworks Sabelli amp Trosti-Ferroni (1985)presented a different kind of structural classification ofsulphate minerals based on the lsquomode of linking of thepolyhedra of the metals present in the mineralsrsquo assigningsulphate minerals to four structural type (insular chainsheet and framework) and 22 sub-types Within their clas-sification brochantite belongs to sub-type 14 in the sheettype as characterized by single undulating layers of copperoctahedra parallel to (100) (Fig 3)
The connection between these layers is ensured not onlyby sulphate tetrahedra but also by hydrogen bondsHelliwell amp Smith (1997) presented a hydrogen bondingsystem on the basis of the hydrogen positions determined
272
Table 4 Bond valence (vu) in brochantite-2M1 (MDO1 polytype)
O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 Sav
Cu1 0409 0387 0494 0494 0154 0168 1952Cu2 0329 0312 0521 0507 0168 0182 2019Cu3 0443 0420 0420 0431 0159 0135 2008Cu4 0431 0420 0409 0443 0154 0115 1972S 1476 1436 1436 1436 5784Scv 1283 1169 1216 1186 1169 1001 1957 1786 1571 1551Srsquocv 1061 1008 1078 1043 0922 1162 1957 2008 1842 181
Scv is the sum of bond strengths reaching the anions Srsquocv after correction for hydrogen bonds
O1-O8iii 271(1) 0222 O5-O9i 302(1) 0126O3-O10iv 296(1) 0138 O5-O10 305(1) 0121O4-O9ii 293(2) 0145 O2-O6v 287(1) 0161
OmiddotmiddotmiddotO distances (Aring) and hydrogen bond strengths (vu) Ineach pair of hydrogen bonded oxygen atoms the first one isthe donor the second one is the acceptor Atom at i x y z+1 ii 12ndashx 12+y -z iii x-12 12-y ziv 12-x 12+y 1-z v x y-1 z
through difference Fourier syntheses Looking at Table 2 ofHelliwell amp Smith (1997) we can see that the D-HAangles are far from ideal and that the O3-H3O9 distancesinvolve two oxygen atoms belonging to the same polyhe-dron
Our hydrogen bonding scheme was derived by lookingat the distances shorter than 31 Aring between oxygen atomsand not belonging to the same polyhedron These distancesare reported in Table 4 together with the bond valencebalance The Scv row shows the sums of bond strengthscalculated following Brese amp OrsquoKeeffe (1991) whereas inthe Srsquocv row these sums are corrected for hydrogen bondcontributions evaluated according to Ferraris amp Ivaldi(1988) The balance can be considered as quite satisfac-tory Among the oxygen atoms of the sulphate group (withthe exception of O7 which is linked to three Cu atoms) O8O9 and O10 are all taken up as acceptors O9 anionreceives two contributions from O4 and O5 hydroxylsthis latter forming a bifurcated bond with O9 and O10anions belonging to different sulphate groups Our datatherefore validate the assignment of the OH bands madeby Schmidt amp Lutz (1993) on the basis of infrared andRaman spectra all the hydrogen bonds shown in Table 4are consistent with those indicated by Schmidt amp Lutz(1993) moreover there is a close inverse relation betweenOO bond lengths given in our Table 4 and the stretchingfrequences reported by Schmidt amp Lutz (1993) Thehighest stretching frequency given in their Table 3 corre-sponds to a bifurcated hydrogen bond of O6 with O9 andO10 not included in our Table 4 For this bond we foundOO distances of 324 Aring (0097 vu) and 321 Aring (vu0100) respectively If we correspondingly correct thebond valence sums for O6 O9 and O10 we obtain sumscloser to the ideal values
Conclusions
In the X-ray diffraction patterns of brochantite weobserve typical features of OD structures These compriseubiquitous twinning disorder along a definite directionnon space-group absences and the presence of distinctdiffraction classes namely family and characteristic reflec-tions Accordingly we show that the crystal structure ofbrochantite may be conveniently described as built up ofOD layers with layer group symmetry P(n)21m moreoverwe derive the two MDO polytypes in the OD family ofbrochantite The X-ray single-crystal study of specimensfrom various Italian localities allows us to define a newpolytype brochantite-2M2 (corresponding to one MDOstructure) in addition to the ldquonormalrdquo brochantite-2M1(corresponding to another MDO structure) This new poly-type is found in specimens from four distinct mineralogicallocalities The crystal structure of this new polytype isoutlined on the basis of OD considerations and successfullyrefined It is possible that more complex polytypes exist atleast as small domains embodied within larger domains ofthe two main polytypes Their presence could be reliablydetermined only through electron diffraction and HRTEMstudies
Whereas our study was carried out on relativelylsquogoodrsquo brochantite crystals it would be interesting toinvestigate brochantite occurring as decay products in theurbanindustrial environment more specif ically as aconstituent of the green patinas formed in the deteriora-tion of copper and bronze manufacts In these patinasbrochantite is commonly found as massive or dustyencrustations not suitable for X-ray single-crystal studyOn the other hand an unambiguous distinction betweenthe brochantite polytypes cannot be made on the basis ofpowder data only as all polytypes exhibit commonlsquofamily reflectionsrsquo with intensities largely dominatingover the characteristic reflections Electron diffractionand HRTEM studies appear necessary to distinguishbetween the two main polytypes and would also be usefulin indicating the presence of other more complex poly-types
Acknowledgement This work was supported by theUniversity of Pisa and MIUR (Ministero dellrsquoUniversitagrave edella Ricerca Scientifica) through grants to the projectlsquoTransformations reactions ordering in mineralsrsquo
Appendix
Discussion of the diffraction pattern on the basis of the OD character of brochantite
It is useful to discuss the common features of all poly-types (and also of the disordered sequences) in the wholeOD family as well as the distinctive features of thedifferent polytypes In particular it is relevant to indicatethe diffractions which characterize the two most importantpolytypes MDO1 and MDO2 It is correct in this respect torefer to the orthogonal cell with AO = 4ao = 2546 AringBO = b = 985 Aring CO = c = 602 Aring In fact this cell is thecommon cell of both polytypes being a B centred cell for
OD character of brochantite 273
Fig 3 The crystal structure of brochantite-2M1 as seen along cshowing the interconnection of the undulating layers of copperoctahedra parallel to (100) with the sulphate groups
S Merlino N Perchiazzi D Franco
the polytype MDO1 and doubly primitive for the polytypeMDO2 (Fig 4)
The single structural layer has symmetry P(n)21m andis repeated by the operation n122 (normal to b with trans-lational component ao+c4) The Fourier transform of thewhole structure (structure factor F) may be obtained bysumming the contributions of the successive layers takingaccount of their relative positions
We shall indicate fo(hkl) as the contribution of the layerL0 The indices k and l are integers and correspond to the band c translations of the layer whereas h is a continuousvariable corresponding to axis A the direction of missingperiodicity The next layer gives a contribution
f1(hkl) = fo(hndashkl) exp[2pi(h4+k2plusmnl4)]
as for every atom at xjyjzj in the layer L0 there is an equalatom at xj+14 12-yj zjplusmn14 in the layer L1 It can be seenthat all the even layers L2p and all the odd layers L2p+1 aretranslationally equivalent to the layers L0 and L1 respec-tively according to the same translation vector
T2p = pA2 + a2pc2 with a2p = 0 1
The Fourier transform of the whole structure may beexpressed as
F(hkl) = fo(hkl) + fo(hndashkl) exp[2pi(h4+k2plusmnl4)] S(hkl) (1)
S(hkl) = 1(2M) Sp exp[2pi(ph2+a2p l2)] (2)
For l = 2L the expression is independent of the param-eter a2p and therefore of the degree of disorder For largevalues of M the expression tends to zero except whenh = h = 2H with integer H Therefore the reflections witheven l (and even h) are common to the whole OD familyand are always sharp (family reflections)
Moreover we observe that for k = 0 (and consideringonly the family reflections namely for even l and h) thefirst factor in expression (1) gives
F(H0L) = fo(H0L) [1 + exp[2pi(H2plusmnL2)]
This factor becomes zero for H+L = 2n+1 The diffrac-tion pattern of the two main polytypes differs only in theodd l reflections In the case of MDO1 (and MDO1rsquo) thevalue of the parameter a2p in the general expression (2) is1 Therefore for l = 2L+1 (the case of l = 2L is alreadyconsidered in a general way)
S(hkl) = (12M) Sp exp[2pi(ph2+(2L+1)2)]
For large values of M this expression tends to zeroexcept when h = h = 2H+1
In the case of MDO2 the value of the parameter a2p is0 therefore for l = 2L+1
S(hkl) = (12M) Sp exp[2pi(ph2]
For large values of M this expression tends to zeroexcept for even integer values of h ie for h = h = 2HFigure 5 presents the diffraction pattern of a crystalpresenting both main polytypes indicating the familyreflections and the characteristic reflections of both MDOstructures Three subsequent planes of the reciprocal latticeare shown with k = 0 1 and 2 As indicated in the Figure0kl reflections are present for odd l values (non-familyreflections) only at k odd values due to the symmetry ofthe single layer
References
Brese NE amp OrsquoKeeffe M (1991) Bond-valence parameters forsolids Acta Cryst B47 192-197
Cocco G amp Mazzi F (1959) La struttura della brochantitePeriod Mineral 28 121-149
274
Fig 4 Relationships between the common orthogonal cell and thecells of the two polytypes MDO1 and MDO2
Fig 5 Diffraction pattern of a brochantite crystal presenting bothmain polytypes The non-family reflections (odd l values) are repre-sented with short (for MDO2 reflections) and long (for MDO1 +MDO1rsquo reflections) dashes
Dornberger-Schiff K (1956) On the order disorder structures(OD-structures) Acta Cryst 9 593-601
mdash (1964) Grundzuumlge einer Theorie von OD-Strukturen ausSchichten Abh Dtsch Akad Wiss Berlin Kl Chem GeolBiol 3 1-107
Egrave urovi S (1979) Desymmetrization of OD structures Krystallund Technik 14 1047-1053
mdash (1997) Fundamentals of the OD theory In Merlino (ed)ldquoModular aspects of mineralsrdquo EMU Notes in Mineralogy 13-28
Ferraris G amp Ivaldi G (1988) Bond valence vs bond length inOmiddotmiddotmiddotO hydrogen bonds Acta Cryst B44 341-344
Gettens RJ (1970) Patina noble and vile In ldquoArt andTechnology A Symposium on Classic Bronzesrdquo (eds SDoeringer DG Mitten and A Steinberg) pp 57-72 The MITpress Boston MA
Guinier A Bokij G B Boll-Dornberger K Cowley J MEgrave urovi S Jagodzinski H Krishna P de Wolff P MZvyagin B B Cox D E Goodman P Hahn Th KuchitsuK Abrahams S C (1984) Nomenclature of polytype struc-tures Report of the International Union of Crystallography ad-hoc Committee on the Nomenclature of Disordered Modulatedand Polytype Structures Acta Cryst A40 399-404
Hawthorne FC Krivovichev SV Burns PC (2000) The crystalchemistry of sulphate minerals In Alpers C N Jambor J Lamp Nordstrom B K (eds) ldquoSulfate mineralsrdquo Reviews inMineralogy amp Geochemistry 40 1-112
Helliwell M amp Smith JV (1997) Brochantite Acta Cryst C531369-1371
Lauro C (1939) Brochantite della miniera di ldquoSa Duchessardquo(Sardegna) Period Mineral 3 327-341
mdash (1941) Sulle costanti reticolari della brochantite PeriodMineral 3 419-427
Mattsson E amp Holm R (1982) Atmospheric corrosion of copperand its alloys In ldquoAtmospheric Corrosionrdquo (ed W H Ailor)Chap 24 pp 365-381 John Wiley New York
Merlino S (1997) OD approach in minerals examples and appli-cations In Merlino (ed) ldquoModular aspects of mineralsrdquo EMUNotes in Mineralogy 1 29-54
Palache C (1939) Brochantite Am Mineral 8 463-481Sabelli C amp Trosti-Ferroni R (1985) A structural classification
of sulphate minerals Period Mineral 54 1-46Schmidt M amp Lutz HD (1993) Hydrogen bonding in basic
copper salts a spectroscopic study of malachite Cu2(OH)2CO3and brochantite Cu4(OH)6SO4 Phys Chem Mineral 2027-32
Woods TL amp Garrels RM (1986) Use of oxidized copperminerals as environmental indicators Appl Geochem 1181-187
Received 8 January 2002Modified version received 29 July 2002Accepted 12 November 2002
OD character of brochantite 275
Mazzi (1959) After some isotropic refinement cyclesanisotropic displacement factors were introduced for all theatoms Refinement readily converged to R1 = 0049 Finalpositional coordinates and displacement isotropic equiva-lent Ueq parameters for MDO1 are reported in Table 2a
The starting atomic coordinates for MDO2 polytypewere derived through OD considerations from the finalpositional coordinates of the MDO1 polytype (matrix trans-formation for coordinates [100010-1201]) The non-stan-dard space group P21n11 was chosen for MDO2 polytypeto allow an easier comparison between the two polytypes
After some isotropic refinement cycles anisotropicdisplacement factors were introduced only for Cu and SThe refinement converged to R1 = 0062 for MDO2
The calculated coordinates are closely similar to thoseobtained from the structural refinement indicating that theOD layers are remarkably similar in the two polytypesThere is also a clear indication that the atomic positionsconform to the symmetry of the single layer Cu3 O6 O7O8 and S are located on the mirror plane at z = 0125(l operation of the single layer) Cu4 and O5 are located onthe mirror plane at z = 0625 while O2 O4 and Cu2 aresymmetrically related to O1 O3 and Cu1 respectively onboth sides of the mirror plane at z = 0125 Clearly thelsquoidealrsquo symmetry of the single layer is not perfectly main-tained in the real structures of the two polytypes whichactually present a slight lsquodesymmetrizationrsquo (Egrave urovi 1979)
OD character of brochantite 271
Table 3 Bond distances (Aring) and angles (deg) in the coordination polyhedra of MDO1 (a) and MDO2 (b) polytypes
a) Brochantite-2M1
Cu1 Cu2 Cu3 Cu4 SO6 194(1) O5iii 192(1) O1 198(1) O4v 198(1) O7 148(1)O5i 194(1) O6 192(1) O4 199(1) O1 199(1) O10 148(1)O1i 201(1) O2i 209(1) O2 199(1) O2v 200(1) O9 150(1)O3ii 203(1) O4iv 211(1) O3 201(1) O3 201(1) O8 150(1)O8ii 234(1) O8iv 230(1) O7 236(1) O5 237(1)O7i 236(1) O7i 234(1) O9v 242(1) O10vi 247(1)
O1i-Cu1-O3ii 1677(3) O2i-Cu2-O4iv1676(3) O1-Cu3-O2 969(3) O1-Cu4-O2v 998(3) O7-S-O8 1084(6)O1i-Cu1-O5i 836(3) O2i-Cu2-O5iii 846(3) O1-Cu3-O3 814(3) O1-Cu4-O3 812(3) O7-S-O9 1085(5)O1i-Cu1-O6 905(3) O2i-Cu2-O6 915(3) O1-Cu3-O4 1747(3) O1-Cu4-O4v 1763(3) O7-S-O10 1094(5)O3ii-Cu1-O5i 901(3) O4iv -Cu2-O5iii 883(3) O2-Cu3-O3 1771(3) O2v-Cu4-O3 1789(3) O8-S-O9 1102(6)O3ii-Cu1-O6 959(3) O4iv -Cu2-O6 953(3) O2-Cu3-O4 822(3) O2v-Cu4-O4v 823(3) O8-S-O10 1097(6)O5i-Cu1-O6 1740(3) O5iii-Cu2-O6 1758(4) O3-Cu3-O4 993(3) O3-Cu4-O4v 967(3) O9-S-O10 1106(5)
Symmetry transformations used to generate equivalent atoms in MDO1 polytypei atom at x 1+y zii 12-x 12 +y 1-ziii x 1+y z-1iv 12 -x 12 +y -zv x y z+1vi x-12 12-y z
b) Brochantite-2M2
Cu1 Cu2 Cu3 Cu4 SO6 196(1) O6 192(1) O3 197(1) O2vi 198(1) O10 151(1)O5i 194(2) O5iii 194(2) O2 200(1) O1 200(1) O10 151(2)O1i 202(1) O2i 208(1) O4 200(1) O3 201(1) O8 151(1)O4ii 202(1) O3iv 209(1) O1 201(1) O4vi 203(1) O7 155(2)O7i 230(1) O8iv 230(1) O7 233(1) O5 238(1)O8ii 233(1) O7i 231(2) O10 242(1) O9v 248(2)
O1i-Cu1-O4ii 1679(6) O2i-Cu2-O3iv 1676(6) O1-Cu3-O2 974(6) O1-Cu4-O2vi 988(6) O7-S-O8 1092(9)O1i-Cu1-O5i 840(6) O2i-Cu2-O5iii 845(6) O1-Cu3-O3 824(6) O1-Cu4-O3 816(6) O7-S-O9 1081(9)O1i-Cu1-O6 903(6) O2i-Cu2-O6 926(6) O1-Cu3-O4 1751(7) O1-Cu4-O4vi 1772(6) O7-S-O10 1076(9)O4ii-Cu1-O5i 887(6) O3iv-Cu2-O5iii 873(6) O2-Cu3-O3 1776(6) O2vi-Cu4-O3 1796(6) O8-S-O9 1116(9)O4ii-Cu1-O6 970(6) O3iv-Cu2-O6 953(6) O2-Cu3-O4 823(6) O2vi-Cu4-O4vi 821(6) O8-S-O10 1095(9)O5i-Cu1-O6 1743(6) O5iii-Cu1-O6 1769(6) O3-Cu3-O4 977(6) O3-Cu4-O4vi 975(6) O9-S-O10 1108(8)
Symmetry transformations used to generate equivalent atoms in MDO2 polytypei atom at x 1+y zii 12-x 12+y 12+ziii x1+y z-1iv 12-x 12+y z-12v x-12 12-Y 12-zvi x y z+1
S Merlino N Perchiazzi D Franco
The table of anisotropic displacement parameters andthe lists of the FoFc data for both polytypes are availablefrom the authors upon request (or through the EJMEditorial Office Paris)
Structure description
The results of the present structural study are given inTables 3 and 4 The main features of the crystal structure ofbrochantite were already outlined by Cocco amp Mazzi(1959) More accurate data were subsequently obtained byHelliwell amp Smith (1997) on a very tiny (015x005x001mm) untwinned crystal from Socorro County NewMexico USA using data collected with a rotating anodediffractometer (MoKa radiation)
As regards the Cu and S coordination polyhedra boththe data of Helliwell amp Smith (1997) and our resultssubstantially agree with Cocco amp Mazzirsquos (1959) modelAs expected from their polytypic nature the coordinationpolyhedra and their linking are essentially the same inMDO1 and MDO2 polytypes (Table 3) so in the followingstructure description we refer only to the data obtained forthe MDO1 polytype The sulphate tetrahedron is veryregular in the MDO1 structure whereas it is slightly largerand a little more distorted in the MDO2 structure As shownin Table 3 Cu octahedra due to the Jahn-Teller effect arestrongly distorted towards an elongated tetragonal bipyra-midal coordination Four hydroxyls with Cu-OH distancesclose to 2 Aring are arranged in a nearly planar square coordi-nation with two additional longer bonds about 23 Aring inlength to complete the sixfold coordination
In Fig 1 and 2 the structures are represented assumingfourfold coordination around the copper atoms Cu3 andCu4 exhibit a nearly square planar coordination with fourCu-O distances between 198 and 201 Aring whereas Cu1 andCu2 exhibit two shorter (192 to 194 Aring) and two longer(201 and 203 Aring in Cu1 209 and 211 Aring in Cu2 coordi-
nation) distances Moreover the oxygen atoms around Cu1and Cu2 slightly deviate from a square-planar coordina-tion which explains the different representation of the twofourfold coordinations in Fig 1 and 2
In these Figures the Cu3- and Cu4-squares are inter-connected through common edges to build infinite planarchains running along c The Cu1- and Cu2-squares repre-sented as strongly squeezed tetrahedra are interconnectedby sharing vertices (O5 and O6 hydroxyl groups) to buildlsquozig-zagrsquo chains running along c Both chains areconnected one to the other by shared vertices to build infi-nite layers parallel to (100) [Cocco amp Mazzi (1959 Fig 8in their paper] The layers are seen along b in Fig 1 and 2where they appear distincly separated from each otherwhich indicates that in the present case the OD layerscorrespond to crystal chemically significant layers whichis not generally the case in OD structures
If we complete the octahedral coordination around eachcopper atom as represented in Fig 3 we can observe thatsubsequent layers are actually connected through thesulphate groups Accordingly in their presentation of astructural hierarchy for sulphate minerals Hawthorne et al(2000) placed brochantite among the structures with infi-nite frameworks as being built up of double chains ofcopper octahedra that are cross-linked by SO4 tetrahedra toform frameworks Sabelli amp Trosti-Ferroni (1985)presented a different kind of structural classification ofsulphate minerals based on the lsquomode of linking of thepolyhedra of the metals present in the mineralsrsquo assigningsulphate minerals to four structural type (insular chainsheet and framework) and 22 sub-types Within their clas-sification brochantite belongs to sub-type 14 in the sheettype as characterized by single undulating layers of copperoctahedra parallel to (100) (Fig 3)
The connection between these layers is ensured not onlyby sulphate tetrahedra but also by hydrogen bondsHelliwell amp Smith (1997) presented a hydrogen bondingsystem on the basis of the hydrogen positions determined
272
Table 4 Bond valence (vu) in brochantite-2M1 (MDO1 polytype)
O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 Sav
Cu1 0409 0387 0494 0494 0154 0168 1952Cu2 0329 0312 0521 0507 0168 0182 2019Cu3 0443 0420 0420 0431 0159 0135 2008Cu4 0431 0420 0409 0443 0154 0115 1972S 1476 1436 1436 1436 5784Scv 1283 1169 1216 1186 1169 1001 1957 1786 1571 1551Srsquocv 1061 1008 1078 1043 0922 1162 1957 2008 1842 181
Scv is the sum of bond strengths reaching the anions Srsquocv after correction for hydrogen bonds
O1-O8iii 271(1) 0222 O5-O9i 302(1) 0126O3-O10iv 296(1) 0138 O5-O10 305(1) 0121O4-O9ii 293(2) 0145 O2-O6v 287(1) 0161
OmiddotmiddotmiddotO distances (Aring) and hydrogen bond strengths (vu) Ineach pair of hydrogen bonded oxygen atoms the first one isthe donor the second one is the acceptor Atom at i x y z+1 ii 12ndashx 12+y -z iii x-12 12-y ziv 12-x 12+y 1-z v x y-1 z
through difference Fourier syntheses Looking at Table 2 ofHelliwell amp Smith (1997) we can see that the D-HAangles are far from ideal and that the O3-H3O9 distancesinvolve two oxygen atoms belonging to the same polyhe-dron
Our hydrogen bonding scheme was derived by lookingat the distances shorter than 31 Aring between oxygen atomsand not belonging to the same polyhedron These distancesare reported in Table 4 together with the bond valencebalance The Scv row shows the sums of bond strengthscalculated following Brese amp OrsquoKeeffe (1991) whereas inthe Srsquocv row these sums are corrected for hydrogen bondcontributions evaluated according to Ferraris amp Ivaldi(1988) The balance can be considered as quite satisfac-tory Among the oxygen atoms of the sulphate group (withthe exception of O7 which is linked to three Cu atoms) O8O9 and O10 are all taken up as acceptors O9 anionreceives two contributions from O4 and O5 hydroxylsthis latter forming a bifurcated bond with O9 and O10anions belonging to different sulphate groups Our datatherefore validate the assignment of the OH bands madeby Schmidt amp Lutz (1993) on the basis of infrared andRaman spectra all the hydrogen bonds shown in Table 4are consistent with those indicated by Schmidt amp Lutz(1993) moreover there is a close inverse relation betweenOO bond lengths given in our Table 4 and the stretchingfrequences reported by Schmidt amp Lutz (1993) Thehighest stretching frequency given in their Table 3 corre-sponds to a bifurcated hydrogen bond of O6 with O9 andO10 not included in our Table 4 For this bond we foundOO distances of 324 Aring (0097 vu) and 321 Aring (vu0100) respectively If we correspondingly correct thebond valence sums for O6 O9 and O10 we obtain sumscloser to the ideal values
Conclusions
In the X-ray diffraction patterns of brochantite weobserve typical features of OD structures These compriseubiquitous twinning disorder along a definite directionnon space-group absences and the presence of distinctdiffraction classes namely family and characteristic reflec-tions Accordingly we show that the crystal structure ofbrochantite may be conveniently described as built up ofOD layers with layer group symmetry P(n)21m moreoverwe derive the two MDO polytypes in the OD family ofbrochantite The X-ray single-crystal study of specimensfrom various Italian localities allows us to define a newpolytype brochantite-2M2 (corresponding to one MDOstructure) in addition to the ldquonormalrdquo brochantite-2M1(corresponding to another MDO structure) This new poly-type is found in specimens from four distinct mineralogicallocalities The crystal structure of this new polytype isoutlined on the basis of OD considerations and successfullyrefined It is possible that more complex polytypes exist atleast as small domains embodied within larger domains ofthe two main polytypes Their presence could be reliablydetermined only through electron diffraction and HRTEMstudies
Whereas our study was carried out on relativelylsquogoodrsquo brochantite crystals it would be interesting toinvestigate brochantite occurring as decay products in theurbanindustrial environment more specif ically as aconstituent of the green patinas formed in the deteriora-tion of copper and bronze manufacts In these patinasbrochantite is commonly found as massive or dustyencrustations not suitable for X-ray single-crystal studyOn the other hand an unambiguous distinction betweenthe brochantite polytypes cannot be made on the basis ofpowder data only as all polytypes exhibit commonlsquofamily reflectionsrsquo with intensities largely dominatingover the characteristic reflections Electron diffractionand HRTEM studies appear necessary to distinguishbetween the two main polytypes and would also be usefulin indicating the presence of other more complex poly-types
Acknowledgement This work was supported by theUniversity of Pisa and MIUR (Ministero dellrsquoUniversitagrave edella Ricerca Scientifica) through grants to the projectlsquoTransformations reactions ordering in mineralsrsquo
Appendix
Discussion of the diffraction pattern on the basis of the OD character of brochantite
It is useful to discuss the common features of all poly-types (and also of the disordered sequences) in the wholeOD family as well as the distinctive features of thedifferent polytypes In particular it is relevant to indicatethe diffractions which characterize the two most importantpolytypes MDO1 and MDO2 It is correct in this respect torefer to the orthogonal cell with AO = 4ao = 2546 AringBO = b = 985 Aring CO = c = 602 Aring In fact this cell is thecommon cell of both polytypes being a B centred cell for
OD character of brochantite 273
Fig 3 The crystal structure of brochantite-2M1 as seen along cshowing the interconnection of the undulating layers of copperoctahedra parallel to (100) with the sulphate groups
S Merlino N Perchiazzi D Franco
the polytype MDO1 and doubly primitive for the polytypeMDO2 (Fig 4)
The single structural layer has symmetry P(n)21m andis repeated by the operation n122 (normal to b with trans-lational component ao+c4) The Fourier transform of thewhole structure (structure factor F) may be obtained bysumming the contributions of the successive layers takingaccount of their relative positions
We shall indicate fo(hkl) as the contribution of the layerL0 The indices k and l are integers and correspond to the band c translations of the layer whereas h is a continuousvariable corresponding to axis A the direction of missingperiodicity The next layer gives a contribution
f1(hkl) = fo(hndashkl) exp[2pi(h4+k2plusmnl4)]
as for every atom at xjyjzj in the layer L0 there is an equalatom at xj+14 12-yj zjplusmn14 in the layer L1 It can be seenthat all the even layers L2p and all the odd layers L2p+1 aretranslationally equivalent to the layers L0 and L1 respec-tively according to the same translation vector
T2p = pA2 + a2pc2 with a2p = 0 1
The Fourier transform of the whole structure may beexpressed as
F(hkl) = fo(hkl) + fo(hndashkl) exp[2pi(h4+k2plusmnl4)] S(hkl) (1)
S(hkl) = 1(2M) Sp exp[2pi(ph2+a2p l2)] (2)
For l = 2L the expression is independent of the param-eter a2p and therefore of the degree of disorder For largevalues of M the expression tends to zero except whenh = h = 2H with integer H Therefore the reflections witheven l (and even h) are common to the whole OD familyand are always sharp (family reflections)
Moreover we observe that for k = 0 (and consideringonly the family reflections namely for even l and h) thefirst factor in expression (1) gives
F(H0L) = fo(H0L) [1 + exp[2pi(H2plusmnL2)]
This factor becomes zero for H+L = 2n+1 The diffrac-tion pattern of the two main polytypes differs only in theodd l reflections In the case of MDO1 (and MDO1rsquo) thevalue of the parameter a2p in the general expression (2) is1 Therefore for l = 2L+1 (the case of l = 2L is alreadyconsidered in a general way)
S(hkl) = (12M) Sp exp[2pi(ph2+(2L+1)2)]
For large values of M this expression tends to zeroexcept when h = h = 2H+1
In the case of MDO2 the value of the parameter a2p is0 therefore for l = 2L+1
S(hkl) = (12M) Sp exp[2pi(ph2]
For large values of M this expression tends to zeroexcept for even integer values of h ie for h = h = 2HFigure 5 presents the diffraction pattern of a crystalpresenting both main polytypes indicating the familyreflections and the characteristic reflections of both MDOstructures Three subsequent planes of the reciprocal latticeare shown with k = 0 1 and 2 As indicated in the Figure0kl reflections are present for odd l values (non-familyreflections) only at k odd values due to the symmetry ofthe single layer
References
Brese NE amp OrsquoKeeffe M (1991) Bond-valence parameters forsolids Acta Cryst B47 192-197
Cocco G amp Mazzi F (1959) La struttura della brochantitePeriod Mineral 28 121-149
274
Fig 4 Relationships between the common orthogonal cell and thecells of the two polytypes MDO1 and MDO2
Fig 5 Diffraction pattern of a brochantite crystal presenting bothmain polytypes The non-family reflections (odd l values) are repre-sented with short (for MDO2 reflections) and long (for MDO1 +MDO1rsquo reflections) dashes
Dornberger-Schiff K (1956) On the order disorder structures(OD-structures) Acta Cryst 9 593-601
mdash (1964) Grundzuumlge einer Theorie von OD-Strukturen ausSchichten Abh Dtsch Akad Wiss Berlin Kl Chem GeolBiol 3 1-107
Egrave urovi S (1979) Desymmetrization of OD structures Krystallund Technik 14 1047-1053
mdash (1997) Fundamentals of the OD theory In Merlino (ed)ldquoModular aspects of mineralsrdquo EMU Notes in Mineralogy 13-28
Ferraris G amp Ivaldi G (1988) Bond valence vs bond length inOmiddotmiddotmiddotO hydrogen bonds Acta Cryst B44 341-344
Gettens RJ (1970) Patina noble and vile In ldquoArt andTechnology A Symposium on Classic Bronzesrdquo (eds SDoeringer DG Mitten and A Steinberg) pp 57-72 The MITpress Boston MA
Guinier A Bokij G B Boll-Dornberger K Cowley J MEgrave urovi S Jagodzinski H Krishna P de Wolff P MZvyagin B B Cox D E Goodman P Hahn Th KuchitsuK Abrahams S C (1984) Nomenclature of polytype struc-tures Report of the International Union of Crystallography ad-hoc Committee on the Nomenclature of Disordered Modulatedand Polytype Structures Acta Cryst A40 399-404
Hawthorne FC Krivovichev SV Burns PC (2000) The crystalchemistry of sulphate minerals In Alpers C N Jambor J Lamp Nordstrom B K (eds) ldquoSulfate mineralsrdquo Reviews inMineralogy amp Geochemistry 40 1-112
Helliwell M amp Smith JV (1997) Brochantite Acta Cryst C531369-1371
Lauro C (1939) Brochantite della miniera di ldquoSa Duchessardquo(Sardegna) Period Mineral 3 327-341
mdash (1941) Sulle costanti reticolari della brochantite PeriodMineral 3 419-427
Mattsson E amp Holm R (1982) Atmospheric corrosion of copperand its alloys In ldquoAtmospheric Corrosionrdquo (ed W H Ailor)Chap 24 pp 365-381 John Wiley New York
Merlino S (1997) OD approach in minerals examples and appli-cations In Merlino (ed) ldquoModular aspects of mineralsrdquo EMUNotes in Mineralogy 1 29-54
Palache C (1939) Brochantite Am Mineral 8 463-481Sabelli C amp Trosti-Ferroni R (1985) A structural classification
of sulphate minerals Period Mineral 54 1-46Schmidt M amp Lutz HD (1993) Hydrogen bonding in basic
copper salts a spectroscopic study of malachite Cu2(OH)2CO3and brochantite Cu4(OH)6SO4 Phys Chem Mineral 2027-32
Woods TL amp Garrels RM (1986) Use of oxidized copperminerals as environmental indicators Appl Geochem 1181-187
Received 8 January 2002Modified version received 29 July 2002Accepted 12 November 2002
OD character of brochantite 275
S Merlino N Perchiazzi D Franco
The table of anisotropic displacement parameters andthe lists of the FoFc data for both polytypes are availablefrom the authors upon request (or through the EJMEditorial Office Paris)
Structure description
The results of the present structural study are given inTables 3 and 4 The main features of the crystal structure ofbrochantite were already outlined by Cocco amp Mazzi(1959) More accurate data were subsequently obtained byHelliwell amp Smith (1997) on a very tiny (015x005x001mm) untwinned crystal from Socorro County NewMexico USA using data collected with a rotating anodediffractometer (MoKa radiation)
As regards the Cu and S coordination polyhedra boththe data of Helliwell amp Smith (1997) and our resultssubstantially agree with Cocco amp Mazzirsquos (1959) modelAs expected from their polytypic nature the coordinationpolyhedra and their linking are essentially the same inMDO1 and MDO2 polytypes (Table 3) so in the followingstructure description we refer only to the data obtained forthe MDO1 polytype The sulphate tetrahedron is veryregular in the MDO1 structure whereas it is slightly largerand a little more distorted in the MDO2 structure As shownin Table 3 Cu octahedra due to the Jahn-Teller effect arestrongly distorted towards an elongated tetragonal bipyra-midal coordination Four hydroxyls with Cu-OH distancesclose to 2 Aring are arranged in a nearly planar square coordi-nation with two additional longer bonds about 23 Aring inlength to complete the sixfold coordination
In Fig 1 and 2 the structures are represented assumingfourfold coordination around the copper atoms Cu3 andCu4 exhibit a nearly square planar coordination with fourCu-O distances between 198 and 201 Aring whereas Cu1 andCu2 exhibit two shorter (192 to 194 Aring) and two longer(201 and 203 Aring in Cu1 209 and 211 Aring in Cu2 coordi-
nation) distances Moreover the oxygen atoms around Cu1and Cu2 slightly deviate from a square-planar coordina-tion which explains the different representation of the twofourfold coordinations in Fig 1 and 2
In these Figures the Cu3- and Cu4-squares are inter-connected through common edges to build infinite planarchains running along c The Cu1- and Cu2-squares repre-sented as strongly squeezed tetrahedra are interconnectedby sharing vertices (O5 and O6 hydroxyl groups) to buildlsquozig-zagrsquo chains running along c Both chains areconnected one to the other by shared vertices to build infi-nite layers parallel to (100) [Cocco amp Mazzi (1959 Fig 8in their paper] The layers are seen along b in Fig 1 and 2where they appear distincly separated from each otherwhich indicates that in the present case the OD layerscorrespond to crystal chemically significant layers whichis not generally the case in OD structures
If we complete the octahedral coordination around eachcopper atom as represented in Fig 3 we can observe thatsubsequent layers are actually connected through thesulphate groups Accordingly in their presentation of astructural hierarchy for sulphate minerals Hawthorne et al(2000) placed brochantite among the structures with infi-nite frameworks as being built up of double chains ofcopper octahedra that are cross-linked by SO4 tetrahedra toform frameworks Sabelli amp Trosti-Ferroni (1985)presented a different kind of structural classification ofsulphate minerals based on the lsquomode of linking of thepolyhedra of the metals present in the mineralsrsquo assigningsulphate minerals to four structural type (insular chainsheet and framework) and 22 sub-types Within their clas-sification brochantite belongs to sub-type 14 in the sheettype as characterized by single undulating layers of copperoctahedra parallel to (100) (Fig 3)
The connection between these layers is ensured not onlyby sulphate tetrahedra but also by hydrogen bondsHelliwell amp Smith (1997) presented a hydrogen bondingsystem on the basis of the hydrogen positions determined
272
Table 4 Bond valence (vu) in brochantite-2M1 (MDO1 polytype)
O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 Sav
Cu1 0409 0387 0494 0494 0154 0168 1952Cu2 0329 0312 0521 0507 0168 0182 2019Cu3 0443 0420 0420 0431 0159 0135 2008Cu4 0431 0420 0409 0443 0154 0115 1972S 1476 1436 1436 1436 5784Scv 1283 1169 1216 1186 1169 1001 1957 1786 1571 1551Srsquocv 1061 1008 1078 1043 0922 1162 1957 2008 1842 181
Scv is the sum of bond strengths reaching the anions Srsquocv after correction for hydrogen bonds
O1-O8iii 271(1) 0222 O5-O9i 302(1) 0126O3-O10iv 296(1) 0138 O5-O10 305(1) 0121O4-O9ii 293(2) 0145 O2-O6v 287(1) 0161
OmiddotmiddotmiddotO distances (Aring) and hydrogen bond strengths (vu) Ineach pair of hydrogen bonded oxygen atoms the first one isthe donor the second one is the acceptor Atom at i x y z+1 ii 12ndashx 12+y -z iii x-12 12-y ziv 12-x 12+y 1-z v x y-1 z
through difference Fourier syntheses Looking at Table 2 ofHelliwell amp Smith (1997) we can see that the D-HAangles are far from ideal and that the O3-H3O9 distancesinvolve two oxygen atoms belonging to the same polyhe-dron
Our hydrogen bonding scheme was derived by lookingat the distances shorter than 31 Aring between oxygen atomsand not belonging to the same polyhedron These distancesare reported in Table 4 together with the bond valencebalance The Scv row shows the sums of bond strengthscalculated following Brese amp OrsquoKeeffe (1991) whereas inthe Srsquocv row these sums are corrected for hydrogen bondcontributions evaluated according to Ferraris amp Ivaldi(1988) The balance can be considered as quite satisfac-tory Among the oxygen atoms of the sulphate group (withthe exception of O7 which is linked to three Cu atoms) O8O9 and O10 are all taken up as acceptors O9 anionreceives two contributions from O4 and O5 hydroxylsthis latter forming a bifurcated bond with O9 and O10anions belonging to different sulphate groups Our datatherefore validate the assignment of the OH bands madeby Schmidt amp Lutz (1993) on the basis of infrared andRaman spectra all the hydrogen bonds shown in Table 4are consistent with those indicated by Schmidt amp Lutz(1993) moreover there is a close inverse relation betweenOO bond lengths given in our Table 4 and the stretchingfrequences reported by Schmidt amp Lutz (1993) Thehighest stretching frequency given in their Table 3 corre-sponds to a bifurcated hydrogen bond of O6 with O9 andO10 not included in our Table 4 For this bond we foundOO distances of 324 Aring (0097 vu) and 321 Aring (vu0100) respectively If we correspondingly correct thebond valence sums for O6 O9 and O10 we obtain sumscloser to the ideal values
Conclusions
In the X-ray diffraction patterns of brochantite weobserve typical features of OD structures These compriseubiquitous twinning disorder along a definite directionnon space-group absences and the presence of distinctdiffraction classes namely family and characteristic reflec-tions Accordingly we show that the crystal structure ofbrochantite may be conveniently described as built up ofOD layers with layer group symmetry P(n)21m moreoverwe derive the two MDO polytypes in the OD family ofbrochantite The X-ray single-crystal study of specimensfrom various Italian localities allows us to define a newpolytype brochantite-2M2 (corresponding to one MDOstructure) in addition to the ldquonormalrdquo brochantite-2M1(corresponding to another MDO structure) This new poly-type is found in specimens from four distinct mineralogicallocalities The crystal structure of this new polytype isoutlined on the basis of OD considerations and successfullyrefined It is possible that more complex polytypes exist atleast as small domains embodied within larger domains ofthe two main polytypes Their presence could be reliablydetermined only through electron diffraction and HRTEMstudies
Whereas our study was carried out on relativelylsquogoodrsquo brochantite crystals it would be interesting toinvestigate brochantite occurring as decay products in theurbanindustrial environment more specif ically as aconstituent of the green patinas formed in the deteriora-tion of copper and bronze manufacts In these patinasbrochantite is commonly found as massive or dustyencrustations not suitable for X-ray single-crystal studyOn the other hand an unambiguous distinction betweenthe brochantite polytypes cannot be made on the basis ofpowder data only as all polytypes exhibit commonlsquofamily reflectionsrsquo with intensities largely dominatingover the characteristic reflections Electron diffractionand HRTEM studies appear necessary to distinguishbetween the two main polytypes and would also be usefulin indicating the presence of other more complex poly-types
Acknowledgement This work was supported by theUniversity of Pisa and MIUR (Ministero dellrsquoUniversitagrave edella Ricerca Scientifica) through grants to the projectlsquoTransformations reactions ordering in mineralsrsquo
Appendix
Discussion of the diffraction pattern on the basis of the OD character of brochantite
It is useful to discuss the common features of all poly-types (and also of the disordered sequences) in the wholeOD family as well as the distinctive features of thedifferent polytypes In particular it is relevant to indicatethe diffractions which characterize the two most importantpolytypes MDO1 and MDO2 It is correct in this respect torefer to the orthogonal cell with AO = 4ao = 2546 AringBO = b = 985 Aring CO = c = 602 Aring In fact this cell is thecommon cell of both polytypes being a B centred cell for
OD character of brochantite 273
Fig 3 The crystal structure of brochantite-2M1 as seen along cshowing the interconnection of the undulating layers of copperoctahedra parallel to (100) with the sulphate groups
S Merlino N Perchiazzi D Franco
the polytype MDO1 and doubly primitive for the polytypeMDO2 (Fig 4)
The single structural layer has symmetry P(n)21m andis repeated by the operation n122 (normal to b with trans-lational component ao+c4) The Fourier transform of thewhole structure (structure factor F) may be obtained bysumming the contributions of the successive layers takingaccount of their relative positions
We shall indicate fo(hkl) as the contribution of the layerL0 The indices k and l are integers and correspond to the band c translations of the layer whereas h is a continuousvariable corresponding to axis A the direction of missingperiodicity The next layer gives a contribution
f1(hkl) = fo(hndashkl) exp[2pi(h4+k2plusmnl4)]
as for every atom at xjyjzj in the layer L0 there is an equalatom at xj+14 12-yj zjplusmn14 in the layer L1 It can be seenthat all the even layers L2p and all the odd layers L2p+1 aretranslationally equivalent to the layers L0 and L1 respec-tively according to the same translation vector
T2p = pA2 + a2pc2 with a2p = 0 1
The Fourier transform of the whole structure may beexpressed as
F(hkl) = fo(hkl) + fo(hndashkl) exp[2pi(h4+k2plusmnl4)] S(hkl) (1)
S(hkl) = 1(2M) Sp exp[2pi(ph2+a2p l2)] (2)
For l = 2L the expression is independent of the param-eter a2p and therefore of the degree of disorder For largevalues of M the expression tends to zero except whenh = h = 2H with integer H Therefore the reflections witheven l (and even h) are common to the whole OD familyand are always sharp (family reflections)
Moreover we observe that for k = 0 (and consideringonly the family reflections namely for even l and h) thefirst factor in expression (1) gives
F(H0L) = fo(H0L) [1 + exp[2pi(H2plusmnL2)]
This factor becomes zero for H+L = 2n+1 The diffrac-tion pattern of the two main polytypes differs only in theodd l reflections In the case of MDO1 (and MDO1rsquo) thevalue of the parameter a2p in the general expression (2) is1 Therefore for l = 2L+1 (the case of l = 2L is alreadyconsidered in a general way)
S(hkl) = (12M) Sp exp[2pi(ph2+(2L+1)2)]
For large values of M this expression tends to zeroexcept when h = h = 2H+1
In the case of MDO2 the value of the parameter a2p is0 therefore for l = 2L+1
S(hkl) = (12M) Sp exp[2pi(ph2]
For large values of M this expression tends to zeroexcept for even integer values of h ie for h = h = 2HFigure 5 presents the diffraction pattern of a crystalpresenting both main polytypes indicating the familyreflections and the characteristic reflections of both MDOstructures Three subsequent planes of the reciprocal latticeare shown with k = 0 1 and 2 As indicated in the Figure0kl reflections are present for odd l values (non-familyreflections) only at k odd values due to the symmetry ofthe single layer
References
Brese NE amp OrsquoKeeffe M (1991) Bond-valence parameters forsolids Acta Cryst B47 192-197
Cocco G amp Mazzi F (1959) La struttura della brochantitePeriod Mineral 28 121-149
274
Fig 4 Relationships between the common orthogonal cell and thecells of the two polytypes MDO1 and MDO2
Fig 5 Diffraction pattern of a brochantite crystal presenting bothmain polytypes The non-family reflections (odd l values) are repre-sented with short (for MDO2 reflections) and long (for MDO1 +MDO1rsquo reflections) dashes
Dornberger-Schiff K (1956) On the order disorder structures(OD-structures) Acta Cryst 9 593-601
mdash (1964) Grundzuumlge einer Theorie von OD-Strukturen ausSchichten Abh Dtsch Akad Wiss Berlin Kl Chem GeolBiol 3 1-107
Egrave urovi S (1979) Desymmetrization of OD structures Krystallund Technik 14 1047-1053
mdash (1997) Fundamentals of the OD theory In Merlino (ed)ldquoModular aspects of mineralsrdquo EMU Notes in Mineralogy 13-28
Ferraris G amp Ivaldi G (1988) Bond valence vs bond length inOmiddotmiddotmiddotO hydrogen bonds Acta Cryst B44 341-344
Gettens RJ (1970) Patina noble and vile In ldquoArt andTechnology A Symposium on Classic Bronzesrdquo (eds SDoeringer DG Mitten and A Steinberg) pp 57-72 The MITpress Boston MA
Guinier A Bokij G B Boll-Dornberger K Cowley J MEgrave urovi S Jagodzinski H Krishna P de Wolff P MZvyagin B B Cox D E Goodman P Hahn Th KuchitsuK Abrahams S C (1984) Nomenclature of polytype struc-tures Report of the International Union of Crystallography ad-hoc Committee on the Nomenclature of Disordered Modulatedand Polytype Structures Acta Cryst A40 399-404
Hawthorne FC Krivovichev SV Burns PC (2000) The crystalchemistry of sulphate minerals In Alpers C N Jambor J Lamp Nordstrom B K (eds) ldquoSulfate mineralsrdquo Reviews inMineralogy amp Geochemistry 40 1-112
Helliwell M amp Smith JV (1997) Brochantite Acta Cryst C531369-1371
Lauro C (1939) Brochantite della miniera di ldquoSa Duchessardquo(Sardegna) Period Mineral 3 327-341
mdash (1941) Sulle costanti reticolari della brochantite PeriodMineral 3 419-427
Mattsson E amp Holm R (1982) Atmospheric corrosion of copperand its alloys In ldquoAtmospheric Corrosionrdquo (ed W H Ailor)Chap 24 pp 365-381 John Wiley New York
Merlino S (1997) OD approach in minerals examples and appli-cations In Merlino (ed) ldquoModular aspects of mineralsrdquo EMUNotes in Mineralogy 1 29-54
Palache C (1939) Brochantite Am Mineral 8 463-481Sabelli C amp Trosti-Ferroni R (1985) A structural classification
of sulphate minerals Period Mineral 54 1-46Schmidt M amp Lutz HD (1993) Hydrogen bonding in basic
copper salts a spectroscopic study of malachite Cu2(OH)2CO3and brochantite Cu4(OH)6SO4 Phys Chem Mineral 2027-32
Woods TL amp Garrels RM (1986) Use of oxidized copperminerals as environmental indicators Appl Geochem 1181-187
Received 8 January 2002Modified version received 29 July 2002Accepted 12 November 2002
OD character of brochantite 275
through difference Fourier syntheses Looking at Table 2 ofHelliwell amp Smith (1997) we can see that the D-HAangles are far from ideal and that the O3-H3O9 distancesinvolve two oxygen atoms belonging to the same polyhe-dron
Our hydrogen bonding scheme was derived by lookingat the distances shorter than 31 Aring between oxygen atomsand not belonging to the same polyhedron These distancesare reported in Table 4 together with the bond valencebalance The Scv row shows the sums of bond strengthscalculated following Brese amp OrsquoKeeffe (1991) whereas inthe Srsquocv row these sums are corrected for hydrogen bondcontributions evaluated according to Ferraris amp Ivaldi(1988) The balance can be considered as quite satisfac-tory Among the oxygen atoms of the sulphate group (withthe exception of O7 which is linked to three Cu atoms) O8O9 and O10 are all taken up as acceptors O9 anionreceives two contributions from O4 and O5 hydroxylsthis latter forming a bifurcated bond with O9 and O10anions belonging to different sulphate groups Our datatherefore validate the assignment of the OH bands madeby Schmidt amp Lutz (1993) on the basis of infrared andRaman spectra all the hydrogen bonds shown in Table 4are consistent with those indicated by Schmidt amp Lutz(1993) moreover there is a close inverse relation betweenOO bond lengths given in our Table 4 and the stretchingfrequences reported by Schmidt amp Lutz (1993) Thehighest stretching frequency given in their Table 3 corre-sponds to a bifurcated hydrogen bond of O6 with O9 andO10 not included in our Table 4 For this bond we foundOO distances of 324 Aring (0097 vu) and 321 Aring (vu0100) respectively If we correspondingly correct thebond valence sums for O6 O9 and O10 we obtain sumscloser to the ideal values
Conclusions
In the X-ray diffraction patterns of brochantite weobserve typical features of OD structures These compriseubiquitous twinning disorder along a definite directionnon space-group absences and the presence of distinctdiffraction classes namely family and characteristic reflec-tions Accordingly we show that the crystal structure ofbrochantite may be conveniently described as built up ofOD layers with layer group symmetry P(n)21m moreoverwe derive the two MDO polytypes in the OD family ofbrochantite The X-ray single-crystal study of specimensfrom various Italian localities allows us to define a newpolytype brochantite-2M2 (corresponding to one MDOstructure) in addition to the ldquonormalrdquo brochantite-2M1(corresponding to another MDO structure) This new poly-type is found in specimens from four distinct mineralogicallocalities The crystal structure of this new polytype isoutlined on the basis of OD considerations and successfullyrefined It is possible that more complex polytypes exist atleast as small domains embodied within larger domains ofthe two main polytypes Their presence could be reliablydetermined only through electron diffraction and HRTEMstudies
Whereas our study was carried out on relativelylsquogoodrsquo brochantite crystals it would be interesting toinvestigate brochantite occurring as decay products in theurbanindustrial environment more specif ically as aconstituent of the green patinas formed in the deteriora-tion of copper and bronze manufacts In these patinasbrochantite is commonly found as massive or dustyencrustations not suitable for X-ray single-crystal studyOn the other hand an unambiguous distinction betweenthe brochantite polytypes cannot be made on the basis ofpowder data only as all polytypes exhibit commonlsquofamily reflectionsrsquo with intensities largely dominatingover the characteristic reflections Electron diffractionand HRTEM studies appear necessary to distinguishbetween the two main polytypes and would also be usefulin indicating the presence of other more complex poly-types
Acknowledgement This work was supported by theUniversity of Pisa and MIUR (Ministero dellrsquoUniversitagrave edella Ricerca Scientifica) through grants to the projectlsquoTransformations reactions ordering in mineralsrsquo
Appendix
Discussion of the diffraction pattern on the basis of the OD character of brochantite
It is useful to discuss the common features of all poly-types (and also of the disordered sequences) in the wholeOD family as well as the distinctive features of thedifferent polytypes In particular it is relevant to indicatethe diffractions which characterize the two most importantpolytypes MDO1 and MDO2 It is correct in this respect torefer to the orthogonal cell with AO = 4ao = 2546 AringBO = b = 985 Aring CO = c = 602 Aring In fact this cell is thecommon cell of both polytypes being a B centred cell for
OD character of brochantite 273
Fig 3 The crystal structure of brochantite-2M1 as seen along cshowing the interconnection of the undulating layers of copperoctahedra parallel to (100) with the sulphate groups
S Merlino N Perchiazzi D Franco
the polytype MDO1 and doubly primitive for the polytypeMDO2 (Fig 4)
The single structural layer has symmetry P(n)21m andis repeated by the operation n122 (normal to b with trans-lational component ao+c4) The Fourier transform of thewhole structure (structure factor F) may be obtained bysumming the contributions of the successive layers takingaccount of their relative positions
We shall indicate fo(hkl) as the contribution of the layerL0 The indices k and l are integers and correspond to the band c translations of the layer whereas h is a continuousvariable corresponding to axis A the direction of missingperiodicity The next layer gives a contribution
f1(hkl) = fo(hndashkl) exp[2pi(h4+k2plusmnl4)]
as for every atom at xjyjzj in the layer L0 there is an equalatom at xj+14 12-yj zjplusmn14 in the layer L1 It can be seenthat all the even layers L2p and all the odd layers L2p+1 aretranslationally equivalent to the layers L0 and L1 respec-tively according to the same translation vector
T2p = pA2 + a2pc2 with a2p = 0 1
The Fourier transform of the whole structure may beexpressed as
F(hkl) = fo(hkl) + fo(hndashkl) exp[2pi(h4+k2plusmnl4)] S(hkl) (1)
S(hkl) = 1(2M) Sp exp[2pi(ph2+a2p l2)] (2)
For l = 2L the expression is independent of the param-eter a2p and therefore of the degree of disorder For largevalues of M the expression tends to zero except whenh = h = 2H with integer H Therefore the reflections witheven l (and even h) are common to the whole OD familyand are always sharp (family reflections)
Moreover we observe that for k = 0 (and consideringonly the family reflections namely for even l and h) thefirst factor in expression (1) gives
F(H0L) = fo(H0L) [1 + exp[2pi(H2plusmnL2)]
This factor becomes zero for H+L = 2n+1 The diffrac-tion pattern of the two main polytypes differs only in theodd l reflections In the case of MDO1 (and MDO1rsquo) thevalue of the parameter a2p in the general expression (2) is1 Therefore for l = 2L+1 (the case of l = 2L is alreadyconsidered in a general way)
S(hkl) = (12M) Sp exp[2pi(ph2+(2L+1)2)]
For large values of M this expression tends to zeroexcept when h = h = 2H+1
In the case of MDO2 the value of the parameter a2p is0 therefore for l = 2L+1
S(hkl) = (12M) Sp exp[2pi(ph2]
For large values of M this expression tends to zeroexcept for even integer values of h ie for h = h = 2HFigure 5 presents the diffraction pattern of a crystalpresenting both main polytypes indicating the familyreflections and the characteristic reflections of both MDOstructures Three subsequent planes of the reciprocal latticeare shown with k = 0 1 and 2 As indicated in the Figure0kl reflections are present for odd l values (non-familyreflections) only at k odd values due to the symmetry ofthe single layer
References
Brese NE amp OrsquoKeeffe M (1991) Bond-valence parameters forsolids Acta Cryst B47 192-197
Cocco G amp Mazzi F (1959) La struttura della brochantitePeriod Mineral 28 121-149
274
Fig 4 Relationships between the common orthogonal cell and thecells of the two polytypes MDO1 and MDO2
Fig 5 Diffraction pattern of a brochantite crystal presenting bothmain polytypes The non-family reflections (odd l values) are repre-sented with short (for MDO2 reflections) and long (for MDO1 +MDO1rsquo reflections) dashes
Dornberger-Schiff K (1956) On the order disorder structures(OD-structures) Acta Cryst 9 593-601
mdash (1964) Grundzuumlge einer Theorie von OD-Strukturen ausSchichten Abh Dtsch Akad Wiss Berlin Kl Chem GeolBiol 3 1-107
Egrave urovi S (1979) Desymmetrization of OD structures Krystallund Technik 14 1047-1053
mdash (1997) Fundamentals of the OD theory In Merlino (ed)ldquoModular aspects of mineralsrdquo EMU Notes in Mineralogy 13-28
Ferraris G amp Ivaldi G (1988) Bond valence vs bond length inOmiddotmiddotmiddotO hydrogen bonds Acta Cryst B44 341-344
Gettens RJ (1970) Patina noble and vile In ldquoArt andTechnology A Symposium on Classic Bronzesrdquo (eds SDoeringer DG Mitten and A Steinberg) pp 57-72 The MITpress Boston MA
Guinier A Bokij G B Boll-Dornberger K Cowley J MEgrave urovi S Jagodzinski H Krishna P de Wolff P MZvyagin B B Cox D E Goodman P Hahn Th KuchitsuK Abrahams S C (1984) Nomenclature of polytype struc-tures Report of the International Union of Crystallography ad-hoc Committee on the Nomenclature of Disordered Modulatedand Polytype Structures Acta Cryst A40 399-404
Hawthorne FC Krivovichev SV Burns PC (2000) The crystalchemistry of sulphate minerals In Alpers C N Jambor J Lamp Nordstrom B K (eds) ldquoSulfate mineralsrdquo Reviews inMineralogy amp Geochemistry 40 1-112
Helliwell M amp Smith JV (1997) Brochantite Acta Cryst C531369-1371
Lauro C (1939) Brochantite della miniera di ldquoSa Duchessardquo(Sardegna) Period Mineral 3 327-341
mdash (1941) Sulle costanti reticolari della brochantite PeriodMineral 3 419-427
Mattsson E amp Holm R (1982) Atmospheric corrosion of copperand its alloys In ldquoAtmospheric Corrosionrdquo (ed W H Ailor)Chap 24 pp 365-381 John Wiley New York
Merlino S (1997) OD approach in minerals examples and appli-cations In Merlino (ed) ldquoModular aspects of mineralsrdquo EMUNotes in Mineralogy 1 29-54
Palache C (1939) Brochantite Am Mineral 8 463-481Sabelli C amp Trosti-Ferroni R (1985) A structural classification
of sulphate minerals Period Mineral 54 1-46Schmidt M amp Lutz HD (1993) Hydrogen bonding in basic
copper salts a spectroscopic study of malachite Cu2(OH)2CO3and brochantite Cu4(OH)6SO4 Phys Chem Mineral 2027-32
Woods TL amp Garrels RM (1986) Use of oxidized copperminerals as environmental indicators Appl Geochem 1181-187
Received 8 January 2002Modified version received 29 July 2002Accepted 12 November 2002
OD character of brochantite 275
S Merlino N Perchiazzi D Franco
the polytype MDO1 and doubly primitive for the polytypeMDO2 (Fig 4)
The single structural layer has symmetry P(n)21m andis repeated by the operation n122 (normal to b with trans-lational component ao+c4) The Fourier transform of thewhole structure (structure factor F) may be obtained bysumming the contributions of the successive layers takingaccount of their relative positions
We shall indicate fo(hkl) as the contribution of the layerL0 The indices k and l are integers and correspond to the band c translations of the layer whereas h is a continuousvariable corresponding to axis A the direction of missingperiodicity The next layer gives a contribution
f1(hkl) = fo(hndashkl) exp[2pi(h4+k2plusmnl4)]
as for every atom at xjyjzj in the layer L0 there is an equalatom at xj+14 12-yj zjplusmn14 in the layer L1 It can be seenthat all the even layers L2p and all the odd layers L2p+1 aretranslationally equivalent to the layers L0 and L1 respec-tively according to the same translation vector
T2p = pA2 + a2pc2 with a2p = 0 1
The Fourier transform of the whole structure may beexpressed as
F(hkl) = fo(hkl) + fo(hndashkl) exp[2pi(h4+k2plusmnl4)] S(hkl) (1)
S(hkl) = 1(2M) Sp exp[2pi(ph2+a2p l2)] (2)
For l = 2L the expression is independent of the param-eter a2p and therefore of the degree of disorder For largevalues of M the expression tends to zero except whenh = h = 2H with integer H Therefore the reflections witheven l (and even h) are common to the whole OD familyand are always sharp (family reflections)
Moreover we observe that for k = 0 (and consideringonly the family reflections namely for even l and h) thefirst factor in expression (1) gives
F(H0L) = fo(H0L) [1 + exp[2pi(H2plusmnL2)]
This factor becomes zero for H+L = 2n+1 The diffrac-tion pattern of the two main polytypes differs only in theodd l reflections In the case of MDO1 (and MDO1rsquo) thevalue of the parameter a2p in the general expression (2) is1 Therefore for l = 2L+1 (the case of l = 2L is alreadyconsidered in a general way)
S(hkl) = (12M) Sp exp[2pi(ph2+(2L+1)2)]
For large values of M this expression tends to zeroexcept when h = h = 2H+1
In the case of MDO2 the value of the parameter a2p is0 therefore for l = 2L+1
S(hkl) = (12M) Sp exp[2pi(ph2]
For large values of M this expression tends to zeroexcept for even integer values of h ie for h = h = 2HFigure 5 presents the diffraction pattern of a crystalpresenting both main polytypes indicating the familyreflections and the characteristic reflections of both MDOstructures Three subsequent planes of the reciprocal latticeare shown with k = 0 1 and 2 As indicated in the Figure0kl reflections are present for odd l values (non-familyreflections) only at k odd values due to the symmetry ofthe single layer
References
Brese NE amp OrsquoKeeffe M (1991) Bond-valence parameters forsolids Acta Cryst B47 192-197
Cocco G amp Mazzi F (1959) La struttura della brochantitePeriod Mineral 28 121-149
274
Fig 4 Relationships between the common orthogonal cell and thecells of the two polytypes MDO1 and MDO2
Fig 5 Diffraction pattern of a brochantite crystal presenting bothmain polytypes The non-family reflections (odd l values) are repre-sented with short (for MDO2 reflections) and long (for MDO1 +MDO1rsquo reflections) dashes
Dornberger-Schiff K (1956) On the order disorder structures(OD-structures) Acta Cryst 9 593-601
mdash (1964) Grundzuumlge einer Theorie von OD-Strukturen ausSchichten Abh Dtsch Akad Wiss Berlin Kl Chem GeolBiol 3 1-107
Egrave urovi S (1979) Desymmetrization of OD structures Krystallund Technik 14 1047-1053
mdash (1997) Fundamentals of the OD theory In Merlino (ed)ldquoModular aspects of mineralsrdquo EMU Notes in Mineralogy 13-28
Ferraris G amp Ivaldi G (1988) Bond valence vs bond length inOmiddotmiddotmiddotO hydrogen bonds Acta Cryst B44 341-344
Gettens RJ (1970) Patina noble and vile In ldquoArt andTechnology A Symposium on Classic Bronzesrdquo (eds SDoeringer DG Mitten and A Steinberg) pp 57-72 The MITpress Boston MA
Guinier A Bokij G B Boll-Dornberger K Cowley J MEgrave urovi S Jagodzinski H Krishna P de Wolff P MZvyagin B B Cox D E Goodman P Hahn Th KuchitsuK Abrahams S C (1984) Nomenclature of polytype struc-tures Report of the International Union of Crystallography ad-hoc Committee on the Nomenclature of Disordered Modulatedand Polytype Structures Acta Cryst A40 399-404
Hawthorne FC Krivovichev SV Burns PC (2000) The crystalchemistry of sulphate minerals In Alpers C N Jambor J Lamp Nordstrom B K (eds) ldquoSulfate mineralsrdquo Reviews inMineralogy amp Geochemistry 40 1-112
Helliwell M amp Smith JV (1997) Brochantite Acta Cryst C531369-1371
Lauro C (1939) Brochantite della miniera di ldquoSa Duchessardquo(Sardegna) Period Mineral 3 327-341
mdash (1941) Sulle costanti reticolari della brochantite PeriodMineral 3 419-427
Mattsson E amp Holm R (1982) Atmospheric corrosion of copperand its alloys In ldquoAtmospheric Corrosionrdquo (ed W H Ailor)Chap 24 pp 365-381 John Wiley New York
Merlino S (1997) OD approach in minerals examples and appli-cations In Merlino (ed) ldquoModular aspects of mineralsrdquo EMUNotes in Mineralogy 1 29-54
Palache C (1939) Brochantite Am Mineral 8 463-481Sabelli C amp Trosti-Ferroni R (1985) A structural classification
of sulphate minerals Period Mineral 54 1-46Schmidt M amp Lutz HD (1993) Hydrogen bonding in basic
copper salts a spectroscopic study of malachite Cu2(OH)2CO3and brochantite Cu4(OH)6SO4 Phys Chem Mineral 2027-32
Woods TL amp Garrels RM (1986) Use of oxidized copperminerals as environmental indicators Appl Geochem 1181-187
Received 8 January 2002Modified version received 29 July 2002Accepted 12 November 2002
OD character of brochantite 275
Dornberger-Schiff K (1956) On the order disorder structures(OD-structures) Acta Cryst 9 593-601
mdash (1964) Grundzuumlge einer Theorie von OD-Strukturen ausSchichten Abh Dtsch Akad Wiss Berlin Kl Chem GeolBiol 3 1-107
Egrave urovi S (1979) Desymmetrization of OD structures Krystallund Technik 14 1047-1053
mdash (1997) Fundamentals of the OD theory In Merlino (ed)ldquoModular aspects of mineralsrdquo EMU Notes in Mineralogy 13-28
Ferraris G amp Ivaldi G (1988) Bond valence vs bond length inOmiddotmiddotmiddotO hydrogen bonds Acta Cryst B44 341-344
Gettens RJ (1970) Patina noble and vile In ldquoArt andTechnology A Symposium on Classic Bronzesrdquo (eds SDoeringer DG Mitten and A Steinberg) pp 57-72 The MITpress Boston MA
Guinier A Bokij G B Boll-Dornberger K Cowley J MEgrave urovi S Jagodzinski H Krishna P de Wolff P MZvyagin B B Cox D E Goodman P Hahn Th KuchitsuK Abrahams S C (1984) Nomenclature of polytype struc-tures Report of the International Union of Crystallography ad-hoc Committee on the Nomenclature of Disordered Modulatedand Polytype Structures Acta Cryst A40 399-404
Hawthorne FC Krivovichev SV Burns PC (2000) The crystalchemistry of sulphate minerals In Alpers C N Jambor J Lamp Nordstrom B K (eds) ldquoSulfate mineralsrdquo Reviews inMineralogy amp Geochemistry 40 1-112
Helliwell M amp Smith JV (1997) Brochantite Acta Cryst C531369-1371
Lauro C (1939) Brochantite della miniera di ldquoSa Duchessardquo(Sardegna) Period Mineral 3 327-341
mdash (1941) Sulle costanti reticolari della brochantite PeriodMineral 3 419-427
Mattsson E amp Holm R (1982) Atmospheric corrosion of copperand its alloys In ldquoAtmospheric Corrosionrdquo (ed W H Ailor)Chap 24 pp 365-381 John Wiley New York
Merlino S (1997) OD approach in minerals examples and appli-cations In Merlino (ed) ldquoModular aspects of mineralsrdquo EMUNotes in Mineralogy 1 29-54
Palache C (1939) Brochantite Am Mineral 8 463-481Sabelli C amp Trosti-Ferroni R (1985) A structural classification
of sulphate minerals Period Mineral 54 1-46Schmidt M amp Lutz HD (1993) Hydrogen bonding in basic
copper salts a spectroscopic study of malachite Cu2(OH)2CO3and brochantite Cu4(OH)6SO4 Phys Chem Mineral 2027-32
Woods TL amp Garrels RM (1986) Use of oxidized copperminerals as environmental indicators Appl Geochem 1181-187
Received 8 January 2002Modified version received 29 July 2002Accepted 12 November 2002
OD character of brochantite 275
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