1 Synthesis and Crystal Structure of New Carbonate2 Ca3Na2(CO3)4 Homeotypic with Orthoborates M3Ln2(BO3)43 (M = Ca, Sr, and Ba)4 Pavel N. Gavryushkin,*,†,‡ Vladimir V. Bakakin,§,† Nadezhda B. Bolotina,∥ Anton F. Shatskiy,†,‡

5 Yurii V. Seryotkin,†,‡ and Konstantin D. Litasov†,‡

6†V.S. Sobolev Institute of Geology and Mineralogy, Russian Academy of Science, Siberian Branch, Novosibirsk 630090, Russia

7‡Novosibirsk State University, Novosibirsk 630090, Russia

8§Nikolaev Institute of Inorganic Chemistry, Russian Academy of Science, Siberian Branch, Novosibirsk 630090, Russia

9∥Shubnikov Institute of Crystallography RAS, Moscow 119333, Russia

10 *S Supporting Information

11 ABSTRACT: Single crystals of the new double alkali carbonate12 Ca3Na2(CO3)4 were synthesized using a high-pressure large volume13 apparatus at 6 GPa by slow cooling of the stoichiometric carbonate mixture14 from 1400 to 1150 °C for 2.5 h. The structure was solved and refined to R =15 0.044 using 7489 independent reflections: P1n1, Z = 8, a = 31.4421(8) Å,16 b = 8.1960(2)Å, c = 7.4360(2) Å, and β = 89.923(2)°. The structure is17 characterized by the maximal number of nonparallel sets of CO3 groups18 among carbonates. The compound is homeotypic with the orthoborates19 M3Ln2(BO3)4 (where M = Ca, Sr, Ba and Ln = Er, Sm, Nd, Pr, La, Y, Gd,20 Eu, Dy, Ho, and Bi). No homeotypic analogs have been found among21 carbonates. The structure is described as a packing of two-capped trigonal22 prisms formed by Na+ and Ca2+ cations and centered by CO3 triangles.

23 ■ INTRODUCTION

24 Na−Ca double carbonates are of significant interest from both25 crystal-chemical and geological points of view.26 From a geological point of view, Na−Ca double carbonates27 constitute one of the most important classes of compounds28 which can control melting temperature of oxidized mantle29 domains and provide formation of mantle carbonatites and30 kimberlites.1−4 From a crystal-chemical point of view, this is a31 surprisingly poorly investigated class of carbonates with two big32 cations that can be homeotypic with orthoborates, which are33 intensively investigated due to their promising applications in34 laser optics.5

35 Our recent research on phase relations in the system36 Na2CO3−CaCO3 at 6 GPa reveals three new compounds:37 CaNa4(CO3)3, Ca3Na2(CO3)4, and Ca4Na2(CO3)5,

6 in addition38 to the known Na2Ca(CO3)2 and Na2Ca2(CO3)3.

7−9 In this39 paper, we present single crystal structure solution and analysis40 of one of these new high-pressure compounds, Ca3Na2(CO3)441 (see the Supporting Information for the .cif structure). This42 compound is the first known double carbonate with a ratio of43 M1+:M2+ = 2:3.

44 ■ EXPERIMENTAL SECTION45 Synthesis. Single-phase aggregate was synthesized using the46 pressless multianvil apparatus BARS at IGM SB RAS (Novosibirsk,47 Russia).6,10,11 The stoichiometric mixture of pure carbonate reagents

48(99.9%, Wako Co. Ltd.), Na2CO3 (25 mol %) and CaCO3 (75 mol %),49was ground in an agate mortar under acetone and loaded as a powder50into a graphite capsule 1 mm in diameter and 1.5 mm in length. The51loaded capsule was dried at 150 °C for 5 h prior to the experiment.52Single crystals of Ca3Na2(CO3)4 were synthesized by the annealing of53the stoichiometric carbonate mixture at 6 GPa and 1000 °C for 30 h.6

54The sample pressure was controlled by varying the oil pressure in the55hydraulic system of the BARS apparatus. Sample heating was achieved56using a tubular graphite heater, 13.0/12.0 mm in outer/inner diameter57and 19.0 mm in height. The sample temperature was controlled using a58PtRh(6/30) thermocouple. The details of high-pressure experiments can59be found elsewhere.10

60Data Collection and Structure Solution. A single crystal sample61with dimensions of 0.08 × 0.1 × 0.08 mm was picked up under a62polarizing microscope. The X-ray diffraction data were collected on the63Oxford Diffraction Gemini R Ultra single-crystal diffractometer (CCD-64detector, graphite-monochromatized Mo Ka radiation) using the65ω-scan technique with a scan width of 1° per frame. Data reduction66was performed with Oxford Diffraction CrysAlisPro. Jana2006 was67used for structure solution and refinement.12 The structure was solved68in the P1 space group using Superflip.13 The details of data collection69and structure refinement are summarized in Table 1. Basic structural70data including atomic coordinates, isotropic displacement parameters,71and site occupancies are listed in Table 2. A mixed occupation is72assumed because of unusually small values of the atomic displacement

Received: May 16, 2014Revised: July 23, 2014

Article

pubs.acs.org/crystal

© XXXX American Chemical Society A dx.doi.org/10.1021/cg500718y | Cryst. Growth Des. XXXX, XXX, XXX−XXX

* UNKNOWN * | MPSJCA | JCA10.0.1465/W Unicode | cg-2014-00718y.3d (R3.6.i5 HF03:4230 | 2.0 alpha 39) 2014/07/15 09:23:00 | PROD-JCA1 | rq_2700154 | 8/06/2014 09:58:43 | 7 | JCA-DEFAULT

73 parameters (ADP) at X1−X6 sites. Such assumption improves the74 R-factor and makes ADP realistic. We failed, however, to refine Na/Ca75 ratios because of unavoidable correlation between ADPs and these76 ratios accompanied by a practically standing R-factor. For this reason,77 the Na:Ca ratios were fixed as 1:1.

78 ■ RESULTS AND DISCUSSION79 Structure Description. Interatomic Ca−O and Na−O80 distances vary in quite a wide range from 2.27 to 2.95 Å. This81 fact leads to an uncertainty in the determination of82 coordination numbers for Ca and Na. Hence, we propose the83 following crystal-chemical formula.84 Ca[9]Ca2

[8]Na2[7]C4

[3]O3(5)O9

(4). The superscripts in square85 brackets and in parentheses indicate the coordination numbers86 of cations and anions, respectively.87 The deviation of the CO3 groups from the planarity varies in88 the range of 0.25°−7° and equal to 1.75° on the average.89 Our analysis of ICSD database shows that Ca3Na2(CO3)490 does not have homeotypic analogs among carbonates, even91 though there exists a family of homeotypic orthoborates with92 chemical formulas M3Ln2(BO3)4 (where M = Ca, Sr, Ba and93 Ln = Er, Sm, Nd, Pr, La, Y, Gd, Eu, Dy, Ho, Bi)5,14−25 and94 Eu5(BO3)4.

26 Twenty-four representatives of these orthobo-95 rates are known up to now.23 In Figure 1, we compare the96 crystal structures of Ca3Na2(CO3)4 and Ba3Nd2(BO3)4. Both97 the a axes and the numbers of formula units of the listed98 borates are two times smaller than those of carbonate. The99 borates crystallized in the space group Pmnb (a nonconven-100 tional setting of Pnma, no. 62) or P21nb (a nonconventional101 setting of Pna21, no. 33) that contain P1n1, the space group of102 Ca3Na2(CO3)4 (Figure 2).

103The crystal-chemical formulas of orthoborates are almost the104same as those for carbonate. For example, the crystal-chemical105formula for Sr3Pr2(BO3)4 is as follows.

14

106Pr2[8]Sr2

[8]Sr[7]B4[3]O3

(5)O9(4). The cation array of the

107Ca3Na2(CO3)4 structure is homeotypic to that of Gd5Si4-type108structures,27 which are known for their giant magnetocaloric109effect.28

110The traditional structure description based on cation111polyhedrons does not work well for these carbonate and112borate structures. In our opinion, the most fruitful approach to113the structure representation is the cation sublattice with anions114filling the cavities,29 as first suggested by A. Vegas30 and applied115for borates in our previous work.31,32 As structures of116orthoborate family M3Ln2(BO3)4 have not yet been described117in this way, we believe that the description will be useful, given118the significant interest in these crystals among researchers.5 The119homeotypic relations between compounds implies that all our120crystal-chemical conclusions will be the same for both121carbonate and orthoborates.122According to the crystal-chemical formula, the total amount123of cation bonds is 51. The balance of anionic bonds is the124following: (5 × 3) + (4 × 9). One fourth of oxygen atoms are125bonded to four additional Na or Ca atoms in addition to the126indispensable bond with carbon, and three-fourth of oxygen127atoms are bonded to three (Na, Ca) atoms. We analyzed the128orthoborate structures and found that the typical coordination129for such a set of bonds of the BO3 triangle is the eight-cornered130polyhedron, typically a two-capped trigonal prism. Thus, the131analysis of the crystal-chemical formula alone suggests that one132can expect that the Ca, Na cation arrangement has main cavities133of a two-capped trigonal prism shape (Figure 1).134The arrangement of Na and Ca is based on the square−135rhombic 32434 net perpendicular to [100] (Figure 2). There136are eight such nets on the a period of the unit cell, alternating137by the law ···AABBAABB···. They superimpose pairwise,138forming right slabs. These slabs are shifted, alternately forming139oblique interjacent slabs. Square prisms of right slabs are140centered by additional (not belonging to the nets) (Na and Ca)141cations (Figure 2). The described cation arrangement results in142a partition of the space on two types of two-capped trigonal143prisms related to the right and oblique slabs. These prisms are144centered by CO3 triangles accordingly to the above reasoning.145It is not hard to distinguish two-capped trigonal prisms in the146right slabs. Their axes are parallel to the a axis of the structure147(Figure 2). Both caps lie in the same slab and are associated148with additional (not belonging to net) (Na and Ca) cations.149The prisms share side faces, two other faces have caps. The slab150is filled with prisms without cavities, except for the tetragonal151pyramid cavities below and above additional cations. These152cavities are included in one-capped trigonal prisms of153underlying and overlying slabs, transforming them into two-154capped prisms. These prisms are not easily distinguishable155visually. They are “lying” prisms with axes parallel to the plane156of the net (Figure 2). One cap of such a prism is located in the157same slab and the other is in the adjacent slab. Each pair of158prisms has a common square face, in the same way as the159prisms of the right slab. The space of a slab is filled with these160prisms almost completely, except for a certain amount of161tetrahedral cavities.162One of the most remarkable crystal-chemical features of the163structure is probably the diversity of CO3 triangle orientations.164Eight nonparallel sets of CO3 groups exist in the structure in165total. For known carbonates, this is the maximum possible

Table 1. Parameters of Single Crystal Data Collection andStructure Refinement

crystal data

formula Ca3Na2C4O12 (Z = 8)formula weight 406.3space group P1n1 (#7; unique axis b, cell choice 2)a (Å) 31.4421 (8)b (Å) 8.1960 (2)c (Å) 7.4360 (2)β (deg) 89.923 (2)V (Å3) 1916.25 (8)calculated density (g cm−3) 2.815F(000) 1616μ (mm−1) 1.9

data collection

instrument Xcalibur, Ruby, Gemini R Ultraradiation type Mo Kα radiation (λ = 0.7107 Å)measured reflections 51005independent reflections 15241reflections with I > 3δ(I) 7140hkl limits −11 ≤ h ≤ 11

−49 ≤ k ≤ 4812 ≤ l ≤ 12

Rint 0.05refinement based on F

R factors [I > 3δ(I)] R = 0.0441; wR = 0.0465R factors (all data) R = 0.1003; wR = 0.0603refined parameters 677residual electron density (e Å−3) max 0.70, min −0.46

Crystal Growth & Design Article

dx.doi.org/10.1021/cg500718y | Cryst. Growth Des. XXXX, XXX, XXX−XXXB

Table 2. Fractional Atomic Coordinates and Isotropic (Equivalent) Displacement Parameters (Å2)

x y z Uiso Occ. (<1)

Ca1 0.33172 (5) 0.91952 (17) 0.0789 (2) 0.0175(4)

Ca2 0.67290 (5) 0.92317 (17) 0.07703 (18) 0.0174(4)

Ca3 0.33529 (5) 0.06638 (17) 0.5759 (2) 0.0185(4)Ca4 0.67416 (5) 0.06442 (18) 0.5767 (2) 0.0213(4)

Ca5 0.08522 (5) 0.42588 (17) 0.6256 (2) 0.0162(4)

Ca6 0.92095 (5) 0.43211 (16) 0.6248 (2) 0.0166(4)Ca7 0.08203 (5) 0.56843 (18) 0.1250 (2) 0.0221(4)Ca8 0.92566 (5) 0.57700 (18) 0.1226 (2) 0.0198(4)Ca9 0.00401 (5) 0.70699 (16) 0.4429 (2) 0.0208(4)Na1 0.31790 (9) 0.4041 (4) 0.9013 (4) 0.0202(8)

Na2 0.68936 (8) 0.4062 (4) 0.9157 (4) 0.0190(8)

Na3 0.06715 (7) 0.0965 (4) 0.3062 (4) 0.0098(6)Na4 0.93865 (9) 0.0933 (4) 0.3040 (4) 0.0193(8)Na5 0.00294 (9) 0.2439 (2) 0.9467 (4) 0.0130(6)X1 (Na,Ca) 0.31631 (6) 0.5971 (4) 0.4172 (4) 0.0251(6) 0.5X2 (Na,Ca) 0.68960 (7) 0.5952 (4) 0.4017 (4) 0.0328(7) 0.5X3 (Na,Ca) 0.94019 (6) 0.9040 (2) 0.7780 (4) 0.0228(6) 0.5X4 (Na,Ca) 0.06640 (7) 0.9014 (4) 0.7801 (4) 0.0370(8) 0.5X5 (Na,Ca) 0.75248 (7) 0.2134 (2) 0.2560 (2) 0.0236(5) 0.5X6 (Na,Ca) 0.25374 (8) 0.2475 (4) 0.2500 (4) 0.0453(8) 0.5C1 0.2534 (2) 0.3818 (8) 0.5942 (9) 0.0188(13)C2 0.7532 (4) 0.3776 (9) 0.5984 (11) 0.0324(17)C3 0.2542 (2) 0.1235 (9) 0.8784 (10) 0.0307(16)C4 0.7559 (4) 0.0902 (9) 0.8613 (11) 0.0291(16)C5 0.3557 (2) 0.2892 (9) 0.2776 (10) 0.0201(13)C6 0.6456 (2) 0.2935 (8) 0.2894 (9) 0.0174(12)C7 0.3578 (2) 0.6936 (8) 0.7708 (8) 0.0145(11)C8 0.6514 (2) 0.7023 (9) 0.7719 (10) 0.0206(14)C9 0.6055 (2) 0.7929 (8) 0.4200 (9) 0.0135(11)C10 0.4014 (2) 0.7887 (8) 0.4156 (8) 0.0128(11)C11 0.6102 (2) 0.1950 (8) 0.9185 (9) 0.0171(12)C12 0.3971 (2) 0.1983 (8) 0.9167 (9) 0.0171(12)C13 0.5031 (2) 0.8870 (7) 0.1155 (8) 0.0130(10)C14 0.50372 (16) 0.1327 (5) 0.5965 (7) 0.0025(7)C15 0.5038 (2) 0.4114 (7) 0.3405 (8) 0.0117(10)C16 0.50394 (16) 0.6355 (7) 0.8184 (7) 0.0054(8)O1 0.28800 (18) 0.3101 (8) 0.5460 (9) 0.040(2)O2 0.21776 (16) 0.3198 (7) 0.5608 (8) 0.0306(17)O3 0.2569 (4) 0.5304 (8) 0.6457 (10) 0.072(3)O4 0.71763 (18) 0.3281 (7) 0.5251 (8) 0.0353(18)O5 0.78858 (18) 0.3237 (7) 0.5375 (9) 0.0383(18)O6 0.7524 (2) 0.4576 (7) 0.7433 (8) 0.047(2)O7 0.2174 (2) 0.0638 (7) 0.8531 (8) 0.042(2)O8 0.2886 (2) 0.0600 (8) 0.8479 (9) 0.048(2)O9 0.25382 (17) 0.2779 (7) 0.9469 (8) 0.0371(18)O10 0.7915 (2) 0.1161 (8) 0.9051 (10) 0.065(3)

O11 0.7238 (4) 0.1026 (9) 0.9561 (13) 0.092(3)

O12 0.7494 (2) 0.0317 (7) 0.7012 (9) 0.057(2)

O13 0.3524 (2) 0.4237 (7) 0.1939 (7) 0.0298(16)O14 0.33170 (18) 0.1690 (7) 0.2545 (7) 0.0327(16)

O15 0.3837 (2) 0.2672 (8) 0.4046 (8) 0.045(2)O16 0.6487 (2) 0.4340 (7) 0.2107 (11) 0.068(3)O17 0.6671 (4) 0.1732 (7) 0.2615 (10) 0.071(3)O18 0.6172 (2) 0.2997 (11) 0.3970 (10) 0.092(3)

O19 0.3596 (2) 0.5648 (7) 0.6841 (9) 0.0359(19)

O20 0.3338 (2) 0.8127 (7) 0.7411 (9) 0.0412(19)O21 0.3831 (2) 0.7127 (9) 0.9074 (9) 0.057(2)O22 0.64972 (18) 0.5759 (7) 0.6763 (10) 0.0405(19)O23 0.67805 (18) 0.8178 (7) 0.7505 (7) 0.0332(17)O24 0.62572 (18) 0.7091 (7) 0.9069 (7) 0.0333(16)

Crystal Growth & Design Article

dx.doi.org/10.1021/cg500718y | Cryst. Growth Des. XXXX, XXX, XXX−XXXC

166 number of sets. The orientation of CO3 triangles inside the167 prisms require extra attention. In the prisms of right slabs, one168 of the edges of a CO3 triangle is almost parallel to the axis of169 the prism and is located near its elongated edge (Figure 3).170 Besides the indispensable bond with a carbon, O2− anions are171 bonded to three or four nearest (Na and Ca) atoms, which are172 located in the vertices of two-capped prisms. In the prisms of an173 oblique slab, the altitude of a CO3 triangle is oriented along the174 axis of the prism. O2− anions form three or four bonds in addition

175to the bond with carbon, in the same way as in the right slabs176(Figure 3).177The above analysis of the Na2Ca3(CO3)4 crystal structure178allows us to make a general conclusion on the genesis of this179structural type.180The partition of the space in two types of two-capped181trigonal prisms is due to the fact that precisely this182configuration of cavities in the cation arrangement is most183favorable for the placement of triangular anion groups (CO3)184or (BO3). In this way, the residue charge of O2− anions185is compensated by forming three or four bonds with big186cations.187Pseudosymmetry Analysis. The crystal structure of188Ca3Na2(CO3)4 is characterized by a substantial amount of189pseudosymmetry, which is reflected in atomic coordinates and190systematic absences. The last fact obstructs the determination191of the correct space group by diffraction pattern, what was the192reason for structure solution in the P1 space group.193The pseudosymmetry was analyzed manually as well as by194PLATON33,34 and KPLOT.35 If we consider only cation195positions without effect of partial occupancy, the space group of196such a cation sublattice is Pmnb (no. 62) with a = 15.72 Å, b =1978.1960 Å, and c = 7.4360 Å. Maximal deviation in the atomic198coordinates of some cations, which must be symmetry-related199in this group, is no more than 0.27 Å. The Ba3Nd2(BO3)4 and200Gd5Si4 compounds are characterized by the same space group201with almost the same lattice parameters in the first case.202Oxygen atoms gradually decrease symmetry through the203intermediate space groups to P1n1 with a doubled a axis, a =20431.4421 Å. The intermediate pseudo space groups are the205following: Pmc21 (no. 26) with a = 15.72 Å, b = 8.196 Å, c =2067.436 Å, Pmn21 (no. 31), and P21/n (no. 14) both with a207doubled a axis. Therefore, we can make a common conclusion208that pseudosymmetry in this case is due to the rotation of the209CO3 groups.

Table 2. continued

x y z Uiso Occ. (<1)

O25 0.6051 (2) 0.9172 (7) 0.5205 (8) 0.0396(19)O26 0.57889 (16) 0.6784 (7) 0.4556 (8) 0.0300(16)O27 0.63069 (16) 0.7672 (7) 0.2886 (7) 0.0243(13)O28 0.4029 (2) 0.9197 (7) 0.5044 (10) 0.049(2)O29 0.42771 (16) 0.6728 (7) 0.4596 (9) 0.0369(17)O30 0.37560 (16) 0.7706 (7) 0.2881 (7) 0.0228(14)O31 0.6071 (2) 0.0722 (7) 0.0066 (8) 0.045(2)O32 0.58538 (17) 0.3101 (8) 0.9594 (10) 0.051(2)O33 0.6350 (2) 0.2314 (9) 0.7803 (9) 0.052(2)O34 0.3966 (2) 0.0615 (7) 0.0056 (10) 0.044(2)O35 0.42372 (16) 0.3003 (7) 0.9783 (10) 0.0424(19)O36 0.37575 (16) 0.2203 (7) 0.7803 (7) 0.0252(14)O37 0.50190 (16) 0.0364 (4) 0.0576 (7) 0.0203(12)O38 0.5387 (2) 0.8211 (7) 0.1340 (9) 0.046(2)O39 0.4687 (2) 0.8150 (7) 0.1488 (9) 0.0354(19)O40 0.50383 (16) 0.0539 (4) 0.4500 (5) 0.0159(11)O41 0.53847 (16) 0.1709 (7) 0.6741 (7) 0.0207(14)O42 0.46834 (12) 0.1707 (5) 0.6736 (7) 0.0127(11)O43 0.5362 (2) 0.3818 (7) 0.2480 (10) 0.054(2)O44 0.4669 (2) 0.3765 (7) 0.2722 (11) 0.072(3)O45 0.50558 (16) 0.4655 (5) 0.4975 (5) 0.0153(11)O46 0.53821 (14) 0.5584 (5) 0.8563 (7) 0.0150(11)O47 0.46847 (16) 0.5525 (5) 0.8539 (5) 0.0154(11)O48 0.50286 (17) 0.7726 (5) 0.7536 (5) 0.0167(12)

Figure 1. Comparison of Ba3Nd2(BO3)4 (Z = 4) (left) andCa3Na2(CO3)4 (Z = 8) (right) crystal structures.

Crystal Growth & Design Article

dx.doi.org/10.1021/cg500718y | Cryst. Growth Des. XXXX, XXX, XXX−XXXD

Figure 2. Right slabs (left) and oblique slabs (right). One of the two-capped trigonal prisms is shown for both types of slabs. The colors of atomsindicate the level of the net, not the type of element.

Figure 3. Orientations of CO3 triangles inside two-capped trigonal prisms. Prisms of right slabs (top); prisms of oblique slabs (bottom); prisms withonly three oxygen−(Na, Ca) bonds (left); and prisms with three and four oxygen−(Na, Ca) bonds (right). Both Na+ and Ca2+ cations are shown ingreen.

Crystal Growth & Design Article

dx.doi.org/10.1021/cg500718y | Cryst. Growth Des. XXXX, XXX, XXX−XXXE

210 In accordance with the described pseudosymmetry, we211 suggest seven new possible polymorphs of Ca3Na2(CO3)4:212 Ca3Na2(CO3)4-I−Ca3Na2(CO3)4-VII (Table 1). Probable213 phase transition between synthesized polymorph Ca3Na2(CO3)4-I214 and some of the new polymorphs took place in the experiment215 during decompression. Indeed, a discontinuous increase in the216 unit cell parameters and volume of Ca3Na2(CO3)4-I was217 observed upon decompression from 1 GPa to 1 atm at room218 temperature.36 It is also possible that some representatives of219 these structures will be found among orthoborates. Group−220 subgroup relationships between Ca3Na2(CO3)4 polymorphs,221 homeotypic orthoborates, and some of the Gd5Si4-type structures222 are presented in Scheme 1. The group−subgroup analysis has223 been done using tools of Bilbao Crystallographic Server.37

224 ■ ASSOCIATED CONTENT225 *S Supporting Information226 CIF structure of Ca3Na2(CO3)4. This material is available free227 of charge via the Internet at http://pubs.acs.org.

228 ■ AUTHOR INFORMATION229 Corresponding Author230 *E-mail: p.gavryushkin@gmail.com.231 Notes232 The authors declare no competing financial interest.

233 ■ ACKNOWLEDGMENTS234 We would like to thank Alex Gavruskin for his very helpful235 advise on group-theoretic aspects of the research and on236 presenting the results and also the reviewers for important237 suggestions, which improved the quality of the manuscript. The238 research was supported by the Russian Foundation for Basic239 Research (Grant 14-05-31051) and Ministry of Education and240 Science of the Russian Federation (Grant 14B25.31.0032).

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Scheme 1. Flow-Chart of Group−Subgroup Relationships between Hypothetical Polymorphs of Ca3Na2(CO3)4 HomeotypicOrthoborates and Some of the Gd5Si4-Type Structuresa

aPotential Ca3Na2(CO3)4 polymorphs are shown in gray. Some space groups are given in a nonconventional setting to make group−subgrouprelations clear. For the atomic coordinates and other crystallographic data, see refs 14, 18, 26, and 28.

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