Sub-Solidus Synthesis and Microwave Dielectric Characterization ofPlagioclase Feldspars

Marjeta Macek Krzmanc,w Matjaz Valant,* Bostjan Jancar, and Danilo Suvorov*

Advanced Materials Department, Jozef Stefan Institute, 1000 Ljubljana, Slovenia

NaxCa1�xAl2�xSi21xO8 plagioclase solid solutions (0rxr1)were synthesized under sub-solidus conditions using a solid-statereaction technique. The plagioclase formation and the sinteringtemperature decreased with an increase in x from the anorthite(CaAl2Si2O8; x5 0) to the albite (NaAlSi3O8; x5 1).

Microwave (MW) dielectric measurements revealed thatslow-cooled ðP1Þ anorthite exhibited higher Q� f values thanfast-cooled ðI1Þ anorthite. Slow cooling also considerably im-proved the Q� f values of the sodium-rich NaxCa1�xAl2�xSi21xO8 solid solutions (0.8rxr1), where the highest Q� fvalue of 17600 GHz was obtained for slow-cooled Na0.8Ca0.2Al1.2Si2.8O8. The temperature coefficient of resonant fre-quency (sf) approached zero for 0.8rxr1.

I. Introduction

CURRENT developments in microwave (MW) circuits are ori-ented toward the miniaturization and integration of passive

components in three-dimensional (3D) modules using low-tem-perature cofired ceramic (LTCC) technology. There is a growingneed in LTCC technology for low-temperature-sinterable subst-rate materials with Q� f values that are higher than commer-cially available today and a temperature-stable permittivity ofless than 12. In addition to cordierite, anorthite (CaAl2Si2O8)has been investigated and regarded as a promising low-permit-tivity LTCC substrate material.1 Currently used commercialtapes are based on recrystallized anorthite, and their Q� f val-ues do not exceed 3000 GHz. Since recrystallization leads to ce-ramics with glassy-phase residuals, which increase the dielectriclosses, a dense, glass-free anorthite ceramic would be expected toexhibit lower dielectric losses. The crystallization and sinteringbehavior of anorthite has been the subject of numerous stud-ies.2–5 The problem of its high crystallization and sintering tem-perature was solved with the use of a nucleating agent (TiO2) ora sintering aid (B2O3).

3–5 The extensive studies of Lo et al.3–5

dealing with the preparation of low-loss anorthite were basedon the densification of fine glass powder (median particlesize5 0.45 mm) before the crystallization of the anorthite. Thecrystallization of anorthite, which followed sintering, was pro-moted by the nucleating agent TiO2. In spite of the recrystalli-zation they reported high Q values (2500 at 10 GHz) for theanorthite prepared in this way.

Anorthite belongs to the feldspar structural family, which arethe most abundant minerals in the earth’s crust. The feldsparcrystal structure is composed of a 3D framework of corner-shared SiO4 tetrahedra with each Si41 ion being surrounded byfour oxygen ions, and each oxygen ion shared between two Si41

ions. The Si41 ions are frequently substituted by Al31 ions, andthe charge is balanced by alkali-metal or alkaline-earth ions that

occupy the crystal site formed by silica/alumina tetrahedra.6 Inthe plagioclase feldspars, this substitution can be described bythe general formula NaxCa1�xAl2�xSi21xO8 (0rxr1). The lit-erature on plagioclase feldspars is vast.6–19 Most of it involvesstudies of minerals in order to shed light on the geological proc-esses that occurred in the past. In the scope of these structuraland mineralogical studies, the researchers devoted much atten-tion to the Al/Si ordering in feldspars while at the same timethey had to confront the structure, which is complicated by thesluggishness of the Al/Si ordering and the small differences inthe X-ray scattering efficiencies of Al and Si.11–18 However, inthe past the X-ray diffraction (XRD) technique was the mostfrequently used for determinations of the Al/Si distributionamong the four non-equivalent tetrahedral sites (T10, T1m,T20, and T2m) in the structure, thus making it possible to dis-tinguish between the low-temperature (ordered) and the high-temperature (disordered) plagioclase feldspars.10 Regardingthe nomenclature, the terminal high and low plagioclases areused for the highly disordered and the ordered plagioclases,respectively.

Extensive studies of the mechanisms and kinetics of Al–Siordering in anorthite by applying the Ginzburg–Landau (GL)rate equation with the introduction of macroscopic long-rangeorder (LRO) parameters (Qod) were made by Carpenter.13,14

Later studies by Phillips et al.15 showed that the ordering infeldspars is far more complicated and cannot be described onlyon the basis of XRD or electron microscopy, which are exper-imental techniques sensitive to long-range structure. The use of29Si magic-angle spinning nuclear magnetic resonance spectros-copy, which gave information about the local Al, Si distribu-tions, showed that a considerable short-range order (SRO)might be present in the phases that are disordered over the cor-relation length of XRD. Since the variations in SRO at fixedLRO can influence the numerous physical properties, includingthe dielectric properties, the SRO must also be considered. Incontrast to albite (NaAlSi3O8) and anorthite where the orderinghas been well investigated, the ordering in plagioclases with anintermediate composition is not yet completely understood.

Because of the variation of the Al:Si molar ratio in theNaxCa1�xAl2�xSi21xO8 (0rxr1) a different type of tetrahe-dral cation ordering occurs along the solid-solubility range. TheAl:Si5 2:2 molar ratio allows the anorthite to be completelyLRO with I1 symmetry. With a decrease in the Al and Ca con-tent in the NaxCa1�xAl2�xSi21xO8 the formation of anorthite-type LRO is constrained and the structure changes to C1 withSRO.16,18 Kroll and Muller9 suggested that the C12I1 trans-formation occurred between x5 0.3 and x5 0.4. Later, thistransformation was more accurately determined by Carpenterand McConnell11 as a steep line passing through the pointsBx5 0.41, 10001C and Bx5 0.23, 14401C in the albite-anort-hite binary phase diagram. The exact determination of theC12I1 transition of the high plagioclases is beyond the scopeof this work.

Although the NaxCa1�xAl2�xSi21xO8 (0rxr1) solid solu-tions belong to the same structural family as anorthite their di-electric properties in the MW frequency region have not beeninvestigated so far. The main objective of our work was to study

Journal

J. Am. Ceram. Soc., 88 [9] 2472–2479 (2005)

DOI: 10.1111/j.1551-2916.2005.00461.x

r 2005 The American Ceramic Society

2472

T. Vanderah—contributing editor

* Member, American Ceramic Society.wAuthor to whom correspondence should be addressed. e-mail: marjeta.macek@ijs.si

Manuscript No. 20313. Received September 3, 2004; approved March 16, 2005.

the effect of the substitution of Na1 for Ca21 and Al31 for Si41

in the plagioclases feldspars NaxCa1�xAl2�xSi21xO8 (0rxr1)on their dielectric properties. Since the cooling rate and sinteringtemperature are parameters that have a significant influence onthe degree of order in the feldspars we investigated their influ-ence on the MW dielectric losses, which are sensitive to theorder/disorder processes in the structure.

II. Experimental Procedure

The NaxCa1�xAl2�xSi21xO8 (0rxr1) solid solutions were syn-thesized using the solid-state reaction technique. Stoichiometricmixtures of reagent-grade oxides (Al2O3, 99.99%, Alfa Aesar,SiO2, 99.9%, Alfa Aesar, Na2CO3, 99.5% Alfa Aesar andCaCO3, 99.99% Alfa Aesar) were homogenized and pre-react-ed under conditions that strongly depend on the composition.The pre-reaction and sintering temperatures (Ts) for particularcompositions are listed in Table I. Because of the eutectic melt-ing that occurred during the synthesis of sodium-rich NaxCa1�xAl2�xSi21xO8 solid solutions (0.6rxr1) these composi-tions required a slightly different procedure for the synthesisthan the plagioclases with compositions closer to anorthite(0rxr0.4). In order to conduct a complete synthesis of sodi-um-rich plagioclases (0.6rxo1) under sub-solidus conditionsthe pre-reactions at certain temperatures, which depended oncomposition, were repeated with intermediate milling (Table I, �

marks the milling before pre-reactions at denoted temperatures).Prior to sintering the powders were ball-milled in ethanol withyttrium-doped zirconium-oxide (Y-ZrO2) balls with a diameterof 3 and 0.8 mm. The milled powders, with median particle sizeof 0.7 mm, were sintered for 15 h at a selected temperature andthen cooled quickly or slowly with a controlled cooling rate(0.51C/min). Fast cooling means uncontrolled cooling in anoven by natural convection, conduction and radiation to roomtemperature. The synthesis of all the plagioclases was performedtwice in order to check its repeatability and compare the struc-tural and dielectric properties from different synthesis runs.

The X-ray powder-diffraction studies were performed with aBruker AXS D4 Endeavor diffractometer using CuKa radia-tion. X-ray powder-diffraction data were collected from 101o2Yo701 with a step of 0.021, a counting time of 12 s, and avariable V6 slit. The DIFFRAC plus TOPAS R program wasused for the determination of the lattice parameters of theNaxCa1�xAl2�xSi21xO8 solid solutions (0rxr1) with Rietveldrefinement of the X-ray powder-diffraction data.

The microstructural studies of the samples were conductedvia scanning electron microscopy (SEM) (Model JXA 840A,JEOL, Tokyo, Japan) coupled with energy-dispersive X-rayspectroscopy (EDX) using software (Series II X-ray micro-analyzer, Tracor Nothern, Middleton, WI).

The electron diffraction and the domain imaging were per-formed with a JEOL 2010F transmission electron microscope(TEM). Samples for these analyses were prepared by mechanicalthinning and subsequent ion-beam milling using a plasma ofargon ions at 4 kV.

The radio-frequency (RF) dielectric measurements wereperformed at frequencies (f) from 1 kHz to 1 MHz on In/Ga-plated disk capacitors using a high-precision LCR meter

(Agilent 4284 A, Palo Alto, CA). The temperature dependenceof the dielectric properties was measured from �1001 to 2501Cby placing the samples in an environmental chamber (Delta De-sign, Delta 9039) and monitoring the temperature with a copper-constantan (T-type) thermocouple. The temperature coefficientof permittivity (tk) was determined from the slope of the DC/Ccurve versus temperature at 1 MHz, where DC represents thedifference between the capacitance at temperature (T) and thecapacitance at 201C (C).

The MW dielectric properties were characterized using theclosed air-cavity method with a network analyzer (HP 8719C).Permittivity and quality factor (Q) values were calculated at theresonant conditions (TE01d mode) from the S11-reflection coef-ficient as proposed by Kajfez et al.20 During the measurementsof theMWdielectric properties of low-loss dielectrics it is crucialto correctly identify the proper eigenfrequency (TE01d). Theidentification is, in the case of a high-permittivity, facilitatedby the fact that this frequency is usually the lowest eigenfre-quency of the resonant system. For low-permittivity dielectrics(o20) the TE01d is not the lowest eigenfrequency anymore andcan only be recognized by a 3D mathematical modeling of theentire resonant structure, which includes the air cavity and theinserted dielectric resonator. We performed such modeling usingMW Studio software packages (Computer Simulation Technol-ogy, Germany) that conduct the calculations based on a finiteintegration technique using Maxwell’s equations. To determinethe temperature dependence of resonant frequency the test cav-ities were inserted into a temperature-controlled chamber. Thedielectric characteristics of the samples were analyzed in thetemperature range from 201 to 601C.

III. Results and Discussion

(1) Solid-State Synthesis of Plagioclase Feldspar Ceramics

The synthesis of the plagioclase feldspars started from amor-phous SiO2, a-Al2O3, Na2CO3 and calcite CaCO3 The reactionsoccurring during the heat treatments were followed by X-raypowder diffraction, which showed that among the plagioclasefeldspars the albite formed at the lowest temperature.

Albite: The pre-reaction of the mixture with the nominalcomposition of albite at 7001C led to partial crystallization ofthe SiO2, decomposition of the Na2CO3 and the formation ofNa2Si2O5 and nepheline (NaAlSiO4) (Table II). The majorityof the Al2O3 remained unreacted at this temperature. At 8001C,the concentration of nepheline further increased and the albitephase started to form. The rate of albite formation was pro-moted by milling the powders before the pre-reactions at 9001C.During firing at 10001rTr10701C, the nepheline and Al2O3

phases completely disappeared and the synthesis of albite wascompleted.

NaxCa1�xAl2�xSi21xO8 (0.6rxo1): The formation andsintering temperatures of plagioclases increases by B501C witha decrease in x of 0.2. The reaction sequences occurring duringthe heat treatment of the samples with the nominal compositionof NaxCa1�xAl2�xSi21xO8 (0.6rxo1) are illustrated for thecase of Na0.8Ca0.2Al1.2Si2.8O8 in Fig. 1, while the phase compo-sitions at different pre-reaction temperatures for all the compo-sitions are represented in Table II.

Table I. Pre-Reaction and Sintering Temperatures for NaxCa1�xAl2�xSi21xO8 (0rxr1) Solid Solutions

Pre-reaction temperatures (1C) Sintering temperature (1C)

NaAlSi3O8 600 700 800 900w 1000–1070Na0.8Ca0.2Al1.2Si2.8O8 700 800 900 1000 1050 1050w 1100Na0.67Ca0.33Al1.33Si2.67O8 800 900 1000 1100 1100w 1135Na0.6Ca0.4Al1.4Si2.6O8 800 900 1000 1100 1100w 1150Na0.4Ca0.6Al1.6Si2.4O8 900 1000 1100 1200 1200Na0.2Ca0.8Al1.8Si2.2O8 1000 1100 1200 1250CaAl2Si2O8 1000 1100 1200 1300–1500

wMilling with yttrium-doped zirconium-oxide balls (with a diameter of 3 mm) before the pre-reaction at denoted temperatures.

September 2005 Sub-Solidus Synthesis and Microwave Dielectric Characterization 2473

The first pre-reaction at 7001C led to the crystallization ofSiO2, the decomposition of CaCO3 and the formation of varioussodium calcium silicates. The presence of CaO in the reactionmixture heat treated at 7001C indicated that the decompositionof CaCO3 proceeded faster than the formation of sodium cal-cium silicates, which were still present at 8001C and disappearedat 9001C. The nepheline, in addition to the plagioclase phase,formed at 8001C (Fig. 1). With a further increase in temperatureto 9001, 10001, and 10501C the concentration of the plagioclasephase increased, while the concentration of Al2O3 and nephelinedecreased. At 9001C the diffraction lines corresponding to thewollastonite (CaSiO3) phase also appeared. When the pre-reac-tion temperature was increased directly from 10501 to 11001Cthe sample with the nominal composition Na0.8Ca0.2Al1.2Si2.8O8

melted at this temperature. The melting could be expected from

the phase diagram of the nepheline-anorthite-silicon oxide sys-tem, where eutectics exist between the nepheline and plagioclaseand between the silicon oxide and plagioclase.21 The pseudobi-nary eutectics albite-nepheline and albite-silicon oxide exist at10681 and 10621C, respectively. Similar to albite, other plagio-clases also form eutectics: plagioclase-nepheline and plagio-clase–SiO2. With a decrease in x in the NaxCa1�xAl2�xSi21xO8 solid solutions the temperatures of the plagioclase-ne-pheline and plagioclase–SiO2 eutectics increase toward theeutectic temperatures of anorthite-nepheline (14501C) andanorthite–silicon oxide (13681C) (Fig. 2). The melting that oc-curred at 11001C indicates that the plagioclase, which formedinitially, contains a very low concentration of Ca21, which ismostly concentrated in the wollastonite. To increase the eutectictemperature above the pre-reaction temperature and ensure the

Table II. Phases Formed During Solid-State Synthesis of NaxCa1�xAl2�xSi21xO8

(Determined from X-Ray Powder-Diffraction Spectra)

x5 1 x5 0.8 x5 0.6 x5 0.4 x5 0.2 x5 0

7001C, SiO2,Al2O3,nepheline,Na2Si2O5

7001C, Al2O3, SiO2,sodium calciumsilicates, CaO

8001C, Al2O3,SiO2, nepheline,sodium calciumsilicates, CaO

9001C, wollastonite, Al2O3,SiO2, nepheline, gehlenite,plagioclase, sodium calciumsilicates

10001C,wollastonite,Al2O3, gehlenite,SiO2, plagioclase,

10001C,gehlenite, Al2O3,wollastonite,anorthite, SiO2

8001C,albite,nepheline,SiO2, Al2O3

8001C, Al2O3, SiO2,nepheline, sodiumcalcium silicates,plagioclase

9001C, plagioclase,wollastonite,Al2O3,SiO2,nepheline

10001C, wollastonite,Al2O3, SiO2, plagioclase,nepheline, gehlenite

11001C,wollastonite,Al2O3,plagioclase,gehlenite, SiO2

11001C, Al2O3,wollastonite,SiO2, anorthite,gehlenite

9001C,albite,Al2O3,nepheline

9001C, plagioclase,Al2O3, SiO2,nepheline,wollastonite

10001C,plagioclase,wollastonite,Al2O3, SiO2,nepheline

11001C, wollastonite,plagioclase, Al2O3, SiO2

12001C,plagioclase,Al2O3

12001C,anorthite, Al2O3

10001–10701C,albite

10001C, plagioclase,Al2O3, wollastonite,nepheline

11001C,plagioclase, Al2O3,wollastonite,nepheline

12001C, plagioclase 12501C,plagioclase

13001–15001C,anorthite

10501C, plagioclase,Al2O3, nepheline,wollastonite

11501C,plagioclase

11001C, plagioclase

Fig. 1. X-ray powder-diffraction patterns of the sample with the nom-inal composition of Na0.8Ca0.2Al1.2Si2.8O8 heat treated at different tem-peratures (N-nepheline, s-SiO2, a-Al2O3,

�-sodium calciumsilicates, W-wollastonite, c-CaO).

Fig. 2. Phase diagram of the system Nepheline-Silicon oxide-Anorthiteafter Schairer.21

2474 Journal of the American Ceramic Society—Krzmanc et al. Vol. 88, No. 9

sub-solidus conditions the pre-reaction must be promoted at10501C. In this way a higher concentration of Ca21 will be in-corporated in the plagioclase and, as a consequence, increase theeutectic melting temperature. To achieve this the powder wasmilled after a pre-reaction at 10501C and then pre-reacted againat this temperature. Because of the smaller particle size theplagioclase phase formation was enhanced, while the nepheline,Al2O3 and CaSiO3 contents were decreased during the addition-al pre-reaction at 10501C (Fig. 3). After that the pre-reactiontemperature was increased to 11001C and the reaction was com-pleted with no intermediate melting. With a decrease in x in theNaxCa1�xAl2�xSi21xO8 solid solutions the eutectic melting wasshifted to higher temperatures. In the case of Na0.6Ca0.4Al1.4Si2.6O8 the pre-reaction should be repeated with intermediatemilling at 11001C before continuing with the synthesis at 11501C(Table I).

NaxCa1�xAl2�xSi21xO8 (0oxr0.4): During the heattreatment of the samples with a nominal composition of NaxCa1�xAl2�xSi21xO8 (0rxr0.4) some differences in the reactionsequences appeared in comparison with the sodium-rich plagi-oclases (0.6rxr1). The firing of the sample with the nominalcomposition Na0.4Ca0.6Al1.6Si2.4O8 at 9001C led to the forma-tion of the gehlenite (Ca2Al2SiO7) phase in addition to the crys-tallization of SiO2 and the formation of wollastonite, nepheline,

sodium calcium silicates and traces of the plagioclase phase.The synthesis of Na0.4Ca0.6Al1.6Si2.4O8 was completed duringsintering at 12001C (Table II). In contrast to sodium-richplagioclases (0.6rxr1), where additional milling before thepre-reactions was indispensable for a complete synthesis under

Fig. 3. X-ray powder-diffraction patterns of a sample with the nominalcomposition of Na0.8Ca0.2Al1.2Si2.8O8 after first pre-reaction at 10501C(10501C�1) and after additional pre-reaction of milled powder at10501C (10501C�2) (N-nepheline, a-Al2O3, W-wollastonite).

Fig. 4. X-ray powder-diffraction patterns of slow-(P1) and fast-(I1)cooled anorthite samples heat treated at different temperatures.

Fig. 5. The parameter D1315 2Y (131)-2Y (131) (a) and g-latticeangle (b) as a function of NaxCa1�xAl2�xSi21xO8 composition: &-Kroll and Muller9 and Kroll and Ribbe.10 J-this study.

Fig. 6. Cell volume of NaxCa1�xAl2�xSi21xO8 solid solutions as afunction of composition. J-refinement with modified albite crystalstructure data (double cell), &-refinement with modified anorthitecrystal structure data.

September 2005 Sub-Solidus Synthesis and Microwave Dielectric Characterization 2475

sub-solidus conditions (Table I), the plagioclases with higher Caand Al contents (0rxr0.4) were milled only prior to sintering.The fact that no melting occurred during the synthesis ofplagioclases with higher Ca and Al contents could be explainedby the nepheline-anorthite–silicon oxide phase diagram(Fig. 2).21 Because of the formation of a plagioclase with acomposition closer to anorthite, the eutectic temperatures be-tween nepheline and plagioclase and between plagioclase andSiO2 are higher than the formation temperature of the plagio-clase phase.

Anorthite: The reactions occurring during the heat treat-ment of samples with the composition of anorthite resembledthat of plagioclases with high Ca and Al contents. Besides theformation of some anorthite phase, the crystallization of SiO2

and the formation of gehlenite and wollastonite phases tookplace at 10001C. With further heat treatments at 11001 and12001C the concentration of anorthite phase increased, while theconcentration of gehlenite, wollastonite and Al2O3 decreased.The synthesis of anorthite was completed during sintering at13001C (Table II). Anorthite crystallizes in the triclinic crystalsystem with I1 symmetry, which during slow cooling inverts to

P1 symmetry. Based on the literature data the anorthite under-goes a displacive phase transition atB2401C to a structure withP1 symmetry.12–14 The I12P1 transformation of anorthiteduring slow cooling can also be seen from the X-ray powder-diffraction patterns. The main difference between the X-raypowder-diffraction patterns of the I1 and P1 structures is theappearance of the ð111Þ diffraction line at 2Y5 12.9941 in theP1 structure. It can be seen from the X-ray powder-diffractionpatterns of the slow- and fast-cooled anorthite samples that slowcooling is required for the I12P1 transformation (Fig. 4).

(2) Crystallographic Considerations for SynthesizedPlagioclases

Because of the sluggish kinetics of Al/Si ordering in the plagi-oclase feldspars the equilibrium state of order is to be expectedonly after several days of heat treatment.9,11,22 In our experi-ments the heat-treatment time was 15 h. This means that ourplagioclase samples most probably did not reach the equilibriumstate of order. When studying the structure of plagioclase feld-spars with X-ray powder diffraction, two facts must be takeninto account. Firstly, the structural information obtained fromXRD studies represents an average structure and gives no in-formation about the local structure. Secondly, X-ray powderdiffraction is not useful for an accurate determination of thetransition from C1 to I1 in anorthite-rich compositions11 be-cause of the small differences in the X-ray scattering efficienciesof Al and Si. Nevertheless, X-ray powder-diffraction, in partic-ular the D131 parameter ðD131 ¼ 2Yð131Þ � 2Dð131ÞÞ and thelattice angle g, are very useful for distinguishing between thehigh and low plagioclases.10 Both the g angle and the D131 pa-rameter are a measure of the difference between the Al occu-pancy of the T10 site and the average Al occupancy over theother T-sites. The dependence of the D131 parameter on thecomposition was determined to be very similar to that obtainedby Kroll and Muller9 and Kroll and Ribbe10 for high plagio-clases prepared by the dry devitrification of glasses at 30–1201Cbelow the solidus temperature (Fig. 5(a)). The values of the D131parameters obtained by Kroll and Muller9 were the expectedvalues at the solidus temperature, which were extrapolated fromD131 values at 301, 601, and 1201C below the solidus tempera-ture. In our case the D131 values were obtained from X-raypowder-diffraction spectra of plagioclases that were preparedunder sub-solidus conditions at lower temperatures (501–2001Cbelow the melting point). For this reason the plagioclases in thisstudy were expected to be slightly more ordered, and thus havesomewhat lower D131 values than would otherwise be expected.

Fig. 7. Selected-area electron-diffraction (SAED) pattern collectedalong the (010) zone axis for fast-cooled anorthite sample heat treatedat 14001C for 15 h (a) and for anorthite sample heat treated at 14751Cfor 24 h and cooled slowly (0.51C/min) (b).

Fig. 8. Dark-field transmission electron micrograph showing b-typeordered domains in the anorthite prepared under conditions as describedin caption of Fig. 7(b).

2476 Journal of the American Ceramic Society—Krzmanc et al. Vol. 88, No. 9

Nevertheless, the values of the D131 parameter for the NaxCa1�xAl2�xSi21xO8 (0rxr1) solid solutions in this study con-firmed their high plagioclase structure.

The unit-cell parameters of the plagioclase solid solutionswere obtained with Rietveld structural refinements of the pow-der data. The best fits for the NaxCa1�xAl2�xSi21xO8 solid so-lutions with 0.6rxr1 were obtained when fitted on the basis ofalbite crystal structure data ðC1Þ that were modified to take intoaccount the composition. In contrast, the structures of NaxCa1�xAl2�xSi21xO8 with 0rxr0.4 could only be fitted on thebasis of a modified anorthite crystal structure with the spacegroup I1. As was already stated, from the lattice angles, the g-angle is the most sensitive to the occupancy of the tetrahedralsite with Si or Al.8 The high plagioclase structure for Nax-Ca1�xAl2�xSi21xO8 in this study was additionally confirmed bythe good agreement of the g-angle values with those values forsynthetic high-temperature plagioclases prepared by recrystalli-zation close to the solidus temperature (Fig. 5(b)).9,10 The in-crease of the cell volume from albite toward anorthite with amaximum near Na0.2Ca0.8Al1.8Si2.2O8 was also in accordancewith the already published data (Fig. 6).8

TEM was found to be a very useful technique for studyingplagioclases, especially those with a composition close to anort-hite, where the I1 and C1 structures could not be distinguishedby X-ray powder-diffraction.7–13 The electron-diffraction pat-tern of I1 anorthite is characterized by the presence of super-structure b reflections (h1k5odd, l5odd) in addition to thebasic a reflections (h1k5 even, l5 even), which are present ineach feldspar pattern.7,9 b-reflections arise because of the alter-nating of the Al and Si atoms. In the P1 anorthite c (h1k5even, l5odd) and d (h1k5odd, l5 even) reflections appearedin addition to the a and b reflections.7,9 The electron-diffraction

pattern of anorthite heat treated at 14001C and cooled fastshowed the presence of a and b reflections, which confirmed itsI1 structure (Fig. 7(a)). In contrast, all four (a, b, c, and d) re-flections are clearly visible in the electron-diffraction pattern ofthe slow-cooled (0.51C/min) anorthite heat treated at 14751C for24 h (Fig. 7(b)). From the dark-field electron micrograph using ab-type superstructure reflection, ordered domains of size 100–200 nm can be estimated (Fig. 8). Based on the b domains sizethis sample represents a well-ordered anorthite. For compari-son, a similar average domain size was obtained after 400–1000h of crystallization for glass with the composition of anorthite at14001C.13

(3) Dielectric Properties

For the analysis of the dielectric properties the powders weresintered to dense ceramics with relative density of B97%. Atypical remaining level of porosity is shown in Fig. 9. The per-mittivity showed no significant frequency dispersion from 1MHz to 10 GHz (Table III). Although there were some varia-tions in the permittivities of the NaxCa1�xAl2�xSi21xO8

(0rxr1) solid solutions, because of the different densitiesof the samples, the permittivity exhibited an increasing trendfrom the albite to the anorthite (Table III). This is to be expectedfrom the decrease in the dielectric polarizability of the NaxCa1�xAl2�xSi21xO8 with x, mainly because of the higher dielec-tric polarizability of Ca21 compared with Na1.

Among the NaxCa1�xAl2�xSi21xO8 (0rxr1) solid solutionsthe anorthite exhibited the most negative temperature coefficient

Table III. The Dielectric Properties of NaxCa1�xAl2�xSi21xO8 (0rxr1) Solid Solutions Determined at 1MHz and in theMicrowaveFrequency Region (at B10.5 GHz)

x-(Ts) 0 (14001C) 0.2 (12501C) 0.4 (12001C) 0.6 (11501C) 0.67 (11351C) 0.8 (11001C)

1

(10001C) (10501C)

e1MHzf 9.3 7.1 6.6 6.8 5.8 6.3 5.1 6.5e1MHzs 8.9 7.2 6.5 6.6 5.6 5.9 5.4 6.3tk (ppm/1C) 280f 93 B20 B10 B10 B10 B10 B10

360s

eMWf 8.0 6.7 6.4 6.6 5.8 6.0 4–5 6.0eMWs 7.4 7.0 6.3 6.7 5.9 5.8 4–5 6.3Q� f (GHz)f 6300 4500 7600 11 250 12 900 9900 8500 4400Q� f (GHz)s 8750 4900 7750 13 300 13 300 17 600 9800 8700tf (ppm/1C) �130f �50 �15 �12 �7 �7 �5 �24

�140s

f and s denote fast, uncontrolled cooling and cooling with a rate of 0.51C /min, respectively.

Fig. 9. Scanning electron micrograph of the anorthite sample sinteredat 14001C.

Fig. 10. Temperature coefficient of resonant frequency (tf) in micro-wave region for NaxCa1�xAl2�xSi21xO8 solid solutions.

September 2005 Sub-Solidus Synthesis and Microwave Dielectric Characterization 2477

of resonant frequency (tf), which approached zero with increas-ing x (Fig. 10). Regarding the equation tf 5�a–0.5tk, where arepresents the thermal expansion coefficient (a5 1–10 ppm/K),the tf and tk showed corresponding trends. The tk of anorthite(280–360 ppm/1C) started to decrease with substitution, ap-proaching zero for solid solutions with 0.8rxr1 (Table III).The tf and tk in the range715 ppm/1C is a very important ad-vantage of NaxCa1�xAl2�xSi21xO8 solid solutions (0.4rxr1)over the anorthite for potential practical applications.

The ratio of Al:Si5 2:2 in anorthite allows, in principle, com-plete ordering with an alternation of Al and Si (Al–O–Si–O–Al).Many studies dealing with ordering in anorthite revealed thatanorthite asymptotically approaches to an equilibrium degree oforder.9,13,15 The increase of Q� f values with sintering temper-ature and slow cooling rate in this study most probably reflectsthis approaching to the ordered state. In the series of fast-cooledðI1Þ anorthite samples the Q� f values increased from 5500GHz (Ts 5 13001C) to 8500 GHz (Ts 5 15001C). Higher Q� fvalues of 7100 GHz (Ts 5 13001C) and 11 000 GHz (Ts515001C) were obtained for ðP1Þ anorthite samples that wereheat treated under the same conditions, but cooled slowly(0.51C/min). Additionally, the Q� f values were also improvedwith an extension of the heat-treatment time to several days.

With substitutions the Al:Si molar ratio in NaxCa1�xAl2�xSi21xO8 starts to deviate from the ideal 2:2 in anorthite. Becauseof the concentration constraints the anorthite–type ðI1Þ long-range ordering, characterized by the alternating of Al and Si

atoms (–Al–O–Si–O–Al–), cannot develop in sodium-richerplagioclases and the structure change to C1.9,11 In spite of theabsence of anorthite-type LRO at intermediate compositions ahigh degree of SRO can develop in the C1 plagioclase feldsparsaccording to several experimental and theoretical studies.15–18

This complicated, and not yet well-understood, ordering at in-termediate compositions certainly affects the dielectric losses.Our study showed that the Q� f values decreased when Ca21

ions were partly substituted with Na1 ions up to x5 0.2. Withfurther substitution theQ� f values started to increase, reachinga maximum at the composition Na0.67Ca0.33Al1.33Si2.67O8 with aSi:Al ratio 2:1, and then decreased again to the Q� f value ofalbite (Fig. 11), which strongly depended on the sintering tem-perature (Fig. 12). The highest Q� f value of an albite sample(8500 GHz) was obtained for a sample sintered at 10001C, whilea more densely sintered sample at 10701C exhibited less thanhalf of this Q� f value (3100 GHz) (Fig. 12). These results referto the samples heat treated for 15 h at a selected temperatureand then cooled without control to room temperature. The di-electric measurements showed that a slow cooling rate of 0.51C/min considerably improved the Q� f values of sodium-richplagioclases NaxCa1�xAl2�xSi21xO8 (0.8rxr1), while smallerimprovements were observed for Ca-richer plagioclases(0rxr0.67) (Table III). The highest Q� f value of 17 600GHz was obtained for Na0.8Ca0.2Al1.2Si2.8O8 when cooledwith a rate of 0.51C/min. Slower cooling rates did not furtherincrease the Q-values.

The Q� f values of the albite samples were also improvedwhen they were cooled slowly (Fig. 12). In contrast to the fast-cooled albite samples, where the Q� f values decreased with thesintering temperature, the Q� f values of the slow-cooled sam-ples at first increased to 11 200 GHz for samples fired at 10251Cand then started to decrease, approaching values typical for afast-cooled sample at 10701C. The increase in the Q� f valuesfor the slow-cooled albite sample at 10251C, compared with thatsintered at 10001C, can be attributed mainly to the higher den-sity of the sample sintered at 10251C. The great differences be-tween the Q� f values of slow- and fast-cooled NaxCa1�xAl2�xSi21xO8 solid solutions (0.8rxr1) most probably reflectthe increase of the SRO, since there is no evidence from theXRD data for an increase of LRO with a slow cooling rate, i.e.,there is no significant change in the g-angle and in the D131parameter in spite of the great difference in the Q� f values.However, the assumption that the slow-cooled samples exhibit-ed higherQ� f values because of an increase in SRO needs to beproved by a technique that is sensitive to the local structure.Based on the extensive structural studies of plagioclase feldsparminerals, Hard Mode Infrared Spectroscopy seems to be themost appropriate technique.22,23

IV. Conclusions

MW dielectric investigations of NaxCa1�xAl2�xSi21xO8 ceram-ics (0rxr1), prepared under sub-solidus conditions, revealedsome advantages of sodium-rich NaxCa1�xAl2�xSi21xO8 solidsolutions (0.8rxr1) over anorthite (x5 0), which is the mainconstituent of commercial LTCC tapes. The sintering tempera-ture decreased with x from 13001C for anorthite to 10001C foralbite (x5 1). While low-loss anorthite ceramics could be ob-tained when heat treated at 15001C, the highest Q� f value of17 600 GHz was obtained for Na0.8Ca0.2Al1.2Si2.8O8 sintered at11001C. In contrast to the anorthite, which exhibited tf5�130to �140 ppm/1C, the tf of the NaxCa1�xAl2�xSi21xO8 solid so-lutions with 0.4rxr1 (�5 to �15 ppm/1C) is close to the valuerequired for LTCC technology.

Composition, cooling rate, and sintering temperature werefound to influence the dielectric losses of plagioclases. Anorthite,which undergoes a displacive I12P1 transition during slowcooling, exhibits higher Q� f values (7100–11 000 GHz) thanfast-cooled I1 anorthite, where Q� f values are 5500–8500GHz. Similarly, the Q� f values of sodium-rich NaxCa1�xAl2�x

Fig. 11. The Q� f values versus composition for fast-cooledNaxCa1�xAl2�xSi21xO8 solid solutions.

Fig. 12. The Q� f-values as a function of the sintering temperature forfast- (-& -) and slow- (-J-) cooled albite samples.

2478 Journal of the American Ceramic Society—Krzmanc et al. Vol. 88, No. 9

Si21xO8 solid solutions (0.8rxr1) were also improved duringslow-cooling. The nearly two times higher Q� f values ofslow-cooled NaxCa1�xAl2�xSi21xO8 solid solutions (0.8rxr1)compared with fast-cooled ones most probably reflects theincrease in SRO, since there is no evidence from the X-raypowder-diffraction data for any increase in the LRO.

Acknowledgments

We would like to acknowledge Mr. Urban Dogler and Mr. Aleksander Figeljfor their important assistance during the extensive experimental work.

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