Dielectric Constants of Diaspore and B-, Be-, and P-Containing Minerals, the Polarizabilities of B2o3and P2os,And the Oxide Additivity Rule

American Mineralogist, Volume 77, pages 101-106, 1992

Dielectric constants of diaspore and B-, Be-, and P-containing minerals, the polarizabilities of B2O3and P2Os,and the oxide additivity rule

Ronrnr D. SnaNnoN, MutstnmLLAM A. SunurvrANrAN Central ResearchDepartment, Experimental Station 356/329, E.I. Du Pont de Nemours, Wilmington, Delaware I 9880-0356, U.S.A. ANrrror.IY N. MlnHNo 48 PageBrook Road, Carlisle, Massachusetts01741, U.S.A. TnunuaN E. Grnn P.O. Box 884, ChaddsFord, Pennsylvania19317, U.S.A- Gnoncn R. RossvHN Division of Geological and Planetary Sciences,California Institute of Technology, Pasadena,California 91125, U.S.A.

Anstnlcr The l-MHz dielectric constantsand loss factors of the minerals diaspore,euclase, hamberyite, sinhalite, danburite, datolite, beryllonite, and montebrasite and of the synthetic oxides IarBe2O5,AlP3Oe, and NdPrO,o were determined. The dielectric polarizabilities of BrO, and PrO, derived from the dielectric constants of these compounds are 6.15 and 12.44 43, respectively. The dielectric constants of the above minerals and oxides, along with the dielectric polarizabilities of LirO, NarO, BeO, MgO, CaO, Al2O3,Nd2O!,La2O3, SiOr, diaspore, and the derived values of the polarizabilities of BrO, and PrOr, were used to calculate dielectric polarizabilities from the Clausius-Mosotti equation and to test the oxide additivity rule. The oxide additivity rule is valid to +0.50/ofor all exceptberyllonite. These compounds with deviations from additivity of 0.5-1.50/0,along with previously studied aluminate and gallate garnets,chrysoberyl, spinel, phenacite,zircon, and olivine- type silicates,form a classof well-behaved oxides that can be used as a basis for compar- ison of compounds that show larger deviations (>50/o)caused by ionic or electronic conductivity, the presenceof HrO or COr, or structural peculiarities.

INrnooucrroN Previous applications of the additivity rule to minerals were reviewed by Shannon and Subramanian (1989). Dielectric polarizability, ao, is related to the mea- The purpose of this paper is to determine the l-MHz sured dielectric constant, x', by the Clausius-Mosotti dielectric constants ofdiaspore and several Be-, B-, and equatron: P-containing oxides and minerals, to derive the polariz- ae: l/bl(V^)(x' - l)/(x' + 2)l (l) abilities of BrO, and PrOr, and to evaluate the validity of the oxide additivity rule in these materials. where Z- is the molar volume in At, b is assumedto be 4tr/3, and r', the real part of the complex dielectric con- ExpnnrvrnNrt stant, was measuredin the range I KHz to l0 MHz (Rob- The sourcesof the crystalswere as follows: diaspore- erts, 1950, l95l). The Clausius-Mosottiequation is strictly grayish green crystal from Turkey; euclase-clear, color- valid only for compounds in which the molecule or ion lesscrystals, one from San Sebastaode Maranhao, Minas has cubic symmetry (Szigeti, 1949;Bosman and Havinga, Gerais, and the other from Diamantina, Minas Gerais, 1963; Duffin, 1980; Kip, 1962; Megaw, 1957; Roberts, Brazll La, n,Ndo o,BerO, - from Allied-Signal Corp.; 1949,1950, l95l; Dunmur, 1972)but has been shown hamberyite-clear, colorless crystal from Antsirabe, Ta- to be approximately valid for a number of noncubic crys- nanarive, Madagascar;sinhalite-greenish yellow crystal tals (Roberts, 1949, 195 | Lasagaand Cygan, I 982; Shan- ; from the Ellawalla River, Ratnapura, Sri Lanka; dan- non et al., 1989,1990). burite-clear, colorless crystal from Charcus, Mexico; The concept of additivity of molecular polarizabilities datolite-clear, colorless crystal from Westfield, Massa- implies that the molecular polarizability of a complex chusetts; AIPO.-clear, colorless crystals grown hydro- substance can be divided into the molecular polarizabil- thermally from a hydrochloric acid-phosphoric acid so- ities of simpler substancesaccording to lution at I 70'C as describedby Ozimek and Chai ( I 978); ao(M,M'X):2a"(MX) + a"(M'Xr). (2) NdPro,o-light purple crystals obtained from Ferrox- 0003404x/ 9210l 02-o I 0 I $02.00 101 r02 SHANNON ET AL.: DIELECTRIC CONSTANTS

Tlau 1, Cell dimensionsand molar volumes

a (A) b(4,fr) c (A) v. (41 Reference Alo*FeoorOOH 4.400s(3) 9.4268(6) 2.U58(2) 29.51 This work BeAISiO4OH 4.7795(4) 14.3320) 4.6323(5) 78.05 This work 100.296(6) La2Beros 7.5356 7.348 7.4387 102.94 Harris and Yakel (1968) 91.55 BeTBOsOH 9.7641(5) 12.2080(8) 4.433s(3) 66.06 This work Mgoe6FeoorAlBOl e.8806(7) 5.6788(4) 4.3295{4) 60.73 This work CaBrSirOs 8.0477(51 8.7628(s) 7.7330(s) 136.3it This work CaBSiOIOH 9.634(2) 7.610(1) 4.8334(7) 88.59 This work 90.15(1) Zn4860r3 7.4659 7.4659 7.4659 209.08 Smith-Verdierand Garcia-Blanco(1 980) BaBrO4 12.547 12.547 12.736 96.46 Eimed et al. (1987) AIPO4 4.9423 4.9423 10.9446 77.17 Thong and Schwatzenbach(1979) AlP3Oe 13.729 13.729 13.729 161.73 NBS Mon 25 NdP50'4 8.7672 8.9948 13.0326 256.93 Allbrand et al. (1974) 90.481 LiAtPOIOH 5.1988(4) 7.1721(7) 5.0415(5) 80.54 This work 112.29(1) 97.840(7) 67.848(6) NaBePO. 8.1354(4) 7.8003(3) 14.2030(6) 75.11 This work 90.000(4)

TABLE2. Summaryof single-crystaldielectric constants

r!., tan d (4.,tan 6 (:., tan d (x') Frequency Reference AlosFeoolOOH 8.335+ 0.05 9.146+ 0.05 7.848+ 0.05 8.443 1 MHz This work 0.0009 0.0008 0.0007 7.70 8.38 7.27 Takubo et al. (1953) 5.7,undefined 1 MHz Olhoeft(1981) orientation o.0264 BeAISiO4OH 6.481+ 0.02 6.663+ 0.05 6.764+ 0.03 6.64 1 MHz This work 0.0005 0.0006 0.0006 LarBerO5 38.74+ 0.8 25.93+ 0.02 22.65! 0.2 29.11 1 MHz This work 0.0010 0.0009 0.0012 BeTBO3OH 4.451! O.O2 4.738+ 0.05 5.28+ 0.1 4.82 1 MHz This work 0.0014 0.0013 0.0011 Mgo$Feo@AlBOl 7.753+ 0.01 8.339+ 0.02 8.113+ 0.01 8.075 1 MHz This work 0.0009 0.0008 0.0007 CaBrSirOu 6.720! 0.01 6.618+ 0.01 6.869+ 0.01 6.735 1 MHz This work 0.0007 0.0009 0.0009 6.35 6.34 6.s8 6.4 500 Hz Takubo et al. (1953) 6.34 6.77 Takubo et al. (1953) 6.9,undefined 1 MHz Olhoeft(1981) orientation CaBS|O.OH 6.84+ 6.2 8.328+ 0.02 6.86+ 0.1 7.34 1 MHz This work 0.020 0.002 0.010 7.2,undefrned 1 MHz Olhoeft(1981) orientation 0.006 Zn4860,3 7.24 7.24 100 KHz Bohaty et al. (1982) BaB2O4 5.78 6.6 6.0s 1 MHz Guo and Bhalla (1989) <0.001 <0.001 AIPO4 4.57r 0.05 4.54+ 0.05 4.56 1 MHz Shannon et al. (1990) 0.001 0.001 Ar%o, 5.185+ 0.05 5.185 1 MHz This work 0.0005 NdP5O14 6.567+ 0.05 5.699 + 0.02 6.722+ 0.06 6.33 1 MHz This woIk 0.0q)9 0.0009 0.0037 uAtPo4oH 6.808+ 0.005 8.342 + O.OO7 8.159+ 0.15 7.77 1 MHz This work 0.005 0.010 0.008 7.7,undefined 1 MHz Olhoeft(1981) orientation 0.0178 NaBePO4 6.34+ 0 06 6.44 + 0.07 6.32+ 0.06 6.37 1 MHz This work 0.0005 0.0005 0.000s Note: xi, : *i. rir.: xL",xL.: (a except for La"BerOu,NbPsO1., euclase, datolite, and montebrasite.See experimentalsection tor details SHANNON ET AL.: DIELECTRIC CONSTANTS 103

Tlele 3. Dielectricconstants and molar polarizabilities

Compound (*') %(4") 4D (43) Reference Liro 8.06 4.11 Osaka and Shindo (1984) Naro 5.59 Shannon(1991) BeO 7.16 13.79 2.213 subramanian et al. (1989) Mgo 9.830 18.69 3.331 Fontanellaet al. (1974) ZnO 8.49 23.55 4.01 Kobiakov (1980) CaO 11.95 27.83 5.22 subramanian et al. (1989) BaO 14.40 41.59 8.11 Jonker and Vansanten (1947) Al203 10.126 42.45 7.627 Fontanellaet al. (1974) Nd,o3 16.3. This work LarO3 17.7* This work sio, 4.559 37.66 4.878 Fontanellaet al. (1974) Alo$FeoolOOH 8.443 29.51 5.021 This work BeAISi04OH 6.64 78.05 12.16 This work LarBe2Os 29.11 102.94 22.21 This work Be"BO"OH 4.82 66.06 8.80 This work Mgo o"AlBOo 8.075 60.73 10.181 This work CaB,SirO"".Feo 6.735 136.33 21.29 This work CaBSiO4OH 7.U 88.59 14.36 This work Zn496013 7.24 209.08 33.71 Bohaty et al. (1982) BaB"O. 6.05 96.46 14.44 Guo and Bhalla(1989) AIPO4 4.56 77.17 10.0 Shannon (unpublisheddata) AlP3Oe 5.185 161.73 22.49 This work NdP5Or4 6.33 256.93 39.24 This work LiAtPOIOH 7.77 80.54 13.32 This work NaBePOn 6.37 75.11 11.502 This work ' - Obtained from ao(Nd,O"): [ao(Nd3GauO,J 2.5ao(Ga,Os)]/1.5;Shannon et al. (1990). '- Obtained from co(LarOJ : co(La.BerO")- 2ao(BeO). cube, Saugerties,New York; beryllonite-clear, colorless a composition of Nar ooBe,ooPr.ooOo, assuming the theo- crystal from Stoneham,Maine; and montebrasite-clear, retical value for Be. A typical analysisof the montebrasite colorless crystal from Minas Gerais, Brazil (USNM crystalsindicated a composition Lir 0oAlrooPr.Ou[(OH)o*- r57924). Foorl.This analysisand the unit-cell volume of 161.08 Crystals of AlP3Oe were grown hydrothermally in an A: indicate a composition close to that of pure monte- Au tube charged with 1.40 g Al2O3, 3.50 g 860/oH3PO4, brasite (Cerna et al., 1972). and 28.0 g polyphosphoric acid (850/oPrO'). The tube was Rectangular- or triangular-shaped samples were cut held 4 h at 900'C and cooled I 'Clh to 800 'C. Clear, from the bulk crystals using a low-speeddiamond wheel colorlesscrystals8x 8 x 5mmwererecovered. saw. Slabs were cut perpendicular to the reciprocal axes Samples were oriented for cutting by polarized light of all crystals, allowing determination of r{r, r'rr, and x\t and by back reflection l-aue photo$aphs. X-ray difrac- in the cubic, hexagonal, and orthorhombic crystals. To tion patterns were obtained using a Guinier-type focusing determine r!, and r'r. of monoclinic crystals, it was nec- camera using CuKa, radiation and Si SRM 640 as an essaryto obtain values ofr' in at least three directions in internal standard. Cell dimensions (Table l) were ob- the (fr0l) plane. Similarly, to determine r!,, x'rr,and rc'yof tained by least-squaresrefinement. triclinic crystals, it was necessaryto measurex' in direc- Electron microprobe analyseswere made using a JEOL tions other than parallel to a*, b*, and c*. A detailed 733 electron microprobe. Electron microprobe data re- description of the determination of r',,, x'rr, and x!. of duction methods are described by Armstrong (1982, anisotropic crystals is given by Takubo (1941). Because 1988).Although no systematiceffcrt was made to obtain of insufficient sample size, slabs were not cut in a third information on possible chemical zonation, significant orientation parallel to b* of the monoclinic crystals or in color variations were not observedin any of the crystals. directions other than perpendicularto the reciprocal axes Microprobe analysesof points on individual crystals did of montebrasite.Thus, valuesof rc{,,xLr, K\r, and x{, were not reveal any significant chemical heterogeneities. not determined for the monoclinic crystals of LarBerOt, The composition of diaspore was determined by mi- NdP4Or4,euclase, or beryllonite, and r'rr,KLr, K\r, K"z, xiz, croprobe analysisto be AlonnFeo.'OOH.Euclase analysis and x'r,were not determined for triclinic montebrasite. gave composition Be,0oAl0eesi,.ooooOH,assuming the However, for LarBerOr, NdPoOro,datolite, and beryllon- theoretical value for Be. The F content of the hambergite ite, the deviations from orthorhombic symmetry are very was determined by electron microprobe analysis.Assum- slight, so the deviations of r{', x'rr,and x'r,from the values ing Be: B : 2:1, the compositionis BerBOr[Fooo(OH)o*]. K'^,,K'o,, and xi. indicated in Table 2 are believed to be Microprobe analysis of the danburite and sinhalite crys- small. For monoclinic euclaseK,* a K6,! x"., so the mean tals led to the compositionsCa,ooB,rrAloo,SirooO. and value of (x') listed in Tables 2 and 3 is probably close to Mgon.FeoorAlreeBoo, respectively, assuming theoretical the actual value of (r'). For triclinic montebrasite, the values for B. Microprobe analysisof beryllonite indicated deviations are probably larger,and the mean value of (x') 104 SHANNON ET AL.: DIELECTRIC CONSTANTS

Tmle 4. Dielectricpolarizability data for BrO" and PrOu TABLE5. Comparisonof observedand predictedberyllate' borate, and phosphatesingle-crystal dielectric polariz- Compound do(total),Ao ao(B.OJ', A3 abilities Bro" Mgoe6Feo@AlBO1 10.181 6.04 Mea- CaB2Siror 21.29 6.31 Pred. sured ZnoBuO," 33.71 5.89 Compound (*') e1 d{exp) L (V") BaBrO. 14.44 6.33 12.11 12.16 +0.4 (ao(BzOJ): 6.15 BeAISiOoOH 6.64 La2Be2O5 29.11 22.23 22.21 0.0 P,O. MgooFeo*AlBOo 8.075 10.24 10.18 -0.6 AIPOl 10.0 12.37 Ca82Si,Oo 6.735 21.13 21.29 +0.8 AlP3Oe 22.49 12.45 AIPO4 4.56 10.03 10.0 -0.3 LiAtPOIOH 13.32 12.49 AlP3Oe 5.185 22.47 22.49 +0.1 NdPsOrl 39.24 12.44 NdP5O14 6.33 39.25 39.24 -0.0 NaBePOl 11 .502 12.98 7.77 13.30 13.32 +o.2 (co(P.Ou)): 12.44omitting NaBePO. LiAtPOIOH NaBePOo 6.37 11.23 11.50 +2.4 :0.5% 'Obtained from a,, : ) (a**). (a)

in Tables 2 and 3 can be expectedto deviate considerably compare our data with previously reported dielectric data from the actual mean (x') value. for diaspore, danburite, datolite, and amblygonite. The The datolite crystal contained numerous veils and a valuesof x" : 7.70, xi : 8.38, and x. : 7.27 for diaspore few small inclusions, and it was difficult to obtain dielec- reported by Takubo et al. ( 1953) are all - 8o/osmaller than tric specimensfree of chipped edges.These imperfections the values reported by us. Becausetheir values obtained resulted in larger estimated errors than found in other for quartz are also - 8ololow, there is apparentlya system- cryslals.The crystalof NdP5Or4showed pronounced {010} atic error in the Takubo et al. technique for measuring cleavage,and most specimens cut perpendicular to b* dielectric constants.The value of 5.7 reported by Olhoeft contained small delaminated areasat the sample perim- (1981) for a sample of diaspore from Rosebud,Missouri, eter. These delaminations may be responsiblefor the un- is anomalously low. The relatively high value of tan 6 : usually high dissipation factors of the samples cut per- 0.0264 suggestspoor sample quality. The value of x' : pendicular to c*. Sample thicknessand area varied from 6.9 reported by Olhoeft for a sample of danburite of un- 0.02 to 0.12 cm and 0.05 to 1.5 cm2,respectively. Sput- known orientation from New York is consistentwith our tered Au electrodeswere applied over the entire parallel mean value of 6.735. The values of Takubo et al. for surfacesof the sample using a Denton Vacuum Desk II danburite from Toroku, Japan, are lower than our values sputtering unit. Sample preparation is describedin detail by -5010.The value of 7.7 obtained for amblygonite by by Subramanianet al. (1989). Olhoeft is in good agreement with our mean value of Dielectric constant measurementswere perfbrned over 7.77, although the dielectric loss of his specimen is sig- the frequency range 30 KHz to 3 MHz with a parallel nificantly higher than that found for our sample of mon- plate capacitance tochnique using a Hewlett-Packard tebrasite. (1984) 42754 LCR bridge and fixture 160348 (Test Tweezers)according to the proceduredescribed by Subra- DrscussroN manian et al. (1989). Edge corrections were made using the expression Table 3 lists mean dielectric constantsand molar volumes of the crystals studied here and the oxides that are c. : (0.019 tn P/t - (3) 0.043)P used to test the oxide additivity rule. Arithmetic, rather where I : sample thickness and p : perimeter in centi_ than geometric, mean values are used. Geometric mean meters. values are smaller by 0.0-0.2o/ofor crystals with little or The overall accuracy of the dielectric constant mea- no anisotropy, whereasthey can amount to 2.7o/oforcrys- surementsusing the above techniquesis estimated to be tals such as LarBerO, with significant anisotropy. Table 1.0-1.50/0.Dielectric loss errors are estimated to be 5- 4 lists the total polarizabilities ofthe ternary oxides and 20o/oat levels of tan D : 0.002 and 50-1000/oat levels of the polarizabilities of BrO, and PrO, derived by subtract- 0.0004-0.0005. ing the components of polarizabilities due to the binary oxides. Composite values for ao(BrO3)of 6.15 A' and Rnsur,rs ao(PrO5) of 12.44 A' were extracted from ao(BrO, or Table I summarizes unit-cell dimensions of the crys- PrOr) : ao(complex oxide) - ao(simple oxide). tals studied here and of ZnoBuO,,and B BaBrO4,used for Table 5 comparesthe total molecular dielectric polar- derivation of the polarizability of BrOr. Table 2lists the izabilities determined from the measureddielectric con- dielectric constantsand dielectric loss (tan 6) values at I stantsusing the Clausius-Mosotti relationship (Eq. l) and MHz of the crystalsstudied here and comparesthem with from the oxide additivity rule using what we believe are previously reported dielectric data. The dielectric con- the most accurate dielectric constants of LirO, NarO, BeO, stantsshowed deviations of lessthan 0.2o/oover the range MgO, CaO, Al2O3,Nd2O3,l-a2o.,, SiOr, and AIOOH (Ta- of frequencies 30 KHz to 3 MHz. In Table 2 we also ble 3). The agreement between the observed dielectric SHANNON ET AL.: DIELECTRIC CONSTANTS 105 polarizabilities and those calculatedfrom the sum ofthe fomia) for microprobe data. This work was supported in part by NSF oxide polarizabilities according to the oxide additivity grant EAR-86 18200. Contribution' no. 5672. rule (Eq. 2) is excellent and is comparable to the typical l0lovariation observed previously for a seriesof aluminates,gallates, and silicates (Shannonand Subramanian, RnrnnpNcns crrED 1989;Subramanian and Shannon,1989; Shannon et al., Allbrand, K.R., Attig, R., Fenner, J., Jeser,J.P., and Mootz, D. (1974) 1989,1990, l99l). Crystal structure of the liaser material NdPiOr4. Materials Research The slightly larger deviation of beryllonite might be Bulletin.9.129-140. causedby the inaccuracyof ao(NarO) estimated from the Armstrong, J.T. (1982) New ZAF and a-factor correction procedures for polarizability of NaF in conjunction with a value of the quantitative analysis ofindividual microparticles. In ICF.J. Hein- 1982, p. 175-180. San FranciscoPress, oo(O'-) : 2.0t A (Shannon,l99l). It might also be caused rich, Ed., Microbeam analysis, San Francisco. by the "rattling cation" effect, which was described by -(1988) Quantitative analysisof silicate and oxide materials:Com- Dunitz and Orgel (1960) as a progressive"loosening of parison of Monte Catlo, ZAF and 6$-J) procedures. In D.E. Newbury, the central cation at the center of its surrounding octa- Ed., Microbeam analysis, 1988, p.239-256. San FranciscoPress, San hedron to off-center displacementscharacteristic of fer- Francisco. Bohaty, L., Haussuhl, S., Liebertz, J., and Stahr, S. (1982) Single crystal roelectric and antiferroelectric substances"as the size of growth and physical properties ofcubicZn'(BO)". Zeitschrift fiir Kris- the central cation in an octahedron decreases.The poly- tallographie,l6l, 157-158. hedron can adjust its configuration to adapt to the small Bosman, A.J., and Havinga, E.E. (1963) Temperature dependenceofdi- cation by movement of the cation, the anions, or both, eleclric constants of cubic ionic compounds. Physical Review, 129, resulting in polyhedral distortion such as in the Nal site l 593- l 600. Brown, I.D., and Altermatt, D. (1985)Bond-valence parameters obtained of beryllonite. When crystal symmetry restricts the mo- ftom a systematic analysis of the inorganic crystal structue database. tion ofboth cation and anion such as is observedin cubic Acta Crystallographica,84 l, 244-247. pyrope, larger than normal bond distancesand thermal Cerna, I., Grn!, P., and Ferguson,R.B. (1972) The Tanco pegmatiteat motion may occur (Shannonand Rossman,1992). In both Bemic Iake, Manitoba. III. Amblygonite-montebrasite. Canadian Mineralogist, I l, 643-659. instancesevidence for rattling cations can be seen from Duffin, W.J. (1980) Electricity and magnetism(3rd edition), p.3O7-329. decreasedapparent bond valences or increasedthermal McGraw-Hill, London. motion. Nal, which occupiesa nine-coordinated site in Dunitz, J.D., and Orgel, L.E. (1960) Stereochemistryof ionic solids. Ad- NaBePOo (Giuseppetti and Tadini, 1973), is character- vances in Inorganic Chemistry and Radiochemistry, 2, l-60. (1972) The local electric field in enisotropic molecular izedby unusually large thermal parametersand by bond Dunmur, D.A. crystals.Molecular Physics,23, 109-l15. valence sums, calculated from the Brown and Altermatt Eimerl, D., Davis, L., Velsko, S., Graham, E.IC, and Zalkin, A. (1987) (1985) parameters,which are somewhat low, 0.87 va- Optical, mechanical and thermal properties ofbarium borate. Journal lence units (vu), relative to its theoretical value of 1.0 vu. of Applied Physics,62, I 968-1 983. Na2 and Na3 occupy distorted octahedral sites and have Fontanella,J., Andeen, C., and Schuele,D. (1974) I.ow frequencydielec- tric constants of a{uartz, sapphire, MgF, and MgO. Journal of Applied more nornal apparentbond valencesof 1.06 and l.l5 Physics,45, 2852-2854. vu, respectively. Giuseppetti, G., and Tadini, C. (1973) Refinement ofthe crystal structure This group of beryllates, borates, and phosphates,along of beryllonite, NaBePOo. Tschermaks Mineralogische und Petrogra.- with several other groups of oxides including Y and RE phische Mitteilungen, 20, l-12. Bhalla, A.S. (l 989) Pyroelectric,piezoelectric and dielectric aluminates, chrysoberyl, spinel, olivine-type silicates, Guo, R., and properties of B-BaBrOo single crysral. Journal of Applied Physics, 66, phenacite,and zircon form a classofwell-behaved oxides 6 186-6188. whose dielectric polarizabilities follow the oxide additiv- Harris, L.A., and Yakel, H.L. (1968) The crystal structurc of Ia"Be'O,. ity rule to +0.5-1.50/0.This group forms a basis for com- Acta Crystallographica, 824, 672-67 6. parison with compounds that show larger deviations Hewlett-Packard (1984) Operating manual for 4275A multi-frequency I,CR meter. Yokogawa-Hewlett-Packard Ltd., Tokyo. (>50/o) ionic conductivity, the becauseof or electronic Jonker, G.H., and VanSanten,J.H. (1947) De dielectrischeeigenshappen presenceof HrO or COr, or structural peculiarities (Shan- van litanalen van het perovkiet-type. Chemisch Weekblad, 43,672- non, l99l). This latter type of deviation is illustrated by 679. several structural groups such as silicate garnets and mel- Kip, A.F. (1962) Fundanenrals of electricity and magnerism, 78-103. ilite-type compounds that contain certain members (py- McGraw-Hill. New York. Kobiakov, I.B. (1980) Elastic, piezoelectric and dielectric properties of rope, hardystonite, akermanite) that show strong devia- ZnO and CdS single crystals in a wide range of temperatures. Solid tions (+ -50lo) from the additivity rule. StateCommunications. 35. 305-3 10. Iasaga, A.C., and Cygan, R.T. (1982) Elecrronic and ionic polarizabilities of silicate minerals. American Mineralogist, 67, 328-334. AcrNowr,rocMENTs Megaw, H.D. (1957) Ferroelectricity in crystals, p. 165-178. Methuen, Iondon. We thank B.H.T. Chai for providing the crystal of Ia,r.NdoorBerOr; Olhoeft, G.R. (1981) Electrical properties ofrocks. In Y.S. Touloukian, T.J. Muro of Ferroxcube, Saugerties, New York; for the crystal of Nd- W.R. Judd, and R.F. Roy, Eds., Physical properties of rocks and min- PrO,n; D.A. Appleman of the Smithsonian Institution for providing the erals,p.257-329. McGraw-Hill, New York crystal of montebrasite (USNM 157924); R.W. Shiffer for sample prep- Osaka, T., and Shindo, I. (1984) Infra-red reflectivity and Raman scat- aration; R.A. Oswald for making the capacitancemeasurements; A. Brown tering of lithium oxide single crystals. Solid State Communications, 5 I , (Studsvik Energiteknik AB, Nykoping, Sweden), L.F. Iardear, and R.L. 421-424. Harlow for crystal orientation and C. Foris for obtaining cell dimensions; Ozimek, E.J., and Chai, B.H.T. (1978) Piezoelectricpropenies of single and J.T. Armstrong (California Institute of Technology, Pasadena, Cali- crystal berlinite. Frequency Control Symposium, 80-87. 106 SHANNON ET AL.: DIELECTRIC CONSTANTS

Robens, R. (1949) Dielectric constantsand polarization ofions in simple Dielectric constants of tephroite, fayalite and olivine and the oxide crystalsand barium titanate. Physical Review, 76, 1215-1220. additivity rule. Physicsand Chemistry of Minerals, 18, 1-6. -(1950) A theory of dielectric polarization in alkali halide crystals. Smith-Verdier, P., and Garcia-Blanco,S. (1980) Redeterrninationofthe Physical Review, 77, 258-263. structure of anhydrous [email protected] fiir Kristallographie, I 5 l, - ( I 9 5 I ) Polarizabilities of ions in perovskite-type crystals. Physical 175-177. Review.8l. 865-868. Subrarnanian,M.A., and Shannon, R.D. (1989) Dielectric constant of Shannon,R.D. (1991) Factors afecting the dielectric constantsofoxides Y-stabilized zirconia, the polarizability of zirconia and the oxide ad- and fluorides. Chemistry of electronic cerarnic materials. Proceedings ditivity rule. Materials ResearchBulletin, 24, 1477-1483. ofthe International Conference on the Chemisry ofElectronic Ceramic Subramanian,M.A., Shannon,R-D., Chai, B.H.T., Abraham, M.M., and Materials, JacksonHole, Wyoming, Aulg.17-22. NIST Special Publi- Wintengill, M.C. (1989) Dielectric constants of BeO, MgO and CaO cation.804. 457-471. using the two-terminal method. Physics and Chemistry of Minerals, Shannon,R.D., and Rossman,G.R. (1992) Delectric constantsof silicate t6,741-746. gamets and the oxide additivity rule. American Mineralogist, 77, 94- Szigeti, B. (1949) Polarizability and dielectric constant ofionic crystals. 100. Transactionsofthe Faraday Society,45, 155-166. Shannon, R.D., and Subramanian, M.A. (1989) Dielectric constants of Takubo, J. (1941)Versuche uber die Dielektricitatskonstanleneiniger Mi- chrysoberyl, spinel, phenacite and forsterite and the oxide additivity neralien and uber das dielektrischen Verhalten derserben bei Erhitzung. rufe. Physicsand Chemistry of Minerals, 16, 74'l -7 5l . Memoirs of the College of Science, Kyoto Imperial University, series Shannon,R.D., Subramanian,M.A., Mariano, A.M., and Rossman,G.R. B, no.2., 16,95-154. (1989) Mineral dielectric constants and the oxide additivity rule. Pro- Takubo, J., Ukai, Y., and Kakitani, S. (1953) On the dielectric constants ceedings of the Materials Research Society Symposium on Materials ofminerals. Mineralogical Journal, 1, 3-24. for Magneto-Optic Data Storage, San Diego, Apnl24-27 . Thong, N., and Schwarzenbach,D. (1979) The useofdielectric field gra- Shannon, R.D., Subramanian, M.A., Allik, T.H., Kimura, H., Kokta, dient calculations in charge density refinemenb. II. Charge density re- M.R., Randles,M.H., and Rossman,G.R. (1990) Dielectric constants finement of the low-quartz structure of aluminum phosphate. Acta of yttrium and rare earth g,amets, the polarizability of gallium oxide Crystallographica,435, 658-664. and the oxide additivity rule. Joumal of Applied Physics,67, 3798- 3802. MnNuscnrrr R-EcErvEDNoveuoen 26, 1990 Shannon,R.D., Subramanian,M.A., Hosoya,S., and Rossman,G.R. (1991) MrNuscmrr ACcEFTEDSsFrElusen I I, l99l