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, ham- beryite, 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 con- ductivity, 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.