Station, Wilmington,. DE 19880356,. U.S.A.. G. R. ROSSMAN. Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA ...
1. Ply.
Chem.
Sohds
Vol
52. No.
9. pp.
IOSJ-1059.
1991
0022.3697,91 13 00 + 0.00 ?:. 1991 Perpamon Press plc
Printed in Great Britain.
DIELECTRIC CONSTANT OF MgAl,O, SPINEL THE OXIDE ADDITIVITY RULE R. E. 1. Du Pont de Nemours
of Geological
SHANNON
and Co., Inc.. Central Station, Wilmington, G.
Division
D.
and Planetary
AND
Research and Development DE 19880356, U.S.A.
Department,
Experimental
R. ROSSMAN
Sciences, California U.S.A.
Institute
of Technology,
Pasadena,
CA 91125,
(Received 28 January 1991; accepred 21 March 1991) Abstract--The dielectric constants and dielectric loss values of five natural and three synthetic spine1 single crystals were determined at I MHz using a two-terminal method and empirically determined edge corrections. The results are: Mg,0zAlI,Fe00104 Mg, ,A4 98Fe00z04 Mg,,Al,,FeO& Mg,,,Al,&, M&,,A&,, Fe,,,Q Mg, ooAl,,O, Mg, ooAl&4 M&,,,,Al>,,O,
K’ K’ K’ K’ K’ K’ K’ K’
= = = = = = = =
8.355 8.322 8.203 8.352 8.302 8.325 8.176 8.572
tan 6 tan 6 tan 6 tan 6 tan 6 tan 6 tan 6 tan6
= 0.0005 = 0.0007 = 0.0007 = 0.0005 = 0.0005 = 0.0008 = 0.0005 =O.OOll
The agreement between measured dielectric polarizabilities as determined from the Clausius-Mosotti equation and those calculated from the sum of oxide polarizabilities according to ro(mineral) = Zzo(oxides) for this group of spinels ranges from + 1.I to + 3.2%. well above the agreement value of 0.5-1.0% found for well-behaved oxides. Possible reasons for these discrepancies are discussed. Ke)lwordr: Spinel, MgAI,O,, Mosotti
dielectric
constants,
dielectric
polarizabilities,
oxide additivity
rule, Clausius-
equation.
lNTRODUCIION
the presence of HZ0 or CO? and/or structural peculiarities [4]. The purpose of this paper is to accurately determine the I MHz dielectric constants of a variety of spinels in order to more carefully evaluate the validity of the oxide additivity rule.
The concept of additivity of molecular polarizabilities implies that the molecular polarizability of a complex substance can be broken up into the molecular polarizabilities of simpler substances according to: zo(M,M’X,)
= 2zo(MX)
where the dielectric polarizability, measured dielectric constant, sius-Mosotti equation: 1, = l/b[(v,,,)(K’
+ a,(M’X:),
(I) EXPERIMENTAL
z,,. is related to the K’, by the Clau-
- l)/(K’ + 2)].
(2)
V, is the molar volume in A’, b is assumed to be 47t/3, and K’, the real part of the complex dielectric constant, is measured in the range I KHz-IO MHz [I, 21. A previous evaluation of additivity in spine1 [3) indicated that the deviation, A, of spine1 was higher than the A of chrysoberyl, phenacite and forsterite. Further studies of oxides indicated that A values of OS-IS% are normal and that deviations are frequently caused by ionic or electronic conductivity,
The natural crystals were from Sri Lanka, Tanzania and Burma. The synthetic crystals were obtained from Union Carbide Corp., D. Viechnicki [S] and A. Mellor Corp., Providence, RI 02906. Crystal source and color are described in Table I. X-Ray diffraction patterns were obtained on a Guinier-type focusing camera using CUKZ, radiation and a Si SRM 640 internal standard. Cell dimensions were obtained by least-squares refinement. Electron microprobe analyses were made using a JEOL 733 electron microprobe. Data reduction methods are described by Armstrong [6,7]. Although no systematic effort was made to obtain information
1055
R. D. S~A~WX and G. R. ROSSMAN
1056
Table 1. Electron microprobe analyses and cell dimensions of spinels Spl MgO AU?, TiOz “203 Cr2
03
MnO Fe0 Total a(A) v, ,(A>) Color
Source
28.60 70.19 0.048 0.140 0.104 0.005 0.40 1 99.49 8.08823 (5) 66.141 Purple Sri Lanka
SP2
$113
27.96 70.07 0.023 0.001 0.148 0.033 0.999 99.23 8.0883 (1) 66,142 Blue-gray Sri Lanka
SP4
27.89 70.31 0.038 0.00 0.077 0.00
1.028 99.34 8.0870 (I) 66.111 Pink Tanzania
27.37 71.52 0.012 0.001 0.049 0.034 0.282 99.27 8.0868 (I) 66.107 Colorless Unknown
sp6 28.24 71.48
0.00 0.00 0.047 0.002 0.002 99.76 8.0824 (2) 65.977 Colorless Union Carbide
SP7 28.24 71.78 0.00 0.00 0.00 0.00 0.01 100.03 8.084 66.037 Colorless Ref. 5
SP8 12.04 87.54 0.091 0.005 0.032 0.00 0.016 99.72 7.9766 (5) 63.440 Colorless A. Mellor
RFSULTS
on possible chemical zonation, significant color variations were not observed in any of the crystals. Microprobe analyses of points on individual crystals did not reveal any significant chemical heterogeneities. Rectangular- or triangular-shaped samples were cut from the bulk crystals using a low-speed diamond wheel saw. Sample thickness and area varied from 0.05 to 0.11 cm and 0.10 to 0.97 cm!, respectively. Sputtered gold electrodes were applied over the entire parallel surfaces of the sample using a Denton Vacuum Desk II sputtering unit. Sample preparation is described in detail in Subramanian et al. 181. Dielectric constant measurements were performed over the frequency range 30 kHz-3 MHz with a parallel plate capacitance technique using a Hewlett Packard 4274A LCR bridge and fixture 16034B (Test Tweezers) [9] according to the procedure described by Subramanian et ui. [8]. Edge corrections were made using the expression: Cc = (0.019 In P/r - 0.043)P.
SPS
28.34 70.25 0.022 0.032 0.203 0.017 0.079 98.95 8.0810(1) 65.963 Pink Burma
Table 1 summarizes unit cell dimensions and chemical compositions of the crystals studied here. Table 2 summarizes the dielectric constants and total polarizabilities of the oxides which are used to test the oxide additivity rule. Table 3 Iists the dielectric constants and dielectric loss (tan 6) values at 1 MHz of the crystals. The dielectric constants showed deviations of less than 0.2% over the range of frequencies 30 kHz-3 MHz. D1SCUSSIOF;
Table 3 compares the total molecular dielectric polarizabilities determined from the measured dielectric constants using the Clausius-Mosotti relationship (eqn (2)) and from the oxide additivity rule using what we believe are the most accurate dielectric constants of MgO, MnO, FeO, Al,03, Fe,O,, Cr20,, V,O, and TiO, listed in Table 2. The agreement between the observed dielectric polarizabilities and those calculated from the sum of the oxide polarizabilities according to the oxide additivity rule (eqn (1)) is + 1.1 to + 3.2%, somewhat higher than the typical OS-l% variation observed previously for a series of aluminates, beryllates. borates, gallates, silicates and phosphates [3, 4, 13, 14. 17-191. The deviations are not random but are
(3)
where I = sample thickness and P = perimeter in cm. The overall accuracy of the dielectric constant measurements using the above techniques is estimated to be 1.0-l .5%. Dielectric loss errors are estimated to be S--20% at levels of tan S = 0.002 and 50-100% at levels of 0.00040.0005.
Table 2. Dielectric constants and molar polarizabilities of MgO, MnO. FeO, Al,O,, Fe,O,, Cr,O,, V,O, and TiO, Compound
K’
(K’)
v, (A’)
d’)
Ella Ellc
9.830 18.10 IS.93 18.23
9.830 18.10 18.70
18.69 22.00 22.00
3.331 4.47 4.49
(10) (11) (12)
Ella E/if
9.395 1I .589
10.126
42.45
4.3 7.627
(13) (10)
Ella Ellc
13.0 I I.8
12.6
48.10
10.51 9.12
(14) (15)
Orientation
MgO MnO Fe0 A&O, Fe,O, Cr,O, “203
TiO,
E;a EN
t Extrapolated from zo(Cr,O,)
86 170
114
31.21 I
= 9.12 A’ and cr,,(Fe,O,) = 10.51 A’.
8 7.258
Reference
(I+&
Dielectric Table
3. Cell dimensions,
molar
v, (A’)
SPl SP2 SP3 Sp4 SP5 Sp6 SP7 Sp8
66.14 66.14 66.11 65.96 66.11 66.00 66.04 63.44
t Estimated
1057
spine1
K’+
tan 6
8.355 8.322 8.203 8.352 8.302 8.325 8.176 8.572
< 0.0005 0.0007 0.0007
