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Dielectric constant of iron pyrite (FeS2)
Solid State Communications, Vol. 27, pp. 1147—1148. © Pergamon Press Ltd. 1978. Printed in Great Britain.
0038—1098/78/0915—1147 $02.00/0
DIELECTRIC CONSTANT OF IRON PYRITE (FeS2) D.E. Husk and M.S. Seehra Physics Department, West Virginia University, Morgantown, WV 26506, U.S.A. (Received 24 May 1978 by E.F. Bertaut) The dielectric constant e’ of FeS2 is measured at 297 K and 77 K and in the frequency range of 500 Hz— 100 kHz using a capacitance bridge. A value of e’ = 10.9 ±0.5 independent of frequency and temperature, is obtained. This value is consistent with the recent reflectivity measurements of Schiegel and Wachter. IRON PYRITE (FeS2) is one of a series of transition metal dichalcogenides with the pyrite structure which have interesting physical properties 2]. Mössbauer 2~in[1, FeS spectroscopy has shown that Fe 2 is in the lowspin configuration resulting in Van-Vleck paramagnetism in FeS2 [3]. This has been further confirmed by the temperature-dependent magnetic susceptibility studies [4]. Electrical resistivity and Hall effect measurements by Horita eta!. [5] have shown that the semiconducting band-gap is about 0.7 eV, whereas the optical studies [1, 6] yielded a room temperature band gap of about 0.9 eV. Infrared studies of the lattice modes in Fe52 have been reported by Verble and Wallis [7] and more recently by Schlegel and Wachter [6]. In this paper we report the first direct measurements of the dielectric constant of FeS2. The measurements were made at 297 and 77K on several natural single crystals of FeS2 using a capacitance bridge (General radio 716 A) and covered the frequency range of 500 Hz to 100 kHz. The dielectric constant was measured by measuring the capacitance of a three terminal capacitor (a cell made of high conductivity copper) in conjunction with the capacitance bridge. The samples, in the form of circular discs of about 1.25mm thickness and 1.0cm diameter, are insulated from the capacitor plates by “crystal clear” (an insulating spray made by Krylon Paints, a Division of Bordon Inc.). In order to reduce edge effects, the two plates of the cell are of considerably different diameter, the larger plate having the diameter of the sample [81. Although a simple equation linking the dielectric constant e’ with the measured capacitance can be derived for the configuration described above, a verification of the equation for several standard materials showed that the edge effects are stillconstant. present and non-linearly with the dielectric Thusthey the vary equation proved to be impractical for deriving the values for e’. In order to solve the above problems, we have calibrated our capacitance cell using several different
materials of known e’ and with nearly the same dimensions as FeS2 samples. This calibration curve of e’ vs measured capacitance is shown in Fig. 1. The dielectric constants of Teflon, Plexiglas, quartz and Corning glass 0080 (100 kHz) are reported by Von Hippel [8] and that of Si by Dunlap and Watters [9]. The three points for Plexiglas are for three different frequencies, and for the rest there is no known or measured dependence in the 500 Hz—I 00 kHz range. The fact that all points fall on smooth curve asserts the validity of our technique. In Fig. 1, we have also indicated the measured capacitance of the “best” pyrite sample which yields c’ = 10.9. This sample is n-type with room temperature resistivity p(RT) = 30.4 &2-cm. (Similar measurements on two other samples, one n-type with p(RT) = 9.2 x l0~~2-cmand the other p-type with p(RT) = 85.2 fl-cm, gave e’ = 12.1 and 10.4 respectively. However, the former sample had visible minute inclusions of calcite and the latter sample had crack defects. We tend to associate the different values of e’ in these materials to the imperfections.) Within limits of experimental error as given by the calibration curve in Fig. 1, no frequency dependence of the measured capacitance was observed in the range of 500 Hz—100 kHz, at room temperature and 77 K. The measured dielectric constant is the same at room temperature and at 77 K. The above facts lead us to suggest that for FeS2 the low frequency (DC) dielectric constant e’ = 10.9 ±0.5, the uncertainty being primarily due to the error in drawing the calibration curve in Fig. 1. As indicated earlier, this is the first direct measurement for e’ for FeS2 From the reflectivity measurements in the 100—800 cm’ range. Verble and Wallis [7] derived e’2 ] /26.1 Thewhere reflectivity R= [(n +for1)2FeS2. + k2], n is the [(n 1)2 index + k and k is the extinction coefficient. In refractive this notation, e’ and e”, the real and the imaginary part of the dielectric function are given by e’ = k2 and = 2nk. It is clear that any systematic errors in the
1147
-
—
—
1148
DIELECTRIC CONSTANT OF IRON PYRITE (FeS2) —-~
~---~
FeS~
.+~f--- Si -‘
10
-
~—-0O80 Cornir~
I F
5
H -
:Air I
- -
k---
H
Tefl~
~
.07
Quartz --~~-~
.10
.15 C
~
.20
(pF)
Fig. 1. Dielectric constant e vs measured capacitance for several standard dielectrics at room temperature. The dotted curve is a visual fit through the points. The measured capacitance of the pyrite sample is indicated, A similar curve, but shifted to the left, is obtained at 77 K. absolute value of R greatly affect the value of e and e”. Near 200cm away from the lattice modes, Verble and Wallis [7] measured R = 0.47 whereas the recent ,
Vol. 27, No. 11
measurements of Schlegel and Wachter [6] giveR = 0.32 at the same wave number. With this later value of R and using k 0, (a reasonable assumption away from the lattice modes [6]) we obtain e’ 13. This is close to our measured value. Thus the higher value of e’ derived by Verble and Wallis is directly traceable to high value of R measured by them. Based on the general concept that in dielectrics, the energy levels are scaled down by a factor (‘)2, the view was put forward 4, [101 the optical energy gap i.e. that (L~.E)n4 = constant. For a variety of semiconductor including Si and Ge, the ~Eshould vary as I/n constant is equal to 77 [10]. Using the Lyddane— Sachs—Teller relation for the phonon modes, Verbie and Wallis [7] showed that for FeS 2 e’(O)/e’(oo) 1 .22. This yield -,
e’(oo) = 2
8.9 for e’(O) = 10.9 and consequently
= 77/(8.9) = 0.96 eV. This derived value of z~J~ is in good agreement with the optically determined energy gap (I 61. ,
Acknowledgements The authors acknowledge useful discussions with P. Burgardt and the assistance of W. Parker in the resistivity measurements. This research was supported in part by the National Science Foundation Grant DMR 74-06684. —
1.
REFERENCES BITHER T.A., BOUCHARD Ri., CLOUD W.H., DONOHUE P.C. & SIEMONS W.J., J. Inorg. Chem. 7,2208 (1968).
2.
WILSON J.A. & YOFFE A.D.,Adv. Phys. 18, 193 (1969).
3.
MONTANO P.A. & SEEHRA MS., Solid State Commun. 20,897 (1976).
4. 5.
BURGARDT P. & SEEHRA M.S., Solid State Commun. 22, 153 (1977). HORITA H. & SUZUKI T., Sd. Repts. Res. Inst. Tohoku Univ. 25A, 124 (1975).
6.
SCHLEGEL A. & WACHTER P., J. Phys. C.: Solid State Phys. 9,3363 (1976).
7. 8.
VERBLE J.L. & WALLIS R.F.,Phys. Rev. 182, 783 (1969). VON HIPPEL A.R., Dielectric Materials and Applications. Technology Press, M.I.T. and Wiley (1954).
9.
DUNLAPW.C., Jr. &WATTERS R.L.,Phys. Rev. 92, 139 (1953).
10.
MOSS T.S., Optical Properties ofSemiconductors, p. 48. Butterworths, London (1959).
0038—1098/78/0915—1147 $02.00/0
DIELECTRIC CONSTANT OF IRON PYRITE (FeS2) D.E. Husk and M.S. Seehra Physics Department, West Virginia University, Morgantown, WV 26506, U.S.A. (Received 24 May 1978 by E.F. Bertaut) The dielectric constant e’ of FeS2 is measured at 297 K and 77 K and in the frequency range of 500 Hz— 100 kHz using a capacitance bridge. A value of e’ = 10.9 ±0.5 independent of frequency and temperature, is obtained. This value is consistent with the recent reflectivity measurements of Schiegel and Wachter. IRON PYRITE (FeS2) is one of a series of transition metal dichalcogenides with the pyrite structure which have interesting physical properties 2]. Mössbauer 2~in[1, FeS spectroscopy has shown that Fe 2 is in the lowspin configuration resulting in Van-Vleck paramagnetism in FeS2 [3]. This has been further confirmed by the temperature-dependent magnetic susceptibility studies [4]. Electrical resistivity and Hall effect measurements by Horita eta!. [5] have shown that the semiconducting band-gap is about 0.7 eV, whereas the optical studies [1, 6] yielded a room temperature band gap of about 0.9 eV. Infrared studies of the lattice modes in Fe52 have been reported by Verble and Wallis [7] and more recently by Schlegel and Wachter [6]. In this paper we report the first direct measurements of the dielectric constant of FeS2. The measurements were made at 297 and 77K on several natural single crystals of FeS2 using a capacitance bridge (General radio 716 A) and covered the frequency range of 500 Hz to 100 kHz. The dielectric constant was measured by measuring the capacitance of a three terminal capacitor (a cell made of high conductivity copper) in conjunction with the capacitance bridge. The samples, in the form of circular discs of about 1.25mm thickness and 1.0cm diameter, are insulated from the capacitor plates by “crystal clear” (an insulating spray made by Krylon Paints, a Division of Bordon Inc.). In order to reduce edge effects, the two plates of the cell are of considerably different diameter, the larger plate having the diameter of the sample [81. Although a simple equation linking the dielectric constant e’ with the measured capacitance can be derived for the configuration described above, a verification of the equation for several standard materials showed that the edge effects are stillconstant. present and non-linearly with the dielectric Thusthey the vary equation proved to be impractical for deriving the values for e’. In order to solve the above problems, we have calibrated our capacitance cell using several different
materials of known e’ and with nearly the same dimensions as FeS2 samples. This calibration curve of e’ vs measured capacitance is shown in Fig. 1. The dielectric constants of Teflon, Plexiglas, quartz and Corning glass 0080 (100 kHz) are reported by Von Hippel [8] and that of Si by Dunlap and Watters [9]. The three points for Plexiglas are for three different frequencies, and for the rest there is no known or measured dependence in the 500 Hz—I 00 kHz range. The fact that all points fall on smooth curve asserts the validity of our technique. In Fig. 1, we have also indicated the measured capacitance of the “best” pyrite sample which yields c’ = 10.9. This sample is n-type with room temperature resistivity p(RT) = 30.4 &2-cm. (Similar measurements on two other samples, one n-type with p(RT) = 9.2 x l0~~2-cmand the other p-type with p(RT) = 85.2 fl-cm, gave e’ = 12.1 and 10.4 respectively. However, the former sample had visible minute inclusions of calcite and the latter sample had crack defects. We tend to associate the different values of e’ in these materials to the imperfections.) Within limits of experimental error as given by the calibration curve in Fig. 1, no frequency dependence of the measured capacitance was observed in the range of 500 Hz—100 kHz, at room temperature and 77 K. The measured dielectric constant is the same at room temperature and at 77 K. The above facts lead us to suggest that for FeS2 the low frequency (DC) dielectric constant e’ = 10.9 ±0.5, the uncertainty being primarily due to the error in drawing the calibration curve in Fig. 1. As indicated earlier, this is the first direct measurement for e’ for FeS2 From the reflectivity measurements in the 100—800 cm’ range. Verble and Wallis [7] derived e’2 ] /26.1 Thewhere reflectivity R= [(n +for1)2FeS2. + k2], n is the [(n 1)2 index + k and k is the extinction coefficient. In refractive this notation, e’ and e”, the real and the imaginary part of the dielectric function are given by e’ = k2 and = 2nk. It is clear that any systematic errors in the
1147
-
—
—
1148
DIELECTRIC CONSTANT OF IRON PYRITE (FeS2) —-~
~---~
FeS~
.+~f--- Si -‘
10
-
~—-0O80 Cornir~
I F
5
H -
:Air I
- -
k---
H
Tefl~
~
.07
Quartz --~~-~
.10
.15 C
~
.20
(pF)
Fig. 1. Dielectric constant e vs measured capacitance for several standard dielectrics at room temperature. The dotted curve is a visual fit through the points. The measured capacitance of the pyrite sample is indicated, A similar curve, but shifted to the left, is obtained at 77 K. absolute value of R greatly affect the value of e and e”. Near 200cm away from the lattice modes, Verble and Wallis [7] measured R = 0.47 whereas the recent ,
Vol. 27, No. 11
measurements of Schlegel and Wachter [6] giveR = 0.32 at the same wave number. With this later value of R and using k 0, (a reasonable assumption away from the lattice modes [6]) we obtain e’ 13. This is close to our measured value. Thus the higher value of e’ derived by Verble and Wallis is directly traceable to high value of R measured by them. Based on the general concept that in dielectrics, the energy levels are scaled down by a factor (‘)2, the view was put forward 4, [101 the optical energy gap i.e. that (L~.E)n4 = constant. For a variety of semiconductor including Si and Ge, the ~Eshould vary as I/n constant is equal to 77 [10]. Using the Lyddane— Sachs—Teller relation for the phonon modes, Verbie and Wallis [7] showed that for FeS 2 e’(O)/e’(oo) 1 .22. This yield -,
e’(oo) = 2
8.9 for e’(O) = 10.9 and consequently
= 77/(8.9) = 0.96 eV. This derived value of z~J~ is in good agreement with the optically determined energy gap (I 61. ,
Acknowledgements The authors acknowledge useful discussions with P. Burgardt and the assistance of W. Parker in the resistivity measurements. This research was supported in part by the National Science Foundation Grant DMR 74-06684. —
1.
REFERENCES BITHER T.A., BOUCHARD Ri., CLOUD W.H., DONOHUE P.C. & SIEMONS W.J., J. Inorg. Chem. 7,2208 (1968).
2.
WILSON J.A. & YOFFE A.D.,Adv. Phys. 18, 193 (1969).
3.
MONTANO P.A. & SEEHRA MS., Solid State Commun. 20,897 (1976).
4. 5.
BURGARDT P. & SEEHRA M.S., Solid State Commun. 22, 153 (1977). HORITA H. & SUZUKI T., Sd. Repts. Res. Inst. Tohoku Univ. 25A, 124 (1975).
6.
SCHLEGEL A. & WACHTER P., J. Phys. C.: Solid State Phys. 9,3363 (1976).
7. 8.
VERBLE J.L. & WALLIS R.F.,Phys. Rev. 182, 783 (1969). VON HIPPEL A.R., Dielectric Materials and Applications. Technology Press, M.I.T. and Wiley (1954).
9.
DUNLAPW.C., Jr. &WATTERS R.L.,Phys. Rev. 92, 139 (1953).
10.
MOSS T.S., Optical Properties ofSemiconductors, p. 48. Butterworths, London (1959).