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Anomalous paramagnetism in pressure quenched CdS
Journal of Non-Crystalline Solids 40 (1980) 369-375 © North-Holland Publishing Company
ANOMALOUS PARAMAGNETISM IN PRESSURE QUENCHED CdS C. HOMAN Benet Laboratories, ARRADCOM, Watervliet Arsenal, Watervllet, New York 12189 USA
and R.K. MACCRONE Department o f Materials Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180 USA
Very large "paramagnetic" on positive magnetization has been observed in "pressure quenched" samples of CdS. Pressure quenching is a formative process involving pressure release rates -10 b bar s-~ . The pressure quenched samples were prepared by pressure quenching at room temperature from above 30 kbar, i.e. from above the insulation-to-metal like transition. The magnetization as a function of magnetic field was measured at 293 and 77 K using a vibrating specimen magnetometer. A linear M versus H behavior is observed in fields above a few hundred gauss, with values of x = (aM/all) ~ 10-4 cgs units. In some specimens saturation occurs, while in others the magnetization passes through a maximum. The maximum value of the magnetic moment M observed is of the order of tens of gauss.
1. Introduction There is interest in the unusual magnetic effects that have been reported in excitonic solids such as CuC1 and CdS which have been subject to high pressure. In this paper we wish to report on the very large positive magnetization (paramagnetism) which we have observed in specimens o f cadmium sulphide which have been subjected to a formative technique k n o w n as pressure quenching which we will describe in detail subsequently. This is the first time, we believe, that such giant paramagnetism with a volume susceptibility Xv---+10-4 cgs units has been observed in any phase o f CdS. This material is normally diamagnetic with a volume susceptibility Xv ~ - 1 . 5 X 10 -6 cgs units. The absolute magnitude of the paramagnetic susceptibility is so large that it is highly likely that some sort o f cooperative behavior is involved. There has been considerable theoretical speculation on the possible phases and cooperative phenomena that in principle could be realized in solids with a high density o f excitons. An early review has been given b y Halperin and Rice [1]. Recently, Abrikosov [2] suggested an excitionic mechanism for the possible forma369
370
c Homan, R.K. MacCrone / Anomalous paramagnetism
tion of Cooper pairs at high (~100 K) temperatures. Brandt et al. [3] subsequently reported large diamagnetic fluctuations in CuC1 which at 5 kbar had undergone rapid temperature fluctuations. Less dramatic, but nevertheless equally suggestive diamagnetic effects have been observed by Chu et al. [4] and by Lefkowitz et al. [5]. Very large diamagnetism X ~ +10 -4 has also recently been observed in pressure quenched CdS by Homan and Kendall [6,7] and Homan et al. [8]. However, pressure quenched CdS is a more complex material in that strong paramagnetism also occurs. This is the subject of this paper. The large paramagnetism of pressure quenched CdS occurs at both 273 and 77 K, and is apparently a "high field limit" of behavior.
2. Experimental The specimens are formed by pressure quenching; that is, by rapidly releasing the pressure previously applied to the material. The specimens in this paper were prepared by quenching, at room temperature, optical grade CdS from above 40 kbar at rates approaching 5 X 10 6 bar s -1 . This starting pressure is above the well known electronic and structural transition reported by Samara and Drickamer [9], Edwards and Drickamer [ 10], and Lewis et al. [ 11 ]. We fred that the electrical resistance changes during the application of pressure provide a sensitive indication of the conditions required to produce specimens with unusually large magnetic properties. The sample resistance during the pressurization is determined by measuring the resistance across the anvils using a constant voltage of 10 v, which produces a field of 250 V cm -1 . A collection of "typical behaviors", depending upon the source material, is shown in fig. 1. Only specimens whose resistance-pressure characteristic is similar to the Alpha Inorganic trace show any anamalousl~, large magnetic behavior. The results in this figure indicate the sensitivity of the magnetic phenomena on the extrinsic impurity content of the starting material, a subject to which we will return subsequently in the paper. The highest specimen currents occur in the high conducting phase and are no more than 10 mA. Since the electrical transition is reversible over many cycles of pressure, electrochemical reactions at the electrodes are unlikely, and cannot account for the magnetic observations. This is borne out by direct micrographica/observations which revealed no evidence of surface reactions. After pressure quenching from Pt to atmospheric pressure, the specimens are black with a dull sheen. The final electrical resistance of the specimen is two orders of magnitude less than the starting material in this condition. Further experimental details are given by Homan and Kendall [6,7]. The magnetic measurements were made using a Princeton Applied Research vibrating sample magnetometer. Extensive previous use has shown no evidence for experimental artifacts. However, a series of tests were also performed during these
¢
C Homan, R.K. MacCrone/Anomalous paramagnetism
371
5xlO ~-
5xlO ~
i0 ~
AlphaInorganic
5xlO:
/
CdS, T = 3 0 0 K 03
102
5xlO ~
EoqlePicker
iO ~
5ol iO
p,~40k bor PRESSURE
Fig. 1. Typical resistance versus pressure curves for CdS. Note the difference in behavior depending upon the starting material.
measurement~ to check for spurious, results. These included measuring comparable signals using known materials (CuSO4, 5 H20 ) and obtaining agreement with literature values of the susceptibility; changing specimen holders; changing geometrical confi~rations of pick-up wires, etc., and running the instrument without the cylinder normally surrounding the vibrating rod. In all cases no' evidence for deviant belravior was observed.
3, Results A typical magnetic response curve is shown in fig. 2 for high fields. At applied' magnetic fields above about 400 Oe, a strong positive linear (paramagnetic) response is observed, followed by either saturation or a maximum in the magnetic moment depending on the temperature. (The experimental work to distinguish between the various possibilities is presently in progress.) The saturation, maximum, or decrease occurs at magnetic fields between 3 and 7 kOe. In the region of the linear positive (paramagnetic) behavior the susceptibility Xv (3M/all) typically has numerical values of+1.0 X 10 -4 cgs at room temperature. The highest value of Xv observed to-data is ~10 -4 cgs units at 77 K. These values
C Homan, R.K. MacCrone / Anomalous paramagnetism
372
[
I
I
I
I
ZYK 60X I0 -s gouss,c m s s
/
/
/
/
/
~
~
\ \ ,,~OO K
///
/ ./ ~/ / I / / I 0.5
0.1
I 1.0
I 5.0
1 I0.0
50.0
H
Fig. 2. Magnetic moment M versus applied magnetic field H for a pressure quenched sample. Magnetic field in kOe.
---JJ .12 M*40
gOUSS
o10
.0 B
.06
.04
-
.02
5
y
9
II
13
H (/rOe)
Fig. 3. Magnetic moment M versus applied field H for a pressure quenched sample (not the same as in fig. 2).
C Homan, R.K. MacCrone /Anomalous paramagnetism
373
should be compared with the room temperature susceptibility of Nd2Oa whose susceptibility ×v "" +2 X 10 -4 cgs. At higher magnetic fields, the linear increase of M with field gives way to a different behavior. The magnetization passes through either a maximum or saturates at both 273 and 77 K. At this stage the magnetization is " 2 . 0 g. The highest value observed to date is 40 g. We note that ~ of this magnetization is sufficient to allow the specimen to be picked up with a bar magnet. These values should be compared with the (saturation) magnetization of metallic Ni, which is ~400 g. The magnetic properties described above are metastable, and decay away in times in the order of days to weeks. At this stage after the decay the material exhibits its normal diamagnetic behavior. More complicated behavior at magnetic fields above 10 kOe is also observed. In fig. 3 is shown the magnetic response of a specimen which at 77 K showed two maxima in M versus H. The specimen was warmed to room temperature, kept there for a day, and then remeasured, the specimen remaining in the magnetometer and not touched in any way. The same behavior was observed, but with the minimum at 5 kOe not as pronounced.
4. Discussion The essential point of this paper is the very strong positive magnetizations, whose origin is presently not known. However, some speculation may not be out of order. Suppose the maximum magnetization results form the almost complete alignment of N elementary magnetic moments, each having moment/a. Then M --~N/a.
(1)
This supposition is of considerable generality, and is not "model specific". It does, however, imply that the effective magnetic moments/a* exist which are sufficiently large than /a*H > > kBT. This could arise from the ferromagnetic-like coupling of elementary spins in clusters, which implies a super-paramagnetic description, namely a non-interacting system o f g t magnetic particles per unit volume each with a magnetic moment/a*. Thus c~ ~t* = N/a.
(2)
The magnetic moment M would be given by M =q~ la'~Oa*H/kT),
(3)
where Z?(o) is the well known Langevin Function. Using the analytical method of van der Giessen [12], we Fred the values for tt*,c)t a n d N shown in table 1 for the specimen shown in fig. 2 for the two temperatures. Thereasonable and almost constant numerical value of N is most intriguing. A temperature dependent/a*, and
374
C Homan, R.K. MacCrone / Anomalous paramagnetism
Table 1 T (K)
#* (number of Bohr magnetons) xlO-3
c~ (cm-3) × 10-17
N (cm-a) X10-21
273 77
9.4 1.33
2.5 25.9
2.35 3.44
hence c~ should not be surprizing in the context of new observations. We assert again that we" have no basis for adopting an empirical superparamagnetic model, which essentially bypasses the physical origin for the ferromagnetic-like coupling. Particularly relevant are the works by Halperin and Rice [1], Ginzburg [13], Abrikosov [2], Collins et al. [14].
5. Specimen characterization There are morphological changes that take place in these pressure quenched samples. The specimens exhibit a layer morphology consisting of opaque lenticular platelets of varying thickness imbedded in a compacted powder matrix. The character of these platelets have been studied by optical and scanning electron microscopy, transmission X-ray analysis, micro-hardness and chemical etching techniques. The platelets are mechanically and chemically different from the matrix material. They are probably amorphous, although micro-crystallinity cannot be ruled out. The volume fraction of the platelets is about 10 to 15%, the larger volume fractions being obtained by quenching from higher pressures. All the previous numerical estimates were made on the basis that the whole volume of the samples contributed to the giant magnetism. Impurities play a profound role in the formation of the magnetic phase, even in the parts per million range. The material used in this work was commerical high purity material, having impurity level of 20 ppm t. In excess of 10 samples from this material with these properties have been studied. Other commerical material from a private source having a nominal impurity level of 5 ppm t t with a slightly paler yellow color did not show the giant magnetism. Flame photometry failed to reveal any difference in the spectrum of metallic impurities between the two froms of starting material. However, a significant variation could occur in the spectrum of non-metallic impurities which were not analyzed. Careful analysis of the impurity spectra of the various materials is planned with attention to spatial distribution of t Alpha Inorganics, Optronic Grade Stock #20130. t t Eagle-Picker,Ultra High Purity.
C Homan, R.K. MacCrone/Anomalous paramagnetism
375
impurities including non-metallic elements and variation in stoichiometry of determine the role of impurities in these effects. This is obviously a research programme of considerable size.
6. Conclusions The experimentally observed giant magnetization of pressure quenched CdS is a challenging observation. At the present time its dependence on physical parameters (such as temperature, magnetic field cycling and reversal, orientation, etc.) have not been fully studied. Experimental work is presently underway to examine some of these dependencies.
Acknowledgements The help and encouragement of D.P. Kendall is gratefully acknowledged. Helpful discussions with J. Bray, E. Brown, P. Cote, G. Capsimalis and C. Herring are acknowledged. We gratefully acknowledge partial support of AFOSR Grant No. 79-0126 and Benet Lab, ARRADCOM Project No. 1560-01-002.
References [1] B.I. Halperin and T.M. Rice, Rev. Mod. Phys. 40 (1968) 755. [2] A.A. Abrikosov, JETP Letters 27 (1978) 219. [3] N.B. Brandt, S.V. Kuvschinnikov, A.P. Rusakov and V. Semenov, JETP Letters 27 (1978) 37. [4] C.W. Chu, A.P. Rusakov, S. Huang, T.H. Early, T.H. Geballe and C.Y. Huang, Phys. Rev. B18 (1978) 2116. [5] 1. Lefkowitz, J.S. Manning and P.E. Bloomfield, Phys. Rev. B20 (1979). [6] C.G. Homan and D.P. Kendall, Bull. Am. Phys. Soc. 24 (1979) 316. [7] C.G. Homan and D.P. Kendall, Tech. Report ARLCB-TR-79004 ARRADCOM, Watervliet, New York 12189, May 1979. [8] C.G. Homan, D.P. Kendall and R.K. MacCrone, Sol. St. Commun. 32 (1979) 521. [9] G.A. Samara and H.G. Drickamer, J. Phys. Chem. Solids 23 (1962) 457. [10] A.L. Edwards and H.G. Drickamer, Phys. Rev. 122 (1961) 1149. [11] G.K. Lewis, E.A. Perez-Albuerne and H.G. Drickamer J. Chem. Phys. 45 (1968) 598. [12] A.A. van der Giessen, J. Phys. Chem. Solids 28 (1966) 343. [13] V.L. Ginzburg, ZLETF Fis. Red. 14 (1971) 572. [14] T.H. Collins, A.B. Kunz and R.S. Weidman, (1979); Bull. Amer. Phys. Soc. 22 (1979) 499, "Recent Advances in Quantum Theory of Polymers", Lect. Notes in Phys. 113 (SpringerVerlag, Berlin, 1979) p. 240.
ANOMALOUS PARAMAGNETISM IN PRESSURE QUENCHED CdS C. HOMAN Benet Laboratories, ARRADCOM, Watervliet Arsenal, Watervllet, New York 12189 USA
and R.K. MACCRONE Department o f Materials Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180 USA
Very large "paramagnetic" on positive magnetization has been observed in "pressure quenched" samples of CdS. Pressure quenching is a formative process involving pressure release rates -10 b bar s-~ . The pressure quenched samples were prepared by pressure quenching at room temperature from above 30 kbar, i.e. from above the insulation-to-metal like transition. The magnetization as a function of magnetic field was measured at 293 and 77 K using a vibrating specimen magnetometer. A linear M versus H behavior is observed in fields above a few hundred gauss, with values of x = (aM/all) ~ 10-4 cgs units. In some specimens saturation occurs, while in others the magnetization passes through a maximum. The maximum value of the magnetic moment M observed is of the order of tens of gauss.
1. Introduction There is interest in the unusual magnetic effects that have been reported in excitonic solids such as CuC1 and CdS which have been subject to high pressure. In this paper we wish to report on the very large positive magnetization (paramagnetism) which we have observed in specimens o f cadmium sulphide which have been subjected to a formative technique k n o w n as pressure quenching which we will describe in detail subsequently. This is the first time, we believe, that such giant paramagnetism with a volume susceptibility Xv---+10-4 cgs units has been observed in any phase o f CdS. This material is normally diamagnetic with a volume susceptibility Xv ~ - 1 . 5 X 10 -6 cgs units. The absolute magnitude of the paramagnetic susceptibility is so large that it is highly likely that some sort o f cooperative behavior is involved. There has been considerable theoretical speculation on the possible phases and cooperative phenomena that in principle could be realized in solids with a high density o f excitons. An early review has been given b y Halperin and Rice [1]. Recently, Abrikosov [2] suggested an excitionic mechanism for the possible forma369
370
c Homan, R.K. MacCrone / Anomalous paramagnetism
tion of Cooper pairs at high (~100 K) temperatures. Brandt et al. [3] subsequently reported large diamagnetic fluctuations in CuC1 which at 5 kbar had undergone rapid temperature fluctuations. Less dramatic, but nevertheless equally suggestive diamagnetic effects have been observed by Chu et al. [4] and by Lefkowitz et al. [5]. Very large diamagnetism X ~ +10 -4 has also recently been observed in pressure quenched CdS by Homan and Kendall [6,7] and Homan et al. [8]. However, pressure quenched CdS is a more complex material in that strong paramagnetism also occurs. This is the subject of this paper. The large paramagnetism of pressure quenched CdS occurs at both 273 and 77 K, and is apparently a "high field limit" of behavior.
2. Experimental The specimens are formed by pressure quenching; that is, by rapidly releasing the pressure previously applied to the material. The specimens in this paper were prepared by quenching, at room temperature, optical grade CdS from above 40 kbar at rates approaching 5 X 10 6 bar s -1 . This starting pressure is above the well known electronic and structural transition reported by Samara and Drickamer [9], Edwards and Drickamer [ 10], and Lewis et al. [ 11 ]. We fred that the electrical resistance changes during the application of pressure provide a sensitive indication of the conditions required to produce specimens with unusually large magnetic properties. The sample resistance during the pressurization is determined by measuring the resistance across the anvils using a constant voltage of 10 v, which produces a field of 250 V cm -1 . A collection of "typical behaviors", depending upon the source material, is shown in fig. 1. Only specimens whose resistance-pressure characteristic is similar to the Alpha Inorganic trace show any anamalousl~, large magnetic behavior. The results in this figure indicate the sensitivity of the magnetic phenomena on the extrinsic impurity content of the starting material, a subject to which we will return subsequently in the paper. The highest specimen currents occur in the high conducting phase and are no more than 10 mA. Since the electrical transition is reversible over many cycles of pressure, electrochemical reactions at the electrodes are unlikely, and cannot account for the magnetic observations. This is borne out by direct micrographica/observations which revealed no evidence of surface reactions. After pressure quenching from Pt to atmospheric pressure, the specimens are black with a dull sheen. The final electrical resistance of the specimen is two orders of magnitude less than the starting material in this condition. Further experimental details are given by Homan and Kendall [6,7]. The magnetic measurements were made using a Princeton Applied Research vibrating sample magnetometer. Extensive previous use has shown no evidence for experimental artifacts. However, a series of tests were also performed during these
¢
C Homan, R.K. MacCrone/Anomalous paramagnetism
371
5xlO ~-
5xlO ~
i0 ~
AlphaInorganic
5xlO:
/
CdS, T = 3 0 0 K 03
102
5xlO ~
EoqlePicker
iO ~
5ol iO
p,~40k bor PRESSURE
Fig. 1. Typical resistance versus pressure curves for CdS. Note the difference in behavior depending upon the starting material.
measurement~ to check for spurious, results. These included measuring comparable signals using known materials (CuSO4, 5 H20 ) and obtaining agreement with literature values of the susceptibility; changing specimen holders; changing geometrical confi~rations of pick-up wires, etc., and running the instrument without the cylinder normally surrounding the vibrating rod. In all cases no' evidence for deviant belravior was observed.
3, Results A typical magnetic response curve is shown in fig. 2 for high fields. At applied' magnetic fields above about 400 Oe, a strong positive linear (paramagnetic) response is observed, followed by either saturation or a maximum in the magnetic moment depending on the temperature. (The experimental work to distinguish between the various possibilities is presently in progress.) The saturation, maximum, or decrease occurs at magnetic fields between 3 and 7 kOe. In the region of the linear positive (paramagnetic) behavior the susceptibility Xv (3M/all) typically has numerical values of+1.0 X 10 -4 cgs at room temperature. The highest value of Xv observed to-data is ~10 -4 cgs units at 77 K. These values
C Homan, R.K. MacCrone / Anomalous paramagnetism
372
[
I
I
I
I
ZYK 60X I0 -s gouss,c m s s
/
/
/
/
/
~
~
\ \ ,,~OO K
///
/ ./ ~/ / I / / I 0.5
0.1
I 1.0
I 5.0
1 I0.0
50.0
H
Fig. 2. Magnetic moment M versus applied magnetic field H for a pressure quenched sample. Magnetic field in kOe.
---JJ .12 M*40
gOUSS
o10
.0 B
.06
.04
-
.02
5
y
9
II
13
H (/rOe)
Fig. 3. Magnetic moment M versus applied field H for a pressure quenched sample (not the same as in fig. 2).
C Homan, R.K. MacCrone /Anomalous paramagnetism
373
should be compared with the room temperature susceptibility of Nd2Oa whose susceptibility ×v "" +2 X 10 -4 cgs. At higher magnetic fields, the linear increase of M with field gives way to a different behavior. The magnetization passes through either a maximum or saturates at both 273 and 77 K. At this stage the magnetization is " 2 . 0 g. The highest value observed to date is 40 g. We note that ~ of this magnetization is sufficient to allow the specimen to be picked up with a bar magnet. These values should be compared with the (saturation) magnetization of metallic Ni, which is ~400 g. The magnetic properties described above are metastable, and decay away in times in the order of days to weeks. At this stage after the decay the material exhibits its normal diamagnetic behavior. More complicated behavior at magnetic fields above 10 kOe is also observed. In fig. 3 is shown the magnetic response of a specimen which at 77 K showed two maxima in M versus H. The specimen was warmed to room temperature, kept there for a day, and then remeasured, the specimen remaining in the magnetometer and not touched in any way. The same behavior was observed, but with the minimum at 5 kOe not as pronounced.
4. Discussion The essential point of this paper is the very strong positive magnetizations, whose origin is presently not known. However, some speculation may not be out of order. Suppose the maximum magnetization results form the almost complete alignment of N elementary magnetic moments, each having moment/a. Then M --~N/a.
(1)
This supposition is of considerable generality, and is not "model specific". It does, however, imply that the effective magnetic moments/a* exist which are sufficiently large than /a*H > > kBT. This could arise from the ferromagnetic-like coupling of elementary spins in clusters, which implies a super-paramagnetic description, namely a non-interacting system o f g t magnetic particles per unit volume each with a magnetic moment/a*. Thus c~ ~t* = N/a.
(2)
The magnetic moment M would be given by M =q~ la'~Oa*H/kT),
(3)
where Z?(o) is the well known Langevin Function. Using the analytical method of van der Giessen [12], we Fred the values for tt*,c)t a n d N shown in table 1 for the specimen shown in fig. 2 for the two temperatures. Thereasonable and almost constant numerical value of N is most intriguing. A temperature dependent/a*, and
374
C Homan, R.K. MacCrone / Anomalous paramagnetism
Table 1 T (K)
#* (number of Bohr magnetons) xlO-3
c~ (cm-3) × 10-17
N (cm-a) X10-21
273 77
9.4 1.33
2.5 25.9
2.35 3.44
hence c~ should not be surprizing in the context of new observations. We assert again that we" have no basis for adopting an empirical superparamagnetic model, which essentially bypasses the physical origin for the ferromagnetic-like coupling. Particularly relevant are the works by Halperin and Rice [1], Ginzburg [13], Abrikosov [2], Collins et al. [14].
5. Specimen characterization There are morphological changes that take place in these pressure quenched samples. The specimens exhibit a layer morphology consisting of opaque lenticular platelets of varying thickness imbedded in a compacted powder matrix. The character of these platelets have been studied by optical and scanning electron microscopy, transmission X-ray analysis, micro-hardness and chemical etching techniques. The platelets are mechanically and chemically different from the matrix material. They are probably amorphous, although micro-crystallinity cannot be ruled out. The volume fraction of the platelets is about 10 to 15%, the larger volume fractions being obtained by quenching from higher pressures. All the previous numerical estimates were made on the basis that the whole volume of the samples contributed to the giant magnetism. Impurities play a profound role in the formation of the magnetic phase, even in the parts per million range. The material used in this work was commerical high purity material, having impurity level of 20 ppm t. In excess of 10 samples from this material with these properties have been studied. Other commerical material from a private source having a nominal impurity level of 5 ppm t t with a slightly paler yellow color did not show the giant magnetism. Flame photometry failed to reveal any difference in the spectrum of metallic impurities between the two froms of starting material. However, a significant variation could occur in the spectrum of non-metallic impurities which were not analyzed. Careful analysis of the impurity spectra of the various materials is planned with attention to spatial distribution of t Alpha Inorganics, Optronic Grade Stock #20130. t t Eagle-Picker,Ultra High Purity.
C Homan, R.K. MacCrone/Anomalous paramagnetism
375
impurities including non-metallic elements and variation in stoichiometry of determine the role of impurities in these effects. This is obviously a research programme of considerable size.
6. Conclusions The experimentally observed giant magnetization of pressure quenched CdS is a challenging observation. At the present time its dependence on physical parameters (such as temperature, magnetic field cycling and reversal, orientation, etc.) have not been fully studied. Experimental work is presently underway to examine some of these dependencies.
Acknowledgements The help and encouragement of D.P. Kendall is gratefully acknowledged. Helpful discussions with J. Bray, E. Brown, P. Cote, G. Capsimalis and C. Herring are acknowledged. We gratefully acknowledge partial support of AFOSR Grant No. 79-0126 and Benet Lab, ARRADCOM Project No. 1560-01-002.
References [1] B.I. Halperin and T.M. Rice, Rev. Mod. Phys. 40 (1968) 755. [2] A.A. Abrikosov, JETP Letters 27 (1978) 219. [3] N.B. Brandt, S.V. Kuvschinnikov, A.P. Rusakov and V. Semenov, JETP Letters 27 (1978) 37. [4] C.W. Chu, A.P. Rusakov, S. Huang, T.H. Early, T.H. Geballe and C.Y. Huang, Phys. Rev. B18 (1978) 2116. [5] 1. Lefkowitz, J.S. Manning and P.E. Bloomfield, Phys. Rev. B20 (1979). [6] C.G. Homan and D.P. Kendall, Bull. Am. Phys. Soc. 24 (1979) 316. [7] C.G. Homan and D.P. Kendall, Tech. Report ARLCB-TR-79004 ARRADCOM, Watervliet, New York 12189, May 1979. [8] C.G. Homan, D.P. Kendall and R.K. MacCrone, Sol. St. Commun. 32 (1979) 521. [9] G.A. Samara and H.G. Drickamer, J. Phys. Chem. Solids 23 (1962) 457. [10] A.L. Edwards and H.G. Drickamer, Phys. Rev. 122 (1961) 1149. [11] G.K. Lewis, E.A. Perez-Albuerne and H.G. Drickamer J. Chem. Phys. 45 (1968) 598. [12] A.A. van der Giessen, J. Phys. Chem. Solids 28 (1966) 343. [13] V.L. Ginzburg, ZLETF Fis. Red. 14 (1971) 572. [14] T.H. Collins, A.B. Kunz and R.S. Weidman, (1979); Bull. Amer. Phys. Soc. 22 (1979) 499, "Recent Advances in Quantum Theory of Polymers", Lect. Notes in Phys. 113 (SpringerVerlag, Berlin, 1979) p. 240.