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The Journal of Physical Chemistry, Vol. 83, No. 6, 1979
TABLE VIII: Band Assignments for the Species Produced in the Matrix Reactions of In and Ga with I6O, frequency,asb cm-' assignmentb In t 1 6 0 2 G a + I6O2 species mode 1084.2 1089.5 332.2 380.0 MO,(C,,) [277.7] 285.5 1 015.9(N, ) 1015.6(N, ) 0,M-MO, (D,d) 443.2(N2) 458.6(N2) MO,M(D,,)
)
I
[816.2]
M-0
\
M
M
{I vv ,, (( AA;, )) VdBl)
v
(B, ), 0-0
VS(B,U)
\
I
O[C,,l
Vl(A1)
M
654 795.3(N2)
M-0
I \
\ I
O-M[D,,]
v(B,)
M M,O, [x > 11 968.0 M,O, [x > 11 952.7(N2) M,O-0 [ X > 11
Values are for Ar matrices unless specified otherwise. Tentative assignments are indicated by brackets.
a
atom into O2 apparently does not occur. This process is either kinetically unfavorable, because of a substantial activation barrier, or thermodynamically unfavorable. There is no reliable evidence that stable dioxide molecules exist for any metals of this family gr0up.l' Hinchcliffe and Ogdeng have reported the existence of a large number of uncharacterized infrared absorptions in experiments concerned with the matrix isolation of In and Ga suboxides. In some of these experiments, the vapor species were produced by passing O2 over the heated condensed metals. This would permit both unreacted metal and O2 to be transported to the matrix. It is pos-
Gough et al.
sible, therefore, that some of the resulting bands belonged to the superoxide species and its various aggregates. A band reported a t 380 cm-', for example, corresponds with the v1 mode of the Ga superoxide. A band reported a t 442 cm-l, which they tentatively assigned as the v1 mode of In20, corresponds with the mode belonging to In021n. A matrix containing sufficient concentrations of metal atoms, 02,and suboxide molecules would likely exhibit a rich infrared spectrum of bands belonging to a variety of reaction products and aggregate species.
References and Notes (1) Research supported in part by a grant from the National Science Foundation. (2) (a) Lamp Materials Research Laboratory, General Electric Co., NELA Park, Cleveland, Ohio 441 12. (b) High Intensity and Quartz Department, General Electric Co., Edison Park, 8499 Darrow Road, Twinsburg, Ohio 44087. (3) M. J. Linevsky, D. White, and D. E. Mann, J . Chem. fhys., 41, 542 (1964). (4) D. M. Makowiecki, D. A. Lynch, Jr., and K. D. Carlson, J. fhys. Chem., 75, 1963 (1971). (5) A. J. Hinchcliffe and J. S. Ogden, J. fhys. Chem., 75, 3908 (1971). (6) J. M. Brom, Jr., T. Devore, and H. F. Franzen, J . Chem. fhys., 54, 2742 (1971). (7) D A. Lynch, Jr., Ph.D. Dissertation, Case Western Reserve University, June 1972. (8) C. P. Marino and D. White, J . fhys. Chem., 77, 2929 (1973). (9) A. J. Hinchciiffe and J. S. Ogden, J. fhys. Chem., 77, 2537 (1973). (10) D. A. Lynch, Jr., M. J. Zehe, and K. D. Carlson, J. fhys. Chem., 78, 236 (1974). (11) L. Andrews, J . Chem. fhys., 50, 4288 (1969); 54, 4935 (1971); J . fhys. Chem., 73, 3922 (1969). (12) L. Andrews, J.-T. Hwang, and C. Trindle, J . fhys. Chem., 77, 1065 (1973). (13) R. R. Smardzewskiand L. Andrews, J. Chem. phys., 57, 1327 (1972); J . fhys. Chem., 77, 801 (1973). (14) B. S. Auk and L. Andrews, J . Chem. fhys., 62, 2312 (1975). (15) H. G. Howell, R o c . R. SOC. London, 57, 32 (1945). (16) L. Brewer and G. M. Rosenblatt, Adv. High Temp. Chem., 2, 1-83 (1969). (17) R. C. Paule, High Temp. Sci., 8, 257 (1976).
Thermal Hysteresis at the Low Temperature Phase Transition of (NH4)H2P04, (NH4)H2As04,Their Deuterated Analogues, and of KH2P04and the Effect of Cr Impurity Ions on the Transition Temperature' S. R. Gough," J. A. Ripmeester, N. S. Dalal,+ and A. H. Reddoch Division of Chemistry, National Research Council of Canada, Ottawa, Canada KIA OR9 (Received September 7, 1978) Publication costs assisted by the National Research Council of Canada
Paraelectric-antiferroelectric phase transition temperatures, determined by dielectric, NMR, EPR, and DSC techniques for ammonium dihydrogen phosphate, ammonium dihydrogen arsenate, and their deuterated analogues, show, in contrast to some previously published reports of others, the thermal hysteresis of the transition to be close to 2' in all cases. The hysteresis is found to be practically independent of technique, crystal orientation, anion type, and deuteration and impurity dopant levels. The influence of Cr impurity ions on the transition appears to be only to lower the transition temperatures by 3.5'1 % impurity. For potassium dihydrogen phosphate, thermal hysteresis is negligible as is the effect on the transition of Cr doping to the 1%level. The nature of the phase transitions and the relevance of the impurity effects to central peak phenomena are discussed.
Introduction In the Course of EPR investigations233 of pretransitional cluster dynamics in some ferro- and antiferroelectric 'Department of Chemistry,West Virginia University, Morgantown,
W. Va. 26506.
0022-3654/79/2083-0664$01 .OO/O
phosphates and arsenates it was observed that certain transition temperatures were a t variance with published values. Particularly, the thermal hysteresis of the transition temperature appeared to be considerably smaller in some cases than indicated in the literature. Hysteresis widths published for the ammonium salts range from 1to
0 1979 American
Chemical Society
Thermal Hysteresis in Phosphates and Arsenates
The Journal of Physical Chemistry, Vol. 83,
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TABLE I: ]Literature Data for Transition Temperatures and Thermal Hysteresis in Ammonium Dihydrogen Phosphates and Arsenates material
author
date
method
Tc& a
ADA
Busch Stephenson and Adams Loiacono Busch Stephenson and Zettlemoyer Matthias, Merz, and Scherrer Eisner Skalyo et al. Boiko and Golovnin Loiacono Peshikov and Mukhtarova Kasturi and Moran Mason and Matt hias Skalyo e t al. Boiko and Golovnin
1938 1944
dielectric heat cap.
220 216
1970 1938 1944
DTA dielectric heat cap.
219 155 147
0.6 1.9
19 10 4
1947
dielectric
14'7
2
11
1960 1969 1970 1970 1971
dielectric neutron diff X-ray diff DTA dielectric
149 151 149 142 147
212 1-4 2 6.4 3.3
16 17 18 19 20
1975
NMR
148
0
21
1952
dielectric
241
6-17
6
1969 1970
neutron diff X-ray diff
235 234
1-4 2
17 18
ADP
DA DP
a
A TC
ref
0.8
10 5
Thte arrow denotes the direction of temperature change.
2' from heat capacity measurement^^,^ to up to 17' from certain dielectric experimenk6 Since no reasonable explanation exists for such a discrepancy and since compounds of this class do have considerable technical potential as dielectric material^^-^ it is desirable that the situation be clarified. First, in view of the many conflicting reports available we shall review the situation in some detail. Busch'O some 40 years ago demonstrated the existence of a pironounced phase change a t low temperatures in the phosphates and arsenates of both potassium and ammonia. Subsequently, Stephenson and c o - ~ o r k e r sby ~ , heat ~ capacity measurements, showed the transition of ammonium dihydrogen phosphate (ADP) and arsenate (ADA) to exhibit thermal hysteresis of width 1.9 and 0.8', respectively, no such hysteresis being observed for the analogous potassium salts (KDP and KDA).42 Matthias, Merz, and Scherrerl' in 1947 obtained a similar figure for ADP via permittivity measurements and they showed also that on repeated cycling through the transition the initial hysteresis decreased by 1 / 3 after the first cycle, to a value of 2'. They also confirmed the effect of a T1+ substitutional impurity to be to lower the transition temperature by -3'/ % impurity.12 Later, for fully deuterated ADP (i.e., DADP), Mason and Matthias13 published dielectric data which indicate from their figure, an hysteresis of some 11 or 14' depending on the crystal orientation, and from their text, either 17 or 6" depending on whether the sample was coated with a plastic cement or not. They also reported the DADP transition to be repeatable on recycling the crystal through the transition temperature. Their results have been widely quoted (e.g., Kanzig (1957, p 126),14 Zheludev (1971, p 448)15) and thus have led to some confusion. In 1960, E i s n e P reported for ADP additional dielectric measurements which confirmed the previously published transition temperatures obtained on cooling but which showed, on warming, an hysteresis of about 12' for both x-cut and z-cut crystals, a value which is in fact six times larger than the previously published values in spite of Eisner's claim16 of agreement with the data of Stephenson and Z e t t l e m ~ y e r Eisner .~ claimed alsox6that the presence of substitutional impurities (e.g., G r o t - up to the 6% level) did not affect the transition temperature. More recently, for both ADP and DADP, Skalyo et al. (1969)17 found, using neutron diffraction, hysteresis values ranging
from 1 to 4', and similarly, but using X-rays, Boiko and Golovnin ( L97O)l8 found values near 2'. Although the latter authors quote the review of Kanzig14which states that the transition "exhibits a pronounced thcrmal hysteresis", they did suggest the magnitude of the earlier data for DADP to have arisen from too great a rate of change of temperature and a consequent lack of thermal equilibrium. These observations were followed by the differential thermal analysis data of Loiaconolg(AT, 3- 6.4' for ADP and 0.6" for ADA), the dielectric data of Peshikov and MukhtarovaZ0(AT, = 3.3' for ADP) and by those of an NMR study by Kasturi and Moran2' who reported the absence of hysteresis for ADP within their claimed experimental accuracy of *0.5'. A summary of the literature data is given for convenience in Table I. On account of the confusion outlined above we have used dielectric, pulsed NMR, and E P R techniques (each operating in essentially different spectral regions) together with differential scanning calorimetry (DSC) measurements to redetermine the temperatures of the phase transitions of ammonium dihydrogen phosphate (ADP), ammonium dihydrogen arsenate (ADA), and of their fully deuterated analogues (DADP and DADA), with both increasing, decreasing, and equilibrated temperatures. In addition, we have investigated the effect of Cr s u b ~ t i t u tional impurity ions on the transition properties since such ions are commonly used as microscopic probes in E P R studies2p3of domain motion in these materials. Our results, Table 11, generally confirm the transition temperatures obtained by others on cooling, but show, on warming, the thermal hysteresis of the transition to be of the order of 2' in all cases. For comparison both as a check of technique and to investigate impurity effects we have examined also two samples of potassium dihydrogen phosphate (KDP).
Experimental Section (a) Sample Preparation. ADA, prepared by reaction of (NH,J2C03 with As205in aqueous solution, was recrystallized several times to eliminate contamination by higher ammonium salts. Stoichiometry of the final product was confirmed by a nitrogen determination. ADP and KDP were reagent grade materials. Deuteration was achieved by successive recrystallization from D20, and doped samples were prepared by adding (NH4)&r04or K2Cr04
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TABLE I1 : Experimental D a t a for Transition Temperatures and Thermal Hysteresis in Ammonium Dihydrogen Phosohates and Arsenatesa material
method
orientation
ADA
dielectric DSC EPR dielectric DSC EPR EPR EPR dielectric
X
DADA ADP
DADP
T , J . ~+ 0.2"
impurity
ZLH, X
ziH, ziH, ZLH,
1%Cr0,2' 1%Cr0,'1%CrOd20.1% CrOa2-
X
dielectric DSC EPR NMR
ZLH,
dielectric
X
EPR EP R dielectric
ZLH, ZLH,
z ZLH,
1%Cr0,'-
0.1% Cr0,'1%CrO,Z-
X
(215.6 216.0 216.2 (214.7 213.0 212.2 303.0 303.0 147.0 (147.0 147.8 147 147.5 145.7 (146.7 143.9 (143.9 148.0 144.0 219.2 (220.2
(237.4 219.2 (219.0 EPR zlH, 237.5 dielectric X 1%Cr0,'238.4 DSC 1%Cr0,'237.3 (237.5 EPR ZLH, 1%Cr0,'239.2 a Data in parentheses obtained on subsequent traverses through the transition. temperature change.
DSC
T,Tb
i
0.2" AT, t0.3"
216.2 217.5 218.5 215.0 215.0 214.6 305.0 305.3 148.9 148.9 149.2 150 149.5 148.8 148.8 144.7 145.0 149.0 145.0 221.4 221.4 238.6 238.6 221.5 221.5 238.8 240.8 239.2 239.2 241.3
0.6) 1.5 2.3 0.3) 2.0 2.6 2.0 2.3 1.9 1.9) 1.4 3 2.0 3.1 2.1) 0.8 1.1) 1.0 1.0 2.2 1.2) 1.2) 2.3 2.5) 1.3 2.4 1.9 1.7) 2.1
%D*1
98.0 98.5
92 92 98.0 98.0 92 92 98 98.2 98.2 98.2 98.2
The arrows denote the direction of
r +-+-%-+
I
t-+-+-+-
DADP ( 92 % D)
1
140
I
i
i
I45
150
T (K) Figure 1. Variation of capacitance of x-cut ammonium dihydrogen phosphate (ADP) in the region of the paraelectric-antiferroelectric phase transition: (0)cooling; (+) subsequent warming; (A) rewarming after conditioning for 24 h at temperatures below 100 K.
to the appropriate solution. D/H ratios were determined by standard NMR techniques and impurity levels were monitored by spectrographic analysis. Large crystals were grown from saturated aqueous solutions and were allowed to dry either in air or over Pz05before grinding to the appropriate shape and orientation. (b) Dielectric Measurements. The dielectric apparatus, described e l ~ e w h e r e ,utilized ~ ~ ~ ~ ~here a parallel plate three-terminal dielectric cell with electrodes supported by a compressed bellows arrangement. Typical results, obtained a t a frequency of 10 kHz under thermally equilibrated conditions with temperatures measured to within
217
220
223
226
T (K) Figure 2. Variation of capacitance of x-cut ammonium-d, dideuterium phosphate (DADP) in the region of the paraelectric-antiferroelectric phase transition. The deuteration level was 92 % : (0)cooling; (+) subsequent warming; (0)subsequent recooling.
*0.05', are illustrated in Figures 1, 2, and 6, for ADP, DADP, and KDP, respectively, the arrows indicating the direction of temperature change during the course of the experiment. We stress the fact that each C and T measurement was made only after the sample had been held a t a particular temperature for a t least 15 min which was sufficient time for thermal (but not necessarily thermodynamic) equilibrium to become established. In most cases the initial cooling run was immediately followed by a warming run from about 10 to 15' below the transition
Thermal Hysteresis in Phosphates and Arsenates
The Journal of Physical Chemistry, Vol. 83, No. 6, 197G1 667
0.5
/-
0.1
(doped )
0.05
8
6.0
6.5
7.0
IOOO/T(K 1 Flgure 3. Variation of spin-lattice relaxation time T , of ammonium dihydroyen phosphate (ADP) in the region of the paraelectric-antiferroelectric phase transition: (0)cooling; (+) subsequent warming; (0) subsequent recooling.
point. To ensure that the initial (cooling) transformation had been complete, some samples were then slowly recooled through the transition point to 77 K where they were held for a period of 18-24 h after which time they were s,lowly warmed and the warming transition again observed (Figure 1). In all cases the original warming transition temperature was reproduced within the limits of f0.15". In the case of DADP where the paraelectric-antiferroelectric phase transition can occur a t temperatures as high as -32 "C we observed large irregularities in the dielectric properties of some of our crystals in the region from - 5 to -20 "C which arose from the presence of supercooled included water. The effect was absent from those crystals dried over P205. Stephenson e t aL4r5 commented also on the difficulty of drying crystals of ADP and ADA grown from aqueous solution. Our observations suggest that contamination by water affects the transition temperatures only to a negligible extent. (c) Pulsed N M R Measurements. Proton spin-lattice relaxation times, T I ,were measured using 90°-~-900 pulse sequences from a Bruker SPX variable frequency pulsed NMR spectrometer operating a t 60 MHz. All measurements were made under thermally equilibrated condition~.~~ Spin-lattice relaxation times, T1, for ADP ( z axis perpendicular to Ho), were measured in the transformation region and are shown in Figure 3 as a function of inverse temperature. The magnitudes of T I reported here are consistent with those of the earlier measurements of Kasturi and Moran.zl The reason for their failure to observe thermal hysteresis is not apparent. (d) EPR Measurements. A Varian E-line spectrometer operating at X-band frequencies (-9.2 GHz) was used to follow the microwave dielectric response of the sample in terms of changes in the Q factor of the microwave cavity as a function of sample temperature. This was achieved by employing a dual sample cavity containing the sample in one part and a paramagnetic reference salt (CuS04. 5H20) in the other. The reference salt was maintained a t room temperature and the change in Q of the microwave cavity monitored by observing changes in the intensity of
Figure 4. Variation of EPR response (see text) for a sample of ammonium dihydrogen arsenate (ADA) containing 1% C r0:in the region of the paraelectric-antiferroelectric phase transition.
the EPR signal from the reference salt as the sample temperature was varied, the magnetic field Ho remaining constant throughout. The data were recorded continuously by means of an X-Y recorder appropriately coupled to the spectrometer and to a copper-constantan thermocouple attached to the sample. Heating and cooling rates of 1°/min were adequate for this sample configuration, there being no decrease in apparent hysteresis a t lower rates. The sample (-0.05 g) was cooled by a stream of cold nitrogen gas in an Air Products Helitran system which permitted control of the temperature to within 0.1". Although the amplitude of the spectrometer output is a complicated function of sample properties and equipment parameters, it nevertheless closely follows the large abrupt changes in sample dielectric properties, such as occur at some phase transitions. The experimental method should be of considerable utility to users of EPR equipment to whom dielectric apparatus is not readily available. It has the advantage of convenience and rapidity not usually associated with the average dielectric system. We suggest the method should also lend itself to use as a high frequency dielectric probe, sensitive to relaxation i3ssociated with extremely rapid dipolar reorientational motion. The general features of the EPR response are illustrated in Figure 4 for an ADA sample doped with 1% CrO:-. (e) DSC Measurements. Differential scanning cailorimetry measurements were made using a Perkin-Elmer Model DSC 1-B instrument operating to temperatures as low as -150 "C and with scanning rates of 5 and lO"/min. The single crystal samples, sealed in aluminum pans, were sufficiently small that no difference in hysteresis was observed between the two scanning rates. Data for DADP are illustrated in Figure 5. Transition temperatures were taken as being indicated by the onset of the theirmal anomaly. Results The transition temperatures (T,) determined as illustrated by Figures 1-5 are presented in Table I1 together with relevant details, the error limits representing the estimated uncertainty in determining T, from the figures. Comparison with the data of Table I shows our results obtained on cooling to be in general agreement with most literature data. Indeed, values of T , derived from our dielectric measurements of x-cut ADP are exactly the same
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The Journal of Physical Chemistry, Vol. 83, No. 6, 1979
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TABLE 111: Experimental Data for Transition Temperatures and Thermal Hysteresis in Potassium Dihydrogen Phosphate material
method orientation impurity dielectric X dielectric X 1%CrOa2The arrows denote the direction of temperature change. KDP
T,lU
?r
0.1"
122.33 122.29
T,ta
~t
0.1"
--
225
T
(K)
220
215
225
220
215
-
210
[-+
T (K)
210
215
220
225
230
T(K)
AT, +0.1,"
0.0
122.33
210
-
u 215
220
225
230
T (K)
DADP ( 9 2 % D) Figure 5. Thermal anomaly at the paraelectric-antiferroelectric phase transition of ammonium-d, dideuterium phosphate (deuterium content 9 2 % ) as observed by differential scanning calorimetry. From left to right, in succession: cooling, warming, cooling, warming.
as those derived by Stephenson and Zettlemoyer4 from heat capacity experiments. We note, for the ammonium salts, that T , is practically independent of the crystalline orientation and of the measurement technique but is dependent both on the substitutional impurity content and, as is well known, more markedly dependent on the deuteration level. The results show the effect of the Cr042substitutional impurity in the normal salts to be lower to T , by about 3 . 5 O a t the 1%level which is contrary to the observation of Eisner16 who reported no effect up to the 6% level. Our result is comparable, however, to the effect produced by both T1+ and Mn3+ substitutional impurities as has been previously d e m ~ n s t r a t e d . l l J ~Spectrographic $~~ analysis of our samples showed a spectrum of metallic impurities between the 0.001 and 0.01% levels which may perhaps be instrumental in determining the exact transition temperature for a given sample.& For the deuterated salts the impurity effect appears to be masked by the effect of differences in the deuteration level between different samples. Thermal hysteresis (AT,) of the phase transition was observed between warming and cooling runs in all cases except that of KDP. Table I1 shows the hysteresis to be a general characteristic of the antiferroelectric ammonium salts of this class. The effect is independent of crystal orientation, impurity content, deuteration level, technique, and the nature of the anion. The isomorphous ferroelectric alkali metal salts are well k n o ~ nto~ exhibit , ~ ~ no such hysteresis effect (Figure 6). We concur with the suggestion of Boiko and Golovninl* that the highest values of AT, of Table I must have arisen from excessively high rates of temperature change during certain experiments and, in addition, we confirm the observations of others1lZz0in that the hysteresis decreased initially for some (but not all) of our samples by about 1/3 on recycling the sample through the transition temperature (Figures 2 and 3). Thereafter we find the hysteresis width to be reproducible over at least five or six successive transformation cycles subsequently traversed. The decrease in AT, probably is related to the
T(K) Figure 6. Variation of capacitance in the region of the paraelectric-ferroelectric phase transition of potassium dihydrogen phosphate (KDP): (0and -I-)cooling and subsequent warming of x-cut KDP; ( 0 ) cooling of x-cut KDP containing 1% C r O t - impurity.
fact that the single crystallinity is usually lost after the initial transformation. For ADA, the hysteresis observed on subsequent transformations approaches values reported by previous w o r k e r ~ . ~ J ~
Discussion That the phase transitions of the ammonium salts are of first order there is little d o ~ b t : ~ ~ J at ~ the J ~ point J~i~~ of transition two distinct phases are present, thermal hysteresis is manifest, and the heat capacity anomaly is typically that of a transition involving a substantial latent heat.4,5In contrast, transitions of second order as defined by ErhenfesP involve no direct change of phase; at T, "the phases are identical in constitution, energy, entropy and volume,29and hysteresis is thermodynamically forbidden. The latter point is clearly stated by and by Loiacono,lgwhereas, incorrectly, the converse is stated by Eisner16and also, indirectly, by KnitteL31 The occurrence of hysteresis a t transitions of the first kind is predicted by theoretical studies32of the appropriate Ising model, the hysteresis arising as a result of incomplete attainment of thermodynamic equilibrium. For transitions of higher order, where the free energy derivative with respect to temperature is continuous, thermodynamic disequilibrium, and hence thermal hysteresis of the transition temperature, obviously becomes impossible. It has been stated previously33 that the magnitude of any experimentally determined hysteresis must depend, in principle, on the thermal equilibration period. For infinitely long times the hysteresis must necessarily be reduced to zero in all cases. In the case of the ammonium salts the dielectric response a t the transition is essentially a step function (Figures 1-4) with hysteresis of near 1 or 2" whereas for KDP the re-
Thermal Hysteresis in Phosphates and Arsenates
sponse, as is well known, is cusp-shaped (Figure 6) and shows no hysteresis (Table 111) within experimental ~ e n s i t i v i t y .KDP ~ ~ undergoes what in modern parlance is described as a “high-order displacive transition”, whether of second order or of mixed-order%being a debatable point. Many studies of materials having second-order displacive transitions have led to an association of “soft phonon modes” (i.em,a phonon mode whose frequency approaches zero as the transition temperature is approached from above) with the mechanism of the transition. These modes, revealed by the inelastic scattering of photons or neutrons, have been shown35for a variety of materials to be accompanied by an exceedingly narrow spectral peak a t v = 0, which increases in amplitude dramatically as T , is approached from above and is somewhat analogous to the strong Rayleigh line familiar in Raman scattering experiments on liquids but €or which the usual hydrodynamic explanation is of course inappropriate for solids. Of several alternative theories dealing with the intrinsic properties of these materials, not one satisfactorily accounts for all of the experimental evid e n ~ e However, .~~ a detailed microscopic theory of defect mechanisms proposed by Halperin and Varma36 relates these central peaks to the presence of impurities or other defects in the crystalline lattice. Their theory, essentially distinguishing between relaxing and frozen defect cells, more adequately represents the experimental data. For the relaxing case stabilization of the low temperature phase is predicted with a consequent increase in T,. For the frozen case a decrease is expected. The latter model has been favored by recent results37obtained for SrTiOs which show a decrease of T, with increasing defect concentration. Although it appears that central peak phenomena have not yet been characterized for the antiferroelectric phosphates and arsenates, our observation of a distinct lowering of T, with impurity (and hence defect) concentration certainly is pertinent to such considerations. For Cr-doped KDP, our null result may argue, however, against the applicability of the theory to that system, although it has been suggested elsewhere3*that the origin of the central peaks observed for KDP may well be related to defects induced by the natural deuterium content. It appears, however, that this suggestion is currently being called in questiona41 Furthermore, although it has been proposed by others39 that Cr5+ions in KDP do form Halperin-Varma type of centers, subsequent E P R studies of line broadening and certain theoretical considerations indicate40 that this proposal is not entirely justified.
References and Notes (1) Issued as NRCC No. 17182. (2) N. S. Dalal and C. A. McDowell, Pbys. Rev. B , 5, 1074 (1972). (3) N. S . Dalal and A. H. Reddoch, Abstracts of the International
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