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Submitted on 1 Jan 1981
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SOFT-MODE SPECTRA AND PHASE TRANSITION
IN KDP CRYSTAL WITH ADP IMPURITIES
Jong-Jean Kim, Jong-Wook Won, Byoung-Koo Choi
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C6, suppldment au n o 12, Tome 42, dgcembre 1981 page C6-427
SOFT-MODE SPECTRA AND PHASE T R A N S I T I O N I N KDP CRYSTAL WITH ADP I M P U R I T I E S
Jong-Jean Kim,Jong-Wook Won and Byoung-Koo Choi
Physics deparhent, Korea Advanced I n s t i t u t e of Science & TechnoZogy, P.O. Box 150 Chongyangni, Seoul, Korea.
Abstract. - O n the basis of the q-dependent coupling interactions between the proton pseudo-spin mode and the lattice phonon mode we could explain qualita- tively the observation that the ferroelectric transition temperature of the KDP crystal was lowered as the ADP impurity concentration in the crystal was increased.
1. Introduction
-
Impurity effects on the dynamical aspects of the phase transition (1,2) The in KDP type crystals have been a great concern of many research workers.local soft-modes of the clusters around impurities are known to have a higher (3,4)
softening temperature T' well above T of the crystal soft-mode.
When the impurity dependent cluster concentration or the temperature dependent cluster size increases to the extent that the nearest neighbor clusters begin to interact, the local soft-modes of the clusters will be correlated in phase to turn into the extended soft-mode of the crystal, and thereby a possible raising of the softening temperature as impurity concentration is increased.
However, we observed from the dielectric constant measurements that T was lowered by 2.9 K when ADP impurities were doped into KIP crystal by 0.13% (Pig. 2). 2. Soft-Node Spectra vs. Phase Transition in KDP
Fig. l(a): a(ba)c Raman spectra of KDP Fig. l(b): a(ba)c low frequency Raman crystal. -at 299.6 K, * - . * at 131.4 K spectra of ADP crystal at room tempera- and
---
at 124.9 K. ture.C6-428 JOURNAL DE PHYSIQUE
The soft-mode Raman spectra of KDP and the Raman spectra of ADP obtained in the same scattering configuration are compared in Fig. 1. This wing spectrum of the soft-mode continues to remain until 90 K much below the transition temperature 122 K.(5) The phonon band at 180 cm-lo< I(H PO does shift significantly when K or P atom
2 4
(6)
is exchanged by different atoms- 145 em-' for KH A 0 and 100 cm-I for C2l2ASO4 ,
2 s 4
From Pig. l(b) we can see that in AIlP both the overdamped ving and the phonon band are extremely weak, and we see an obvious coupling between the soft-mode and a lattice phonon mode in KDP-type crystals. The uncoupled soft-mode frequency depen- dence on temperature obtained from the two-oscillator coupled mode analysis can be interpreted either as w- of the coupled pseudo spin-phonon soft mode or as
aT
of the-1
bare pseudo-spin soft-mode depending on whether we consider the 180 cm oscillator as another simple phonon of B2 symmetry or as the IC-PO4 lattice w+ vibration of the
2
coupled soft-mode. :Je have the temperature dependence of QT, = A(T-T ) different T
from that of w-,
4
= B(T-Tc). Another difficulty arises that the same :bserved spectra may be fitted equally well by a number of solutions(7), and indeed we have many different results rep~rted(~)for the temperature dependence of the 1;DP soft- mode, To from 30 K to 117.1 K. Scarparo et al!j)recently emphasized the non-linear behaviour of the soft-mode, denunciating the fits to the w2 = K(T-T ) behaviour. 3. Extension of ICobayashimodel-
The q-dependent coupling interaction of Koba~ashi(~) can be written as1J - + % + + -t
leiq+(xj
- x ~ ) ( ~ - ~
-iq. a ) for K3P crystal,vhere one KDP per unit cell is assumed, the Coulomb interaction energy between the
-th
+
+i proton and the j'th ion, v(xi
-
2.).
is Fourier transformed and a, the distance1
between the two minima of the double ~&ll potential, and
+
for ADP crystal, where A is the distance between the two ADP molecules in the primi- tive unit cell involved in the antiferroelectric ordering. Suppose an impure KDP
crystal where AD? impurities are homogeneously distributed so that an AOP molecule sees another h I P molecule at every n-th nearest neighbor site and KDP molecules in between. As in the case of antiferromagnetic impurites in a ferromagnetic crystal where the antiferro interaction persists even at large distances between impurities and a spin glass transition occurs'''), we assume the N)P impurities persist to con-
trzbute the antiferrv pseudo spin interactions. Then we haye,
for
the @?-dopedand we obtain
2 2 2 -+ -+ -+ + + -+
lB,12 cc 4n (11411 ) (6
-
lcos(2n-1)q.A+
2cos2nq-A-
4 ~ 0 s ;.x}(l-
cos q.a)( 1
-
cos6.2
)In the limit of q + 0 , as for Xaman
1 scattering, this is reduced to give
Fig. 2: Temperature dependence of di- Thus we can see the ferroelectric tran- electric constant at f = 1 KHz; (pure),
x(0.13Yb ADP) sition temperature is reduced as ADP
impurity concentration p is increased,
f' d e- Id- as depicted in Fig. 2. 2 2 2 l&m
IF;~
a (n-1) In '-lo-
= 1-
2/n+
1/n2 o: (1-
zp1I3
+
p2I3),where the first term 1 corresponds to
I F?
1
of pure KDP and p,
the ADP im- purity concentration per unit volume. Veanwhile,
.re have (9)2 2 Tc = To
+
iIB / K ~ R ~,
and substituting B' for F we obtain
* € 3 n o ! j o * u l a o l a
References
1. A. D. Bruce and R. A. Cowley, Adv. in Phys. 29, 219(1980).
2. V. L. Ginzburg, A. P. Levanyuk and A. A. Sobyanin, Phys. Lett. C 5 J , 151(1980). 3. K. H. HSck and H. Thomas, 2. Physik B z , 267(1977).
4. B. I. Halperin and C. M. Varma, Phys. Rev. B14, Pt030(1976).
5. M. Scarparo, R. S. Katiyar, R. Srivastava, and S. Parto, Phys. Stat. Sol. (b)s, 543(1978).
6. R. S. Katiyar, J, F. Ryan and J. F. Scott, Phys. Rev. BA, 2635(1971). R. P. Lowndes, N. E. Tornberg and R. C. Leung, Phys. Rev. B s , 911(1974). 7. A. S. Barker, Jr. and J. J. Hopfield, Phys. Rev.
135,
A1732(1964).8. C. Y. She, T. W. Broberg, L. S. Wall, and D. F. Edwards, Phys. Rev. BA, 1847 (1972) and references quoted therein.
N. Lagakos and H. 2 . Cummins, Phys. Rev. B s , 1063(1974).
9.
K.
K. Kobayashi, J. Phys. Soc. Japan 24, 497(1968). R. Blinc and B. Zeks, Adv. in Phys. 2l, 693(1972).10. T. Oguchi, Theories of Random Spin Systems, invited paper #1
-
Korean Phys. Soc. spring meeting(l980). See also spin glass papers in J. Physique 39,colloq. C6(1978).
TEw~wwslt) = T
