DYNAMICAL STUDY OF PHONONS IN FERROELECTRIC LEAD TITANATE

R. S. Katiyar, J. D. Freire
1981 Le Journal de Physique Colloques  
L a t t i c e dynamical formalism using r i g i d ion model with long range coulomb forces and s h o r t range a x i a l l y symmetric forces has been applied t o t h e c r y s t a l of lead t i t a n a t e i n t e t r a g o n a l phase. A l l zone center phonons and a few zone boundary phonons were used i n determining t h e f o r c e constant paramet e r s both a t room temperature and c l o s e t o Tc by nonlinear l e a s t squares analysis. The r e s u l t s i n d i c a t e t h a t the T i
more » ... e t h a t the T i 4 short range f o r c e s a r e a t l e a s t one order of magnitude l a r g e r than t h e Pb-0 forces. Moreover oxygens r e t a i n an e f f e c t i v e charge of 73% of t h e i r f r e e ion value, whereas t i t a n i u m possess only 67% of t h e i r f r e e ion charge. The eigenvector c a l c u l a t i o n s of t h e lowest o p t i c mode of E-symmetry correspond t o t h e prediction by Last, whereas i n BaTi03 t h e computed eigenvectors confirm the d e s c r i p t i o n of the s o f t mode clue t o S l a t e r . The parameters obtained, have been u t i l i z e d t o compute e l a s t i c and piezoelect r i c p r o p e r t i e s of PbTi03. The calculations of t h e zone centre phonons near Tc reveal t h a t the small anharmonic forces could lead t o the observed frequency changes. The importance of l a t t i c e dynamics i n studying t h e s t r u c t u r a l phase t r a n s i t i o n s i n cubic perovskite s t r u c t u r e s was f i r s t r e a l i z e d by Cochran. l No work has, however, appeared i n l i t e r a t u r e dealing with t h e interatomic forces i n tetragonal phase and t h e i r v a r i a t i o n s with temperature. Lead t i t a n a t e is one example of t h i s c l a s s and undergoes a ferroelectric-paraelectric phase t r a n s i t i o n a t 493'C, below which the c r y s t a l symmetry is tetragonal (C1 ) with one formula u n i t i n the u n i t 4v c e l l . According t o Shirane e t a1.2 the u n i t c e l l s t r u c t u r e may be described by placing Pb (K=l) a t t h e c e l l corners, Ti (K=2) a t (1,3,u) and oxygens (K=3,4,5) a t (f , i , v ) , (f,O,w), (O,i,w); where u = 0.541, v = 0.112 and w = 0.612 with a. = 3.904 A and c o = 4.15 A. Group t h e o r e t i c a l a n a l y s i s f o r zone c e n t r e phonons shows t h a t t h e 12 o p t i c a l modes should be c l a s s i f i e d as follows: 3A1(Pb,Ti,0)= + 4E(Pb,Ti,0)x,y + B1(OlZ The s u b s c r i p t s x,y,z denote the displacement d i r e c t i o n s of t h e ions included i n bracket. I n t h e r i g i d ion formalism t h e p o t e n t i a l energy of an i o n i c c r y s t a l can be w r i t t e n as the sum of short range repulsive and long range coulomb forces. For lead t i t a n t e considering ion p a i r p o t e n t i a l s f o r a l l i n t e r a c t i o n s f o r distances l e s s than 3.5 A, the s h o r t range p a r t of p o t e n t i a l energy may be elaborated as follows: t l 9 1 $S,R. = 4$13(r13) + 4'$14(r14) + 4$14(r14) + $23(r23) + '$23(r23) + 4$24(r2/+) + 8'$34(r34) + 4 6 4 5 ( r~5 ) Article published online by EDP Sciences and available at http://dx.
doi:10.1051/jphyscol:19816127 fatcat:oapw5p7wmragjpyvi2ae35iy6i