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LATTICE DYNAMICS OF YAl2 AND LaAl2 - A FURTHER CONTRIBUTION TO THE La-Y PUZZLE
C. Yeh, W. Reichardt, B. Renker, N. Nücker, M. Loewenhaupt
To cite this version:
C. Yeh, W. Reichardt, B. Renker, N. Nücker, M. Loewenhaupt. LATTICE DYNAMICS OF YAl2 AND
LaAl2 - A FURTHER CONTRIBUTION TO THE La-Y PUZZLE. Journal de Physique Colloques,
1981, 42 (C6), pp.C6-371-C6-373. �10.1051/jphyscol:19816107�. �jpa-00221167�
JOURNAL DE PHYSIQUE
CoZZoque C6, suppZ6ment au n o 12, Tome 42, de'cembre 1981 page C6-371
LATTICE DYNAMICS OF Y A I Z AND LaA12 - A FURTHER CONTRIBUTION TO THE La-Y PUZZLE
C.T. ~ e h * , W. R e i c h a r d t , B. Renker, N. Niicker and M. Loewenhaupr * *
Kemforschungszentmun KarZsruhe, I n s t i t u t fiir Angaandte Kemphysik I , 0-7500 KQrZsruhe, Postfach 3640, F.R.G.
A b s t r a c t . - By means of i n e l a s t i c n e u t r o n s c a t t e r i n g we have measured t h e phonon d i s p e r s i o n c u r v e s i n t h e main symmetry d i r e c t i o n s o f t h e c u b i c Laves phases Y A 1 2 and LaA12. The phonon f r e q u e n c i e s i n LaA12 a r e c o n s i d e r a b l y
s o f t e r t h a n t h o s e of Y A ~ which cannot be e x p l a i n e d s o l e l y by t h e d i f f e r e n t atomic masses of La and 3. The e x p e r i m e n t a l d i s p e r s i o n c u r v e s a r e w e l l de- s c r i b e d by a x i a l l y symmetric Born v. Khrmh models t a k i n g i n t o account i n t e r - a c t i o n s up t o the fifth n e a r e s t neighbors. From t h i s a n a l y s i s we f i n d t h a t t h e n e a r e s t neighbor A1-A1 and TM-TM l o n g i t u d i n a l f o r c e - c o n s t a n t s o f YA12 a r e about t w i c e t h o s e of LaA12 whereas t h e TM-A1 i n t e r a c t i o n s a r e n e a r l y e q u a l . YA1 and LaAl belong t o t h e group o f c u b i c Laves-phases of type AB2. I n t h i s s t r u c -
2 2
t u r e t h e A-atoms form a diamond l a t t i c e . The remaining t e t r a h e d r a l s i d e s a r e occu- p i e d by r e g u l a r t e t r a h e d r a of t h e B-atoms. The B r a v a i s l a t t i c e i s FCC, t h e p r i m i t i v e c e l l c o n t a i n s 6 atoms. Today more t h a n 150 r e p r e s e n t a t i v e s of t h i s s t r u c t u r e a r e known, a b o u t 35
o fwbich a r e superconaucting. T h e ~ o t k % r = t i ~ ~ s f o r o u r s t u d i e s of Y . a 2 and LaAl a r e twofold: On one hand we want t o have a b e t t e r understanding of t h e l a t -
2
t i c e dynamics of such a common s t r u c t u r e ; on t h e o t h e r hand it i s of i n t e r e s t t h a t LaAl h a s a superconducting t r a n s i t i o n temperature of 3.2K whereas YA12 i s nonsuper-
2
conducting a t l e a s t down t o 0 . 3 4 ~ ' . Recently r e l a t i o n s between superconducting and l a t t i c e dynamical p r o p e r t i e s have been s t u d i e d f o r two o t h e r p a i r s of compounds:
YB6 (Tc=7 .IK) -LaB6 (Tc=.45K) 2 and YS (Tc=2 .8K) -LaS ( ~ ~ = . 8 4 ~ ) ~ ' ~ . Note t h a t i n t h o s e c a s e s t h e Y compounds have t h e h i g h e r Tc v a l u e s . For YB6 t h e high Tc i s c o r r e l a t e d w i t h a
s t r o n g r e d u c t i o n of t h e t r a n s l a t i o n a l phonon f r e q u e n c i e s compared with LaB
6 whereas f o r YS and LaS almost i d e n t i c a l dynamical f o r c e s have been found.
C a l o r i m e t r i c measurements5 and i n v e s t i - g a t i o n s o f t h e e l a s t i c c o n s t a n t s 6 have shown, t h a t t h e Debye temperature of LaM2 behaves anomalously compared t o o t h e r r e l a t e d nonsuperconductinq com- Table 1: Debye temperature of v a r i o u s
MeA1, compounds pounds ( s e e Table 1). A f t e r c o r r e c t i n g
L
-
a e l a s t i c c o n s t a n t s 6 b s p e c i f i c h e a t 5 t h e experimental OD-values f o r t h e i r de- pendence on t h e molecular masses almost i d e n t i c a l v a l u e s a r e o b t a i n e d f o r YA12,
* P r e s e n t a d d r e s s : I n s t i t u t e of Atomic Energy, Academia S i n i c a , Peking, China
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816107
JOURNAL DE PHYSIQUE
REWCED WAVE VECTW CCCRWTE
S=g
qFig. 1 phonon d i s p e r s i o n c u r v e s of Y A l l and LaAl2 a t 296K. F u l l c u r v e s were calcu- l a t e d w i t h l o parameter BvK models. For some r p o i n t f r e q u e n c i e s t h e c o r r e - sponding v i b r a t i o n a l modes a r e i n d i c a t e d . The c u r v e s t o t h e r i g h t were c a l - c u l a t e d w i t h t h e parameters o f Y A 1 2 u s i n g t h e a t o m i c mass o f La.
GdA12 and LuA12 whereas t h e v a l u e s f o r LaA12 a r e c o n s i d e r a b l y lower.
W e performed measurements of both t h e phonon d e n s i t i e s o f s t a t e s and t h e phonon d i s - p e r s i o n c u r v e s o f YA12 and LaA12 a t t h e K a r l s r u h e r e s e a r c h r e a c t o r FR2 by means o f i n e l a s t i c n e u t r o n s c a t t e r i n g . F i g . 1 shows t h e d i s p e r s i o n c u r v e s o f YA12 and LaA12 a t 296K i n t h e t h r e e main symmetry d i r e c t i o n s . The f u l l c u r v e s were c a l c u l a t e d with a 10 parameter a x i a l l y symmetric Born v. K 6 m h model f i t t e d t o t h e experimental d a t a . The d a s h e s l i n e s i n d i c a t e t h e s l o p e s of t h e a c o u s t i c branches a t t h e r p o i n t a s c a l c u l a t e d from t h e e l a s t i c c o n s t a n t s 6 . The d i s p e r s i o n c u r v e s f o r t h e Cl00l d i - r e c t i o n on t h e r i g h t s i d e of F i g . 1 have been c a l c u l a t e d w i t h t h e model parameters of YAl b u t u s i n g t h e atomic mass of La. By comparing t h i s s e t of d i s p e r s i o n c u r v e s
2
with t h e corresponding experimental d a t a o f LaA12 " t r i v i a l " e f f e c t s caused by t h e d i f f e r e n t atomic masses o f Y and La a r e e l i m i n a t e d . B e s i d e s t h e t o r s i o n a l mode a t 24 meV a l l branches o f LaA12 a r e c o n s i d e r a b l y lower.
Q u a n t i t a t i v e i n f o r m a t i o n about t h e i n t e r a c t i o n s can be o b t a i n e d from t h e parameters
of t h e Born v . MrmSn models which a r e l i s t e d i n Table 2 . The t h r e e l o n g i t u d i n a l
f o r c e - c o n s t a n t s o f t h e n e a r e s t neighbor i n t e r a c t i o n s of
A l - A l ,Me-A1, Me-Me (Me=Y,
L a ) , r e s p e c t i v e l y a r e dominant. They l a r g e l y determine t h e p o s i t i o n s of t h e v a r i o u s
phonon branches. For YA12 t h e f o r c e - c o n s t a n t s f o r t h e A1-A1 and Y-Y i n t e r a c t i o n s a r e
about t w i c e a s l a r g e a s t h e corresponding v a l u e s of LaA12. I n c o n t r a s t t h e Me-A1
f o r c e - c o n s t a n t s a r e a b o u t e q u a l f o r t h e two compounds. The Table g i v e s a l s o t h e in-
v e r s e t h i r d moment of t h e phonon d e n s i t i e s of s t a t e s c a l c u l a t e d from t h e models.
Table
*INTER- ACTION A1-A1
Me-A1 Me-Me A l - A 1 Me-A1
2: Force-constants [ i n dyn/cm]
- ~ i g . 2 Generalized phonon d e n s i t y of
of a x i a l l y symmetric Born v. s t a t e s determined from neutron KBrm2n models f o r LaA12 and s c a t t e r i n g experiments and from
YA12. models f i t t e d t o t h e experimental
d i s p e r s i o n c u r v e s .
They a g r e e w e l l w i t h t h o s e v a l u e s o b t a i n e d from t h e e l a s t i c c o n s t a n t s . The compari- son with t h e Debye temperatures from c a l o r i m e t r i c measurements seems t o i n d i c a t e t h a t t h e phonon d e n s i t i e s of s t a t e s do n o t change much between OK and 300K. However, d i s - c r e p a n c i e s e x i s t between t h e c a l c u l a t e d and experimental s p e c i f i c h e a t s i n t h e tem- p e r a t u r e xange between 5 and 20K which might be e x p l a i n e d by a pitonon s o f t e n i r i g out- s i d e t h e e l a s t i c r e g i o n a t low t e m p e r a t u r e s . I n F i g . 2 we compare t h e g e n e r a l i z e d phonon d e n s i t i e s of s t a t e s c a l c u l a t e d from our models w i t h t h o s e determined from s c a t t e r i n g law measurements u s i n g powder samples. From r e c e n t b a n d s t r u c t u r e c a l c u l a - t i o n s of Hasegawa and yanase7 we must conclude t h a t t h e anomalously s o f t phonon spectrum of LaA12 i s n o t caused by t h e i n f l u e n c e o f f - e l e c t r o n s . The f-bands of LaA12 l i e about 3 eV above t h e Fermi energy EF and t h e f-components i n t h e e l e c t r o n s t a t e s n e a r EF a r e l e s s t h a n 10%. Below EF t h e b a n d s t r u c t u r e s o f LaAl and
Y A 1 2a r e v e r y
2
s i m i l a r , o n l y c l o s e t o EF t h e r e a r e some d i f f e r e n c e s which a c c o r d i n g t o t h e s e a u t h o r s a r e caused by a s t r o n g e r p-d h y b r i d i s a t i o n i n t h e c a s e of LaA12. Whether t h e s e d i f - f e r e n c e s account f o r t h e occurence of s u p e r c o n d u c t i v i t y and e x p l a i n t h e r a t h e r s o f t phonon spectrum o f LaA12 cannot he answered a t p r e s e n t .
r/ao .3536 .4146 -4330 -6124 .6494
B.W. Roberts, J.Phys.Chem. Ref. Data, Vol 5 , No 3 (1976) G. S h e l l , W. Winter, H . R i e t s c h e l and F. Gompf, t o be published
P. Roedhammer, W . R e i c h a r d t and
F.Holtzberg, Phys. Rev. L e t t . 40 465 (1978) W. R e i c h a r d t , P. Roedhammer and
F.Holtzberg, KfK Report 2670 p . 1 (1978) R.E. Hungsherg and K.A. Gschneider, J.Phys.Chem. S o l i d s 33, 401 (1972) R.J. S c h i l t z and J . F . Smith, J.Appl.Phys. 45, 4681 (1974)
A. Hasegawa and A. Yanase, J.Phys. F 10, 847 (1980) and J.Phys. F 0, 2207 (1980) 493
475 473
E)-3
