ISOTOPE EFFECTS IN SUPERCONDUCTING TRANSITION METAL HYDRIDES

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ISOTOPE EFFECTS IN SUPERCONDUCTING TRANSITION METAL HYDRIDES

J. Hauck

To cite this version:

J. Hauck. ISOTOPE EFFECTS IN SUPERCONDUCTING TRANSITION METAL HYDRIDES.

Journal de Physique Colloques, 1978, 39 (C6), pp.C6-1395-C6-1400. �10.1051/jphyscol:19786578�.

�jpa-00218069�

ISOTOPE EFFECTS IN SUPERCONDUCTING TRANSITION METAL HYDRIDES

J . Hauck

Kernfovschungsanlage Jillieh, Institut fifr Festkd'rperforsohung, D-5170 Julidh, FRG

Resume.- Les effets isotopiques dans les hydrures des metaux de transition peuvent etre relies a. une stabilisation differente du champ eristallin pour les atomes H et D aux sites intersti- tiels tetraedriques ou octaedriques. Les metaux avec une faible electronegativite ou travail de sortie montrent l'effet isotopique normal avec une temperature de transition de la supraconduc- tivite plus basse pour le deuteride, une energie d'octivation plus elevee pour la diffusion et une temperature plus elevee pour la lacune de miscibilite de la phase a. Les metaux avec une electronegativite superieure a 4,5 V montrent l'effet inverse. La dilatation volumetrique rela- tive peut etre reliee a 1'electronegativite et est un peu plus petite pour 1'echantillon deute- rogene.

Abstract.- Isotope effects, in transition metal hydrides can be related to a different crystal- field stabilization for H and D atoms at tetrahedral or octahedral interstices. Metals with low electronegativity or electron work function exhibit the normal isotope effect with a lower su- perconducting temperature for the deuteride, a higher activation energy of diffusion and a higher temperature for the miscibility gap of the a-phase. Metals with an electronegativity lar- ger than about 4.5 V exhibit the reverse behaviour. The relative volume expansion can be related to the electronegativity and is somewhat smaller for the deuterated sample.

Since the discovery of superconductivity in thorium and palladium hydride in 1970 /l/ and 1972 /2/ resp.

many metal-hydrogen systems were investigated /3/

with the aim for a better understanding of super- conductivity in such simple compounds. The major in- terest concentrated on the transition metal hybrides where hydrogen enters interstitial sites without major changes of the metal lattice structure but some variation of the average number of valence electrons with hydrogen content. In figure 1 part of the periodic table with the transition metals is shown.

metals which can form hydrides - that are the elements of the third, fourth and fifth group, chromium, nickel and palladium.

Two schematic phase diagrams are shown in figure 2 as an example for hydride formation.

m m.

^(2.7)

4.9 6.0

m

Tcr-0.39

w,.

^0.65

Ws

0.13 5.4

9.2

V&

4.5

W

Mo 0.92 W 0.015

Mn

Tc 7.8 Re 1.7

Fe

Ru 0.49 Os 0.66

Co

Rh

Ir 0.11

V//A

fay,

w.

Pt Cu

Ag

Au Zn 0.86 Cd 0.52

Hg 4.15 3.95 Fig. 1 : Superconducting temperatures of transition metals at 1 atm. or at high pressure (values in brackets) and ability for hydride formation (hatched fields).

The numbers below the elements indicate the criti- cal temperatures of superconductivity of the"pure metals with maximum values for the fifth and the

seventh group. The hatched fields indicate those

Fig. 2 : Schematic phase diagrams for hydrides at equilibrium conditions (a) VD and for a metastable non-stoichiometric solid solution (b) PdH.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786578

C6-

1

396

JOURNAL D E PHYSIQUE

Above about 100

-

3 0 0 ' ~ t h e metal can absorb hydro- e f f e c t changes from normal t o r e v e r s e 1 3 1 . A t low gen o r deuterium i n t h e a-phase up t o a concentra-

t i o n of about one hydrogen p e r m e t a l atom w i t h a random d i s t r i b u t i o n of t h e hydrogen atoms a t t h e i n - t e r s t i c e s . A t lower temperature s e v e r a l m i s c i b i l i t y gaps occur between o r d e r e d phases. A t very low tem- p e r a t u r e s , which a r e o f p a r t i c u l a r i n t e r e s t f o r su- p e r c o n d u c t i v i t y , only c e r t a i n s t o i c h i o m e t r i c com- pounds can e x i s t a t e q u i l i b r i u m c o n d i t i o n s a s i t i s shown i n t h e schematic VD-phase diagram i n f i g u r e 2a. I n o t h e r systems l i k e t h e palladium-hydrogen phase diagram a non-stoichiometric s o l i d s o l u t i o n remains m e t a s t a b l e w i t h i n t h e approximate concentra- t i o n range PdH0.6 t o PdH ( f i g u r e 2b). I n such metas- t a b l e systems t h e superconducting behaviour changes c o n t i n u o u s l y o t h e r w i s e d i s c o n t i n u o u s l y .

There a r e f o u r p o s s i b i l i t i e s f o r such a change, a s a r e o u t l i n e d i n f i g u r e 3 f o r some t e r n a r y compounds : t h e c r i t i c a l temperature can d e c r e a s e w i t h i n c r e a - s i n g hydrogen c o n t e n t o r i t i n c r e a s e s a t a c e r t a i n composition and it a l s o can have a maximum o r a minimum v a l u e i n between.

H f j / H o w p d n

VHo 5 ,,NbHo75

Hf HfV2 V W Rh Pd Ag Pd WNb Nb

La- H Pd-H(rl Pd-Cu-H(n,r) Pd-NI-Hlr)

Ti+. Zr-H Pd-Rh-H(r) Pd-Ag-H(n.r) Pd-Ti-H V-H. Nb-H.To-H Pd-Pt-H Pd-Au-H Pd-Nb-H

TiB Au-H (n.s.1 Nb-Ru-H Pd-Ru-H

Hf Vz-H(n) Nb-Rh-H

(Th -H) F i g . 3 : S u p e r c o n d u c t i v i t y of b i n a r y and t e r n a r y hy- d r i d e s and d e u t e r i d e s w i t h normal i s o t o p e e f f e c t (n) o r r e v e r s e i s o t o p e e f f e c t ( r ) . Some examples of t e r - n a r y systems w i t h a change of Tc a l o n g t h e dashed

l i n e s a r e given i n t h e upper p a r t .

Some t e r n a r y systems a r e sketched w i t h a change of Tc a l o n g t h e dashed l i n e l i k e Hf Yp charged w i t h H, PdRhH, PdAgH and PdNbH. Usually one o b t a i n s d i f f e - r e n t v a l u e s i f hydrogen i s r e p l a c e d by deuterium.

This i s r e f e r r e d t o a s t h e normal i s o t o p e e f f e c t a s i n d i c a t e d by a

n

a s f o r HfV2-H, i f Tc i s lower f o r t h e d e u t e r a t e d sample. The r e v e r s e i s o t o p e e f f e c t i s o b t a i n e d i f T, i s h i g h e r f o r t h e d e u t e r a t e d sample a s i n d i c a t e d by a

r

a s f o r PdH system. I n some systems l i k e Pd-Ag-H and Pd-Cu-H, t h e i s o t o p e

s i l v e r c o n t e n t of t h e a l l o y Tc of t h e d e u t e r a t e d sample i s h i g h e r , a t h i g h e r s i l v e r c o n t e n t it i s lower than f o r t h e h y d r i d e . The a c t i n i d e element tho- rium may a l s o b e included and e x h i b i t s a d i s c o n t i - nuous change of Tc w i t h a minimum. Thorium m e t a l i s superconducting below 1.4 K, ThH2 i s n o t supercon- d u c t i n g above 1.2 K and ThH3,75 hecomes superconduc- t i n g below about 8 K. No i s o t o p e e f f e c t was found f o r t h i s compound w i t h i n t h e experimental u n c e r t a i n - t y / I / .

The t h e o r i e s f o r t h e s u p e r c o n d u c t i v i t y of h y d r i d e s were mainly developed f o r palladium a l l o y s . One con- d i t i o n f o r o b t a i n i n g superconducting h y d r i d e s seems t o b e t h e quenching of s p i n f l u c t u a t i o n s . Palladium m e t a l f o r example i s paramagnetic. The s u s c e p t i b i l i -

t y

^{i s} decreased by a d d i t i o n of hydrogen and a l s o by a l l o y i n g w i t h s i l v e r . At about t h e composition PdHo,7 i t becomes superconducting w i t h a T i n c r e a s i n g with hydrogen c o n t e n t t o about 9 K i n t h e b i n a r y and t o a maximum v a l u e of about 15.6 K a t t h e composition Pdo,70Aga,soHo,s of t h e t e r n a r y system 131. I n t h e b i n a r y Pd-Ag a l l o y t h e s p i n f l u c t u a t i o n s a r e a l s o quenched above about 60 a t % s i l v e r b u t i t does not be- come superconducting. From t h i s one might conclude that t h e r e should be an a d d i t i o n a l c o n d i t i o n f o r super- c o n d u c t i v i t y . From McMillan's formula f o r Tc i n t h e form given by Dynes / 4 / one might conclude t h a t electron-phonon coupling w i t h a c o u s t i c a l o r o p t i c a l phonons i s important f o r s u p e r c o n d u c t i v i t y .

w i s t h e phonon frequency,

X

t h e phonon induced a t t r a c t i v e e l e c t r o n - e l e c t r o n coupling and vx t h e p a i r b r e a k i n g Coulomb p s e u d o p o t e n t i a l which i s usu- a l l y about 0.1 f o r superconductors. The o p t i c a l and t h e a c o u s t i c a l branch of t h e phonon s p e c t r a a r e w e l l s e p a r a t e d i n h y d r i d e s because of t h e d i f f e r e n t mas- s e s of t h e metal and hydrogen atoms. The o p t i c a l phonons can be r e l a t e d t o t h e metal hydrogen bonding t h e a c o u s t i c a l t o metal-metal i n t e r a c t i o n s . Roughly speaking t h e r e a r e t h r e e k i n d s of e x p l a n a t i o n s f o r t h e superconductivity of h y d r i d e s :

A t t h e f i r s t p o s s i b i l i t y mainly t h e a c o u s t i c a l pho- nons a r e c o n s i d e r e d t o be e n f o r c e d by t h e introduc- t i o n of hydrogen i n t o t h e metal l a t t i c e ,

-

t h a t i s e i t h e r t h a t t h e metal-metal d i s t a n c e d e c r e a s e s by i n t r o d u c i n g small m e t a l l i c hydrogen / 5 / o r by cou- p l i n g between a c o u s t i c a l phonons and d - e l e c t r o n s /6/ o r s p e l e c t r o n s

171,

o r

-

c o n s i d e r i n g t h e i s o - tope exchange of H by D

-

t h e volume c o u l d change

because of a s m a l l e r z e r o p o i n t motion 181, o r

-

c o n s i d e r i n g a l l o y s l i k e t h e t e r n a r y system PdAgH

-

a volume change could l e a d t o d i f f e r e n t o s c i l l a - t i o n s of hydrogen atoms 191. However t h e r e a r e se- v e r a l reasons t h a t i n d i c a t e t h a t t h e a c o u s t i c a l phonons a r e n o t s o important i n hydride systems.

One major p o i n t i s t h e n e g a t i v e p r e s s u r e e f f e c t of PdH

-

t h a t means w i t h i n c r e a s i n g p r e s s u r e t h e vo- lume d e c r e a s e s and t h e metal-metal i n t e r a c t i o n should i n c r e a s e . T however d e c r e a s e s i n s t e a d of i n c r e a s i n g 131.

Another p o s s i b i l i t y i s t h e coupling between o p t i c a l phonons and t h e e l e c t r o n s . Because of t h e r e l a t i o n between o p t i c a l phonons and metal hydrogen bonding Ganguly / l o / reduced t h e formula of Dynes t o t h e e x p r e s s i o n

-

1 Tc

= <

^exp

^(-1

Elf1

where f i s t h e f o r c e c o n s t a n t , M t h e e f f e c t i v e mass and C i s an e l e c t r o n i c f a c t o r which i s c o n s i d e r e d t o be c o n s t a n t by Ganguly. A h i g h Tc should b e o b t a i n e d f o r small f v a l u e s because of t h e exponen- t i a l f u n c t i o n . The h i g h e r Tc of t h e d e u t e r a t e d p a l - ladium sample was r e l a t e d t o a s m a l l e r f o r c e cons- t a n t due t o anharmonic v i b r a t i o n s / l o / . An anharmo- n i c i t y was a l s o p o s t u l a t e d f o r t h e t e r n a r y system PdAgH w i t h an asymmetric neighborhood of t h e hydro- gen atoms / 1 1 / . The n e g a t i v e p r e s s u r e e f f e c t was e x p l a i n e d by t h e s t i f f e n i n g of t h e f o r c e c o n s t a n t 131. For PdH an anharmonic p o t e n t i a l a l o n g

P

^{1 0 1}

d i r e c t i o n was found e x p e r i m e n t a l l y 1121.

Other a u t h o r s r e l a t e a change of f t o d i f f e r e n t e l e c t r o n i c p r o p e r t i e s . M i l l e r and S a t t e r t h w a i t e 1131 concluded f o r t h e i s o t o p e e f f e c t of PdH t h a t t h e s m a l l e r motion of deuterium c a u s e s a s m a l l e r overlapp of wave f u n c t i o n s between Pd and D. The a d d i t i o n a l e l e c t r o n s i n c r e a s e t h e Fermi energy and cause a h i g h e r T

.

For PdAgH system an i n c r e a s i n g e l e c t r o n d e n s i t y a t t h e hydrogen atom was conside- r e d f o r i n c r e a s i n g H o r Ag c o n t e n t 1141. I n PdD a h i g h e r e l e c t r o n d e n s i t y t h a n i n PdH was found by N M R 1151.

The l a t t e r two groups of t h e o r i e s can e x p l a i n w e l l t h e s u p e r c o n d u c t i v i t y and t h e i s o t o p e e f f e c t of PdH b u t t h e r e a r e some d i f f i c u l t i e s f o r t e r n a r y systems where T h a s a maximum o r a minimum and f o r t h o s e

systems where t h e r e v e r s e i s o t o p e e f f e c t changes t o normal w i t h t h e composition of t h e a l l o y .

A t t h e LT 15 conference i n Grenoble a sirnple'model was p r e s e n t e d which can b e c o r r e l a t e d t o t h e s e theo- r i e s b u t has some new a s p e c t s , which can be summa-

r i z e d s h o r t l y i n two t h e s e s :

( 1 ) Hydrides w i t h s m a l l thermal s t a b i l i t y have

s m a l l f o r c e c o n s t a n t s and a r e f a v o u r a b l e f o r super- c o n d u c t i v i t y .

( 2 ) There e x i s t s a q u a l i t a t i v e r e l a t i o n between f r e e energy of h y d r i d e f o r m a t i o n and t h e e l e c t r o n e - g a t i v i t y o r e l e c t r o n work f u n c t i o n of t h e m e t a l . The f i r s t p o i n t might b e e x p l a i n e d by f i g u r e 4 , where t h e hydride f o r m a t i o n i s considered i n t h r e e

s t e p s of a t h e o r e t i c a l p r o c e s s 1161.

F i g . 4 : T h e o r e t i c a l p r o c e s s of t r a n s i t i o n metal h y d r i d e formation (D d i s s o c i a t i o n energy of HZ, 6A volume work of t h e metal and t h e gas phase, 6 (I-E) p a r t i a l c o n t r i b u t i o n of i o n i s a t i o n energy and e l e c t r o n a f f i n i t y , M Madelung l a t t i c e energy CFE c r y s t a l f i e l d energy, AEkin k i n e t i c energy-of H atoms).

We s t a r t on t h e l e f t s i d e w i t h N moles of HZ gas and a p i e c e of m e t a l w i t h t h e volume VM. I n a f i r s t endothermic s t e p of t h i s t h e o r e t i c a l p r o c e s s t h e metal l a t t i c e g e t s expanded by AV. Hydrogen disso- c i a t e s and t h e volume i s changed i n such a way t h a t t h e volume of t h e gas and t h e m e t a l phase a r e t h o s e of t h e h y d r i d e a f t e r t h e r e a c t i o n . I n a second s t e p t h e hydrogen atoms a r e allowed t o d i f f u s e i n t o t h e channels of t h e expanded m e t a l l a t t i c e s i m i l a r a s i n t h e Gay-Lussac experiment f o r i d e a l g a s e s w i t h no i n t e r a c t i o n s w i t h t h e m e t a l . I n a t h i r d s t e p t h e i n t e r a c t i o n between hydrogen and t h e m e t a l i s c o n s i d e r e d , which i s an exothermic p r o c e s s . The hydrogen atoms can g a i n e l e c t r o n d e n s i t y o r can l o o s e i t . For b o t h p r o c e s s e s p a r t i a l c o n t r i b u t i o n s t o t h e i o n i s a t i o n energy and e l e c t r o n a f f i n i t y must b e considered. The hydrogen and t h e metal atoms change t h e i r e f f e c t i v e charge which l e a d s t o a g a i n of Madelung l a t t i c e energy and c r y s t a l f i e l d energy. By t h e s e i n t e r a c t i o n s between t h e H atoms and t h e metal l a t t i c e t h e h y d r i d e g e t s s t a b l e w i t h a n e g a t i v e v a l u e f o r t h e f r e e energy of formation.

T h i s c o n t r i b u t i o n i s considered f u r t h e r on f i g u r e 5 , where t h e e l e c t r o n d e n s i t y f o r m e t a l s w i t h d i f - f e r e n t e l e c t r o n e g a t i v i t i e s i s sketched. The e l e c - t r o n e g a t i v i t y o r t h e e l e c t r o n work f u n c t i o n of t h e

C6-1398

JOURNAL DE PHYSIQUE elements give qualitatively the tendency to exchange

electrons from the hydrogen to the metal atoms.

, , i _{I ,} 8 ,

M H M M H M M H M

oct t e t

-

Coulomb energy

-

electronegat~v~ Cwlomb energy ty temperature ---c

concentrat~on +

soto ope exchange-

Fig.

5

: Schematic drawing of the electron density distribution in transition metal hydrides at diffe- rent electronegativity, H concentration, temperatu- re and at an isotope exchange.

There is very few exchange at about equal electro- negativity values of hydrogen and the metal, only a little Coulomb energy is gained. In that case, the bonding between metal and hydrogen is weak and has a small force constant, which is supposed to be fa- vourable for superconductivity. At large electrone- gativity values of the metal the hydrogen atoms loose some charge

6,

at low values they gain some.

In both cases the Coulomb energy increases. Because of the non-spherical distribution of the d orbitals of transition metals, crystal field energy is also gained. The electron density of the metal d-orbitals is higher at octAhedral interstices than at tetrahe- dral interstices as was discussed in a former inves- tigation 1171. Therefore octahedral sites are pre- ferred by hydrogen atoms with a partial positive charge, otherwise hydrogen with a partial negative charge is repelled to tetrahedral sites. The elec- tronegativity however is no constant value but depends slightly on temperature, concentration and isotope exchange. With increasing temperature, in- creasing hydrogen concentration or by exchange of H by

D

the effective positive charge at the hydro- gen atoms decreases and/or the electron concentra- tion nearby the

D

atoms increases because of the smaller thermal motion. Both lead to the same effect as a smaller electronegativity of the metal (figure 5 ) .

At figure 6 the relation between free energy of hy- dride formation and electronegativity is shown.

Metals with small electronegativity like La, Zr, Hf, Ti, Nb, Ta have

H&-

at tetrahedral sites. The stability decreases with increasing electronegati- vity of the elements. At high electronegativity like for Cu, Cr, Mo, Ni and Pd

H&+

occupies octahe- dral sites. The stability of the hydride increases

with increasing electronegativity.

A G (kcallmole M x H I

0

-

Hf V 2 H I n )

-

P-VH05ins l

TaH i n s )

at at

octahedral sates

W N b H W Ru H

Pd T I H W R h H l r l N b R h H P d N f H I r l s~tes TI^ Au H2 ~ ( n s Pd AU H

3 L 5 6 ~ ' ( v o l t l

-

chonge of Coulomb ~nteracttons w ~ t h lncreaslng

-

temperature,H concentrat~on or HID Isotope exchange

Fig.

6

: Variation of the free energy of hydride formation for transition metals with different electronegativities

4%

correlated to a reverse iso- tope effect of superconductivity (r) for metals with high

4'

and normal isotope effect (n) at low

@*,

^{(n. s. =} not s~~erconducting)

.

The best superconductor should be found at small thermal stability with small interaction between metal and hydrogen and small force constants.

An

exchange of hydrogen by deuterium should decrease the force constant for the elements at the right side leading to a reverse isotope effect which is indicated by a

r .

For metals with low electronega- tivity the isotope exchange leads to a stronger force constant where the normal isotope effect can be expected as for HfVz-H. If the Coulomb interac- tion is too large with stronger force constants the hydrides are not superconducting like LaH2, ZrH2, TiH2, niobium hydrides, TaH and B-VHo.~. In between are listed those alloys containing a metal with low electronegativity and one with a high va- lue like TisAu, Nb-Rh etc. Usually the electronega- tivity of an alloy changes with the composition and should cause an inversion of the isotope effect Only for PdCuH and PdAgH the isotope effect was measured. For both systems Tc has a maximum and the isotope effect changes from normal to reverse.

In the system Pd-Cu-H the highest Tc of hydride systems was found by Stritzker with about 16.6 K 131.

Because of these relations between small Coulomb interactions and superconductivity we had searched for new superconducting hydrides at the middle af the field and had found VH2 with a Tc (midpoint) of

3.9 K

/18/. In VHz the vanadium atoms form a fcc lattice similar as palladium, the H atoms however are at tetrahedral sites, VDP exhibits a

0

= 4.215

1

compared t o a = 4 . 2 3 6 A f o r VH2 because of t h e i n c r e a s e d Coulomb i n t e r a c t i o n and had no su- perconducting t r a n s i t i o n above 1.5

K.

I n t a b l e I some f o r c e c o n s t a n t s a r e l i s t e d which were c a l c u l a t e d w i t h t h e two mass model because of weak coupling a t l a r g e mass d i f f e r e n c e s 1161. There a r e small v a l u e s f o r PdH w i t h a r e v e r s e i s o t o p e e f f e c t and f o r 6-VH and l a r g e r v a l u e s f o r t h e o t h e r elements. These v a l u e s show t h a t t h e r e i s only a q u a l i t a t i v e r e l a t i o n and t h a t t h e f o r c e c o n s t a n t s f o r example might a l s o depend on c r y s t a l s t r u c t u r e . Table I : MH-force c o n s t a n t s from f = 0.59

MH (v/ 1000)

PdH PdD B-VH 8-VD a-VH a-VD a-TaH 8-NbH NbHz T i H l . 6

TiH2 Z r H 2

There a r e o t h e r s i m i l a r r e l a t i o n s f o r t h e mean squa- r e amplitude of hydrogen o s c i l l a t i o n , f o r t h e a c t i - v a t i o n energy of d i f f u s i o n and t h e volume expansion a s i t i s o u t l i n e d i n f i g u r e 7

1161.

I n h y d r i d e s w i t h s m a l l f o r c e c o n s t a n t s t h e hydrogen atoms usual-

l y have a l a r g e mean s q u a r e amplitude of o s c i l l a - t i o n . I f t h e r e a r e s m a l l Coulomb i n t e r a c t i o n s b e t - ween t h e metal and t h e hydrogen atoms t h e a c t i v a t i o n energy of hydrogen d i f f u s i o n i s s m a l l . VH2 and PdH have t h e s m a l l e s t a c t i v a t i o n energy of f c c m e t a l s , a-VH t h e s m a l l e s t f o r a bcc l a t t i c e . The a c t i v a t i o n e n e r g i e s e x h i b i t t h e same i s o t o p e e f f e c t s a s super- c o n d u c t i v i t y . Metals w i t h small e l e c t r o n e g a t i v i t y show t h e normal i s o t o p e e f f e c t w i t h a h i g h e r a c t i - v a t i o n energy f o r t h e d e u t e r a t e d sample l i k e a-VH, Ta and Nli h y d r i d e s , t h o s e w i t h h i g h e r e l e c t r o n e g a - t i v i t y t h a n jV l i k e Cu, N i and Pd e x h i b i t t h e r e v e r s e i s o t o p e e f f e c t w i t h a s m a l l e r value. At high tempe- r a t u r e s of about 500 ^{O C} t h e i s o t o p e e f f e c t dimini- s h e s , probably because of t h e r e l a t i v e l y s m a l l crys- t a l f i e l d s t a b i l i z a t i o n . The r e l a t i v e volume

expansion h a s no maximum b u t can b e r e l a t e d q u a l i t a -

t r o n e g a t i v i t y t h e metal t a k e s more e l e c t r o n s from t h e hydrogen atoms and expands more.

02A-

mean square amplitude of H oscrllat~on

0

energy of

U \ K C U I I

diffusion

L.

Zr Hf TI Nb Ta V Pd electronegat~vlty

- ^HID

soto ope exchange

-

F i g . 7 : Sketch f o r t h e v a r i a t i o n of t h e mean square amplitude of H o s c i l l a t i o n , t h e a c t i v a t i o n energy of d i f f u s i o n and t h e r e l a t i v e volume expansion w i t h e l e c t r o n e g a t i v i t y and a t an i s o t o p e exchange.

D e u t e r i d e s u s u a l l y have a s m a l l e r volume t h a n hydri- des. This r e l a t i o n shows t h a t t h e occupation of H a t t e t r a h e d r a l o r o c t a h e d r a l i n t e r s t i c e s of t h e metal l a t t i c e i s no s i z e e f f e c t b u t depends on crys- t a l f i e l d s t a b i l i z a t i o n .

Another i s o t o p e e f f e c t . c a n b e found by comparison of h y d r i d e and d e u t e r i d e phase diagrams. T r a n s i t i o n m e t a l s w i t h low e l e c t r o n e g a t i v i t y l i k e Nb and Ta e x h i b i t a m i s c i b i l i t y gap o f t h e a-phase below PI

( f i g u r e 2) a t about 10

-

2 0 ' ~ h i g h e r temperatures f o r D t h a n f o r H s o l i d s o l u t i o n /20/. T h i s can be a t t r i b u t e d t o t h e l a r g e r c r y s t a l f i e l d s t a b i l i z a - t i o n of o r d e r e d MD phases. Metals w i t h h i g h e l e c t r o - n e g a t i v i t y l i k e Pd and N i show a r e v e r s e e f f e c t w i t h a lower temperature v a l u e of PI f o r t h e deute- r a t e d sample, because of t h e decreased thermodyna- mic s t a b i l i t y . The VH and VD systems e x h i b i t d i f f e - r e n t phase diagrams w i t h d i f f e r e n t c r y s t a l s t r u c t u -

C6- 1400 ^JOURNAL

^{D E}

^PHYSIQUE

res, where H or D can occupy tetrahedral or octahe- References dral sites /16/. At the composition VHo.5 or VD0.5

octahedral interstices are occupied in the ordered compounds, but change to tetrahedral in the a-phase with random distribution at about 440 and 405 K, resp. This large isotope effect can be explained by addition of two effects in the ordered and the di- sordered phase. 8-VDoe5 with octahedral occupancy has a lower crystal field stabilization than 8-VDo.5, the disordered a-VD however has a stronger crystal field stabilization than a-VH. Therefore a-VD stays stable at lower temperatures than a-VH.

At higher deuterium concentrations deuterides with an occupancy of tetrahedral sites are formed at the composition VDo.75,VD and VD2 (figure 2a). In contrast to this hydrogen occupies octahedral sites in different phases with the composition VHo.67and probably VH and changes to tetrahedral occupancy only at the composition VH2 1201. The different behaviour of H and D in vanadium can be explained qualitatively by small changes of the crystal field stabilization which is leading to a preference of tetrahedral sites with increasing temperature, H or D concentration and at the exchange of H by D as it was outlined in figure 6 1161.

It was the aim of this investigation, to show that there are some qualitative relations between diffe- rent physical properties like superconductivity, thermodynamic stability, the activation energy of diffusion, optical phonons, mean square amplitude of H oscillation and the relative volume expansion.

/I/ Satterthwaite, C.B. and Toepke, I.L., Phys.Rev.

Lett. 3 (1970) 741.

/2/ Skoskiewicz, T., Phys. Stat. Sol. (a) 11 (1972) K123.

/3/ Stritzker, B., and ~iihl, H., "Superconductivity in Metal-Hydrogen Systemst' in Topics in Applied Physics (G. Alefeld, ed.) 1978

/4/ Dynes, R.C., Solid State Commun. 10 (1972) 615.

151 Auluck, S., Lett. Nuovo Cimento 7 (1973) 545.

161 Bennemann, K.H. and Garland, J., Z. Physik 260

(1973) 367.

/7/ Hertel, P., Z. Physik 268 (1974)

1 1 1 .

181 Nakajima, T., Phys. Stat. Sol. (b) 11 ⁽¹⁹⁷⁶⁾

K147.

191 Gomersall, I.R. and Gyorffy, B.L., J. Phys. F

:

Metal Phys. 2 (1973) L138.

/I01 Ganguly, B.N., Z. Physik 265 (1973) 433 and B22

(1975) 127.

/Ill Burger, J.P. and MacLachlan, D.S., J. de Physi- que 37 (1976) 1227

1121 Drexel, W., Murani, A., Tocchetti, D., Kley,W., Sosnowska, I., and Ross, D.K., J. Phys. Chem.

Solids 37 (1976) 1135.

1131 Miller, R.J. and Satterthwaite, C.B., Phys.Rev.

Lett. 24 (1975) 144.

1141 Klein, B.M., Economou, E.N. and Papaconstanto- poulos, D.A., Phys. Rev. Lett. 39 (1977) 574.

1151 Jena, P., Wiley, C.L. and Fradin, F.Y., Phys.

Rev. Lett. 5 (1978) 578.

1161 Hauck.J., Proc. 2nd Int. Conf. Hydrogen in Me- tals, Paris 6-10 June 1977, Abstr. IDI.

1171 Hauck, J. and Schenk, H.J., J. Less-Common Me- tals 2 (1977) 251.

1181 Hauck, J., J. de Physique Colloq. 39 (1978) C6-426.

The isotope effect is a very sensitive indicator of 1191 Hauck, J. in "Crystal Field Effects in Metals this, if other factors like temperature, H-concen- and Alloys" A. Furrer, ed.) (Plenum Publ. Corp)

1977 p. 239.

tration and crystal structure remain unchanged. On

/20/ Hauck, J., Acta Cryst. (1978) 389.

the search for new superconducting hydrides mate-

rials with small Coulomb interactions seem to be

favourable. A small Coulomb interaction can be

estimated for materials with low thermodynamic sta-

bility, small activation energy of diffusion, large

mean square amplitude of H oscillation and small

optical phonon energies.