Transition Metal Hydrides - American Chemical Society

19 Electronic Structure of Transition Metal Hydrides ALFRED C. SWITENDICK

Downloaded by RUTGERS UNIV on March 12, 2016 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/ba-1978-0167.ch019

Sandia Laboratories, Albuquerque, NM 87115

Metal hydrides form crystalline solids of various types ranging from ionic crystals through semiconductors to metals. They also can be considered as perhaps the simplest example of a class of solid state systems called interstitial alloys wherein a nonmetallic element (hydrogen) is incorporated into an empty hole in a simple metal lattice. The effect of this incorporation on the structure and electronic properties of the metal has been investigated theoretically using the solid state counterpart of molecular orbital theory-band structure theory. Results of these calculations are given for a prototype dihydride system TiH and the well-studied monohydride PdH. In particular, the nature of the metal-hydrogen bond and hydrogen-hydrogeninteractions are elucidated. 2

T

he incorporation of h y d r o g e n into metal lattices leads to f o r m a tion of m e t a l - h y d r o g e n compounds called metal hydrides. T h e properties of these systems have been discussed i n numerous monographs and review articles ( i , 2 , 3 ) . S i m i l a r l y a n u m b e r of theoretical papers have been w r i t t e n about the change i n electronic properties i n d u c e d b y hydrogen i n various m e t a l lattices (4-11). In this chapter, some of these theoretical results w i l l be s u m m a r i z e d . In particular, the nature of the b o n d i n g between the h y d r o g e n a n d the metal (hydrogen) w i l l be examined to assess the factors leading to the stability of these systems. T h e occurrence of transition and rare earth metal hydrides is shown i n F i g u r e 1. N o t shown are the alkali hydrides and alkaline earth d i h y d r i d e s that bear a close resemblence to their halide counterparts. Also not shown are compounds f o r m e d f r o m elements to the right that are the topic of m u c h of the rest of this s y m p o s i u m volume. W e shall address ourselves to the systems shown i n F i g u r e 1 and discuss two particular systems i n detail, showing h o w m a n y of the regularities of these m a terials c a n be understood. G e n e r a l l y speaking, these materials are metals w i t h 0-8412-0390-3/78/33-167-264/$05.00/0 © American Chemical Society

Bau; Transition Metal Hydrides Advances in Chemistry; American Chemical Society: Washington, DC, 1978.

19.

Electronic

SWITENDICK

265

Structure

the exception of the rare earth trihydrides, that become semiconducting. T h e major feature of F i g u r e 1 is the preponderance of d i h y d r i d e s o n the left, w h i c h become increasingly unstable and display competing phases along the line f r o m c h r o m i u m to tantalum.

O n the right, the monohydride of nickel and p a l l a d i u m

f o r m , but p l a t i n u m does not h y d r i d e . These factors are of interest i n terms of an electronic structure model. A distinct d i h y d r i d e phase is the strongest c o n f i r m a t i o n of the m a g n i t u d e of the influence of h y d r o g e n o n the metal systems.

As the m e t a l is exposed to

h y d r o g e n gas, spontaneous uptake occurs w i t h i n the m e t a l lattice. T h i s c o n centration is usually very small but can have strong influence on the mechanical properties, a phenomenon k n o w n as embrittlement.

W i t h further increase of


hydrogen, the metal lattice transforms to a c u b i c close p a c k e d lattice w i t h 1MB

IVB

Sc^

YH2 Y H

ZrH2

VB

VI IB

VH

CrH

(Mn)

(Fe)

(Co)

Ni Η

NbH

(Mo)

(Tc)

(Ru)

(Rh)

PdH

--

--

-

-

(W)

(Re)

(0s)

NbH 2

3

See Rare Earth Series

TaH

Pm HH2_3

C e H

Figure

2-3

1.

PrH 2 _ 3

NdH 2 _ 3

Occurrence

V111Β

VIB

SmH,

EuH,

GdH 2

?

of binary transition

7b H 2

(Ir)

(Pt)

DyH 2

HoH 2

DyH3

HoH 3 E r ^

ErH ? TmH 2

YbH 2

LuH 2

YbH^?) LuH 3

and rare earth metal

hydrides

nominally two hydrogens per metal. In the rare earth systems, trihydride phases are even possible, but w e shall l i m i t this discussion p r i m a r i l y to these d i h y d r i d e phases. V e r y h i g h hydrogen densities can be obtained i n these metals, w h i c h leads to their a p p l i c a t i o n for h y d r o g e n storage a n d for reactor moderator mate rials. As w e indicated earlier a n d as is pointed out i n the recent review article b y M c C l e l l a n and H a r k i n s (12), hydrogen plays a somewhat ambivalent role, as it is both the alkali a n d the halide i n its p e r i o d ; this leads to alternative models for the electronic structure of these systems. In the anion model, the hydrogen states are presumed to lie below the metal states. E a c h state c a n be f i l l e d w i t h t w o electrons, and since the hydrogen only contributes one electron, electrons f r o m the transition metal f i l l the l o w - l y i n g hydrogen states, l o w e r i n g the F e r m i level i n the metal m a n i f o l d . In the proton m o d e l , the h y d r o g e n states are higher i n


266

TRANSITION M E T A L HYDRIDES

energy than the metal states, and the electrons from the hydrogen fill up the metal states.

T h e r e is experimental evidence for both viewpoints, a n d the questions

for a m o d e l become:

where do the states associated w i t h the hydrogen lie a n d

w h i c h states are f i l l e d b y the added electrons? O u r results w i l l be based on the one electron energy b a n d theory of solids (13) that forms the basis for the present-day understanding of metal a n d s e m i conductor physics.

It is the counterpart of the chemist's molecular orbital theory,

a n d we shall try to relate our results back to the u n d e r l y i n g atomic structure.


Results and Discussion W e now turn to the formation of some of these h y d r i d e structures. T h e majority of them are based on a fee array of metal atoms, as shown by the open circles i n F i g u r e 2. T h e d i h y d r i d e structure comes f r o m f i l l i n g the tetrahedral interstice (large solid circles) i n the lattice w i t h hydrogens a n d gives the w e l l k n o w n C a F or calcite structure. Similarly, if one fills the octahedral interstice (small solid circles), one gets the N a C l or rocksalt structure found i n nickel hydride a n d p a l l a d i u m h y d r i d e , w h i c h we w i l l discuss near the end of this chapter. 2

T i t a n i u m D i h y d r i d e . T h e first candidate for study is T i H w h i c h forms a prototype d i h y d r i d e system. F i g u r e 3 indicates schematically what the c a l culations (14) show, w h i c h we w i l l examine further i n some detail. T i t a n i u m atoms are put together to f o r m a m e t a l , starting on the left w i t h the atomic c o n 2

F i g u r e 2. Fee hydride structures. Large open circles represent metal atom positions, solid large circles represent hydrogen atom positions in dihydride structure, small solid circles represent hydrogen atom positions in NiH and PdH.


19.

SWITENDICK

Electronic


Ti atom

0

—

-1.0

—

Ti solid

267

Structure TiH2

H atom/ion

Figure 3. Energy level diagram indicating modification of energy levels of titanium and hydrogen upon formation of titanium dihydride. The diagonally shaded line indi cates the potential between the atoms. figuration d s and w i t h u n o c c u p i e d ρ levels. T h e a t o m i c potentials overlap in the metal; this leads to a lowering of the energy between the atoms. As i n the molecular case, the degeneracy of the isolated atom levels is broken by the for m a t i o n of a variety of b o n d i n g a n d a n t i b o n d i n g states f r o m the 1 0 atomic s, p, and d levels. As i n the molecular case, the accommodation of electrons i n low l y i n g electronic states leads to bonding and cohesion. T h e states broaden about their atomic values, and we have a broad s b a n d now partly below the d states a n d a fairly w e l l - d e f i n e d d band. T h e relative numbers of l o w - l y i n g s and d states and the number of electrons determine the highest filled energy, the F e r m i level. 2

2

2 3

O n the right, we have the levels associated w i t h the h y d r o g e n atom (ion): the Is level at —1 R y d b e r g and the H ~ ion at —0.72 e V . It seems clear that the lowest valence energy of the c o m b i n e d system is associated w i t h the h y d r o g e n


268


Is, that the highest is Is , a n d that some compromise between these extremes w i l l be met i n the solid. T h e h y d r o g e n level shown is d o u b l e d since there are two hydrogens i n each unit cell. As the h y d r i d e forms, the h y d r o g e n Is levels interact with each other to form a bonding and antibonding pair. Also, the overall potential is lowered by the presence of the hydrogens. Interactions with transition metal d s, and ρ electrons are i n d i c a t e d i n the second a n d t h i r d columns. T h e magnitudes of the lowerings are sizeable ( 5 eV). T h e d b a n d m a n i f o l d largely is m a i n t a i n e d . T h e major result is that the h y d r o g e n - d e r i v e d s states are low a n d can be f i l l e d w i t h electrons both f r o m the transition m e t a l a n d f r o m the hydrogen. T h e results of the b a n d structure calculations show i n detail how this comes about. Instead of labels like II, σ, a\ B\ , etc., the three-dimensional periodic nature of the solid defines s y m m e t r y labels that are vectors. These vectors are defined i n the B r i l l o u i n zone that is complementary to the real space unit cell of F i g u r e 2. Instead of plotting 1 0 levels one above the other, we spread t h e m out, g i v i n g quasi-continuous points (lines) £ vs. k. T h e i m p o r t a n t fact is that each line (band) can hold two electrons per unit cell, and the lowest bands are filled first. 2

y


gy

u

2 3

F i g u r e 4 shows our results for fee t i t a n i u m . W e see the l o w - l y i n g states derived from the titanium s states. W e also see the fairly narrow d band structure

0.0 -04 W

Χ

Γ

L

W

Κ

Γ

Journal of the Less-Common Metals

Figure 4. Energy levels (bands) for fee titanium. The symbols at the bottom designate specific values of k (see Figure 2, Ref. II). The Fermi energy is indicated by the horizontal line (14).



19.

Electronic

SWITENDICK

269

Structure

-0.2)-

W

Χ

Γ

L

W

Κ

Γ

Journal of the Less-Common Metals

Figure

5.

Energy bands for titanium dihydride, same remarks as Figure 4(14)

TiH

2

with

d e r i v e d f r o m the atomic d states W 2 ' - W 1 ' , L 1 - L 3 , K 1 - K 2 , a n d X 1 - X 5 . T h e states at zone center k = 0, Γ, of t and e symmetry are those familiar i n ligand field theory, only they are now called Γ25' and Γ12, respectively. F i l l i n g the states of F i g u r e 4 w i t h the four electrons of titanium gives a F e r m i energy i n the 2g

g

lower part of the d complex. F i g u r e 5 shows what happens w h e n we a d d h y drogen i n the tetrahedral site to f o r m the d i h y d r i d e structure. As already i n d i cated, the lowest levels drop. B u t most i m p o r t a n t l y , a new b a n d ( Γ 2 ' at zone center) appears mostly below the d complex; this b a n d is f o r m e d largely f r o m the antibonding combination of hydrogen s levels w i t h some d admixture. This band can be filled w i t h the electrons added by the hydrogen. It is this result that accounts for the occurrence a n d stability of the d i h y d r i d e phase. W e can look at this result another way by plotting line density as a function of energy, the so called density of states as shown i n F i g u r e 6. T h e major feature is the occurrence of the low energy peak that is associated largely w i t h the h y drogens. This peak is observed by Eastman (15) i n photo-emission from a sample of t i t a n i u m exposed to hydrogen where a peak develops below the m a i n d b a n d peak of titanium. H o w e v e r , we can go even further and decompose the density of states according to wave function character around the titanium and hydrogen sites, as shown i n F i g u r e s 7-12. Thus, F i g u r e 7 confirms our earlier statement that the l o w - l y i n g peak is associated w i t h the hydrogens w h i l e F i g u r e s 8 a n d 9 display the b o n d i n g and a n t i b o n d i n g parts of the h y d r o g e n s character, respec-



270

TRANSITION M E T A L

0 . 0

J I l _l L _l I 1^11

5 . 0

10. ENERGY

Figure 6.

0

1 5 . 0

2 0 . 0

C E L E C T R O N - V O L T S D

Density of states for TiH . There are two electrons per spin state. 2

HYDROGEN

S - L I K E

SUM

—!—τ—ι—ι—ι—ι—ι—ι—ι—r—ι—ι—ι—ι——ι—ι—τ

g M I Ε Ν

G Y

5 . 0 ENERGY

Figure

7.

1 0 . 0

1 5 . 0

2 0 . 0

C E L E C T R O N - V O L T S D

Density of states associated with character about the hydrogens

s-like


HYDRIDES

Electronic Structure

SWITENDICK

H Y D R O G E N

B O N D I N G

Fι

~Ί—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι

ι—ι—ι—ι—ι—ι—ι—ι—r

I M


I Ε Ν

-5.0

0 . 0 E N E R G Y

5 . 0

ΥδΓυ

Γ 6 7 0

2 0 . 0

( E L E C T R O N - V O L T S )

Figure 8. Density of states associated with bonding s-like character about the hydrogens

H Y D R O G E N

A N T I B O N D I N G

~i—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι—ι

τ

ι

ι—ι—ι—ι—ι—ι—ι—ι—Γ

I

M I Ε Ν

G Y

l.oL

I - 5 .

0

0 . 0 E N E R G Y

5 . 0

I i ι 1 0 . 0

ι

ι

ι n*i 1 5 . 0

I

I 2 0 . 0

C E L E C T R O N - V O L T S )

Figure 9. Density of states associated with antibonding s-like character about the hydrogens


272

TRANSITION M E T A L


d

- 5 .

0

D E N S I T Y

0 . 0 E N E R G Y

Figure 10.

5 . 0

OF

S T A T E S

1 0 . 0

1 5 . 0

C E L E C T R O N - V O L T S 3

Density of states associated with d-like character

T I T A N I U M τ—r

2 0 . 0

T 2 G

titanium

C H A R G E

ι—ι—ι—ι—ι—ι—ι—r—ι—ι—ι—r

^

ι—ι—ι—ι—ι—ι—ι—ι—r

M I

4 . 0

Ε Ν Ε R G Y

2 3 3 .

0

2 .

0

CL CO LU Ζ Ο

ο

- 5 .

0

0 . 0 E N E R G Y

Figure

11.

5 . 0

1 0 . 0

1 5 . 0

2 0 . 0

C E L E C T R O N - V O L T S )

Density of states of titanium character

tg 2


HYDRIDES

19.

Electronic

SWITENDICK

273

Structure

TITANIUM

EG CHARGE —ι—ι—»

~ι—ι—ι—ι—ι—ι—ι—ι—I

£

ι—ι—ι—r~

M I


Ε Ν

0. 0 L - 5 .

0

0.

ι ιιιι

0

ENERGY Figure

12.

5 .

0

1111 L 1 0 .

0

1 5 .

0

2 0 . 0

CELECTRON-VOLTSD

Density of states of titanium character

e

g


274


tively. F i g u r e 10 shows that the upper three peaks of F i g u r e 6 largely are asso ciated with d character around the titanium. Figure 10 also shows some evidence of d bonding w i t h the hydrogen. Figures 11 and 12 show the t (xy, yz, zx) and e (x — y , Sz — r ) decomposition of the t i t a n i u m d character, respectively. F i g u r e 11 shows that the d b o n d i n g w i t h the hydrogen is exclusively of t character, as is most of the structure i n F i g u r e 10, while most of the occupied states are of e character. These site and character decompositions are useful and serve as further check on the theory when used i n conjunction w i t h spectral probes that are site and character sensitive such as soft x-ray emission a n d absorption and A u g e r spectra. 2g

g

2

2

2

2

2g


g

W e see that these calculations can account for the stability of the d i h y d r i d e structure i n terms of l o w - l y i n g hydrogen states that can be f i l l e d a n d are con siderably detailed i n the explanation of the nature of the interactions between the atomic system. C a n this approach also explain w h y p a l l a d i u m doesn't f o r m a d i h y d r i d e but forms a m o n o h y d r i d e instead (8)?

P a l l a d i u m H y d r i d e . T h e energy b a n d structure for PdH2 is shown i n F i g u r e 13. C o m p a r i s o n w i t h F i g u r e 5 shows the states associated w i t h the a n tibonding hydrogen band (Γ2') now are well above the d manifold, and the added two electrons must be accommodated i n empty d states of p a l l a d i u m and i n these higher a n t i b o n d i n g states above Γ 2 . T h e reason these states are h i g h i n p a l l a d i u m but low i n titanium becomes clear w h e n we recall the energy dependence of the b o n d i n g Σ and a n t i b o n d i n g Σ states of the h y d r o g e n molecule shown in F i g u r e 14. T h e a n t i b o n d i n g states rise more r a p i d l y as the hydrogens come /

β

ίΛ

(Λ CE

-1

c LU

ο

2

3

4

Quantum Theory of Molecules and Solids

Figure

14.

Total energy curves for hydrogen molecule to Ref. 16

according



19.

SWITENDICK

275


Figure 15. Position of state Γ 2 ' relative to Fermi energy Δ = E = Γ 2 ' as a function of tetrahedral hydrogen-hydrogen spacing in dihydride structures 2

F

closer together. T h i s behavior of the a n t i b o n d i n g states i n d i h y d r i d e s also has been observed where Γ 2 ' is low w h e n the hydrogens are far apart, a n d it is e n ergetically favorable to f i l l this b a n d — l a r g e atoms left side of periodic table larger h y d r o g e n - h y d r o g e n spacing. T h i s behavior is s u m m a r i z e d i n F i g u r e 15 where the Δ = E F Γ 2 ' is plotted vs. the tetrahedral-tetrahedral hydrogen spacing or e q u i v a l e n t l y , the m e t a l atoms size R . W e observe that a l l stable d i h y d r i d e s have h y d r o g e n - h y d r o g e n spacing > 2 . 1 4 A a n d Δ > .10, w h i l e the unstable d i h y d r i d e s have h y d r o g e n - h y d r o g e n < 2 . 1 4 A a n d Δ < .10. O f the two borderline cases, v a n a d i u m a n d tantalum, F i g u r e 1 shows V H exists w h i l e T a H does not. T h e validity of various approximations, i n c l u d i n g the lack of self consistency, prevents these results f r o m b e i n g even relatively q u a n t i t a tive. 2

—

m

2

2

2

2

T o introduce our picture of P d H , we again show the energetics as we go from isolated p a l l a d i u m a n d hydrogen atoms to p a l l a d i u m a n d p a l l a d i u m h y d r i d e i n


276


F i g u r e 16.

T h e overall trend of levels going d o w n i n energy is favorable to sta

b i l i t y , as the s level drops to become occupied i n p a l l a d i u m metal a n d d states e m p t y (holes).

F i g u r e 16 also shows significant H-s a n d H - p lowerings such

that unoccupied ρ states i n p a l l a d i u m are lowered a n d w i l l become o c c u p i e d i n PdH.

T h e detailed bandstructures and densities of states are given i n F i g u r e s

Pd

PdH

Η


Pd

Figure 16. Energy level diagram indicating modification of energy levels of palladium and hydrogen upon formation of palladium hydride. Same remarks as those in Figure 3. 17-25. As indicated i n F i g u r e 17, the bandstructure of p a l l a d i u m consists of an almost-full d band X 1 - X 5 , L 1 - L 3 , K 1 - K 2 , overlapped by the s-p band Π — X 4 ' , T l - L 2 , Γ 1 - Κ 1 , w i t h the highest filled state d e t e r m i n i n g the F e r m i energy, E , falling just below the top of the d bands. T h e total density of states for palladium is shown i n F i g u r e 18, where it is seen that the F e r m i energy falls i n a region of high density of states that is r a p i d l y decreasing above it. T h e results of b a n d /

F



19.

SWITENDICK

277


Figure 17. Energy bands for palladium metal. The Fermi energy Epis indicated by the dashed horizontal line.

DENSITY OF S T A T E S

). 0 -5.0

/ 0.0

ENERGY

Figure 18.

1

5. 0

10. 0

τ^^ΓΤ^ 15. 0

, 20.0

CELECTRON-VOLTSD

Total density of states for metal

palladium


278



Figure 20.

Total density of states for hydride

palladium


19.

279


SWITENDICK

HYDROGEN S-LIKE CHARGE

0.50,

r ι ι ι ι ι ι ι ? ι ι ι ι τ ι ι ι ι—ι—r F

τ ι—Γ*Τ"

I M I

5I

>

LU


Γ 0.23L

0.00L -5.0

0.0 ENERGY

5.0

1 10.0 1 1 1 Γ 15.0 I I 1 I— I— 20.0

(ELECTRON-VOLTS)

Figure 21. Density of states associated with s-like character about the hydrogen

PALLADIUM S-LIKE CHARGE t

0.01 -5.0 Figure

22.

t

τ

ι—r—ι—ι—ι—?—ι—ι—ι—ι—ι—ι—ι—ι—ι—rill—r~

. 0.0 5.0 10.0 15.0 ENERGY (ELECTRON-VOLTS) Density palladium

of states associated s-like character

20.0 with


280

TRANSITION M E T A L H Y D R I D E S


structure calculations for P d H are shown i n F i g u r e 19. T h e d - l i k e states ( X 5 , Γ12, Γ25'; L 3 K 2 ) are affected little by the presence of the hydrogen. States h a v i n g s-like character (h) a r o u n d the h y d r o g e n site Γ 1 , L 2 ' , W 2 ' are l o w e r e d significantly. T h i s l o w e r i n g reflects m e t a l s-h, p-h, d-h type interactions as outlined i n F i g u r e 16. In p a r t i c u l a r , the e m p t y states L 2 ' of p a l l a d i u m are lowered 5 e V and become filled i n P d H . This lowering and filling of empty states (as i n the dihydrides) contributes to the formation of P d H and N i H . These states already are filled i n p l a t i n u m a n d presages the lack of P t H f o r m a t i o n i n d i c a t e d i n F i g u r e 1. T h e total density of states for P d H is shown i n F i g u r e 20. A g a i n , the l o w - l y i n g states below the d b a n d are characteristic of h y d r o g e n influence on the host electronic states a n d have been observed i n photoemission (7).

Figure

23.

Density of states associated palladium p-like character

with

H o w e v e r , since these states were largely f i l l e d i n p a l l a d i u m a n d the states asso ciated w i t h L 2 ' contain only about 0.4 electrons, the r e m a i n i n g 0.6 electron is accommodated: 0.36 electron i n the d b a n d holes a n d 0.24 electron go to i n creasing the F e r m i energy such that the state density is m u c h lower i n P d H than i n P d but not as low as P d + 1 electron. C o m p a r i s o n of F i g u r e s 17 a n d 19 a n d Figures 18 and 20 indicates several similarities as well as considerable differences i n detail. As before, the total density of states can be b r o k e n d o w n into site a n d wavef unction character to better reveal the details of the h y d r o g e n - p a l l a d i u m interaction. F i g u r e 21 shows hydrogen s-like character contributing to the lowest peak as well as being present and increasing (while the total is decreasing) at the F e r m i energy. These latter facts have explained the occurrence of supercon-



19.

SWITENDICK

Figure


24. Density of states associated palladium t2 -like character

281

with

g

Figure 25. Density of states associated with palladium e -like charge in palladium hydride g


282


ductivity in P d H (17) while their antibonding nature and arguments, similar to those in discussing Figures 14 and 15, can account for the pressure dependence of T (18). Figure 22 shows states with s-like character around the palladium c

showing sizeable evidence of s-h interaction associated with the lowest peak. This is also seen in Figure 23 for the palladium ρ character. 24 and 25 show the t

2g

spectively.

Finally, Figures

and e d character associated with the palladium, re g

This time, the hydrogen interacts primarily with the e d-character g

overlap, which the octahedral site occupancy in P d H favors.


Conclusions In conclusion, calculations for metal hydride systems have shown evidence of sizeable metal-hydrogen and hydrogen-hydrogen interactions. Stable hydride formation is favored by filling energetically low states. The more of these that are empty in the metal, the better. The added electrons should go into states associated with the hydrogen and not in states associated with the metal (at Ε ρ — h i g h and empty). We also have seen that detailed wavef unction infor mation can be derived from such calculations, which can help put the results on a firmer basis.

Literature Cited 1. Lewis, F. Α., "The Palladium Hydrogen System," Academic, London, 1967. 2. Libowitz, G. G., "Solid State Chemistry of Binary Metal Hydrides," W. A. Benjamin, Inc., New York, 1965. 3. Mueller, W., Blackledge, J. P., Libowitz, G. G. Eds. "Metal Hydrides," Academic, 1968. 4. Switendick, A. C., Solid State Commun. (1970) 8, 1463. 5. Ibid. (1970) 34. 6. Switendick, A. C., Int. J. Quantum Chem. (1971) 5, 459. 7. Eastman, D. E., Cashion, J. K., Switendick, A. C., Phys. Rev. Lett. (1971) 27, 35. 8. Switendick, A. C., Ber. Bunseges. Phys. Chem. (1972) 76, 535. 9. Switendick, A. C., "Hydrogen in Metals—A New Theoretical Model," Hydrogen Energy, Part B, T. N. Veziroglu, Ed., Plenum, New York, 1975. 10. Gelatt, C. D. Jr., Weiss, J. Α., Ehrenreich, H., Solid State Commun. (1975) 17, 663. 11. Zbasnik, J., Mahnig, M., Z. Phys. (1976) 23, 15. 12. McClellan, R. B., Harkins, C. G., Mater. Sci. Eng. (1975) 18, 5. 13. Callaway, J., "Energy Band Theory," Academic, New York, 1964. 14. Switendick, A. C., J. Less Common Met. (1976) 49, 283. 15. Eastman, D. E., Solid State Commun. (1972) 10, 933. 16. Slater, J. C., "Quantum Theory of Molecules and Solids," Vol. 1, McGraw-Hill, New York, 1963. 17. Papaconstantopoulos, D. Α., Klein, Β. M., Phys. Rev. Lett (1975) 35, 110 18. Switendick, A. C., Bull. Am. Phys. Soc. (1975) 20, 420. R E C E I V E D October 5, 1977. This work was supported by the United States Energy Re search and Development Administration, ERDA, under Contract AT(29-1)789.


Transition Metal Hydrides - American Chemical Society

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