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VIBRATIONAL PROPERTIES OF HYDROGEN IMPURITY IN HIGH-PRESSURE PALLADIUM DEUTERIDE Kuzovnikov M.A. ISSP RAS, Chernogolovka kuz@issp.ac.ru Local vibrations of a light-atom defect chemically identical to heavy atoms of the host lattice were experimentally studied only once in the work of ref. [1], in which a solid solution of 3.7 at.% H in PdD0.6 was investigated by inelastic neutron scattering (INS). The experiment demonstrated the occurrence of a local-mode peak shifted beyond the band of optical vibrations of the D atoms. No other details of H or D vibrations could be seen in the INS spectrum because it was broadened due to the non-stoichiometric composition of the deuteride. Homogeneous samples of stoichiometric PdD and PdH can only be prepared at high pressures. The present work reports on an INS study of three PdD1-x Hx powder samples with x = 0.050, 0.072 and 0.091 synthesised in a deuterium-hydrogen atmosphere at P = 50 kbar and T = 600 K. To analyse and interpret the obtained spectra, the lattice dynamics of PdD1-x Hx solid solutions was simulated using the Born-von K`rman model. a` The PdD1-x Hx samples weighing about 2 g each were prepared at ISSP RAS and studied with the IN1-BeF neutron spectrometer at the Institute Laue-Langevin in Grenoble. The background from the sample holder and cryostat was separately measured under similar conditions and subtracted from the INS spectra. The resulting INS spectra normalized to the sample weight and the number of incoming neutrons are shown in Fig. 1. The optical spectra in Fig. 1 can formally be split into the contribution SPdD from the undisturbed PdD matrix and the contribution SH resulting from neutron scattering on the H atoms and also the neighbouring D atoms, whose motions are influenced by the H impurity. If the hydrogen content x is low and the interaction among the H atoms is negligibly small, the total scattering intensity S can be written as: S = xSH + (1 - x)S
PdD

Pd D

arb. units

x

1{

x Hx

= 0 .0 5 0 0 .0 7 2 0 .0 9 1

S(Q, !),
0

40

80

!,

meV

120

160

200

Fig. 1. The dynamic structure factor, S (Q, ), of powder PdD1-x Hx samples measured at 5 K using the IN1-BeF neutron spectrometer at ILL, Grenoble. The peaks at 40 and 70 meV are mostly due to the optical vibrations of D and H atoms, respectively. The spurious intensity at energies below 30 meV results from two- and three-phonon scattering of admixed neutrons of half the wavelength in the incoming monochromared beam.
Pd D

.

(1)

From the experimental S spectra written in the form of equation (1) for any two different PdD1-x Hx samples one can get SPdD and SH . Figs. 2 and 3 show these dependences calculated for the pairs of samples with x = 0.05 and 0.091 and with x = 0.05 and 0.072. The calculated two SPdD spectra (Fig. 2) coincide within the line thickness and the two SH spectra (Fig. 3) are close to each other, too. This suggests the applicability of equation (1) to the solid PdD1-x Hx solutions with hydrogen concentrations up to x = 0.091 at least. The SPdD spectrum in Fig. 2 is very similar to the experimental spectrum S (Q, ) of stoichiometric PdH [2] if the latter is plotted as a function of /1.51. The deviation of the scaling factor from the 1

S(Q, !),

arb. units

PdH scaled

!/

1 .5 1

0

40

80

!,

meV

120

160

200

Fig. 2. Solid line: INS spectrum for PdD, extracted from the experimental PdD1-x Hx spectra. Dashed line: INS spectrum for PdH [2], scaled /1.51. harmonic value mD /mH 2 well agrees with earlier estimates [3]. The contribution SH from the H impurity (Fig. 3) proved to have a rather unexpected profile. First, it showed a negative scattering intensity at energies near 35 meV, in the energy range of the main peak


arb. units

x x

H in Pd D = 0 .0 5 0 ; 0 .0 9 1 = 0 .0 5 0 ; 0 .0 7 2

to g (j, ) =
q BZ

( - (j, q ))dq = =
(j,q )=

d2 q , |q (j, q )|

(2)

S(Q, !),

where q is varied over the BZ. Hereafter, the eigenvectors are normalized as j, q : mi |ei (j, q )|2 = 1,
i

0

40

80

!,

meV

120

160

200

Fig. 3. INS spectrum corresponding to H impurity in PdD, extracted from two different pairs of experimental PdD1-x Hx spectra. of D optical vibrations (see Fig. 2). Second, the broad H peak at 70 meV with an intense shoulder towards lower energies demonstrated no tendency to transforming into a narrow local-mode peak with decreasing H concentration in the deuteride. To ascertain the origin of such an unusual profile, we have calculated the lattice dynamics for Pd4 D3 H (x = 0.25), Pd8 D7 H (x = 0.125), Pd16 D15 H (x = 0.0675) and PdD crystals using the Born-von K`rman model. The Pd-Pd, Pd-D and D-D force a` constants were taken from ref. [4]. The constants for H atoms were set equal to those for D atoms. The dispersion curves calculated for PdD without H impurities (NaCl-type cubic crystal structure, space group F mЇm) are shown in Fig. 4. 3
60 50
, meV
ў § ¤

mi being the mass of atom i. To integrate in equation (2), we interpolated (j, q ) linearly within tetrahedrons with vertices at the nearest sampling points chosen so as to completely fill the BZ. The total number of the sampling points varied from 32000 for PdD to 1000­2000 for the PdD1-x Hx structures. Fig. 5 shows the total density of phonon states (phonon DOS) for PdD calculated as g ( ) = g (j, ). One can see that the optic part of g ( )
j

qualitatively reproduce the intensity distribution in the experimental S (Q, ) spectrum of PdD.
) , a rb . u n i t s
0.12

P dD

0.10

g(!), cal S(Q, ! ),

c. exp.

0.08

S( Q , !
) , m eV ;
-1

0.06

0.04

0.02

g( !

0.00 0 10 20

!

30

, m eV

40

50

60

40 30 20 10 0
2

Fig. 5. Solid line: the phonon DOS of PdD calculated using 32000 sampling points in the irreducible BZ. Dashed line: the experimental INS spectrum of PdD from Fig. 2.
2

2

2 X U (K ) Ў L

Ў

The calculated g ( ) spectra of the PdD1-x Hx solutions cannot be directly compared with their experimental S (Q, ) spectra because of the significantly different cross-sections for neutron scattering by H and D atoms. To calculate the S (Q, ) spectra from the g ( ) spectra, we did the following. First, a partial generalized phonon density of Gi (j, ), was computed for each states, Gi ( ) =
j

!
Fig. 4. Phonon dispersion curves for PdD calculated in the Born-von K`rman model using force a` constants from ref. [4]. The numbers indicate the degeneracy; = 1. Eigenvalues 2 (j, q ) and eigenvectors ei (j, q ) for each atom i in the unit cell were calculated for sampling points uniformly distributed over the irreducible part of the Brillouin zone (BZ) and further used to obtain densities of phonon states according 2

atom in the unit cell using Gi (j, )'s calculated as: Gi (j, ) =
q BZ

|ei (j, )|2 ( - (j, q ))dq = =
(j,q )=

|ei (j, )|2 d2 q , | (j, q )|

(3)

Second, the computed Gi ( ) were used to calcu-


7 6 5 4 3 2 1 0 -1 20

a rb . u n i t s

S S

H H

f o r P d D H , ca l c.
4 3

e x p.

30

40

50

!
8

, m eV

60

70

80

90

7 6 5 4 3 2 1 0 -1 20

a rb . u n i t s

S S

H H

f o r P d D H , ca l c.
7

e x p.

30

40

50

7 6 5 4 3 2 1 0 -1 20

S (!

H

),

a rb . u n i t s

S S

!

, m eV

60

70

80

90

H H

f o r P d D H , ca l c.
16 15

e x p.

30

40

50

!

, m eV

60

70

80

90

Fig. 6. Contributions SH (Q, ) to the total dynamical structure factor of the solid PdD1-x Hx solutions due to the presence of H impurity. The dashed curves represent the experimental SH from Fig. 3. The solid curves are results of the model calculations. late the dynamical structure factor S (Q, ) at 0 K according to: S (Q, ) = Q2 2
2

is the Debye-Waller factor for atom i. Finally, using the S (Q, ) spectra calculated for PdD and for each of the three model solutions, Pd4 D3 H, Pd8 D7 H and Pd16 D15 H, the contribution SH due to the H impurity in these solutions was calculated via equation (1). The resulting SH contributions convoluted with the resolution function (a Gaussian with FWHM = 0.05 ) of the IN1-BeF spectrometer are shown in Fig. 6. As seen from Fig. 6, the decrease in the H concentration and, correspondingly, in the H-H interaction leads to a sharpening of peaks in the calculated SH spectra. At the same time, even in the Pd16 D15 H structure with the minimum x = 0.0675, this interaction is strong enough to broaden the peak of local H vibrations over a wide interval of 60­75 meV. Regretfully, none of the calculated spectra in Fig. 6 can quantitatively reproduce the profile of the experimental SH spectrum because of the simple model used [4]. Nevertheless, the calculation confirms and explains some principle features of the SH contribution. One of these features is the broad peak at 40­50 meV. According to the calculation, it originates from the low-frequency modes of co-vibrations of H atoms together with the D atoms. In its turn, the involvement of the D atoms in co-vibrations with the H atoms leads to the increase in their vibrational frequencies. The resulting shift of the main peak of optical D vibrations to higher energies produces a negative scattering intensity near 36 meV in the calculated difference spectra SH . The negative intensity in the experimental SH spectrum is observed at the same energies therefore it is likely to have this very origin. To briefly summarize, three samples of solid PdD1-x Hx solutions with x = 0.050, 0.072 and 0.091 synthesised at high pressures are studied by inelastic neutron scattering. The vibrational spectrum of stoichiometric palladium deuteide has been constructed for the first time. The contribution from H impurity to the vibrational spectrum of PdD is shown to significantly differ from earlier estimates [1]. The main features of the obtained experimental profile of this contribution are explained by simulating the lattice dynamics of the solid PdD1-x Hx solutions using the Born-von K`rman model. a` This work was supported by grant No. 08-0200846 from RFBR and by the Program `Physics of Strongly Compressed Matter' of RAS. 1. 2. 3. 4. Rush J.J, Rowe J.M., Richter D. // Phys. Rev. B 1985. V. 31. No. 9. P. 6102. Ross D. K., Antonov V. E. Bokhenkov E. L., Kolesnikov A. I., Ponyatovsky E. G., Tomkinson J. // Phys. Rev B 1998, V. 58. No. 5. P. 2591. Rush J.J, Rowe J.M., Richter D. // Z. Phys. B: Condensed Matter 1984. V. 5. P. 283. Rahman A., Skold K., Pelizari C., Sinha S.K., and Flotow H. // Phys. Rev. B 1976. V. 14. P. 3630.

S (!

H

),

S (!

H

),

i

i exp(-2Wi (Q))Gi ( ), mi

where i is the total (incoherent and coherent) neutron scattering cross section for atom i and Wi (Q) = Q 12m
2 2 i

Gi ( ) d 3