VIBRATIONS AND DIFFUSION OF ATOMS IN SUPERIONIC CRYSTALS AND MELTS

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VIBRATIONS AND DIFFUSION OF ATOMS IN SUPERIONIC CRYSTALS AND MELTS

R. Elliott, M. Dixon

To cite this version:

R. Elliott, M. Dixon. VIBRATIONS AND DIFFUSION OF ATOMS IN SUPERIONIC CRYSTALS AND MELTS. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-175-C6-177.

�10.1051/jphyscol:1981651�. �jpa-00221587�

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JOURNAL DE PHYSIQUE

CoZZoque C6, supp26ment au n ' 1 2, Tome 42, d&mnbre 1981 page C6-175

V I B R A T I O N S AND D I F F U S I O N OF ATOMS I N SUPERIONIC CRYSTALS AND MELTS

R.J. Elliott and M. Dixon

Department of TheoreticaZ Physics, Oxford University, Oxford, U . K.

Abstract.- Recent computer simulation studies contain sufficient

information about the atomic disorder and motion to allow a calctlation of the dynamical response of superionic crystals and melts which may be com- pared with measurements of inelastic neutron scattering and Raman scattering.

The high frequency part of this response is essentially that of anharmonic vibrations in a disorderd lattice. The low frequency part results from correlated jump diffision of the atoms.

1. Introduction.

-

The exact nature of the transition which occurs in superionic crystals is still imperfectly understood, in spite of the intensive study of materials like A g I and particularly the fluorites (1). In the latter the anion lattice certainly disorders to some extent (2) and these ions are able to diffuse.

However it now seems unlikely that the disorder is simply due to partial occupation of the empty cube centre sites with consequential vacancies in the normal sites Rather there appears to be a density variation along the (100) anion chains and a strongly correlated motion in these directions.

The experimental observations cannot readily be interpreted in terms of simple models of disorder. The extensive computer simulation studies of Gillan and Dixon (3) and others (4), elucidate some aspects of the problem. Most recently Gillan and Dixon (5) have studied in more detail the dynamical response in SrCR2 using a 96 ion sample and rigid ion potentials. The result for the anion structure factor (defined belowlis shown in figure I .

Partial dynamical structure factor S--(&,w) at k = (2r/aO) (2.5,0,0) from simulations at 938K (broken line) and T = 14 4K (full line).

!I

The peaks at 1.4 and 4.0 x 10 rad. s-I are due to longitudinal acoustic and optical

-

phonons. The peak at w = 0 in the full line is due to diffusive motion.

Phonon structure is still visible in the high T phase although experiments by

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981651

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C6- 176 JOURNAL DE PHYSIQUE

neutron scattering ( 6 ) and Raman scattering (7) show greater broadening. This is interpreted (7) as due to anharmonicity which is effective at relatively low T and the destruction of the k-selection rule by disorder at high T.

2. Theory.

-

The structure factor which is related to neutron scattering is defined as

1 B

S (k,w) _aB =

-

_2.nIdt eiwt<z X exp[i&.gy(t)

-

^R.^{( 0 ) D}

i j -3

where

Ri

a is the position of atom i of type a and < > indicates thermal average.In harmonic theory ~ ( t ) is expanded about its equilibrium position, but in the simulations the full expression is used. The motions at high T are roughly described as oscillations around some point, followed by a jump to a new position.

The Raman scattering is proportional to the correlation between the polarisabilities

1 iwt

Rab = ~ j ; Idt e <Pab(t) Pab(0) >.

Here P is the polarisation due to the fields Ea,E' of the incoming and outgoing b

photons.

where r(i) is the relative electron co-ordinate on atom i. There are two import- ant contributions to P, one local when i=j involving the electronic quadrupole or the electronic orbit size, for combinations of the indices a, b appropriate to second and zero order harmonics respectively. The other arises for the induced dipoles on different atoms i # j, which is effectively the modulation of the van der Waals interation (8). Extensive discussion of the latter mechanism has been given for rare gas liquids but because of the long range non-local character computer simulations are unreliable (9). We have assumed a local polarisation which depends on the relative local atomic displacements via a term like the Born-Meyer potential A The two components depend on the density and quadrupole distortion of the local environment.

3.

Melts. -

We have estimated these effects on a computer simulation of molten NaI using a rigid ion model (10). Figure 2 shows results for the number-number and charge-charge combinations.

The Raman scattering intensity is shown in figure 3 for the two symmetry types.

Since the polarisability is due to relative atomic displacements the vibrational part is emphasised, although the 'optical phonon' peak is less pronouncedthan it is in Scc. The narrow diffusive peak seen in S is absent.

nn

Computer simulations are proving extremely valuable in determining the atomic structure and atomic motion in superionics and melts. They allow an effective separation of vibrational and diffusive motions because of the jump diffusive character of these.

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Fig.3 : Raman scattering intensities predicted from a simulation of NaI at lOOOK using local polarisabilities.

References

1) W. Hayes 1978 Contemp. Phys. 19, 469.

R. Catlow 1980 Comments on Solid State Physics

9,

157.

2) M.H. Dickens et al. 1978 J. Phys. C.

2,

L583.

3) M. Dixon and M.J. Gillan 1980 J. Phys. C.

2,

1901, 1919.

4) G. Jacucci and A. Rahman 1978 J. Chem. Phys.

69,

4117.

5) M.J. Gillan and M. Dixon 1980 J. Phys. C.

12,

L835.

6) M.H. Dickens, W. Hayes and M.T. Hutchings 1976 J. de Phys.

21,

Suppl. C7-353.

7) R.J. Elliott et al. 1978 Proc. Roy. Soc.

H ,

317.

8) B.J. Adler et al. 1979 J. Chem. Phys.

70,

^4091.

9) A.J.C. Ladd et al. 1980 J. Chem. Phys.

72,

1759.

J.H.R. Clarke and L.V. Woodcock 1981 Chem. Phys. Lett.

2,

121.

10) M. Dixon (to be published).