Model Chudley-Elliott

The theoretical basis of all these QENS studies is the Chudley-Elliott model [59], which in its basic form involves the following postulates. 

In this basic form the Chudley-Elliott model describes the H diffusion in f c.c. Pd. 

A first generalization of the Chudley-Elliott model has been developed in order to deal with crystallographically different hydrogen sites. Crystallographically different sites occur, e.g., for H diffusion over the tetrahedral interstices in b.c.c. metals like Nb. In this case the hydrogen sublattice consists of six superimposed b.c.c. 

From the Q dependence a mobility range of about 10 A is obtained. For the mobile state the isotropic Chudley-Elliott model is assumed. The result of a fit with this two-state model is shown by the solid line in Fig. 26.8 obviously a reasonable agreement between model and fit is achieved. In particular, the diffusion process in between traps is considerably faster than in crystalline Pd, whereas, as a consequence of trapping, the long-range diffusion coefficient is of the same order. At small Q the character of the narrow mode already crosses over from diffusive to localized behavior this explains a Q exponent smaller than... 

The dashed curves correspond to the Chudley-Elliott model with L = 1.5 (line b) and 1.8 A (line d) and the dolled curve to the Random Jump Diffusion model with = q.93 (line c) and 1.22 A (line e). 

Figures (A) Scattering at 0=0.87 A- and 360K from ZrTijHjg. The fit (soiid iine) to the data ( ) is the sum of the quasieiastic scattering with a Lorentzian line shape, (dashed line) and elastic scattering from the metal atoms (dotted line). (B) Line width of the Lorentzian component as a function of Q for T = 295, 330 and 360 K. The solid lines are fits from the Chudley-Elliott model (Eqn [8]) with / = 2.8 A. (Data recorded with IN10 at the ILL). Reproduced with permission from Fernandez JF, Kemali M, Johnson MR and Ross DK (1997) Quasieiastic neutron scattering measurements on the ZrTi2H3e C-15 Laves phase compound. P/ij4s/ca 6234-236 903-905.

It is not possible here to go into the details of the various proposed models . Let us briefly note that in the simplifying assumption of a cubic lattice of parameter L the Chudley-Elliott (CE) model gives... 

Fig. 30.S. Halfwidth AQ/(t>o of the elastic peak S(Q,

Chudley and Elliott (CE) [ 13] in this model, the jump distance d is a constant and the HWHM is given by... 

---