Hydrogen motion in single-crystal palladium hydride as studied ultrasonically

A lattice gas model for the Zener relaxation

“…Further, a model calculation for the relaxation kinetics of the short-range order parameters was performed [21], yielding identical relaxation rates for all the order parameters considered. Therefore, this calculation cannot explain different relaxation rates for different elastic compliances such as, for instance, experimentally observed in the PdH x system [11].…”

“…Using the orthogonal and normalized strain ˜ (2) as in (11), and proceeding identically as in section 3, the correlation function for ˜ (2) is given by (see (13))…”

“…Since the (interstitial) sites of such a lattice gas are either populated by interstitial atoms (component 1) or by vacancies (component 2), Zener relaxation can take place precisely as in a two-component substitutional alloy. Metalhydrogen systems are an interesting realization of such a lattice gas because of the high diffusivity of the hydrogen interstitials [5,6], so the Zener relaxation in these systems was 0953-8984/96/397233+15$19.50 c 1996 IOP Publishing Ltd intensively investigated, for instance in Pd [7][8][9][10][11][12] and in Sc and Y [13][14][15][16][17]. It is worth mentioning that a pure Zener relaxation was studied in these cases since the symmetry of the interstitial sites of the hydrogen (octahedral sites in face-centred cubic (fcc) Pd and tetrahedral ones in hexagonal close-packed (hcp) Sc and Y) excludes the occurrence of a Snoek relaxation.…”

“…Because of the complex nature of the Zener relaxation, the presently existing theoretical models for this process [1,2,11,12,[18][19][20][21][22][23][24] are still very crude and approximate. Even in the simplest case of dilute alloys, where the relaxation can be traced to pairs of the solute atoms [1,2,18], the relaxation kinetics has only been treated in a highly simplified manner.…”

“…The situation is much more complex in concentrated alloys where the atomic order is no longer describable in terms of isolated pairs of atoms of one of the alloy constituents. In this case, expressions for the relaxation strength were derived in model calculations [1,2,11,12,19,20,[22][23][24] which considered, in most cases, the effects of a stress-induced change of short-range order parameters (a critical discussion of the merits and the problems of this concept is given in [22]). Further, a model calculation for the relaxation kinetics of the short-range order parameters was performed [21], yielding identical relaxation rates for all the order parameters considered.…”