DEFECTS. DISLOCATIONS. PHYSICS OF STRENGTH
Kinetics of the

˜
␣
transformation and the hierarchical nature of structure
defects in the two-phase state in the Pd–H system
A. A. Katsnel’son
*
)
and M. A. Knyazeva
M. V. Lomonosov Moscow State University, 119899 Moscow, Russia
A. I. Olemsko
Sumy State University, 244000 Sumy, Ukraine
͑Submitted January 21, 1999͒
Fiz. Tverd. Tela ͑St. Petersburg͒ 49, 1621–1626 ͑September 1999͒
Possible types of time dependences p(t) describing the kinetics of the

→
␣
transformation in
the Pd–H system are presented based on the theory of hierarchical structures. It is shown
that one factor influencing the change in the time dependence p(t) is the degree of regularity in
the distribution of defects in the hierarchical complexes and the strength of the hierarchical
coupling determining the number of hierarchically coupled levels. Analysis of the relations
obtained and the experimental data made it possible to distinguish the most likely physical
causes for the retardation of the

→
␣
transformation. © 1999 American Institute of Physics.
͓S1063-7834͑99͒01809-2͔
The problem of the interaction of hydrogen with metals
and alloys is becoming increasing more pressing in connec-
tion with the use of hydrogen in many branches of technol-
ogy. For example, the use of palladium–hydrogen systems in
hydrogen energetics involves storage, transport, and extrac-
tion of hydrogen. The effect of hydrogen on service charac-
teristics such as longevity and reliability of membranes used
as filters for purifying hydrogen and separating its isotopes is
extremely important. These applications make it necessary to
study the mechanical properties of the Pd–H and Pd–Me–H
systems determined by the phase composition
1
and state of
the defect structure.
2,3
Specifically, it is found that the high-
strength state is formed as a result of repeated cycling of the
phase transformation.
1–3
In recent years the idea has developed
4–6
that a strongly
deformable crystal is a synergetic system, where the defect
density is so high that collective effects show up in their
behavior. This means that a coherent coupling is established
in an ensemble of defects between the constituents of the
ensemble, and this coupling leads to self-localized formation
of the structural elements of a high level. Simple examples of
this phenomenon are: clustering of vacancies leads to dislo-
cation loops, clusters of dislocations transform into disloca-
tion walls, and so on. As a result, a hierarchical system of
defects arises and, since a definite relation exists between
different structural levels, it is more accuracte to call it a
hierarchically subordinated system.
4,6–9
A theory of hierar-
chical coupling is proposed in Ref. 9.
According to Refs. 10–14, a defect structure develops by
generation of defects in the process of an
␣
↔

transforma-
tion, leading to dilatation of the lattice. As a result of fine-
scale fragments assembling into a large-scale structure, the
evolution of a defect structure consists of a process in which
a complex, hierarchically subordinated, system of defects
arises. According to Ref. 15, the picture of the development
of such a system of defects also depends on the phase state.
We note that characteristic features of the kinetics of the
reverse phase transformation are determined by the state of
the defect structure.
12–14
It has been shown in Refs. 12, 14,
and 16 that the time dependence of the volume fraction of
the

phase does not reduce in the degassing process to very
simple exponential-type relations, but rather it possesses a
power-law or logarithmic dependence. In Refs. 12 and
16–18 it was determined that the

→
␣
transformation pro-
ceeds in multiple stages. It was established that the staged
nature of the degassing process is associated with stagewise
development of a defect structure.
19
Our objective in the present work is to describe the ki-
netics of the reverse transformation

→
␣
on the basis of the
concept of a hierarchical defect system arising in the two-
phase system Pd–H.
This paper is organized as follows. In Sec. 1, the basic
experimental data, generalizing the results of Refs. 12–19,
are expounded and analyzed on the basis of ideas developed
in Ref. 15, on the staged evolution of the defect structure. A
discussion based on the theory of hierarchical structures
7
is
given in Sec. 2. A number of basic relations are derived in
the Appendix.
1. EXPERIMENTAL RESULTS
In Ref. 13 it was shown by x-ray diffraction that the
kinetics of the

→
␣
transformation in Pd ribbons deformed
by rolling is described by an exponential dependence, if the
ribbons were saturated for 15 min by a current density 2.5
mA/cm
2
. At the same time it was observed in these samples
that the density of randomly distributed dislocations or large-
radius dislocation loops increases appreciably during phase
transformations. As the current density and saturation time
PHYSICS OF THE SOLID STATE VOLUME 41, NUMBER 9 SEPTEMBER 1999
14861063-7834/99/41(9)/5/$15.00 © 1999 American Institute of Physics