Journal of Alloys and Compounds 404–406 (2005) 332–334
Modeling high-temperature TDS-spectra peaks of
metal–hydrogen systems
Yu. Zaika
a, ∗
, I. Chernov
a
, I. Gabis
b
a
Institute of Applied Mathematical Research, Karelian Research Centre of RAS, 185610 Petrozavodsk, Russia
b
V.A. Fock Institute of Physics, St. Petersburg State University, 198504 St. Petersburg, Russia
Received 30 May 2004; received in revised form 1 March 2005; accepted 4 March 2005
Available online 6 July 2005
Abstract
In the paper we present several mathematical models of dehydrogenation kinetics of metals for the TDS (thermal desorption spectrometry)
method. Diffusion is assumed to be fast. This allows considering only ordinary differential equations.
© 2005 Elsevier B.V. All rights reserved.
Keywords: Gas–solid reactions; Metals; Thermal analysis
1. Introduction
In this paper we discuss some models applied to the
widely used experimental method of thermal desorption
spectrometry (TDS) [1–6] applied to dehydrogenation of
metals. A sample of studied material (e.g. hydride) is placed
into an evacuated vessel and heated. The desorption flux of
hydrogen from the sample is measured. We are interested
in kinetics of dehydrogenation of metals. We assume that
temperature is rather high so that diffusion is relatively fast.
Then it is possible to make models using ordinary differential
equations.
The material is a powder. We consider a single particle
and model it as a sphere of radius L. Real particles of hydride
powders are not spherical; yet the sphere is a good approx-
imation for small particles when diffusion is fast. Inside the
particle there is a hydride core ( phase) of radius ρ. A spher-
ical layer of width L - ρ is metal with dissolved hydrogen
( phase). Usually the heating is linear: T (t ) = υt + T
0
.
Let c
(t, r),c
(t, r) be the concentrations of hydrogen dis-
solved in and phases at time t, r is for radius. Since dif-
fusion is fast, we can assume that c
(t, r) = c
(t ),c
(t, r) =
∗
Corresponding author. Tel.: +7 8142 766312; fax: +7 8142 766313.
E-mail address: zaika@krc.karelia.ru (Yu. Zaika).
c
(t ). For some materials one can also assume that c
(t ) =
c
crit
= const. Otherwise c
(t ) ≥ c
crit
. Here c
crit
is the criti-
cal concentration in hydride. We model the desorption flux
density with a square dependence on the concentration:
J (t ) = b(T )c
2
(t, L) (bulk desorption). The boundary-value
problems of dehydrogenation of metals with surface des-
orption are considered in [7,8]. We assume also that all pa-
rameters are Arrhenius temperature dependent, in particular
b(t ) = b(T (t )) = b
0
exp{-E
b
/[RT (t )]}.
2. Constant concentration in hydride
Here we consider the case when c
(t ) = c
crit
. The concen-
tration dynamics is driven by two fluxes: the desorption flux
and the flux of hydrogen decomposition. To avoid singular-
ity in the obtained differential equations at t = 0 we should
consider a thin ”initial cover”: a layer of metal with dissolved
hydrogen around the hydride core. Let V (r) and S(r) be the
volume and area of a sphere of radius r. The balance equation
for decomposing hydride is
c
V (ρ(t )) + c
(t )(V (L) - V (ρ(t ))) + S(L)
t
0
b(τ )c
2
(τ )dτ
= const. (1)
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.jallcom.2005.03.095