Appl. Phys. A 67, 183–192 (1998)
Applied Physics A
Materials
Science & Processing
Springer-Verlag 1998
GeneralizedWagner’s diffusion model of surface modification
ofmaterials by plasma diffusion treatment
V.I. Dimitrov
∗
, G. Knuyt, L.M. Stals, J. D’Haen, C. Quaeyhaegens
Materials Physics Division, Institute for Materials Research, Limburgs Universitair Centrum, Science Park, Universitaire Campus, B-3590 Diepenbeek,
Belgium
Received: 26 February 1998/Accepted: 15 March 1998
Abstract. A general model of surface modification of ma-
terials by plasma diffusion techniques has been developed.
This model takes into account the erosion effects at the
plasma/solid interface occurring due to the ion bombard-
ment of the surface. For constant sputtering rate, which is
the usual situation during plasma treatment, the growth of the
sub-layers (and the total compound layer) is well described
by the analytical expression g(t) = g
0
f
−1
(t/t
0
),whereg(t)
is the sub-layer thickness at time t, g
0
and t
0
are parameters
that dependon the treated material and plasma characteristics,
and f
−1
is the inverse function of f(x) =−(ln(1 −x) + x),
where x = g(t)/g
0
,0≤x≤1. Under negligible erosion ef-
fects, the model becomes of Wagner’s diffusion model type
and the expression for g(t) reduces to the parabolic law. The
model can be simplified by considering the compound layer
as a united one. The general and simplified models can be
used as a method for the experimental determining of the
effective diffusion coefficients and the erosion rate during
plasma treatment of material surfaces.
PACS: 68.65; 68.66
Recently a diffusion model of metal surface modification dur-
ing plasma nitriding has been proposed [1]. Plasma treatment
of materials however is a modern technology used not only
for plasma nitriding but also in an incredibly diverse range
of materials processing applications, see for example [2–9].
Surface modification of materials by plasma is usually asso-
ciated with low-density glow-discharge plasma processes. In
such a plasma energetic electrons collide with and dissociate
and ionize low-temperature neutral species, creating highly
reactive free radicals and ions. These byproductsenable many
traditional “high-temperature” chemical processes to occur
with low-temperature feedstock and surfaces [3].
Plasma nitriding of metal can be assigned to the group
of plasma diffusion treatments (PDTs). PDT is a plasma-
activated thermochemical process involving the diffusional
∗
Corresponding author. Sofia University, Faculty of Physics, Department of
Solid State Physics, 5 J. Bouchier Bld., BG-1126 Sofia, Bulgaria (E-mail:
Dimitrov@phys.uni-sofia.bg)
addition of elements such as nitrogen, carbon, and boron to
the treated specimen [4]. The flexibility of plasma processing
allows the structure and properties of the sub-layers, formed
at the material surface, to be varied within broad limits. For
example, metal nitrides can be produced by plasma nitriding
even for high-carbon materials. A combination of carbides
and nitrides of metals can provide unique properties of metal
surfaces: heat resistance, anticorrosion properties, wear resis-
tance, surface hardening, etc. PDT techniques have become
a powerful method for creating new materials and a need
for accurate models describing material surface modification
during plasma treatment is obvious. Different kinds of PDT,
namely plasma nitriding, nitrocarburizing, carburizing, and
boridingare verysimilar to each other. This enables us to gen-
eralize the plasma-nitriding model [1] to surface modification
by PDT.
In fact, PDT can be considered as a kind of chemical heat
treatment, which combines thermal, chemical, and significant
sputtering action on the material surface. During any PDT an
energetic flux of neutral atoms and ions is generated, which
produces significant sputtering, surface heating, and a large
number of surface defects such as dislocations and vacancies.
The ion bombardment, followed by surface erosion, is so in-
tensivethat it is used as an independenttechnologicalprocess,
for example, in ion plating [10] and surface cleaning [11,12].
Lakhtin and Krymskii [13] refer to a localized temperature
increase of 40000–50000K at the surface in the area of ion
impact. The erosion and local heating effectsat the surface re-
sult in a decrease of the activation energy for diffusion of the
plasma particles into the material. Thus, the effective diffu-
sionduringthe plasmaprocess is greatly enhanced. Diffusion,
in turn, causes changes in the chemical composition of the
material surface, and different phase transformations, con-
trolled by the diffusion, take place. A system of new phases
forms an outer compound layer that differs significantly from
the initial material (the matrix).
In the present paper we show that the generalized Wag-
ner’s diffusion model, proposed in the present study, de-
scribes rather well the metal surface modification by any
plasma diffusion treatment. The only qualitative difference
between a conventional chemical heat treatment and the