Environmental Engineering Reference
In-Depth Information
) implies that relaxation
occurs toward (and not away from) the bulk lattice constant with increasing
The minus sign of the proportionality constant (
1/
δ
ξ
,
and
is a positive quantity having the dimensions of length that determines how
slowly or quickly the relaxation takes place with increasing distance from the
metal substrate. It is thus expected that
δ
will be a characteristic of the oxide
medium and in particular will depend on the elastic constants of the medium.
The predictions of Eq. 5.107 have been illustrated by Fromhold [52] in a
qualitative way as shown in Fig. 5.24. In these schematic diagrams, sketch (a)
indicates the difference in the metal substrate and oxide periodicities that might
be ordinarily expected if each substrate had its normal bulk lattice constant.
Sketch (b) illustrates a situation in which the metal substrate influences the first
monolayer to take on a ''reduced'' value for the lattice constant in order to make
the periodicities the same for the two substances, in which case
δ
0. Sketch
(c) illustrates the alternative situation in which the metal substrate influences the
first oxide monolayer to take an ''expanded'' value for the lattice constant in
order to equalize the periodicities of the two substances, in which case
γ
γ
0.
Thus the stresses developed in scales may be related to epitaxial relationships
and oxide-metal mismatch. Such stresses are the largest at the metal-oxide inter-
face. Studies of epitaxial relationship have, for example, been reported for oxide
film formation on copper [55]. It has been shown by means of x-ray diffraction
studies that there existed a strain of 2-2.5% at the copper-oxide interface while
there was no strain at the oxide-oxygen interface. Epitaxial relationships are a
function of the orientation of metal grains.
In polycrystalline materials stresses may also develop at grain boundaries ow-
ing to the difference in oxidation rates between neighbouring grains and a prefer-
ential diffusion and oxide formation along grain boundaries.
5.8.3 Compositional Changes in the Metal
and Surface Oxide
Compositional changes in the metal as well as in oxide scale are likely to alter
the mechanical properties of both phases. Differential doping of the growing scale
by second or third alloying element or by the presence of impurity elements in
the scale has been experimentally observed during oxidation of dilute alloys for
which a theoretical model has also been proposed. Thus nonstoichiometry will
vary from the inner to outer interface of the oxide layer. Accordingly, it is ex-
pected that different segments of the total oxide will have different creep proper-
ties or stress relaxations. The dopant may enrich either in the outer layer or at
the metal-oxide interface, as, for example, segregation of sulfur at the metal-
oxide interface often leads to decohesion of scale. Similarly, difference in inter-
diffusivity values of elements in the metallic phase or internal precipitation of
oxide, carbide, nitride, etc., will also greatly influence the mechanical properties
