Full text of DOI:10.1557/JMR.2002.0363

ARTICLES
High-temperature oxidation of CoGa: Influence of the
crystallographic orientation on the oxidation rate
U. Koops
Institute of Physical Chemistry, Darmstadt University of Technology, Petersenstraße 20,
D-64287 Darmstadt, Germany
D. Hesse
Max Planck Institute of Microstructure Physics, Weinberg 2, D-06120 Halle, Germany
M. Martina)
Institute of Physical Chemistry I, Aachen University of Technology (RWTH), Templergraben 59,
D-52056 Aachen, Germany
(Received 8 February 2002; accepted 10 June 2002)
The crystallographic orientation plays an important role in high-temperature oxidation of
the intermetallic compound CoGa. When CoGa is exposed to air at elevated temperatures,
the oxide ␤–Ga2O3 is formed, and different scale growth rates are observed, depending
on the crystallographic orientation of the CoGa grains. This dependence is a consequence
of the anisotropy of the gallium diffusion rate through the ␤–Ga2O3 scale and of a
topotaxial orientation relationship occurring between ␤–Ga2O3 and CoGa. The
combination of ex situ techniques, such as transmission electron microscopy and electron
backscatter diffraction with optical microscopy, applied in situ resulted in a thorough
understanding of these relations and of the oxidation process in general.
oxide. The orientation of the forming oxide can in turn be
I. INTRODUCTION
expected to depend on the orientation of the underlying
metal substrate, at least if a topotaxial oxidation mecha-
nism occurs. This expectation is supported by studies of
the very early oxidation states of CoGa.7–9 However,
these experiments were performed under high vacuum
conditions, and single-crystalline samples of CoGa were
exposed to small amounts of oxygen corresponding to
coverages in the monolayer regime. The resulting islands
of ␤–Ga2O3 were analyzed by low energy electron dif-
fraction (LEED) showing certain orientation relation-
ships (see below). As a result, it appears that the rate of
high-temperature oxidation of CoGa should depend on
its crystallographic orientation, resulting in a different
scale thickness on differently oriented grains of a poly-
crystalline CoGa intermetallic. A better knowledge of
these relations is necessary if one aims at an optimization
of the oxidation resistance of CoGa. With this goal in
mind, experimental investigations on polycrystalline
CoGa samples were performed, in which the rate of scale
growth in dependence on the crystallographic orientation
of the CoGa grains was studied.
The intermetallic compound CoGa shows an excellent
high-temperature oxidation resistance. When exposed to air
at elevated temperatures, Ga is selectively oxidized, and a
compact and dense oxide scale of ␤–Ga2O3 forms. Through
time-resolved, in situ x-ray powder diffraction it could be
shown that after an induction period the scale growth fol-
lows a simple parabolic rate law.1–3 This means that the rate
determining step is diffusion through the oxide layer. Dur-
ing the oxidation process pores are formed in the interme-
tallic CoGa at the metal/oxide interface. This observation
gives clear evidence that ␤–Ga2O3 grows by diffusion of
Ga ions from the metal/oxide to the oxide/gas interface.
Diffusion of oxygen ions in the opposite direction can
be excluded, since in this case ␤–Ga2O3 would grow at the
metal/oxide interface and no pores could grow (they would
be filled by the growing oxide). ␤–Ga2O3 is known to be a
semiconductor;4,5 thus it can be concluded that ␤–Ga2O3
grows by ambipolar diffusion of Ga ions and electronic
defects through the oxide scale,1–3 resulting in the observed
parabolic rate law as described by Wagner’s oxidation
rate theory.6
Since ␤–Ga2O3 has an anisotropic crystal structure as
described below, an orientation dependence of the gal-
lium diffusion rate through the oxide can be expected,
which in turn should result in different rates of scale
growth for different crystallographic orientations of the
II. EXPERIMENTAL
A. Applied methods
To study the influence of sample orientation on the
growth rate of the oxide scale, the crystallographic ori-
entation of the respective metal sample must be known.
Depending on the method of determining the growth
a)Address all correspondence to this author.
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U. Koops et al.: High-temperature oxidation of CoGa: Influence of the crystallographic orientation on the oxidation rate
kinetics, different possibilities exist, which required
samples of different types. For example, if thermogra-
vimetry or in situ x-ray diffraction is used to follow the
oxidation rate, a number of single-crystal samples with
differently oriented surfaces must be cut and polished.
This is elaborate, and, moreover, the above methods do
not allow determination of the oxide layer thickness with
any sensible lateral resolution because the measured sig-
nal is integral over the whole sample. Less-elaborate ex-
periments are possible if polycrystalline samples are
used, provided that the crystallographic orientation of
the individual grains can be determined and the growth
rate of the scale can be measured with sufficient spatial
resolution.
AAS). All samples used in this study have a slight Co-
excess (Co52.6 0.2Ga48.3 0.3), but they will always be de-
noted “CoGa.” Disks were cut from the ingots with a
diamond wire saw (Well, Mannheim, Germany). Grind-
ing and polishing were performed by standard metallo-
graphic methods, whereby SiC papers and a diamond
polishing paste were used to reduce the surface rough-
ness. The final polishing step was performed using an
alumina-silica suspension of 60-nm grain size (Master-
met I, Wirtz-Buehler, Du¨sseldorf, Germany) on a velvet
disc. For the TEM investigations, thin plan-view and
cross-sectional specimens were prepared by mechanical
polishing and subsequent argon ion milling (DuoMill,
Gatan, Mu¨nchen, Germany) following the well-known
established techniques; see Ref. 10.
A method that reveals the scale thickness with high
lateral resolution, and in addition allows determination of
the orientation relationships, is transmission electron
microscopy (TEM) in combination with selected-area
electron diffraction (SAED). The TEM investigations
were performed in a standard transmission electron mi-
croscope with 200-keV primary beam energy, equipped
with a 45° double-tilt holder (CM20T, Philips, Eind-
hoven, The Netherlands). This method can, however, be
applied only after oxidation, i.e., as an ex situ technique.
To measure the oxidation rate during oxidation in
dependence on the grain orientation of the polycrystal-
line intermetallic substrate, a method with a spatial reso-
lution better than the grain size of the metal has to be
used. In polycrystalline CoGa samples obtained by arc
melting, the grain size varies from 10 to 1000 ␮m. Thus
optical microscopy is a suitable method, provided that
the required temperatures can be reached and maintained
in the microscope during the measurement. We chose
this option, measuring the thickness of the oxide scale on
polycrystalline CoGa samples via the interference colors
of the scale. The experiments were performed in situ in a
specially designed hot stage adapted to an optical micro-
scope (Leica DMRM, Germany). The orientation of the
CoGa grains was determined prior to the oxidation ex-
periments by electron backscatter diffraction (EBSD) via
selected-area channeling (SAC) in a scanning electron
microscope (SEM; Zeiss 962, Germany), equipped with
a special beam control for SAC, and via orientation map-
ping (demonstration laboratory of Oxford Instruments,
Wiesbaden, Germany).
III. RESULTS
A. TEM investigations
1. Crystallographic orientations and
topotaxial relationships
The lattice parameters and space groups of the in-
volved materials, i.e., CoGa and ␤–Ga2O3, are shown in
Table I.11,12 A number of interplanar distances and
angles common to both CoGa and ␤–Ga2O3 can be found
(Sec. III), which make the presence of a topotaxial ori-
entation relationship most probable. Accordingly, an in-
vestigation of the crystallographic orientation of the
␤–Ga2O3 scale relative to the underlying CoGa grain(s)
was carried out by SAED in TEM.
Figure 1(a) shows a bright-field cross-sectional image
of the gallium oxide scale developed on a CoGa grain
during 24 h of oxidation at 800 °C in air. The entire
CoGa region imaged in Fig. 1(a) belongs to one CoGa
grain. While the oxide/metal interface is smooth and pla-
nar (except for the presence of pores, the role of which is
considered below), the surface of the oxide scale is rather
rough, most probably due to the surfacial facets of the
columnar grains forming the scale. On average, the thick-
ness of the oxide scale is 135 nm. The columnar structure
of the oxide scale is particularly easy to see in the dark-
field image [Fig. 1(b)]; the width of a column is on the
order of 30 nm (for the different brightness of the col-
umns, see below). A closer inspection of these and other
TEM images reveals the presence of many planar de-
fects, most probably stacking faults, in addition to the
boundaries between the columnar grains. The fact that
B. Sample preparation
Polycrystalline samples of the intermetallic compound
CoGa were obtained by arc melting the elements Co and
Ga under argon in the desired stoichiometric ratio. The
phase purity of the samples was checked by x-ray dif-
fraction (XRD), and analysis of the stoichiometry was
performed using SEM energy dispersive x-ray (EDX),
electron probe microanalysis (EPMA), as well as a wet
chemical analysis (atomic absorption spectroscopy,
TABLE I. Crystallographic parameters of the involved materials
CoGa and ␤–Ga2O3.11,12
Material
Space group
Lattice parameters
CoGa
␤–Ga2O3
Pm3m (No. 221)
C2/m (No. 12)
a ס b ס c ס 0.2878 nm
␣ ס ␤ ס ␥ ס 90°
␣ ס ␥ ס 90°
␤ ס 103.87°
a ס 1.2214 nm
b ס 0.3037 nm
c ס 0.5798 nm
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U. Koops et al.: High-temperature oxidation of CoGa: Influence of the crystallographic orientation on the oxidation rate
Fig. 2, Table II shows the number of the original negative,
the experimental sample tilt angles (x;y), the calculated di-
rection B of the electron beam and the (hkl) indexing of the
three reflections closest to the zero spot, all for each of
the two materials, CoGa and ␤–Ga2O3.
From an evaluation of these and other diffraction pat-
terns, all taken from the sample region shown in Fig. 1,
the following orientation relationship was deduced:
¯
(201) ␤–Ga2O3 ꢀꢀ (110) CoGa
[010] ␤–Ga2O3 ꢀꢀ [001] CoGa
;
.
(1)
Figures 2(c) and 2(d) are drawn under the assumption
that Eq. (1) is exactly fulfilled. However, a close inspec-
tion of Figs. 2(a) and 2(b) (and other diffraction patterns)
shows that small angular deviations (up to about 2.5°)
from this orientation relationship occur. Moreover,
Figs. 2(a) and 2(c) show that the (100) plane of ␤–Ga2O3
makes a small angle (about 5°) with the (100) plane of
CoGa, whereas Figs. 2(b) and 2(d) reveal that the (010)
plane of ␤–Ga2O3 is almost exactly parallel to the (001)
plane of CoGa. We may therefore suggest that small
deviations from Eq. (1) occur and that the second part of
Eq. (1) is the fundamental orientation relationship:
(010) ␤–Ga2O3 ࿣ (001) CoGa
.
(2)
According to a LEED-study8 on the very early oxidation
state of CoGa under high vacuum conditions (100) ␤–
Ga2O3 was reported to be exactly parallel to (100) CoGa
(see Fig. 3 below), but in our case this is only approxi-
mately true.
The following values of the interplanar distances and
lattice mismatches for the three principal space directions
were calculated assuming that the orientation relation-
ship Eq. (1) is exactly fulfilled.
Misfit in the direction [001] of CoGa [i.e., to the left in
Fig. 2(d)]:
FIG. 1. (a) Cross-sectional bright-field TEM and (b) ␤–Ga2O3 dark-
field image of the ␤–Ga2O3 scale developed on a grain of the inter-
metallic compound CoGa during 24 h of oxidation at 800 °C in air.
P designates a pore formed at the oxide/metal interface.
d(010) ␤–Ga2O3 ס 0.3037 nm
d(001) CoGa ס 0.2878 nm
f1 ס +5.4%
the long axis of the columns makes a definite angle
around 80° with the substrate plane already points to a
definite orientation relationship of the oxide with respect
to the metal grain. This relationship was analyzed by
SAED using various definite tilts of the specimen in a
45° double tilt holder.
Misfit in the direction [110] of CoGa [i.e., downwards in
Figs. 2(c) and 2(d)]:
¯
d(402) ␤–Ga2O3 ס 0.2340 nm
d(110) CoGa ס 0.2035 nm
f2 ס +13.9%
Figures 2(a) and 2(b) show two of the SAED patterns
obtained, together with schematic patterns in Figs. 2(c)
and 2(d), which display the locations of the CoGa and
␤–Ga2O3 reflections and their (hkl) indices. From an
analysis of these and other diffraction patterns, taking the
well-known magnetic rotation between images (Fig. 1)
and diffraction patterns (Fig. 2) into account, the normal
to the grain surface in Fig. 1 was derived to be [110]
CoGa, as also schematically shown in Figs. 2(c) and 2(d).
Furthermore, the diffraction patterns were analyzed in de-
tail. For example, for each of the two SAED patterns of
¯
Misfit in the direction [110] of CoGa [i.e., to the left in
Fig. 2(c)]:
d(402) ␤–Ga2O3 ס 0.1834 nm
d(110) CoGa ס 0.2035 nm
¯
f3 ס −10.4%
The smallest of the three values f1, f2, and f3 corresponds
to Eq. (2), which confirms that this relation is the funda-
mental one. It appears that the lattice misfit along the
CoGa/␤–Ga2O3 interface is not very small, if Eq. (1) is
strongly obeyed. However, our investigations pointed to
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U. Koops et al.: High-temperature oxidation of CoGa: Influence of the crystallographic orientation on the oxidation rate
the possible presence of two deviations from Eq. (1),
both of which may contribute to a reduction of the overall
misfit. (i) Twins are present in the oxide, the nature of
which was not investigated in detail. In fact, the different
brightness of the ␤–Ga2O3 grains in Figs. 1(a) and 1(b)
(dark or bright) most probably goes back to this twin-
ning. (ii) There are the already mentioned small angular
deviations from Eq. (1), e.g., small azimuthal rotations of
the ␤–Ga2O3 lattice around the [010] ␤–Ga2O3 ࿣ [001]
CoGa axis. The orientation relationship reported in
Ref. 8 is such an orientation. As an example of the ori-
entations resulting from small rotations, Fig. 3 shows a
schematic diagram of the situation described in Ref. 8,
i.e., when (100) CoGa ࿣ (100) ␤–Ga2O3. The (100) sur-
face of a CoGa grain is drawn horizontally. The
␤–Ga2O3 lattice has been arranged in such a way that
the (100) plane of ␤–Ga2O3 is exactly parallel to the
CoGa (100) grain surface.8 The “viewing direction” (per-
pendicular to the plane of the paper) is [010] ␤–Ga2O3 ࿣
[001] CoGa, so Eq. (2) is obeyed. The orientation drawn
in Fig. 3 deviates from Eq. (1) by about only 5°. A de-
tailed consideration shows that the situation of Fig. 3
results in small misfit values. In summary, small devia-
tions from the three-dimensional orientation relationship
Eq. (1) may occur in the form of twins or small angular
rotations.
As a result of these investigations, the following
should be pointed out. If small rotations and the presence
of twins are neglected, the three-dimensional crystallo-
graphic orientation of the ␤–Ga2O3 scale with respect to
FIG. 2. (a,b) Two selected-area diffraction patterns taken at different sample tilt angles from the sample region visualized in Fig. 1.
(c,d) Corresponding schematic drawings showing the calculated indexing and the assignment of the spots to the CoGa (᭹) and the ␤–Ga2O3 phase
¯
(᭿), respectively. The hkl indices for CoGa are given in roman letters, for ␤–Ga2O3 in italic letters. The beam direction in (a) and (c) is [001]
¯
¯
CoGa ࿣ [010] ␤–Ga2O3, (b) and (d) it is [110] CoGa ࿣ [102] ␤–Ga2O3. Note that there is an angle of 90° between the beam directions of (a) and
(b). For other details, see Table II.
TABLE II. Parameters of the SAED patterns shown in Fig. 2.
Figure
no.
Negative
no.
B
B
Closest spots
(CoGa)
Closest spots
(␤–Ga2O3)
(x;y)
(CoGa)
(␤–Ga2O3)
¯
200, 001, 201
010, 201, 211
Fig. 2(a)
Fig. 2(b)
×304
×302
(−45°; +12°)
(+45°; +12°)
[001]
[110]
[010]
[102]
010, 110, 100
001, 110, 111
¯
¯ ¯
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U. Koops et al.: High-temperature oxidation of CoGa: Influence of the crystallographic orientation on the oxidation rate
by far too elaborate, this method was applied to one only
sample, in order to find out whether indeed differences in
scale thickness from grain to grain occur.
Figures 4 and 5 show TEM images of the ␤–Ga2O3
scale grown on two different CoGa grains of the same
sample oxidized at 800 °C for 48 h, as well as some of
the SAED patterns used to determine the crystallographic
indexing of the surface normal of each CoGa grain. The
sample regions shown in Figs. 4 and 5 were part of
the same TEM sample; the grains had a mutual separa-
tion of several hundred micrometers. Carefully studying
a large section of each grain and finding sample regions
where the scale had not been attacked during ion thinning
confirmed that, indeed the entire scale thickness is visu-
alized in Figs. 4 and 5. The fact that the scale surface was
not affected during the ion thinning process (i.e., during
TEM sample preparation) can also be deduced from the
glue residues still present on the surface of the scale in
both images. Whereas the scale shown in Fig. 4 has a
thickness of 260 nm, the one in Fig. 5 is only 130 nm
thick—a surprisingly large difference, by a factor of two,
on parts of the same sample. The SAED investigation
showed that the CoGa direction perpendicular to the
¯
¯
grain surface was [110] in Fig. 4, whereas it was [310] in
Fig. 5 (see the given SAED patterns).
FIG. 3. Schematic drawing showing the arrangement of the atoms
near a (100) CoGa/(100) ␤–Ga2O3 interface constructed in accordance
with Eq. (2). The crystallographic axes of ␤–Ga2O3 (top) are shown in
the upper left.
¯
¯
Since the angle between the [ 110] and [310] directions
in CoGa is only 26.6°, the above result shows that an
angular difference of only 26.6° in the orientation of the
CoGa surface results in a decrease of the oxidation
kinetics by as large as a factor of two. Such a drastic
effect can only be explained by two different crystallo-
graphic orientations of the ␤–Ga2O3 scale in Figs. 4 and
5 in accordance with the discussion in the previous para-
graph. This observation was the starting point for the
more detailed investigations of the growth kinetics in
dependence on grain orientation presented in Sec. III.B
and III.C.
the CoGa lattice is given by Eq. (1) for all CoGa grains
of the sample. This makes it most probable that a topo-
taxial reaction mechanism occurs. The crystallographic
indexing (hkl) of the metal/oxide interface is, of course,
different from grain to grain; i.e., the indexing of the top
and bottom plane of the ␤–Ga2O3 scale depends on the
indexing of the underlying CoGa surface plane. With
respect to the scale growth rate, it is worthwhile to point
out that the direction into which the gallium ions have to
diffuse (through the growing oxide scale) is roughly per-
pendicular to the CoGa grain surface and that the corre-
sponding direction in the ␤–Ga2O3 lattice of the scale
varies from grain to grain. It is thus reasonable to expect
corresponding variations from grain to grain in scale
growth kinetics and oxide scale thickness.
3. Pore shape and size
Due to the selective oxidation of gallium from the
intermetallic compound CoGa to form ␤–Ga2O3, pores
are formed on the metal side of the metal/oxide interface
(compare with Fig. 1). For the detailed reaction mecha-
nism involving the formation of pores, see Ref. 2. The
TEM investigations on cross-sectional samples were also
used to answer the question whether such pores are
already present in the early stage of the oxidizing reac-
tion, and if so, to visualize them and to study their shapes
and sizes.
As can be deduced from Figs. 4 and 5 above, these
pores at the CoGa/oxide interface tend to partly adopt a
crystallographic shape, whereby the pores in different
CoGa grains have clearly different shapes. For example,
in Fig. 4 the pore shape is rounded with a more or less
2. Oxide scale thickness
TEM cross-sectional investigations allow a precise de-
termination of the scale thickness while SAED provides
information on the grain orientation. It is thus possible in
principle to determine the scale growth kinetics as a func-
tion of the grain orientation by TEM and SAED. How-
ever, this requires a large number of cross sections of
different regions of the same sample to be prepared, and
moreover, the investigation of different samples oxidized
for different times is necessary. Since this procedure is
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U. Koops et al.: High-temperature oxidation of CoGa: Influence of the crystallographic orientation on the oxidation rate
¯
FIG. 4. (a) Cross-sectional TEM bright-field image of a scale grown on a CoGa grain having the normal to the surface along the [110] CoGa
direction, and (b–d) three corresponding SAED patterns of the CoGa grain obtained under various sample tilt angles. Tilt is around the normal
¯ ¯
to the CoGa surface plane. The beam direction is [113] in (b), [111] in (c), and [001] in (d). In all SAED patterns, the reciprocal vector g ס
¯
(110) is marked by an arrow and is perpendicular to the surface plane in (a). Scale grown during 48 h at 800 °C in air. Note the pores and their
shape.
flat part of the inner surface pointing to the interior of the
grain, whereas in Fig. 5 the shape is roughly triangular,
with an oblique corner pointing into the depth of the
grain. Finally, in Fig. 1 (showing, however, a sample
different from the one in Figs. 4 and 5) the pore is more
lens shaped. It is reasonable to assume that the shape of
the pores is determined by the orientation of the CoGa
grain. Accordingly, it can be assumed that qualitative
differences in the orientations of various grains can al-
ready be noticed by observation of the pore shape.
In TEM cross sections, the apparent lateral size of the
pores varied rather extensively between 0.1 ␮m and
more than 1 ␮m, depending on scale thickness and oxi-
dation time (24 h or 48 h). This extensive variation
at least in part might have been an effect of the
cross-section preparation because the apparent pore size
image depends on whether the pore had been cut cen-
trally or rather peripherally during mechanical cutting.
To avoid this problem, the pore sizes were also investi-
gated using plan-view samples. Figure 6 shows the
bright-field TEM image of a plan-view sample oxidized
for 24 h at 800 °C. The dark areas are thick regions of
one CoGa grain covered with the oxide scale, whereas
the pores are visible as bright polygonally shaped re-
gions. The pores are also covered by the oxide scale
(compare with Fig. 1), and the latter appears to contain a
high density of crystal defects. In the image shown, the
lateral pore size varies between 0.2 and 2 ␮m, which is
typical for this sample. Thus it appears that the above-
described influence of the cross-section geometry on the
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U. Koops et al.: High-temperature oxidation of CoGa: Influence of the crystallographic orientation on the oxidation rate
¯
FIG. 5. (a) Cross-sectional TEM bright-field image of a scale grown on a CoGa surface having the normal to the surface along the [310] CoGa
direction, and (b–d) three corresponding SAED patterns of the CoGa grain obtained under various sample tilt angles. Tilt is around the normal
to the CoGa surface plane. The beam direction is [135] in (b), [133] in (c), and [001] in (d). In all SAED patterns, the reciprocal vector g ס
¯
(310) is marked by an arrow and is perpendicular to the surface plane in (a). Scale grown during 48 h at 800 °C in air. Sample is identical to that
of Fig. 4. Note the pores and their shape.
pore size determination is not important. Note also that
the larger of the pores all have more or less the same
shape. Again, different shapes were found on different
CoGa grains (not shown).
system by recording the modulation of the intensity of the
backscattered electrons due to diffraction at near-surface
lattice planes. This intensity modulation results in patterns
very similar to the Kikuchi patterns known from TEM.
Figure 7 shows an example of an electron backscatter dif-
fraction pattern obtained by SAC.
B. Grain orientation determined by EBSD
Before an in situ oxidation experiment of a polycrystal-
line bulk CoGa-sample can be performed in an optical mi-
croscope, the crystallographic orientations of the CoGa
grains to be oxidized have to be determined. For this
purpose, a technique working in reflection geometry has to
be used to avoid thinning of the sample. Such a method,
EBSD, is available if a corresponding additional detector is
present in a SEM. EBSD is capable of measuring the ori-
entation of crystal areas relative to the laboratory coordinate
Accordingly, the same crystallographic computation
methods as in TEM can be used to analyze the obtained
intensity pattern and to deduce the crystallographic
orientation of the crystal area investigated.13 By analyz-
ing several spots via a mapping function, one can cover
large sample areas and obtain the different orientations
of various grains in the polycrystalline sample. Such
an EBSD mapping is shown in Fig. 8, where the orien-
tations of the grains in a certain sample region, to be
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U. Koops et al.: High-temperature oxidation of CoGa: Influence of the crystallographic orientation on the oxidation rate
oxidized subsequently in the in situ experiment, are
determined. Two of the obtained orientations are in-
dicated in the figure. These two orientations differ by
an angle of 70.5°. Whereas the (001)CoGa plane is
densely packed by either Co or Ga atoms, the (221)
plane is certainly not densely packed. Thus we may
expect a difference in oxidation kinetics to occur in
this case.
colors resulting from destructive interference can be used to
determine the oxide layer thickness during the oxidation
process performed in the hot stage of an optical microscope:
2k + 1
4n
⌬x t͒ = ␭ t͒ и
.
(3)
͑
͑
Here, ⌬x(t) is the time-dependent scale thickness, ␭(t) the
time-dependent wavelength of the color, n the refractive
index, and k the order of interference, k ס 0,1,2…14 This
method was already used by Tamman;15 however, it was
performed ex situ, i.e., after an oxidation reaction. Our
experiments were performed in situ at 650 °C in air, us-
ing the same sample regions for which the grain orien-
tations had been determined by EBSD. Figure 9 shows a
series of images taken during oxidation of that very area,
for which the orientation determination is demonstrated
in Fig. 8. The original version of Fig. 9 is in color. From
video images taken at well-defined oxidation times, the
colors and the corresponding wavelengths of individual
grains were obtained by comparing the colors with a
standard color card, and then Eq. (3) was used to derive
the scale thickness.
C. Oxidation kinetics determined by in situ
optical microscopy
Since monoclinic ␤–Ga2O3 is transparent and the refrac-
tive index is known (n ס 1.92), the wavelengths of the
Figure 10 shows the deduced layer thickness for the
two grains visualized in Figs. 8 and 9 in a plot of
the square of the thickness [⌬x(t)]2 against time t. The
lines were drawn following the simple parabolic rate law
2
0
͌
⌬x t͒ =
x + 2k t − t ͒
,
(4)
͑
͑
p
0
where kp is the parabolic rate constant, x0 is the thickness
of the scale after an induction period of length t0 where
the oxide grows by a different rate law (nucleation, island
growth, and coalescence of the islands).
FIG. 6. Plan-view bright-field TEM image of pores in a CoGa grain
covered by a ␤–Ga2O3 scale. Scale grown during 24 h at 800 °C in air.
Note the different pore sizes and the most similar pore shapes.
FIG. 8. EBSD map of a selected area of a CoGa sample to be oxi-
dized. Different gray levels indicate different orientations. The [hkl]
indices indicate the deduced normal to the sample surface. (The origi-
nal image is colored. The EBSD measurements were performed by G.
Frosch at Oxford Instruments, Wiesbaden, Germany.)
FIG. 7. EBSD intensity modulation in SEM obtained by electron
backscatter diffraction from the sample area shown on top right. Note
the similarity to Kikuchi patterns in TEM.
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U. Koops et al.: High-temperature oxidation of CoGa: Influence of the crystallographic orientation on the oxidation rate
FIG. 9. Series of images taken from the CoGa area shown in Fig. 8 during in situ oxidation at 650 °C in air. (The original images are colored.)
TABLE III. Parabolic rate constants of the oxidation of the interme-
tallic compound CoGa in dependence on the grain orientation, deter-
mined by in situ optical microscopy. The [hkl] given describe the
direction of the surface normal of the grain.
Orientation
Parabolic rate constant kP [cm2s−1
]
[001]
[221]
6.3 × 10−17
2.6 × 10−16
constants for the two grains. As shown in Table III, the
parabolic rate constant for the scale growth on the CoGa
surface with the [221] surface normal is about five times
larger than on the one with the [001] surface normal.
Since the measured parabolic rate constants are smaller
than the diffusion coefficients of Co or Ga in CoGa,16 it
can be concluded that the rate-determining step for scale
growth is diffusion through the oxide scale and not dif-
fusion in the intermetallic CoGa. Consequently, it can be
concluded that the observed orientation effect is not due
to orientation dependent mechanical damage in CoGa
caused by the initial mechanical polishing. However, if
FIG. 10. Square of the scale thickness, [⌬x(t)]2, determined by in situ
optical microscopy, in dependence on time t for the two grains shown
in Figs. 8 and 9. For the lines, see the text.
From Fig. 10 it is obvious that after the induction pe-
riod the ␤–Ga2O3 scale grows on both grains following a
parabolic rate law, but with different parabolic rate
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U. Koops et al.: High-temperature oxidation of CoGa: Influence of the crystallographic orientation on the oxidation rate
the results presented in the previous section are taken into
account, the drastic orientation effect can be explained
by two different crystallographic orientations of the
␤–Ga2O3 scale on the two grains, leading to two different
diffusion coefficients of gallium ions through the scale in
the direction perpendicular to the grain surface. These
results obtained in situ agree well with the findings ob-
tained by TEM in Sec. III.A.2 in which scales of different
thickness on differently oriented CoGa-grains were
found after oxidation for a certain time. However, it was
impossible to deduce the rate law for oxide scale growth
from the latter findings, since no time dependence was
studied. The parabolic rate law with different parabolic
rate constants found in our in situ optical experiments
confirms that after an induction period, diffusion is the
rate-limiting step for scale growth. Interface control as
the rate-determining step can now be ruled out, since this
would result in a linear rate law.17
property but varies from grain to grain if the scale has an
anisotropic crystal structure. It is thus important to study
the crystal structure of the scale in detail. Second, the
scale thickness on, and the oxidation resistance of a specific
metal surface can be influenced at will by a specially cho-
sen surface orientation or texture of the metal.
ACKNOWLEDGMENTS
We are grateful to G. Frosch from Oxford Instruments,
Wiesbaden, Germany, for the EBSD measurements as
well as O. Pompe from the Institute of Physical Metal-
lurgy and S. Zaefferer from the Institute of Chemical
Analysis, both at Darmstadt University of Technology,
for the SAC measurements. We also gratefully acknowl-
edge financial support of Deutsche Forschungsgemein-
schaft (DFG MA 1090/8) for part of this work. D.H.
acknowledges the support of DFG via the Coordinated
Research Center SFB 418 at Martin-Luther-Universita¨t
Halle-Wittenberg, Germany.
IV. CONCLUSIONS
This paper is dedicated to Professor Hermann Schmal-
zried on the occasion of his 70th birthday.
During the high-temperature oxidation of the interme-
tallic compound CoGa in air, a protective oxide layer
consisting of ␤–Ga2O3 is formed. Through TEM, EBSD,
and in situ optical microscopy it was shown that during
this process the crystallographic orientations play an im-
portant role. After an induction period, the growth of
␤–Ga2O3 follows a parabolic rate law with parabolic rate
constants kp depending on the crystallographic orienta-
tion of the CoGa grains. This dependence is a conse-
quence of the anisotropy of the gallium diffusion rate
through the monoclinic scale and of a topotaxial orientation
relationship occurring between ␤–Ga2O3 and CoGa.
These results can be generalized, and they apply to all
high-temperature oxidation processes in which oxides
with anisotropic crystal structure are formed. Important
examples are aluminum oxides (Al2O3) growing on Al-
containing intermetallics, such as NiAl. As described in
this paper for ␤–Ga2O3, the orientation of the anisotropic
oxide scale influences the transport rate through the scale
and thereby its growth rate. The orientation of the oxide
is in turn controlled by the orientation of the metal grains
due to topotaxial orientation relationships occurring
between the metal and the oxide. Therefore the oxidation
rate of the metal in effect depends on the crystallographic
orientation of the surface of the metal grains.
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At least two consequences of these results have to be
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crystalline metal, and thus also the resistance of the metal
against high-temperature oxidation, is not a uniform
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