158
5 Compositionally Modulated and Multilayered Deposits
of the middle zone of the grains far from the layer interfaces do not differ
significantly from those in a bulk deposit since the impact of the adjacent layers
decays fast in the interfacial zone.
2. If the layer thicknesses are smaller than the crystallite size (at least along the
growth direction) but are large enough so that the natural bulk lattice distances
can manifest themselves in the middle of the layers, the heteroepitaxial growth
is accompanied with an effective strain relaxation. The strain originates from the
difference of the nearest neighbour distances of the bulk forms of the constituent
layers. The stress-induced deformation is effective only in the close vicinity of
the layer boundary.
3. When the layer thicknesses are small enough so that the natural lattice distances
of the layers cannot be set in, oscillating stress and strain fields occur along the
growth direction, which impact the growth of the coating.
For Case 1 of the above list, the multilayer growth is determined by the same
factors as those being effective during any plating process. For Cases 1 and 2 of the
above list, the X-ray diffraction pattern of the multilayer deposit shows the lines of
the constituent layers independently of each other (depending on the texture, not all
lines of the powder diffraction data may appear). For Case 3, however, the structural
features of the individual layers do not manifest themselves, which leads to new
features not seen at larger layer thicknesses. This occurs usually when the bilayer
thickness is less than 20 nm [97], which will be called hereinafter as the “small layer
thickness case”.
If the layer thicknesses are small enough, the lattice mismatch is small and the
deposition is assumed to produce truly planar layers perpendicular to the growth
direction, the X-ray diffraction pattern of the multilayer changes as compared to the
thick layer case. The individual diffraction lines of the layer types disappear and
a single line are obtained for a particular reflection in the weighted average lattice
distance of the bulk form of the constituent layers. This line merging is due to the very
small thickness of the coherently scattering domains in the direction of the scattering
vector. The analysis of the diffraction behaviour of a coherently grown multilayer
system was accounted for in detail by Michaelsen [97], offering a thorough guideline
for the diffraction study of any multilayer system.
Concerning the mean atomic distances for the “small layer thickness case”, the
Vegard law can be applied, which tells that the mean lattice parameter can be obtained
as the weighted average of the relaxed lattice parameter of the constituent layers.
However, a scrutiny of the structure tells that the in-plane and out-of-plane lattice
distances are not necessarily the same. Since the atomic volume for an element can
be taken constant regardless of the neighbourhood of a certain atom, the in-plane
compression draws an out-of-plane dilatation and vice versa. The exact deformations can be calculated by using the relevant elastic constants. For the quantitative
treatment, the reader is advised to consult some relevant literature resources [93, 98,
99]. Regardless of the stress effect, the Vegard law can be used for estimating the
mean atomic distances in multilayers and the corresponding position of the lines in
the XRD pattern.
5 Compositionally Modulated and Multilayered Deposits
of the middle zone of the grains far from the layer interfaces do not differ
significantly from those in a bulk deposit since the impact of the adjacent layers
decays fast in the interfacial zone.
2. If the layer thicknesses are smaller than the crystallite size (at least along the
growth direction) but are large enough so that the natural bulk lattice distances
can manifest themselves in the middle of the layers, the heteroepitaxial growth
is accompanied with an effective strain relaxation. The strain originates from the
difference of the nearest neighbour distances of the bulk forms of the constituent
layers. The stress-induced deformation is effective only in the close vicinity of
the layer boundary.
3. When the layer thicknesses are small enough so that the natural lattice distances
of the layers cannot be set in, oscillating stress and strain fields occur along the
growth direction, which impact the growth of the coating.
For Case 1 of the above list, the multilayer growth is determined by the same
factors as those being effective during any plating process. For Cases 1 and 2 of the
above list, the X-ray diffraction pattern of the multilayer deposit shows the lines of
the constituent layers independently of each other (depending on the texture, not all
lines of the powder diffraction data may appear). For Case 3, however, the structural
features of the individual layers do not manifest themselves, which leads to new
features not seen at larger layer thicknesses. This occurs usually when the bilayer
thickness is less than 20 nm [97], which will be called hereinafter as the “small layer
thickness case”.
If the layer thicknesses are small enough, the lattice mismatch is small and the
deposition is assumed to produce truly planar layers perpendicular to the growth
direction, the X-ray diffraction pattern of the multilayer changes as compared to the
thick layer case. The individual diffraction lines of the layer types disappear and
a single line are obtained for a particular reflection in the weighted average lattice
distance of the bulk form of the constituent layers. This line merging is due to the very
small thickness of the coherently scattering domains in the direction of the scattering
vector. The analysis of the diffraction behaviour of a coherently grown multilayer
system was accounted for in detail by Michaelsen [97], offering a thorough guideline
for the diffraction study of any multilayer system.
Concerning the mean atomic distances for the “small layer thickness case”, the
Vegard law can be applied, which tells that the mean lattice parameter can be obtained
as the weighted average of the relaxed lattice parameter of the constituent layers.
However, a scrutiny of the structure tells that the in-plane and out-of-plane lattice
distances are not necessarily the same. Since the atomic volume for an element can
be taken constant regardless of the neighbourhood of a certain atom, the in-plane
compression draws an out-of-plane dilatation and vice versa. The exact deformations can be calculated by using the relevant elastic constants. For the quantitative
treatment, the reader is advised to consult some relevant literature resources [93, 98,
99]. Regardless of the stress effect, the Vegard law can be used for estimating the
mean atomic distances in multilayers and the corresponding position of the lines in
the XRD pattern.