Diploma Thesis - Erich Schmid Institute

The relations between the compliance tensor and matrix are:
sijkl = smn when m and n are 1, 2 or 3.
2 sijkl = smn when either m or n are 4, 5 or 6.
4 sijkl = smn when both m and n are 4, 5 or 6.
Mechanical properties of crystals
The advantage of working with matrix notation is the compacter formalism, though
the rotation of the compliance and the stiffness matrix is more complicated than the
rotation in the tensor notation. For example an isotropic material can be
characterized by the following stiffness matrix:
⎛ c11
c12
c12
0 0 0 ⎞
⎜
⎟
⎜c12
c11
c12
0 0 0 ⎟
⎜c
⎟
12 c12
c11
0 0 0
c = ⎜
⎟
(equ. 4.14)
⎜ 0 0 0 c44
0 0 ⎟
⎜ 0 0 0 0 c ⎟
44 0
⎜
⎟
⎜
⎟
⎝ 0 0 0 0 0 c44
⎠
Isotropic materials have only two independent components, so the third one can be
calculated:
4.3. Intrinsic and extrinsic stress
1
c44 = ( c11
− c12
)
2
The residual stresses in thin films results from a growth procedure and from a cooling
down to the operation temperature after the deposition with specific intrinsic and
extrinsic stress contributions, respectively. The intrinsic stresses originate from a
specific microstructure development and the film densification during the growth [5].
An atomic disorder caused by foreign atoms integrated into the lattice can serve as
an example of the intrinsic stress origin. An impurity atom can substitute a lattice
atom or it can be found in lattice gaps as an interstitial atom. The compressive/tensile
stress is getting higher if the atomic radius of the impurity atoms is larger/smaller than
the atomic radius of the original lattice atoms. Intrinsic stresses can be reduced by
applying high substrate temperatures during deposition, because of the high mobility
of the atoms reduces the disorder. An additional part of intrinsic stresses occur in
sputtered layers. The incoming sputtered atoms are hitting the layer and this is like
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