Diploma Thesis - Erich Schmid Institute

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$dissertation global and local fracture properties of metal matrix ...$

Basic X-ray diffraction Equation 3.9 is valid for all crystal systems, and the components of G can be replaced by the points of intersection u1, u2 and u3 of the net plane with the elongated translation vectors a1, a2 and a3. Figure 3.1: Crystallographic plane and surface normal The components of G are for that reason: 1 h = u1 1 k = u2 1 l = (equ. 3.10) u 3 5
4. Mechanical properties of crystals 4.1. Stress, strain and displacement Mechanical properties of crystals Internal stresses are produced by external forces acting on a body [2]. These external forces can be separated into two categories, like the distribution of forces over the surface, such as hydrostatic pressure, and distributed forces over the volume, for example gravitational forces or magnetic forces. A motion of the body is also able to influence the internal stresses. The most important expression to describe stresses can be derived by assuming the conservation of impulse. ρ a = div( σ) + f (equ. 4.1) Where ρ is the density of the body, a is the acceleration, f denotes the distributed forces over the volume and σ, a second ranked tensor, represents the internal stresses. σ σ n n = (equ. 4.2) The distributed forces or stresses over a surface are written in equation 4.2 that is the product between the stress tensor and the surface normal vector n, and can be understood as a boundary condition for equation 4.1. In the case of stress measurement on thin films, which is a static problem, the acceleration is zero and the volume forces are neglected. div ( σ ) = 0 (equ. 4.3) A body under stresses will deform, this means that a point P of the unstressed body moves to the position P’. The vector connecting P and P’ is called displacement u. We consider a short and a long rod with same cross section and made of the same material. Let us say that the change of length is the displacement, than one can see that the displacement of the longer rod is greater than the displacement of the small rod, if the same stress is applied at the ends of both rods. An assessment based on strains to characterize the deformation will show same results for both rods. This means that the influence of geometry does not play a role. 6
Page 1 and 2: Thermal Behaviour of Al/Si(0 0 1) a
Page 3 and 4: Content: i Content 1. Motivation...
Page 5 and 6: iii Content 14. Conclusion and Outl
Page 7 and 8: 2. Introduction Introduction Alread
Page 9: ⎛ a1 . b1 ⎜ ⎜a 2 . b1 ⎜ ⎝
Page 13 and 14: Mechanical properties of crystals B
Page 15 and 16: Mechanical properties of crystals s
Page 17 and 18: ⎛x 1'⎞ ⎛ cos( e1' , e1) ⎜
Page 19 and 20: The last step is the rotation aroun
Page 21 and 22: Basic Physical Properties The compo
Page 23 and 24: Basic Physical Properties Group III
Page 25 and 26: Basic Physical Properties The plane
Page 27 and 28: Basic Physical Properties The elast
Page 29 and 30: 7. Polycrystalline and monocrystall
Page 31 and 32: e = The transformation matrix writt
Page 33 and 34: 2π hkl, R 1 λ λ λ λ λ λ λ
Page 35 and 36: Polycrystalline and monocrystalline
Page 37 and 38: Polycrystalline and monocrystalline
Page 39 and 40: 8.2. Molecular beam epitaxy of GaN/
Page 41 and 42: X-ray Diffraction - Measurements an
Page 43 and 44: 9.3. The High-Resolution Monochroma
Page 49 and 50: I / counts s -1 83000 82000 81000 8
Page 51 and 52: Aluminium on silicon measurement Th
Page 53 and 54: Aluminium on silicon measurement cr
Page 55 and 56: 11. GaN and GaBN on sapphire measur
Page 57 and 58: GaN and GaBN on sapphire measuremen
Page 59 and 60: GaN and GaBN on sapphire measuremen
Page 61 and 62:
GaN and GaBN on sapphire measuremen
Page 63 and 64:
11.5. Theta scans: GaN and GaBN on
Page 65 and 66:
I (2 2 0 5) / counts s -1 500 400 3
Page 67 and 68:
Results of aluminium on silicon Suc
Page 69 and 70:
Results of aluminium on silicon Ten
Page 71 and 72:
12.4. Lattice spacing of silicon su
Page 73 and 74:
Results of aluminium on silicon Aft
Page 75 and 76:
ε 33 0,002 0,000 -0,002 -0,004 12.
Page 77 and 78:
Results of aluminium on silicon ela
Page 79 and 80:
13. Results of GaN/GaBN/Al2O3(0 0 0
Page 81 and 82:
Results of GaN/GaBN/Al2O3(0 0 0 1)
Page 83 and 84:
a 0 / A 3,194 3,192 3,190 3,188 3,1
Page 85 and 86:
ε 11 ε 11 0,0000 -0,0002 -0,0004
Page 87 and 88:
14. Conclusion and Outlook Conclusi
Page 89 and 90:
[10] G. Harsch, R. Schmidt Kristall
Page 91 and 92:
[28] Steffen Weber JWulf http://jcr
Page 93 and 94:
16.2. Stereographic projection of S
Page 95:
16.4. Stereographic projection of s
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Diploma Thesis - Erich Schmid Institute

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