Grain Boundary Properties: Energy (L21) - Materials Science and ...

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14 Dihedral Angles • An material with uniform grain boundary energy should have dihedral angles equal to 120°. • Likely in real materials? No! Low angle boundaries (crystalline materials) always have a dislocation structure <strong>and</strong> therefore a monotonic increase in energy with misorientation angle (Read- Shockley model). • The inset figure is taken from a paper in preparation by Prof. K. Barmak <strong>and</strong> shows the distribution of dihedral angles measured in a 0.1 µm thick film of Al, along with a calculated distribution based on an GB energy function from a similar film (with two different assumptions about the distribution of misorientations).
15 Unequal energies • If the interfacial energies are not equal, then the dihedral angles change. A low g.b. energy on boundary 1 increases the corresponding dihedral angle. 1 2 3 χ 1>120° γ 1
Page 1 and 2: 1 Carnegie Mellon MRSEC Grain Bound
Page 3 and 4: 3 Outline • Motivation, examples
Page 5 and 6: 5 Properties, phenomena of interest
Page 7 and 8: 7 • Grain boundary sliding should
Page 9 and 10: 9 Measurement of GB Energy • We n
Page 11 and 12: 11 Zero-creep Method • The zero-c
Page 13: 13 Definition of Dihedral Angle •
Page 17 and 18: 17 Wetting • For a large enough r
Page 19 and 20: 19 Triple Junction Quantities • G
Page 21 and 22: 21 Derivation of Herring Equs. A vi
Page 23 and 24: 23 γ S2 Analysis of Thermal Groove
Page 25 and 26: Bi impurities in Ni have the opposi
Page 27 and 28: 27 Grain boundary energy: current s
Page 29 and 30: 29 Read-Shockley model • Start wi
Page 31 and 32: 31 Read-Shockley contd. • For an
Page 33 and 34: 33 Read-Shockley contd. • If the
Page 35 and 36: 35 Exptl. vs. Computed E gb Tilts
Page 37 and 38: 37 2 i i+2 r ij1 l’ ij j 1 j 3 r
Page 39 and 40: 39 Tilt versus Twist Boundaries Iso
Page 41 and 42: 41 λ(Δg, n) λ(n|5°/[100]) λ(n|
Page 43 and 44: 43 For all grain boundaries in MgO
Page 45 and 46: 45 Symmetric [110] tilt boundaries
Page 47 and 48: 47 Inclination Dependence • Inter
Page 49 and 50: 49 The torque term Change in inclin
Page 51 and 52: 51 Herring’s Relations
Page 53 and 54: 53 Aluminum foil, cross section •
Page 55 and 56: 55 How to Measure Dihedral Angles a
Page 57 and 58: 57 Calculation of G.B. Energy • I
Page 60 and 61: 60 3 ⎪⎪⎧⎧ ∑ ⎨⎨σ ˆ j
Page 62 and 63: 62 Grain Boundary Energy Calculatio
Page 64 and 65:
64 # of total TJs : 8694 # of {111}
Page 66 and 67:
66 Capillarity Vector • The capil
Page 68 and 69:
68 Capillarity vector definition
Page 71 and 72:
71 Computer Simulation of Grain Gro
Page 73 and 74:
73 • Steady state population deve
Page 75 and 76:
75 G.B. Energy: Summary • For low
Page 77 and 78:
77 Supplemental Slides
Page 79:
79 Expanded Young Equations • Pro
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