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

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30 Tilt boundary Each dislocation accommodates the mismatch between the two lattices; for a or misorientation axis in the boundary plane, only one type of dislocation (a single Burgers vector) is required. b D
31 Read-Shockley contd. • For an infinite array of edge dislocations the longrange stress field depends on the spacing. Therefore given the dislocation density <strong>and</strong> the core energy of the dislocations, the energy of the wall (boundary) is estimated (r 0 sets the core energy of the dislocation): γ gb = E 0 θ(A 0 - lnθ), where E 0 = µb/4π(1-ν); A 0 = 1 + ln(b/2πr 0 )
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 and 14: 13 Definition of Dihedral Angle •
Page 15 and 16: 15 Unequal energies • If the inte
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: 29 Read-Shockley model • Start wi
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

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

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