William Stratton Ph.D. Thesis - MINDS@UW Home

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X 2( α + β ) g 1 ∝ d 1 = d hkl 2( α + β ) Figure 2.3: Reciprocal space representation of the contributions to Δθ. α and β are the illumination convergence half angle and the objective aperture half angle respectively. θc is the acceptance angle of the Ewald sphere with the shape function of the lattice points which is proportional to 1/d. θc is the dominant factor in the Bragg active function calculation. Figure from 87 . accepts rays with a half angle β = Qλ with respect to the optic axis, effectively increasing the Ewald shell thickness. The second contribution comes from the small size of the nanocrystals. For a finite crystal, each reciprocal lattice point is replaced by a shape function, which for a spherical crystal is a series of concentric shells. The width of the first shell is ~1 d . For a θc 32
eciprocal lattice point 1 d hkl away from the origin, where dhkl is the plane spacing for {hkl}, the crystal can be rotated through an angle θc ≈ dhkl d and still have the shape function in contact with the Ewald sphere. The total acceptance angle is just the sum of these contributions, ( ) Δ θ = θ + 2 α + β 100 . For our VC-FEM experiments on a TEM α = 4 × 10 -3 radians and β = 6 c × 10 -4 radians. For d = 1 nm and the {111} reflection of Al, θc = 0.2 radians, so θc dominates Δθ and we will neglect α and β where convenient. Ahkl also depends on the multiplicity and geometry of a family of reflections {hkl}. For a given reflection( hkl ) , the incoming beam directions that satisfy the Bragg condition will map − −− out half of a great circle on the unit sphere; the corresponding hkl ⎛ ⎞ ⎜ ⎟ reflection maps out the ⎝ ⎠ other half. Δθ gives this great circle width, making it a “great ribbon”. Ahkl is then the fraction of the unit sphere and surface area covered by all the ribbons from an {hkl} family. Figure 2.4 shows an example of A111 for a cubic crystal and d = 2.0 nm. The number of ribbons is the multiplicity of a family of planes, Mhkl, divided by two, and the fraction of the surface area occupied by the ribbons is approximately ( M ) 2πΔθ hkl 2 1 Ahkl = = MhklΔ θ , (2.24) 4π4 following Freeman et al. 100 . This is an overestimate for Ahkl, since it assumes that the great ribbons are flat and that there are no intersections of the great ribbons on the unit sphere. These approximations are acceptable when the width of the ribbons is small, but fail as they grow larger. We have also calculated Ahkl numerically including these effects, and compare the results as a function of Δθ to 33
Page 1 and 2: MEDIUM RANGE ORDER IN HIGH ALUMINUM
Page 3 and 4: To my wife Elisabeth i
Page 5 and 6: Abstract High Al-content metallic a
Page 7 and 8: Table of Contents List of Figures
Page 9 and 10: List of Figures Figure Page Figure
Page 11 and 12: Figure 2.8: V(Φ) at varying values
Page 13 and 14: electron beam exposure. The sharp f
Page 15 and 16: Figure 5.7: FEM data for Al88Y7Fe5
Page 17 and 18: Chapter 1. Introduction Amorphous m
Page 19 and 20: Material Type Tg ( o C) Reference P
Page 21 and 22: dH / dt (arb. units) time Figure 1.
Page 23 and 24: enough to avoid any nucleation onse
Page 25 and 26: nanocrystals are thermally stable u
Page 27 and 28: The structural difference between t
Page 29 and 30: Structures for various metallic gla
Page 31 and 32: ( , ) V k Q = ( r, , ) − ( r, , )
Page 33 and 34: of 1-3 nm is readily achievable in
Page 35 and 36: than the STEM FEM V 66,67,84 . This
Page 37 and 38: interesting behavior upon devitrifi
Page 39 and 40: Λ is a characteristic ordering len
Page 41 and 42: amorphous matrix crystal l R d R bi
Page 43 and 44: For a crystal oriented to a Bragg c
Page 45 and 46: number of crystals in a column will
Page 47: 3 d π 2 Rt max Zmax Φ = . (2.21)
Page 51 and 52: A hkl 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Page 53 and 54: V(C hklΦ,d) 0.4 0.3 0.2 0.1 0.4 0.
Page 55 and 56: V(C 111 Φ) 0.12 0.10 0.08 0.06 0.0
Page 57 and 58: Φ = 6π d ( 72 − 6π + π ρ) m
Page 59 and 60: V(t) 0.16 0.14 0.12 0.10 0.08 0.06
Page 61 and 62: ⎛ 3 ⎛ 4 6tΩ⎞⎞ d = ⎜ Chkl
Page 63 and 64: Chapter 3. Experimental Set-up Prep
Page 65 and 66: A B 0.25 1/Å 0.25 1/Å Figure 3.1:
Page 67 and 68: 〈IBF〉, to the bright field inte
Page 69 and 70: Once the relative thickness is know
Page 71 and 72: Given that FEM is a quantitative el
Page 73 and 74: eam at a uniform intensity across t
Page 75 and 76: Low Filtering Limit ω l (Å -1 ) 0
Page 77 and 78: sample 101 . Much of the influence
Page 79 and 80: 3.07 Thickness Dependant Thinning A
Page 81 and 82: Residual XRD Intensity (arb. units)
Page 83 and 84: Intensity (arb. units) 0.30 Al 88 Y
Page 85 and 86: 3.08 Beam Induced Crystallization o
Page 87 and 88: Fraction of Atoms 0 120 keV 100 200
Page 89 and 90: V(k) x10 -3 10 8 6 4 2 Al 92 Sm 8 P
Page 91 and 92: to produce an accurate FEM data set
Page 93 and 94: Deformation Al 92Sm 8 sample: Rapid
Page 95 and 96: intensity (arb. units) 3 4 {111} {2
Page 97 and 98: Al2O3 Al hkl d (1/nm) hkl d (1/nm)
Page 99 and 100:
easons. First, the as-spun V(k) for
Page 101 and 102:
atoms locally organized into an FCC
Page 103 and 104:
in Figure 4.6. Still, this begs the
Page 105 and 106:
Φ 0.20 0.15 0.10 0.05 0.00 10 21 A
Page 107 and 108:
Chapter 5. Al88Y7Fe5 and Al88Y7Fe4C
Page 109 and 110:
diffracting condition through the m
Page 111 and 112:
increases the number of Al nanocrys
Page 113 and 114:
Fraction of nanocrystals x10 -3 Fra
Page 115 and 116:
Al 88 Y 7 Fe 5 Enthalpy (J/g) 0 -1
Page 117 and 118:
Al 88Y 7Fe 5 100 nm Al 88Y 7Fe 4Cu
Page 119 and 120:
5.04 Al88Y7Fe4Cu1 Discussion The de
Page 121 and 122:
FEM is sensitive to both critical a
Page 123 and 124:
devitrified structure has the possi
Page 125 and 126:
fraction between the as quenched ma
Page 127 and 128:
number, etc.) can give insight to t
Page 129 and 130:
24. Liquid Metals Website, http://w
Page 131 and 132:
66. Voyles, P. M., Gibson, J. M. &
Page 133:
105. Zuo, J. M. Electron detection
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