Chapter 7 Introduction to Crystallography

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Interference condition: the difference in path lengths of adjacent lattice points must be a multiple integral of the wavelength. AD-CB = a·s-a·s 0 = Or, The derivation of the Laue equation a·(s-s 0 ) = hλ a(cosα- cosα 0 ) = hλ Where, a— lattice parameter α α 0 α 0 —angle which a makes with s 0 α— angle which a makes with s Expanded to 3D lattice a·(s-s 0 ) = a(cosα-cosα 0 ) = hλ b·(s-s 0 ) = b(cosβ-cosβ 0 ) = kλ c·(s-s 0 ) = c(cosγ-cosγ 0 ) = lλ where, a,b,c—lattice parameter α 0 ,β 0 ,γ 0 —angle which a makes with s 0 α,β,γ —angle which a makes with s h,k,l — indices of diffraction, integers
In the diffraction direction, the difference between the incident and the diffracted beam through any two lattice points must be an integral number of wavelengths. The vector form (000) to (mnp): T mnp = ma + nb +pc The differences in wavelengths: Δ =T mnp ·(s-s 0 ) =(ma +nb +pc) ·(s-s 0 ) = ma ·(s-s 0 )+nb ·(s-s 0 )+pc ·(s-s 0 ) =mhλ+ nkλ+plλ =(mh+nk+pl)λ 2. The Bragg’s Law Bragg discovered that you could consider the diffraction to have arisen from reflection from lattice planes Δ=AD+DB = 2d (hkl) sinθ n s 0 s Condition for diffraction: 2d (hkl) sinθ n = nλ (n=1, 2, 3, … ) θ n : the angle of reflection n: the order of the reflection 2⋅d nhnknl ⋅sinθ nh,nk,nl =λ Reformulated Laue equations: 2d hkl ⋅sinθ = λ hkl — reflection indices θ O θ A B D (d nhnknl =d hkl /n) d hkl
Page 1 and 2: Chapter 7 Introduction to Crystallo
Page 3 and 4: 2. Fundamental characteristics of c
Page 5 and 6: •Definite sharp melting points T
Page 7 and 8: . Lattice and its unit in 2D: T = m
Page 9 and 10: Five 2D lattices a=b γ=120° Primi
Page 11 and 12: Crystal structure = lattice + struc
Page 13 and 14: Atomic Coordinates: Fractional coor
Page 15 and 16: . Bravais Lattice: (14) Unit Cell:
Page 17 and 18: Face-centered cell and its primitiv
Page 19 and 20: * Cubic a=b=c α= β = γ =90º c 9
Page 21 and 22: Monoclinic F = C a.Primitive rhomoh
Page 23 and 24: .Miller indices (hkl) Miller indice
Page 25 and 26: Example: Directions on the (111) pl
Page 27 and 28: 7.1.5 Real crystals and Crystal def
Page 29 and 30: . Point symmetry elements compatibl
Page 31 and 32: ⎡0 ⎢ R(4) = ⎢1 ⎢ ⎣ 0 1 0
Page 33 and 34: Summary of symmetry elements and sy
Page 35 and 36: 7.2.3 The description and applicati
Page 37 and 38: X-rays produced by electronic trans
Page 40 and 41: SPring-8, at Osaka, Japan. www.spri
Page 44 and 45: diffraction crystal planes - (100),
Page 46 and 47: The contribution of the scattering
Page 48 and 49: 2. The intensity of diffraction bea
Page 50 and 51: Types of reflecti on hkl okl 00l sy
Page 52 and 53: Automated diffractometer method 2.
Page 54 and 55: (7) Index and calculate h 2 +k 2 +l
Page 56 and 57: . Applications of powder diffractio
Page 58: Crystal Quasi-crystal There is no t

Chapter 7 Introduction to Crystallography

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