Test01_solution - 1 Test # 1 – Solution Problem # 1 The...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Test # 1 – Solution Problem # 1 The CsCl structure is simple cubic with two non-equivalent atoms in a unit cell which have coordinates 1 = r and 2 ˆ ˆ ˆ ( / 2)( ) = + + r x y z a . Denoting the atomic form-factors of the two atoms 1 f and 2 f and taking into account that the reciprocal lattice vector is 2 ˆ ˆ ˆ ( ) h k l a π = + + G x y z , we obtain for the structure factor [ ] 1 1 2 2 1 2 1 2 2 ˆ ˆ ˆ ˆ ˆ ˆ exp( ) exp( ) exp ( ) ( ) 2 exp ( ) a S f i f i f f i h k l a f f i h k l π π & ¡ =- ⋅ +- ⋅ = +- + + ⋅ + + = ¢ £ ¤ ¥ = +- + + G G r G r x y z x y z If 1 2 f f ≠ , for any h , k and l one can observe diffraction peaks provided that the diffraction condition is met. The latter is given by 2 2 G = ⋅ k G . It follows from this expression that 2 sin 2 2 G G kG kG k θ = = = k G & , where 2 k π λ = . Since for cubic lattice 2 2 2 2 2 G h k l d a π π = = + + , we find that 2 2 2 sin 2 h k l a λ θ = + + . The allowed values of h , k and l are therefore limited by the existence of the solution of this equation. Thus, we find that there are 12 planes (non-equivalent by symmetry of the lattice) and the associated scattering angles which are { } { } { } { } { } { } { } { } { } { } { } { } 100 16.57 110 23.79 111 29.60 200 34.78 210 39.62 211 44.31 220 53.77 221 58.82 222 81.08 300 58.82 310 64.40 311 71.06 ° ° ° ° ° ° ° ° ° ° ° ° If 1 2 f f = the diffraction peaks corresponding to odd values of ( h + k + l ) vanish, which is the case for the bcc lattice. Therefore, only scattering from the {110}, {200}, {220}, {222}, and {310} planes will be observed. 2 Problem # 2...
View Full Document

Page1 / 5

Test01_solution - 1 Test # 1 – Solution Problem # 1 The...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online