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The reflexion of X-rays from the ‘anti-phase nuclei’ of AuCu 3 . II

1966; Royal Society; Volume: 290; Issue: 1423 Linguagem: Inglês

10.1098/rspa.1966.0066

2053-9169

Arthur James Cochran Wilson, L. Zsoldos,

Theoretical and Computational Physics

A simplified method of calculating the diffraction patterns of crystals showing mistake broadening is outlined, and used to correct three results published by Wilson in 1943. Wilson’s model 3 (mistakes on {110} planes) is extended in the light of probable differences of the energy of interfaces between domains of different types. The apparent particle sizes obtained, when differences in interfacial energy are ignored, are: formistakes on { 100 } planes 3 N 1 2 / 2 ( h + k + l ) δ ; formistakes on { 110 } planes 3 ( 2 N ) 1 2 / 4 ( 2 h + k ) δ ; formistakes on { 111 } planes 3 ( 3 N ) 1 2 / 8 h δ if h ≥ k + l , 3 ( 3 N ) 1 2 / 4 ( h + k + l ) δ if h < k + l ; where δ is the probability of a mistake per unit length, h, k, l are the positive values of the indices of reflexion arranged in the order h ≥ k ≥ 1, and N = h 2 + k 2 + l 2 . When differences in interfacial energy are taken into account the apparent particle size for mistakes on {100} planes becomes 2 N 1 2 / { 2 ( h + k + l − u ) δ ′ + ( h + k + l + u ) δ ′ ′ } , where u is the impaired index, and that for mistakes on {110} planes becomes ( 2 N ) 1 2 / { 4 h δ ′ + 2 ( h + k ) δ ′ ′ } when ( 2 N ) 1 2 / { 2 ( h + k ) δ ′ + ( 3 h + k ) δ ′ ′ } when k or l is the unpaired index. All {111} interfaces have the same energy in AuCu 3 , so the expressions for mistakes on {111} planes are not altered.