Crystallography

NST IA Materials and Mineral Sciences Course Course A, Lecture Lecture 4 Lattice Vectors, Lattice Planes and Miller Indices

The ‘language’ of crystallography crystallography

How does the arrangement arrangement of atoms in crystals cr ystals affect growth (morphology), deformation etc?

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General lattice vector: t = U a + a + V b + b + W c























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After deformation Cd crystal before deformation Easy slip occurs along close-packed planes slip steps

slip planes

constructive interference of diffracted x-rays occurs when: λ = 2 d h k l s i n θ (Bragg’s law) h k l are ‘Miller indices’










































Astrobiology Magnetotactic bacteria






















morphologies of iron oxide crystals



































































origin at corner of unit cell















































1 s t plane away from origin
























1 s t plane away from origin













































































































































































































































































































































































































(1) intercepts of plane with axes


choose an origin ( 2 ) c h o o s e 1 st plane away from origin

b / k a / h

Defines

(2 1) planes 1 s t plane away from origin procedure (a) select an origin at corner of unit cell from which intercepts of planes along axes can be seen. (b) determine the positions of intercepts of the first plane away from the origin along x, y and z axes. (c) intercepts are at a/h, b/k and

origin

1 st

(3) look at intercepts a / = a / ; h = 2 h 2 b / = b / ; k = 1 k 1

Intercepts x-axis at 1 a / = a / ; h = 1 h 1 Intercepts y-axis at ∞

plane from origin ∞

(1 0) planes

= b / k = b / 0 ; k = 0
























b / k a / h

Defines


origin

1 st




(1 0) planes

= b / k = b / 0 ; k = 0
























b / k a / h

Defines


origin

1 st




(1 0) planes

= b / k = b / 0 ; k = 0
























b / k a / h

Defines


origin

1 st




= b / k = b / 0 ; k = 0

(1 0) planes a /

h =

a /

2 ; h=2
























b / k a / h

Defines


origin

1 st




= b / k = b / 0 ; k = 0

(1 0) planes a / b

h =

a /

2 ; h=2

























b / k a / h

Defines

(2 1) planes 1 s t plane away from origin

choose an origin ( 2 ) c h o o s e 1 st plane away from origin (3) look at intercepts a / = a / ; h = 2 h 2 b / = b / ; k = 1 k 1 Intercepts x-axis at 1 a / = a / ; h = 1























(1)

b / k a / h (2 1) planes

choose an origin ( 2 ) c h o o s e 1 st plane away from origin (3) look at intercepts a / = a / ; h = 2 h 2 b / = b / ; k = 1 k 1 Intercepts x-axis at 1 a / a / ; h = 1























(1)



origin y

x























(1)



origin y a/3 x























(1)



origin y a/3

-b/1

x

























(1)

choose an origin ( ) c h o o s e 1 st























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Crystallography

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