Crystallography Basics - Review

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Crystallography Basics

(continued)

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Identical (same) environment: Same environment and basis positions after 2 different lattice translations in ‘blue’ :

- They can fill an infinite plane and can be arranged in different ways on lattice

Crystallography Basics

(continued)

lattice parameters

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Translation (lattice) vector

For example, if we want to go from one corner to another across a body diagonal…….

R

Crystallography Basics

(continued)

3-D lattice showing position vector (R or r) = primitive (or

lattice) vectors a, b and c with integer coefficients u, v and w

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If a,b,c cell lengths are

different, e.g. orthorhombic

If a,b,c cell lengths are

equal, e.g. cubic

[011]

[111]

[110]

[uvw]:

[001]

[101]

[100]

[325]=?

The Four 2-D Crystal Systems (Shapes)

2-D lattice showing position vector (R) = primitive (or

lattice) vectors a and b with integer coefficients u and v:

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The four 2-D crystal systems: (a) square, (b) rectangular, (c)

hexagonal and (d) oblique:

These are

the only 4

possible

2-D crystal

systems

Crystallography Basics

(continued)

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Mirror

planes

(reflection)

Mirror planes

180° in-

plane

rotation

Crystallography Basics

(continued)

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**Recently quasicrystals were discovered and do not belong to 1 of 230

8These are the only 7 possible 3-D crystal systems

(know them and their 6 lattice parameters)

Unit cell: smallest repetitive volume

which contains the complete lattice

pattern of a crystal.

The Seven 3-D Crystal Systems (Shapes)

“from your Callister Book”

Trigonal - has 3-fold

rotation (120°) normal to the

body diagonal, e.g. {11ī}

has 3-fold symmetry

denoted with triangle shape.

Monoclinic- has 2-fold

rotation (180°) normal to the

centers of 2 unit cell edges going

through the opposite sides of the

cell, e.g. {01ī} has 2-fold symmetry

denoted with diad shape.

The Seven 3-D Crystal Systems

(continued)

Cubic- has 2,3 and 4-fold

(90°) rotations, e.g. {001}

has 4-fold symmetry denoted

with square shape.

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Cubic Crystal System Symmetry

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From John D. Verhoeven, Fundamentals of Physical Metallurgy,

Wiley, New York, 1975, p. 16

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Summary of the

Seven 3-D Crystal Systems