材料化学全英文课件PPT课件

h
12
c
(1 1 0)
a
[100 ]
[110 ]
(100)
Planes and their negatives are identical. Therefore, (02)0(020).
In some situation, p identical.
In cubic systems, a direction that has the same indices as a plane is perpendicular to that plane.
h
2
2.5.2 Plane indices
1. Steps to determinate the plane indices: Establish a set of coordinate axes. Find the intercepts of the planes to be indexed on a, b and c axes (x, y, z).
Lesson five
h
1
2.5 Indices of Crystal Planes and Directions
2.5.1 What’s crystal planes and directions?
The atomic planes and directions passing through the crystal are called Crystal Planes and Crystal Directions respectively.
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9
2. The important direction in cubic crystals: <100> : crystal axes <110> : face diagonal <111> : body diagonal <112> : apices to opposite face-centers
1 1 2 [ 1 1 2 ] [ 1 1 2 ] [ 1 1 2 ] [ 1 1 2 ] [ 1 2 1 ] [ 1 2 1 ] [ 1 2 1 ] [ 1 2 1 ] [ 2 1 1 ] [ 2 1 1 ] [ 2 1 1 ] [ 2 1 1 ] [ 1 1 2 ] [ 1 1 2 ] [ 1 1 2 ] [ 1 1 2 ] [ 1 2 1 ] [ 1 2 1 ] [ 1 2 1 ] [ 1 2 1 ] [ 2 1 1 ] [ 2 1 1 ] [ 2 1 1 ] [ 2 1 1 ]
h
5
6
7
{11}2(11)2(112)(112)(112) (12)1(121)(121)(121) (21)1(211)(211)(211)
Total: 12
{123}(123)(123)(123)(123)(132)
(132)(132)(132)(231)(231)
(231)(231)(213)(213)(213)
c
z
yb
x
a
h
3
Take the reciprocals of the intercepts 1/x, 1/y, 1/z.
Clear fractions but do not reduce to lowest integers.
Enclose them in parentheses, (h k l)
材料科学基础
Fundamental of Materials Science
Prof: Tian Min Bo
Tel: 62795426 ，62772851 E-mail: tmb@
Department of Material Science and Engineering Tsinghua University. Beijing 100084
② Find the coordinates of another point on the direction in questions.
③ Reduce to three smallest integers: u, v, w. ④ Enclose in square brackets [u v w].
3. Family of directions consists of crystallographically equivalent directions, denoted <u v w>
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10
100[100][010][001] [100][010][001]
110[110][110][110][101 ][101 ] [101][011 ][011 ][011]
(213)(312)(312)(312)(312)
(321)(321)(321)(321)
Total: 4×3！=24
h
8
3.5.3 Direction indices
1. Derivation for the crystallographic direction
① As the first above, set the origin on the direction to be indexed.
Example: 1/2,1,2/3 2,1,3/2 (423)
Plane indices referred to three axes a, b and c are also called Miller Indices.
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4
Several important aspects of the Miller indices for planes should be noted:
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11
2.6 Hexagonal Axes for Hexagonal Crystals
2.6.1 Why choose four-axis system?
Four indices has been devised for hexagonal unit cells because of the unique symmetry of the system.