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ME 2203 Engineering Materials: Dr. Kazi Md. Shorowordi

The document discusses crystallographic points, directions, and planes in crystalline solids. It describes how to specify the coordinates of points within a unit cell and determine the Miller indices that represent crystallographic directions. Examples are provided on locating points with given coordinates, specifying coordinates for all atom positions in a body-centered cubic unit cell, and drawing a specified crystallographic direction within a cubic unit cell.

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Tahmim Alam
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35 views9 pages

ME 2203 Engineering Materials: Dr. Kazi Md. Shorowordi

The document discusses crystallographic points, directions, and planes in crystalline solids. It describes how to specify the coordinates of points within a unit cell and determine the Miller indices that represent crystallographic directions. Examples are provided on locating points with given coordinates, specifying coordinates for all atom positions in a body-centered cubic unit cell, and drawing a specified crystallographic direction within a cubic unit cell.

Uploaded by

Tahmim Alam
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Lecture: 05

ME 2203 Engineering Materials


Topic: The Structure of Crystalline Solids (Contd.)
Materials Science and Engineering, WD Callister, Jr. and DG Rethwisch, 8th
Edition, SI Version, John Wiley and Sons, 2011 (Chapter 3)

Dr. Kazi Md. Shorowordi


Department of MME
Bangladesh University of Engineering and Technology, Dhaka - 1000
CRYSTALLOGRAPHIC POINTS, DIRECTIONS AND PLANES
POINT COORDINATES
• The position of any point located within a unit cell may be
specified in terms of its coordinates as fractional multiples
of the unit cell edge lengths (i.e., in terms of a, b and c).

2
EXAMPLE 01 Location of Point Having Specified Coordinates
• For the unit cell shown in the accompanying sketch (a),
locate the point having coordinates ¼ 1 ½.

3
EXAMPLE 02 Specification of Point Coordinates
• Specify point coordinates for all atom positions for a BCC
unit cell.

4
CRYSTALLOGRAPHIC DIRECTIONS
• Certain directions in the unit cell are of particular importance.

• Miller indices for directions are the shorthand notation used to describe these directions.

• The procedure for finding the Miller indices for directions is as follows:

1. A vector of convenient length is positioned such that it passes through the origin of
the coordinate system. Any vector may be translated throughout the crystal lattice without
alteration, if parallelism is maintained.

2. The length of the vector projection on each of the three axes is determined; these are
measured in terms of the unit cell dimensions a, b, and c.

3. These three numbers are multiplied or divided by a common factor to reduce them
to the smallest integer values.

4. The three indices, not separated by commas, are enclosed in square brackets, thus:
[uvw]. The u, v, and w integers correspond to the reduced projections along the x, y, and z axes,
respectively.

• The [100], [110], and [111] directions are common ones; they are drawn in the unit cell shown
in the Figure. 5
6
Determination of Directional Indices

7
Construction of Specified Crystallographic Direction
• Draw a [110] direction within a cubic unit cell.

8
Determine the Miller indices of directions A, B, and C

Crystallographic directions and coordinates

100  Direction A
111  Direction B
122  Direction C
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