تكملة المقدمة مواد هندسية It is understood that properties of materials depend on their crystal structure, and many of these properties are directional in nature. For example: elastic modulus of BCC iron is greater parallel to the body diagonal than it is to the cube edge. Thus it is necessary to characterize the crystal to identify specific directions and planes. Specific methods are employed to define crystal directions and crystal planes. Methodology to define crystallographic directions in cubic crystal:
- a vector of convenient length is placed parallel to the required direction.
- the length of the vector projection on each of three axes are measured in unit cell dimensions.
- these three numbers are made to smallest integer values, known as indices, by multiplying or dividing by a common factor.
- the three indices are enclosed in square brackets, [uvw]. A family of directions is represented by . Methodology to define crystallographic planes in cubic crystal:
- determine the intercepts of the plane along the crystallographic axes, in terms of unit cell dimensions. If plane is passing through origin, there is a need to construct a plane parallel to original plane. - take the reciprocals of these intercept numbers.
- clear fractions. - reduce to set of smallest integers.
- The three indices are enclosed in parenthesis, (hkl).
A family of planes is represented by {hkl}. For example, if the x-, y-, and z- intercepts of a plane are 2, 1, and 3. The Miller indices are calculated as: - take reciprocals: 1/2, 1/1, 1/3.
- clear fractions (multiply by 6): 3, 6, 2.