Page 123 - Materials Science and Engineering An Introduction

Summary • 95

Anisotropy • Anisotropy is the directionality dependence of properties. For isotropic materials,
properties are independent of the direction of measurement.

X-Ray Diffraction: • X-ray diffractometry is used for crystal structure and interplanar spacing determina-
Determination of tions. A beam of x-rays directed on a crystalline material may experience diffraction
Crystal Structures (constructive interference) as a result of its interaction with a series of parallel atomic
planes.
• Bragg’s law specifies the condition for diffraction of x-rays—Equation 3.21.

Noncrystalline Solids • Noncrystalline solid materials lack a systematic and regular arrangement of atoms or
ions over relatively large distances (on an atomic scale). Sometimes the term amor-
phous is also used to describe these materials.

Equation Summary

Equation Page
Number Equation Solving For Number
3.1 a = 2R12 Unit cell edge length, FCC 54
volume of atoms in a unit cell V S
3.3 APF = = Atomic packing factor 55
total unit cell volume V C
4R
3.4 a = Unit cell edge length, BCC 56
13
nA
3.8 r = Theoretical density of a metal 60
V C N A
lattice position referenced to the x axis Point coordinate referenced 64
3.9a q =
a to x axis

3.10a u = na x 2 - x 1 b Direction index referenced 67
a to x axis
1 Direction index conversion 70
3.11a u = (2U - V)
3 to hexagonal

3.12a u = 3na a 1 - a 1 b Hexagonal direction index 71
a referenced to a 1 axis
na
3.14a h = Planar (Miller) index referenced 75
A
to x axis
number of atoms centered on direction vector
3.16 LD = Linear density 81
length of direction vector
number of atoms centered on a plane
3.18 PD = Planar density 82
area of plane
Bragg’s law; wavelength–interplanar 89

3.21 nl = 2d hkl sin u spacing–angle of diffracted beam
a
3.22 d hkl = Interplanar spacing for crystals 89
2
2

2h + k + l 2 having cubic symmetry