## Elements of X-ray Diffraction |

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Page 31

Table 2-1 Crystal Systems and

nonequality by reason of symmetry. Accidental equality may occur, as shown by

an example in Sec. 2-4.) * Also called trigonal. spaced and mutually

perpendicular, the unit cell is cubic. In this case the vectors a, b, c are all equal

and at right angles to one another, or a = b = c and a = /3 = 7 = 90°. By thus giving

special values to the axial lengths and angles, we can produce unit cells of

various shapes and therefore ...

Table 2-1 Crystal Systems and

**Bravais Lattices**(The symbol ^ impliesnonequality by reason of symmetry. Accidental equality may occur, as shown by

an example in Sec. 2-4.) * Also called trigonal. spaced and mutually

perpendicular, the unit cell is cubic. In this case the vectors a, b, c are all equal

and at right angles to one another, or a = b = c and a = /3 = 7 = 90°. By thus giving

special values to the axial lengths and angles, we can produce unit cells of

various shapes and therefore ...

Page 43

The cardinal principle of crystal structure is that the atoms of a crystal are set in

space either on the points of a

points. It follows from this tLc^ the atoms of a crystal will be arranged periodically

in three dimensions and that this arrangement of atoms will exhibit many of the

properties of a

simplest crystals one can imagine are those formed by placing atoms of the same

kind on ...

The cardinal principle of crystal structure is that the atoms of a crystal are set in

space either on the points of a

**Bravais lattice**or in some fixed relation to thosepoints. It follows from this tLc^ the atoms of a crystal will be arranged periodically

in three dimensions and that this arrangement of atoms will exhibit many of the

properties of a

**Bravais lattice**, in particular many of its symmetry elements. Thesimplest crystals one can imagine are those formed by placing atoms of the same

kind on ...

Page 47

For example, if the structure is based on a body-centered

must be possible to go from an A atom, say, to another A atom by the translation

22^- (2) The set of A atoms in the crystal and the set of B atoms must separately

possess the same symmetry elements as the crystal as a whole, since in fact they

make up the crystal. In particular, the operation of any symmetry element present

must bring a given atom, A for example, into coincidence with another atom of the

...

For example, if the structure is based on a body-centered

**Bravais lattice**, then itmust be possible to go from an A atom, say, to another A atom by the translation

22^- (2) The set of A atoms in the crystal and the set of B atoms must separately

possess the same symmetry elements as the crystal as a whole, since in fact they

make up the crystal. In particular, the operation of any symmetry element present

must bring a given atom, A for example, into coincidence with another atom of the

...

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### Common terms and phrases

absorption coefficient absorption edge alloy atomic number austenite axes axis back-reflection Bragg angle Bragg law Bravais lattice calculated camera chart circle composition constant copper cos2 counter counting rate cubic curve Debye ring Debye-Scherrer decreases determined diffracted beam diffraction lines diffraction pattern diffractometer direction distance effect electrons elements equation error example face-centered face-centered cubic factor film filter given grain hexagonal incident beam indices integrated intensity lattice parameter Laue method martensite measured metal normal obtained orthorhombic parallel percent phase photograph pinhole plotted point lattice pole figure position powder pattern preferred orientation produced pulses rays reciprocal lattice reflecting planes relative rhombohedral rotation sample scattering shown in Fig sin2 slit solid solution spacing specimen sphere stereographic projection stress structure substance surface symmetry temperature tetragonal thickness tion transmission twin twin band unit cell vector voltage wave wavelength x-ray beam x-ray diffraction x-ray tube zero zone