International notation, 218
Interplanar spacing, 49, 53, 65, 66, 115, 154,
156–162, 174–176, 273, 275–278, 280,
281, 285, 287, 292, 294–296, 340, 341,
343–346, 349–351, 372
Inversion operation, 221
Isomorphic group, 244
L
Lattice centering, 18, 21–25
Laue
equation, 274
method, 355
Linear atomic density, 114–116, 131, 132
M
Matrices
adjoint, 232
inverse, 232
orthogonal, 225, 229
singular, 232
square, 232
Miller Bravais Indices, 149, 151–153, 173
Mirror
plane, 95–97, 209–216, 218, 222, 226–228,
241, 248, 251, 258
symmetry, 18, 95–97, 209, 211, 212, 226,
251
Monoclinic, 10, 15, 18, 20–24, 52, 53, 56, 89,
110, 157, 214, 226, 252, 259, 309
N
Neutron diffraction, 284
O
Oblique lattice, 4, 20, 21, 34, 72, 74
Oblique system, 103, 104, 156
Order of the group, 239, 240, 242, 247
Orthogonal axes, 24, 50, 100, 138, 148, 154,
220, 223–225
Orthogonal matrix, 236–238
Orthorhombic, 6, 14, 18, 20, 23, 24, 35, 36, 38,
53, 110, 111, 113, 139, 141, 144, 155,
157, 161, 169, 175, 182–184, 195, 196,
202, 204, 205, 214, 215, 227, 228, 252,
259, 346
Oscillation method, 361
P
Packing efficiency, 120–123, 125–127
Planar atomic density, 114–116, 132
Plane
group, 97, 241, 248
lattice, 190, 192
Point group, 17, 18, 96, 97, 230, 238, 240–242,
244–251, 259–261
Powder method, 339
Primitive lattice, 16, 17, 19–21, 23, 24, 155,
190, 192, 199–201
Proper rotation, 209, 212, 222, 223, 230
R
Reciprocal lattice, 48–57, 59–69, 71–80, 82,
88–90, 156, 164, 179, 194, 274, 301
Rectangular lattice, 4, 10, 17, 21, 22, 34, 50,
74, 115, 131
Reflection symmetry, 209, 212, 218
Representation of
directions, 145
planes, 145
Rotation/oscillation method, 361
Rotational symmetry, 99–102, 127, 128, 210,
213, 220, 251
Rotoinversion, 18, 209–211, 218, 230
Rotoreflection, 18, 209–211, 218, 230
S
Schoenflies notation, 209, 218
Space
group, 246
lattice, 1–3, 8, 9, 16–18, 51, 57, 59, 89, 274
Square lattice, 5, 6, 11–13, 21, 35, 69, 70, 82,
87, 91, 112, 115, 130, 132, 134
Structure factor, 299–302, 304–306, 308–311,
313–335
Subgroup, 246, 247
Super group, 246, 247
Symmetry element, 20, 96, 97, 209, 214–218,
238–244, 246, 248–252, 260, 261
Symmetry operations, 95–97, 209, 219, 222,
224, 228, 238, 248, 249
T
Tetragonal lattice, 24, 86
Transformation of indices of
crystal planes, 180
directions, 193
Triclinic lattice, 18, 20, 53, 95, 98, 104, 105,
110, 127, 156, 157
Trigonal lattice, 46, 198
Two dimensional lattice, 2, 17, 18, 55, 213
U
Unit cell
calculation, 95
composition, 1
construction, 41
386
Index
Interplanar spacing, 49, 53, 65, 66, 115, 154,
156–162, 174–176, 273, 275–278, 280,
281, 285, 287, 292, 294–296, 340, 341,
343–346, 349–351, 372
Inversion operation, 221
Isomorphic group, 244
L
Lattice centering, 18, 21–25
Laue
equation, 274
method, 355
Linear atomic density, 114–116, 131, 132
M
Matrices
adjoint, 232
inverse, 232
orthogonal, 225, 229
singular, 232
square, 232
Miller Bravais Indices, 149, 151–153, 173
Mirror
plane, 95–97, 209–216, 218, 222, 226–228,
241, 248, 251, 258
symmetry, 18, 95–97, 209, 211, 212, 226,
251
Monoclinic, 10, 15, 18, 20–24, 52, 53, 56, 89,
110, 157, 214, 226, 252, 259, 309
N
Neutron diffraction, 284
O
Oblique lattice, 4, 20, 21, 34, 72, 74
Oblique system, 103, 104, 156
Order of the group, 239, 240, 242, 247
Orthogonal axes, 24, 50, 100, 138, 148, 154,
220, 223–225
Orthogonal matrix, 236–238
Orthorhombic, 6, 14, 18, 20, 23, 24, 35, 36, 38,
53, 110, 111, 113, 139, 141, 144, 155,
157, 161, 169, 175, 182–184, 195, 196,
202, 204, 205, 214, 215, 227, 228, 252,
259, 346
Oscillation method, 361
P
Packing efficiency, 120–123, 125–127
Planar atomic density, 114–116, 132
Plane
group, 97, 241, 248
lattice, 190, 192
Point group, 17, 18, 96, 97, 230, 238, 240–242,
244–251, 259–261
Powder method, 339
Primitive lattice, 16, 17, 19–21, 23, 24, 155,
190, 192, 199–201
Proper rotation, 209, 212, 222, 223, 230
R
Reciprocal lattice, 48–57, 59–69, 71–80, 82,
88–90, 156, 164, 179, 194, 274, 301
Rectangular lattice, 4, 10, 17, 21, 22, 34, 50,
74, 115, 131
Reflection symmetry, 209, 212, 218
Representation of
directions, 145
planes, 145
Rotation/oscillation method, 361
Rotational symmetry, 99–102, 127, 128, 210,
213, 220, 251
Rotoinversion, 18, 209–211, 218, 230
Rotoreflection, 18, 209–211, 218, 230
S
Schoenflies notation, 209, 218
Space
group, 246
lattice, 1–3, 8, 9, 16–18, 51, 57, 59, 89, 274
Square lattice, 5, 6, 11–13, 21, 35, 69, 70, 82,
87, 91, 112, 115, 130, 132, 134
Structure factor, 299–302, 304–306, 308–311,
313–335
Subgroup, 246, 247
Super group, 246, 247
Symmetry element, 20, 96, 97, 209, 214–218,
238–244, 246, 248–252, 260, 261
Symmetry operations, 95–97, 209, 219, 222,
224, 228, 238, 248, 249
T
Tetragonal lattice, 24, 86
Transformation of indices of
crystal planes, 180
directions, 193
Triclinic lattice, 18, 20, 53, 95, 98, 104, 105,
110, 127, 156, 157
Trigonal lattice, 46, 198
Two dimensional lattice, 2, 17, 18, 55, 213
U
Unit cell
calculation, 95
composition, 1
construction, 41
386
Index