Incommensurate and commensurate modulated structures

Janssen, T.; Janner, A.; Looijenga-Vos, A.; Wolff, P. M. de

doi:10.1107/97809553602060000624

Abelian module 9.8.4.1

Ambiguities in modulated structure notation 9.8.3.6

Aperiodic lattice 9.8.4.1

Approximations

commensurate 9.8.1.3.2

Arithmetically equivalent point groups 9.8.4.2.2

Arithmetic crystal classes 9.8.1.4.5, 9.8.3.1, 9.8.3.2, 9.8.4.2.2, A9.8.2

(3 + 1)-dimensional 9.8.3.3

Arithmetic equivalence 9.8.1.4.3, 9.8.4.2.2

Arithmetic point groups 9.8.2

Average structure 9.8.2

Basic structural features 9.8.1.1

Basic structure 9.8.1.3.1

Basis

conventional A9.8.2

standard A9.8.2

vectors A9.8.1

Bravais classes 9.8.1.4.1, 9.8.1.4.5, 9.8.2, 9.8.4.3, 9.8.4.3.3, 9.8.4.3.3, A9.8.2

(3 + l)-dimensional 9.8.1.4.5

one-line symbols 9.8.3.1, 9.8.3.3.1

two-line symbols 9.8.3.1, 9.8.3.3.1

Bravais classes

(2 + 1)-dimensional 9.8.3.1

(2 + 2)-dimensional 9.8.3.1

(3 + l)-dimensional 9.8.3.2

Bravais lattice 9.8.2

Centring conditions 9.8.3.3.2

Centring reflection conditions 9.8.3.3.2

for (3 + 1)-dimensional Bravais classes 9.8.3.6

Commensurate approximation 9.8.1.3.2

Compensating transformations 9.8.4.4.1

Compensating translations 9.8.4.4.1

Composite crystal structures 9.8.1.2, 9.8.5.1

Conventional basis A9.8.2

Conventional unit cell 9.8.2

Crystal(s)

definition of 9.8.1.2

displacively modulated 9.8.1.3

ideal 9.8.1.2

intergrowth 9.8.5.1

modulated 9.8.1.2

normal 9.8.1.2

Crystal classes

arithmetic 9.8.1.4.5, 9.8.3.1, A9.8.2

geometric 9.8.1.4.3, 9.8.1.4.5

Crystallographic system 9.8.4.3.2

Dimension of a lattice 9.8.4.1

Direct lattice 9.8.1.4.2

Displacive modulation 9.8.1.1

Equivalent superspace groups 9.8.4.4.1

External space A9.8.1

Full symbols for superspace groups 9.8.3.3.1, 9.8.3.4

Geometric crystal classes 9.8.1.4.3, A9.8.2

Gittergeister (lattice ghosts) 9.8.1.1, 9.8.1.1

Higher-dimensional crystallography 9.8.1.2

Holohedry 9.8.4.3.1, A9.8.2

Ideal crystals 9.8.1.2

Incommensurate modulated structures 9.8.1.1

Intergrowth crystal structures 9.8.1.1

Internal

space 9.8.1.4.4, 9.8.4.1, A9.8.1

translation 9.8.1.4.4

Intrinsic component 9.8.3.3.1

Intrinsic part of a space group 9.8.4.4.1

Lattice(s)

aperiodic 9.8.4.1

Bravais 9.8.2

dimension 9.8.4.1

direct 9.8.1.4.2

holohedry 9.8.4.3.1

rank 9.8.4.1

Lattice bases, standard 9.8.4.1

Lattice ghosts (Gittergeister) 9.8.1.1, 9.8.1.1

Laue class 9.8.4.2.1

Laue point group 9.8.1.2, 9.8.2, 9.8.4.2.1

Main reflections 9.8.1.1

Modulated crystal structures 9.8.1.1, 9.8.1.1

examples 9.8.3.5

types defined 9.8.1.1, 9.8.1.1

Modulation

displacive 9.8.1.1

occupation 9.8.1.1, 9.8.1.5

relations 9.8.4.4.2

Normal crystal 9.8.1.2

Occupation modulation 9.8.1.1, 9.8.1.5

One-line symbols for Bravais classes 9.8.3.1, 9.8.3.1, 9.8.3.3.1

Point group(s) 9.8.4.2

arithmetic 9.8.2

arithmetically equivalent 9.8.4.2.2

definition of A9.8.2

equivalence class 9.8.4.2.2

geometrically equivalent 9.8.4.3.2

Laue 9.8.1.2, 9.8.2

reducible 9.8.4.3.1

Quasicrystals 9.8.1.1

Rank of a lattice 9.8.4.1

Reducible point groups 9.8.4.3.1

Reflection

conditions, special 9.8.3.3.2

Reflections

main 9.8.1.1

satellite 9.8.1.1

Satellite

reflections 9.8.1.1

Short symbols for superspace groups 9.8.3.3.1

Space groups

one-line symbol 9.8.3.3.1

two-line symbol 9.8.3.3.1

Special reflection conditions 9.8.3.3.2

for (3 + 1)-dimensional space groups 9.8.3.3.2

Split basis A9.8.2

Standard basis A9.8.2

Standard lattice bases 9.8.4.1

Structure factor(s) 9.8.4.4.3

Superspace A9.8.2

embedding 9.8.1.2

Superspace groups 9.8.1.2, 9.8.1.4.3, 9.8.3.3, 9.8.4.4, A9.8.2

(2 + 1)-dimensional (table) 9.8.3.4

equivalent 9.8.4.4.1

full symbols 9.8.3.3.1

short symbols 9.8.3.3.1

symbols for 9.8.3.3.1, 9.8.3.4

Superspace groups

(2 + 2)-dimensional (table) 9.8.3.4

(3 + 1)-dimensional (table) 9.8.3.5

Superstructure 9.8.1.3.1

Symmetry

elements, non-crystallographic 9.8.1.1

group 9.8.1.2

Transformation(s)

compensating 9.8.4.4.1

Translation, internal 9.8.1.4.4

Translations, compensating 9.8.4.4.1

Two-line symbols for Bravais classes 9.8.3.1, 9.8.3.3.1

Unit cell

conventional 9.8.2

Vector(s)

basis A9.8.1

module 9.8.1.1, 9.8.4.1, A9.8.1, A9.8.2

Wyckoff positions 9.8.2, 9.8.2

Z-module 9.8.1.1

Chapter 9.8. Incommensurate and commensurate modulated structures

Chapter index