Glossary
https://xraytools.com/glossary
One table for the words that decide an answer — asymmetric unit, setting, zone, multiplicity, centring. Each row says what this site means by it and where somebody else’s meaning would cost you a number rather than an error message.
How to read this
Every row is one word this site uses in a particular way. On this site says what is meant by it here and what it decides; elsewhere names a different meaning common enough to give you a wrong number rather than a puzzled pause.
The row to read first if you are about to type an atom list is asymmetric unit. Supplying a whole cell where a page wants the asymmetric unit is the one mistake here that produces a complete, confident, badly wrong answer with no error message anywhere.
Symbols are next door, on Notation.
Terms
| Term | What it is | On this site | Elsewhere |
|---|---|---|---|
| asymmetric unit | the part of the cell that the symmetry has not yet copied | every page that takes an atom list wants THIS and not the cell contents: the space group does the expanding, so listing the copies as well multiplies every atom by the order of the group and reports a density, a formula weight and an |F| several times too large | a CIF may hold either — _atom_site loops are conventionally the asymmetric unit, but files exported from modelling programs often list a whole cell or a whole molecule |
| Used on: HKL Calculator · Structure Factor Calculator · Crystal Density Calculator · Interatomic Distances and Angles · Displacement Parameters and NPD Atoms | |||
| centring | the extra lattice points a conventional cell carries besides its corners — I, F, A/B/C, R | a property of the LATTICE, which removes whole classes of reflection and never moves one: the peaks a centred cell keeps sit exactly where a P lattice of the same cell dimensions would have put them. Not where “the primitive cell” would — the primitive cell of an F lattice is a different shape with different indices, and it describes the same reflections rather than a subset of them | “centred” is also said loosely of a cell drawn with an atom at its middle, which is a fact about the motif and causes no absence at all |
| Used on: Lattice Explorer · HKL Calculator · Powder Indexing · Reduced Cell and Bravais Lattice · The Ewald Construction · Space Group Reflection Conditions · Space Group from Absences · Wilson Plot and E Statistics | |||
| general position | a point that no operation of the group other than the identity leaves where it is, so the group sends it to as many distinct points as it has operations | the default everywhere an atom is typed: a coordinate like 0.4697 0 0.1666 that happens to sit ON a symmetry element is a special position instead, and the page says so rather than assuming it | the International Tables print the general position first, as the block of coordinate triplets at the head of each group — so “the general position” often means that printed LIST rather than any one point |
| Used on: Space Group Reflection Conditions · Structure Factor Calculator · CIF Parser · Displacement Parameters and NPD Atoms · Wilson Plot and E Statistics | |||
| Wyckoff position | one class of points of a space group that are all held by the same site symmetry, taken together — the general position is one of them and every special position is another | the rows of the table on the space-group page: each is a Wyckoff position, with its multiplicity, its site symmetry and the coordinate triplet that generates it. A point you type is reported as the position it lies ON rather than as a position of its own | the International Tables label them with a letter from a upwards, and that letter is an arbitrary index rather than a property — the same site in a different setting of the same group can carry a different letter |
| Used on: Space Group Reflection Conditions | |||
| point group | the symmetry a crystal has about a point, with every translation dropped: the rotations, mirrors and inversions alone, of which there are 32 in three dimensions | what is left of a space group when the screws become rotations and the glides become mirrors — and, on the reduction page, the symmetry of the lattice METRIC, which is what names the crystal family from the shape of the cell alone | a molecule has a point group too, in Schoenflies notation, and it is the symmetry of one object rather than of a periodic structure — the same symbols, a different subject |
| Used on: Space Group Reflection Conditions · Reduced Cell and Bravais Lattice · HKL Calculator | |||
| holohedry | the point group of the LATTICE — there are seven, one per lattice system rather than one per Bravais type, of which there are 14, and no structure built on that lattice can exceed it. Note this is not always the highest class of the crystal system: a trigonal crystal on a hexagonal P lattice has lattice symmetry 6/mmm, while the highest trigonal class is 3̄m | written holohedral of a Laue class and holohedry of a lattice, which are the adjective and the noun for one thing; the HKL calculator assumes the holohedral class because a crystal system does not fix a point group, and the reduction page reports the holohedry it measured | some texts use “holosymmetric” for the same idea, and a few use “full symmetry” loosely for the space group rather than the point group |
| Used on: HKL Calculator · Reduced Cell and Bravais Lattice | |||
| Laue class | a point group with a centre of symmetry added: 11 classes, not 32 | what decides which reflections are EQUIVALENT, and therefore which arrive at one powder line; to a very good approximation a diffraction pattern cannot see the difference between a class and the same class centrosymmetrised, which is Friedel’s law and is why 32 collapse to 11. The law is exact only while resonant scattering is negligible — it is the small violation that the Friedif page is entirely about | “Laue group” is the same thing and is at least as common in print; neither is the crystal class, which a diffraction experiment on its own cannot determine |
| Used on: Space Group from Absences · HKL Calculator · Space Group Reflection Conditions | |||
| multiplicity | a count of equivalents — and the equivalents are of two quite different things | on the HKL calculator it counts the REFLECTIONS symmetry makes equivalent to the one you asked for, which is what scales a powder peak — strictly, the peak is the sum over every reflection at that angle, and multiplying one |F|2 by the count is exact only while they share it; on the displacement and geometry pages it counts the POINTS a site has in the cell, which is what a Wyckoff letter carries. Same word, different objects, and a page says which by what it is a table of | a CIF’s _atom_site_symmetry_multiplicity is always the second sense — so a value read off a CIF must not be used to scale an intensity. Z′ is not derived from it: it is Z divided by the multiplicity of the general position, one figure for the whole group, and an atom on a special position has a smaller one |
| Used on: HKL Calculator · Intensity Corrections · Structure Factor Calculator · CIF Parser · Displacement Parameters and NPD Atoms · Space Group Reflection Conditions | |||
| setting | which of several axis choices a space group is written in | part of the answer rather than a formatting choice: Pnma, Pbnm and Pmcn are one group with its axes labelled differently, and they give different reflection conditions on the same crystal. The 230 groups have 531 settings here and each has its own table | the ordinary English word turns up on this site too — a monochromator setting, a tube setting — and means nothing crystallographic |
| Used on: Reduced Cell and Bravais Lattice · Space Group Reflection Conditions · Structure Factor Calculator · Interatomic Distances and Angles · Displacement Parameters and NPD Atoms · Space Group from Absences · HKL Calculator | |||
| site symmetry | the operations of the space group that leave a given point exactly where it is | what decides how much of an atom is free to refine: the displacement page derives from it how many of the six components of U a refinement could vary, and it is six only at a general position | also called the site-symmetry group or the stabiliser; papers usually give it as a Hermann–Mauguin symbol in the site’s own axes, which are not always the cell axes |
| Used on: Displacement Parameters and NPD Atoms · Space Group Reflection Conditions | |||
| zone | a set of planes that all contain one common direction, the zone axis | usually named by the class of reflection it produces — h0l, hk0 — because that is the form a reflection condition is written in. A condition on a zone is a glide, and it says nothing whatever about the general reflections | in metallurgy and electron microscopy a “zone axis” is the direction the beam is sent down, which is the same geometry named from the other end |
| Used on: Powder Indexing · Reciprocal Cell Calculator · Space Group Reflection Conditions · Space Group from Absences · Structure Factor Calculator · Interatomic Distances and Angles · Displacement Parameters and NPD Atoms · Wilson Plot and E Statistics · The Patterson Function | |||
A word that is deliberately not here
Form. In crystallography a form is the set of planes symmetry makes equivalent, written {hkl}. It is not a row here because this site uses the word twenty times in its ordinary English sense — the general form of an equation, a closed form, a contact form — and once in the crystallographic one, in the brace-notation row on Notation, where it belongs, because the word is inseparable from the brackets.