Notation
https://xraytools.com/notation
One table for the symbols that change role between pages — F, I, s, d, B, U, R, brackets and stars. Each row says what this site means by it, and where another field means something else by the same letter.
How to read this
Every row is one symbol. This site says what it means here and how it is written; elsewhere names a convention common enough in neighbouring fields to give you wrong numbers rather than an error message. The reciprocal-cell row is the one to read first if you have come from solid-state physics.
Symbols
| Symbol | Read as | Quantity and unit | On this site | Elsewhere |
|---|---|---|---|---|
| d | dee | interplanar spacing, Å | the spacing of a NAMED set of planes, d(hkl), with the order n folded into the indices — except dmin, the resolution of a whole data set: the smallest spacing it reaches, which names no planes | texts that keep nλ = 2d sin θ use d for the first-order spacing only |
| Used on: Bragg Calculator · HKL Calculator · Reciprocal Cell Calculator · Powder Indexing · Refinement Statistics and R Factors | ||||
| θ, 2θ | theta, two theta | Bragg angle and scattering angle, degrees | the Bragg calculator takes whichever you say, and every other form labels the one it wants; a powder pattern is always plotted against 2θ | single-crystal work quotes θ more often, so a “27.5° data set” usually means θ |
| Used on: Bragg Calculator · HKL Calculator · Peak Finding · Intensity Corrections · Refinement Statistics and R Factors | ||||
| s | ess | sin θ / λ, Å−1 | always sin θ/λ, which is half the scattering vector and is what scattering-factor fits are tabulated against | s or q for 4π sin θ/λ is standard in scattering physics — a factor of 4π out |
| Used on: Structure Factor Calculator · Wilson Plot and E Statistics | ||||
| (hkl) | a plane, spoken “aitch kay ell” | one family of lattice planes | round brackets are always a PLANE; a bar over a digit is the negative | some software writes −1 for the bar, which sorts differently and reads the same |
| Used on: HKL Calculator · Reciprocal Cell Calculator · Space Group Reflection Conditions · Space Group from Absences | ||||
| [uvw] | a direction | a direction in the crystal | square brackets are always a DIRECTION, and it is not the normal to the plane with the same numbers unless the metric makes it so | universal — but the fact that it differs from (hkl) is the thing most often assumed away |
| Used on: Reciprocal Cell Calculator · The Ewald Construction | ||||
| {hkl}, ⟨uvw⟩ | a form, a family | all planes or directions symmetry makes equivalent | braces and angle brackets are the SET; the count of members is the multiplicity that scales a powder peak | universal, and frequently omitted in prose where the set is meant |
| Used on: HKL Calculator · Space Group Reflection Conditions | ||||
| a*, b*, c* | a star | reciprocal cell edges, Å−1 | no 2π: a* = bc sin α / V, so |d*(hkl)| = 1/d. This is the crystallographic convention | solid-state physics puts 2π in, making every reciprocal magnitude 6.283 times larger. Nothing errors; every number is wrong |
| Used on: Reciprocal Cell Calculator · The Ewald Construction · Reduced Cell and Bravais Lattice | ||||
| F, |F| | the structure factor, its modulus | the summed scattering of one cell for one reflection, electrons | F is complex — amplitude and phase. |F| alone is what survives a measurement | Fo and Fc for observed and calculated are universal and appear here in the R-factor definitions |
| Used on: Structure Factor Calculator · Fourier Synthesis and the Phase Problem · Charge Flipping · Difference Map · Wilson Plot and E Statistics · Refinement Statistics and R Factors | ||||
| I | intensity | what a detector records, counts | always the MEASURED or simulated quantity, proportional to |F|² once corrected — never used as a synonym for |F| | widely used loosely for |F|² itself, which hides the corrections between them |
| Used on: HKL Calculator · Intensity Corrections · The Patterson Function · Wilson Plot and E Statistics | ||||
| E | ee, a normalised structure factor | dimensionless | |F| divided by the root mean square |F| of its own resolution shell — |E|² = |F|²/⟨|F|²⟩, so the angle dependence is removed, ⟨|E|²⟩ is 1 by construction and the statistics become comparable. Dividing by the mean |F| instead would put ⟨|E|²⟩ at 1.27 or 1.57 and every threshold on the Wilson page out of reach | E is also energy in the radiation pages — different quantity, same letter, and the context is always the page |
| Used on: Wilson Plot and E Statistics · Direct Methods and the Sign Relation | ||||
| U, B | you, bee | displacement parameters, Å2 | B = 8π²U. U is a mean-square displacement and is what a CIF stores; B is the older form and is what a Wilson plot’s slope gives | both are in current use, so a number near 0.02 is almost certainly U and one near 1.6 almost certainly B |
| Used on: Displacement Parameters and NPD Atoms · Wilson Plot and E Statistics · Interatomic Distances and Angles | ||||
| Z, V | zed, vee | formula units per cell; cell volume, Å3 | beside a cell, Z counts FORMULA UNITS, not atoms and not molecules where the two differ. Beside an element it is the atomic number, which is the sense on the radiation pages and wherever a scattering factor is discussed | Z′ for formula units per asymmetric unit is common in papers and is a different number |
| Used on: Crystal Density Calculator · Reciprocal Cell Calculator · Structure Factor Calculator | ||||
| μ, μ/ρ | mew, mew over rho | linear and mass attenuation coefficient, mm−1 and cm² g−1 | μ/ρ is the property of the SUBSTANCE and μ the property of the SPECIMEN — only the second depends on density, and only the second decides a crystal size | μ is quoted in mm−1 by CIFs and in cm−1 by much of the older literature |
| Used on: Absorption Coefficient Calculator · Intensity Corrections | ||||
| R1, wR2, S | are one, weighted are two, the goodness of fit | refinement residuals; dimensionless | R1 on F over the observed reflections, wR2 on F² over all of them — two quantities, not one measured twice | plain R in older papers is almost always today’s R1 |
| Used on: Refinement Statistics and R Factors | ||||
| Rint | are internal | agreement between symmetry equivalents; dimensionless | computed from the equivalents as they merge, so it describes the MEASUREMENT and bounds no other R | Rmerge and Rsym name close variants with different denominators |
| Used on: Refinement Statistics and R Factors | ||||
| x, u(x) | the Flack parameter and its standard uncertainty | fraction of the inverted component; dimensionless | always quoted as the pair — x without u(x) is not a weak determination, it is none | e.s.d. is the older name for the same quantity and appears in the papers cited here |
| Used on: Refinement Statistics and R Factors · Friedif Calculator | ||||
| K | kay | three different dimensionless constants | three senses, by page: the Scherrer shape constant on the broadening page, about 0.9; the scale factor between observed and absolute intensities on the Wilson and corrections pages; and, further down the corrections page, the polarisation ratio of a monochromator, cos² 2θM, which is 1 without one. None is the others | the overall scale factor of a refinement is as often a lower-case k, and SHELXL calls it OSF — which is the reason the letter is worth checking before a formula is copied between pages |
| Used on: Line Broadening · Intensity Corrections · Wilson Plot and E Statistics | ||||
| f0, f′, f″ | eff nought, eff prime, eff double prime | atomic scattering factor and its resonant parts, electrons | f″ is the part that breaks Friedel’s law and so the whole of the absolute-structure signal | Δf′ and Δf″ are the same quantities in the International Tables |
| Used on: Friedif Calculator · Structure Factor Calculator · Absorption Coefficient Calculator | ||||