Reading and sources

The papers behind each calculation

This list is books, tables and programs. The method papers — Scherrer and Williamson–Hall behind the line broadening, Wilson behind the intensity statistics, Niggli and Gruber behind the cell reduction, Moseley, Cochran, Oszlányi and Sütő, de Wolff and Smith–Snyder — are cited on the pages whose calculations they are, in a Where this comes from panel at the foot of each: 53 papers across 27 pages, each with the DOI. A source sits beside the thing it is the source of, which is why they are not repeated here.

Start here

One book, if you are going to read one. It assumes no crystallography and gets as far as space groups and diffraction without ever asking you to take a symmetry argument on trust, which is rarer than it sounds. Its author has kept a blog on the same subject for years, and that is where the book carries on.

Introduction to Crystallography

Frank Hoffmann, Springer, 2020

Symmetry from the ground up: point groups, the 230 space groups, how to read an International Tables page, and what a diffraction pattern is telling you. It is the book to read alongside the space group tables here.

Faszination Kristalle und Symmetrie

Frank Hoffmann, Springer Spektrum, 2016

The German original of the same book, under a different title.

The Fascination of Crystals and Symmetry

Frank Hoffmann, Universität Hamburg

The same author’s blog, named after the German edition above, and the one place on this list that is still being written. Its space group diagrams are worked through group by group, and there is a long run of posts on nets and topology that this site does not touch at all. It is the nearest thing to a commentary on the space group tables here.

The tables this site computes from

These are the published sources the calculators are built on. Where a dataset is shipped with the site it was generated from the source below by a script in the repository, never transcribed by hand.

International Tables for Crystallography

International Union of Crystallography

The reference work. Volume A is the 230 space groups — their symmetry operations, general and special positions, and reflection conditions; Volume C carries the atomic scattering factors behind the structure factor.

spglib

Atsushi Togo and contributors

A crystal symmetry library whose database encodes the symmetry operations of all 530 settings the Tables list. It is the machine-readable route to Volume A used here: the operations are read from it, and everything this site says about a space group — the conditions, the elements, the general position — is derived from those operations rather than transcribed.

Atomic weights and isotopic compositions

NIST, Physical Measurement Laboratory

The isotope masses and representative abundances behind the isotope pattern. Every mass on this site that is not a standard atomic weight comes from here.

Standard atomic weights

CIAAW, the IUPAC commission

The atomic weights and their uncertainties, which is what an elemental analysis and a molar mass are built from. For a dozen elements the value is an interval rather than a number, because the isotopic composition of normal materials genuinely varies.

XrayDB

Matthew Newville and contributors

A public-domain compilation of X-ray data, and the route this site takes to Chantler’s relativistic tabulation (NIST FFAST). The anomalous scattering factors f′ and f″ behind the Friedif value, the mass attenuation coefficients behind the absorption calculator, and every absorption-edge energy this site states come from here. It also carries the Elam, Ravel and Sieber tables, which the gate over that data uses as an independent second opinion rather than as a source.

X-Ray Diffraction Procedures for Polycrystalline and Amorphous Materials

H. P. Klug and L. E. Alexander, Wiley, 2nd edition, 1974

The mass absorption coefficients this site shipped until August 2026, for Z up to 83 at three wavelengths; the absorption calculator computes them at any wavelength now and its numbers differ from these by a few per cent. It is also the standard account of powder diffraction as an experiment — specimen preparation, line broadening, quantitative analysis — which is the half this site does not compute, and the reason it stays on this list.

The programs a determination actually uses

Everything on this site computes one quantity from a structure you already have. Getting that structure out of measured intensities, refining it, and deciding whether it is right are jobs for the programs below — which is what a working crystallographer spends the day in, and what this site deliberately does not try to be.

SHELX

George M. Sheldrick, Universität Göttingen

The programs most small-molecule structures are solved and refined with: SHELXT determines the space group and the structure from the intensities, SHELXL refines it. The phase problem that Patterson, direct methods and charge flipping demonstrate here is what SHELXT solves for real, and the difference map is the step SHELXL runs at every refinement cycle.

A short history of SHELX

George M. Sheldrick, Acta Cryst. A64, 112 (2008)

The paper to cite, and a readable account of how the direct-methods era gave way to the dual-space algorithms these programs use now.

Olex2

OlexSys, Durham University

A graphical environment that drives solution, refinement and reporting in one place, with a structure viewer beside the numbers. It is where most people meet SHELX rather than at a command line, and it writes the CIF that the parser here reads.

OLEX2: a complete structure solution, refinement and analysis program

Dolomanov, Bourhis, Gildea, Howard & Puschmann, J. Appl. Cryst. 42, 339 (2009)

The paper to cite.

PLATON

Anthony L. Spek, Utrecht University

The validation program: it checks a finished structure for the mistakes that survive a good refinement. Several pages here answer questions it made standard: the missed-symmetry search on the geometry page is its ADDSYM, and the distances, angles, torsions, hydrogen bonds and solvent-accessible voids beside it are its geometry report. Two it does that this site does not: SQUEEZE, which takes the scattering of disordered solvent out of the data before refinement, and the full set of validation tests behind the IUCr’s checkCIF report — this site borrows a few of its thresholds, not the list.

Structure validation in chemical crystallography

Anthony L. Spek, Acta Cryst. D65, 148 (2009)

The paper to cite, and the argument for validating a structure at all: what an R factor cannot tell you.

Formats, dictionaries and structures

Where to look a definition up, and where to find a structure to put through the calculators here.

The CIF format

International Union of Crystallography

The specification and the data dictionaries for the file format the CIF parser reads.

Online Dictionary of Crystallography

International Union of Crystallography

Short, careful definitions, written by the people who set the terminology. Useful whenever a word on this site is doing more work than it looks like it is.

Crystallography Open Database

COD

Open-access crystal structures, as CIFs. A good source of real files to drop into the parser or the geometry page.