Powder Indexing

A powder pattern is a list of angles and nothing else. Indexing is the step that turns it into a lattice: find the cell that puts a reflection at every one of those angles, and name the reflection at each. This page does it exhaustively for the three systems where it can be done exhaustively — cubic, one unknown, and tetragonal and hexagonal, two — so it either finds every cell that works or proves there is none.

You supply

A wavelength and a list of peak positions in degrees 2θ, one per line. No intensities and no widths: indexing uses positions alone. Three lines are the minimum the page will accept and eight or more is where the answer starts to be worth something — the panel on the floor says why.

Reading it

Finding a cell is not the same as being right, and in the two-parameter systems it is barely evidence at all: given eight random angles, a tetragonal cell accounting for every one of them turns up 385 times in 400. What separates a real lattice from an accidental fit is completeness — of the lines the cell predicts inside the range you measured, how many you actually saw. A real lattice comes out at 1.00 and the best accidental fit measured here reached 0.066. And every cell edge scales with the wavelength: index a Cu pattern as Mo and the whole cell is wrong by 2.168 with a perfect completeness.

Worked examples: quartz, twelve lines – one answer · α-iron, three lines – six cells, and no way to choose · NaCl – one lattice, two descriptions

See also: Bragg Calculator · HKL Calculator · Peak Finding · Line Broadening · Reduced Cell and Bravais Lattice · Space Group from Absences