---
title: "Laue and the Braggs: from spots to a crystal model"
description: "What extra measurements turn a diffraction photograph into evidence for an atomic arrangement?"
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[Diffraction, phase and surface structure](https://sandboxphysics.com/stories/probe-evidence/#structure)

Apparatus · Observation · Inference

# Laue and the Braggs: from spots to a crystal model

Sandbox Physics · 2026-10-22

What extra measurements turn a diffraction photograph into evidence for an atomic arrangement?

1. X-ray source and collimation
2. Oriented crystal
3. Plate or angular intensity scan
4. Test spacings and a basis

Laue photographs use a range of incident wavelengths; an angle scan with selected radiation is a different measurement.

## A crystal supplied the missing grating

Laue’s proposal joined two uncertain ideas: X-rays might be waves, and crystals might contain a regular three-dimensional arrangement. Friedrich and Knipping performed the 1912 experiments. Discrete spots around the transmitted beam, with symmetry tied to crystal orientation, gave those ideas a common quantitative test.

The pattern was not an enlarged picture of atoms. A broad incident spectrum allowed different directions to satisfy interference conditions at different wavelengths. Assigning every spot the same wavelength would change the experiment being interpreted.

Sources: [1]

## A rotating spectrometer changed the question

W. L. Bragg expressed the condition using families of crystal planes. W. H. Bragg’s spectrometer made angular intensity measurements with selected characteristic radiation practical. Source, crystal and detector geometry then constrained plane spacing through peak positions.

The Bragg angle below is measured from the reflecting planes, not from their normal. The angle between the incident forward direction and diffracted direction is twice that angle. Order is a positive integer; the equation specifies a constructive condition, not the measured strength of a reflection.

$$
2d\sin\theta_{\mathrm B}=n\lambda
$$

Sources: [2]

## The weak reflections carry structural information

Salts with related geometry could show very different relative intensities. The Braggs compared such differences to arrangements with a basis of unlike atoms. For sodium chloride, the interpenetrating sublattices matter; a lattice of identical points discards the contrast that distinguishes the ions.

In a single-scattering description, the structure factor sums complex amplitudes from atoms at fractional coordinates. The scattering factors depend on the probe and scattering vector. Measured intensities also need absorption, geometry and thermal corrections. Copying an electron scattering weight into an X-ray calculation has no physical justification.

$$
F_{hkl}=\sum_j f_j\exp\!\left[2\pi i(hx_j+ky_j+lz_j)\right]
$$

Sources: [2]

## Intensities do not retain every phase

A detector generally records intensity, not the complex phase of each structure factor. Peak indexing, chemical composition, symmetry and complementary constraints therefore participate in a structure solution. A plausible arrangement reproducing one pattern is weaker evidence than a model tested against independent reflections and alternatives.

Laue’s 1914 prize and the Braggs’ 1915 prize recognize connected but distinct contributions. The hosted lectures were delivered later: Laue in 1915 and W. L. Bragg in 1922. Keep the experiment, award and retrospective account on separate dates.

Sources: [1] [2]

## Read positions before intensities

Compare the first spot photographs with the spectrometer scans, then follow the salt examples in the Bragg lecture. Separate the geometrical question of which reflections are allowed from the structural question of how strong they should be. The linked models let these two questions be varied independently.

Sources: [1] [2]

## Explore the related models

Each link states what the existing model can explain and where the historical measurement goes further.

### [Explore reciprocal-space geometry](https://sandboxphysics.com/labs/crystal-diffraction-reciprocal-space/)

Rotate a crystal and compare accessible reflections.

This optical teaching model does not calibrate historical X-ray intensities or solve an unknown crystal.

### [Compare a different probe](https://sandboxphysics.com/labs/electron-diffraction/)

Compare voltage and ring positions with a fixed specimen.

Electron multiple scattering and scattering factors differ from X-rays; shared geometry does not make the records interchangeable.

## Sources and reading notes

Historical apparatus and salt arguments come from the hosted primary accounts. The displayed structure factor is a modern single-scattering explanation, not a digitized historical refinement.

1. [M. von Laue, Concerning the detection of X-ray interferences (1915 lecture; 1914 prize)](https://www.nobelprize.org/uploads/2018/06/laue-lecture.pdf)

   Historical apparatus and interference account read, together with the 1914 presentation. Lecture date and award year are distinct. [Read the hosted original](https://www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics01-21-2.pdf)

2. [W. L. Bragg, The diffraction of X-rays by crystals (1922 lecture; 1915 prize)](https://www.nobelprize.org/uploads/2018/06/wl-bragg-lecture.pdf)

   Angle scans, spectrometer and salt-structure discussion read; the lecture was delivered 6 September 1922. [Read the hosted original](https://www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics01-21-2.pdf)

[Probes, light and measurement: reading the evidence](https://sandboxphysics.com/stories/probe-evidence/) [Zernike: a reference wave makes transparent structure visible](https://sandboxphysics.com/stories/probe-evidence/zernike-phase-reference/) [STM: a current contour is not simply a height map](https://sandboxphysics.com/stories/probe-evidence/stm-current-and-surface-inference/) [Electron diffraction: two experiments, one wavelength test](https://sandboxphysics.com/stories/electron-evidence/electron-diffraction-crystal-records/) [Ruska: making an electron image was only the beginning](https://sandboxphysics.com/stories/electron-evidence/ruska-electron-microscope-resolution/) [Kai Siegbahn: when electron energies began to reveal chemistry](https://sandboxphysics.com/stories/electron-evidence/siegbahn-electron-spectroscopy-chemical-shifts/)