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William Lawrence Bragg introduced the plane interpretation; his father William Henry Bragg built the X-ray spectrometer. Their joint 1913 paper, The Reflection of X-rays by Crystals, reports the experiment. ^{[ref] [ref]}

An X-ray tube supplied radiation through lead slits to a crystal mounted with its cleavage face through the rotation axis. A rotating ionization chamber replaced a spectrometer telescope; electric current measured the scattered signal, and a circular scale supplied angular readings. They first scanned the chamber at fixed crystal orientation, then swept crystal and chamber together to follow the reflection. ^[ref]

Changing chamber gas checked detector dependence; readings on opposite sides checked face-setting errors. Repeated peaks with sines of half-deflections in integer ratios, together with matching absorption coefficients, distinguished repeated diffraction orders of the same wavelength from different radiation components. Comparing crystal faces constrained interplanar spacings. Their limits included slit broadening, face alignment and incomplete interception at glancing incidence; assigning absolute wavelengths still required a structural choice for $d$. ^[ref]

William Lawrence Bragg's 1913 structure paper connects a slit-selected beam, an oriented crystal and an ionization chamber to strength-versus-angle curves. Repeated sine ratios and matching absorption coefficients identify common radiation. Narrower slits resolve blended lines. Absolute wavelengths remain undetermined there; intercrystal comparisons first give relative scales. The Bragg crystal reflection experiment of 1913 covers the alignment controls.^[ref]

William Henry Bragg's 1915 Bakerian lecture, X-rays and Crystal Structure, separates the geometric and intensity arguments. Its Figure 9 compares reflection positions and strengths from three sodium chloride orientations; odd and even diffraction orders differ in strength along one orientation. The interpretation uses alternating scattering layers. Later, the calcite example identifies an internal oxygen coordinate that symmetry alone cannot fix. Improved wave intensity measurements revise a previously rough estimate. Thus a lattice assignment can precede determination of positions inside the unit cell; intensity interpretation also has experimental and theoretical limits. This is the father's 1915 lecture, distinct from the joint 1913 reflection paper.^[ref]

A crystal structure specifies the chemical species and spatial arrangement of the chemical atoms or ions in a crystal. For an ideal periodic structure, separate two ingredients: a Bravais lattice specifies the translations that repeat the arrangement, and an atomic basis of a crystal specifies the chemical motif repeated at every lattice point. The outward shape, or crystal habit, is a different description: the internal arrangement is what this article describes.

For a concrete two-dimensional model, choose primitive lattice translation vectors $a_1=(2,0)$ and $a_2=(0,1.5)$ in arbitrary length units. At every lattice point $R=m{a}_1+n{a}_2$, with integers $m,n$, place species A at $R$ and a different species B at $R+(0.65,0.55)$. Translating by $a_1$ or $a_2$ preserves both the positions and their chemical labels. Translating by $(0.65,0.55)$ sends one A position to a B position, so it is not a translation symmetry of the labeled structure. A picture of dots with the labels erased can therefore conceal essential chemical information.

A primitive unit cell contains one lattice point, but may contain several chemical atoms. A conventional unit cell can contain several lattice points to display the symmetry more clearly. Thus the conventional cube of a face-centered cubic lattice contains four lattice points, whereas a body-centered cubic lattice has two. Neither lattice name alone specifies which chemical species occupies the repeated motif. The NaCl conventional cell and coordination example makes the distinction explicit.

This separation is useful experimentally: interplanar spacings constrain the repeating geometry, while relative wave intensities also depend on the atomic basis of a crystal through the crystal basis structure factor. The Bragg crystal reflection experiment of 1913 describes the X-ray spectrometer, angular scans and detector checks in detail. Its conversion from angle to length is developed under Bragg's law; a geometrically possible reflection can still have zero wave intensity.

William Lawrence Bragg's 1913 structure determination supplied a complementary test. He directed X-rays through sodium chloride sections cut parallel to a cube face and recorded spots on photographic plates. Comparing section thicknesses tested how transmission altered the pattern: the relative spot strengths changed. Comparing related salts led him to two interpenetrating face-centered cubic lattices, one for each kind of constituent. He explicitly distinguished evidence for that arrangement from the still-needed identification of a single chemical atom with each scattering center. The photographs were evidence for a structural model, not direct pictures of labeled ions.^[ref]

By William Lawrence Bragg, credited as W. L. Bragg, pp. 531–539 in Fifty Years of X-ray Diffraction, edited by Paul Peter Ewald. The chapter author is distinct from the volume editor. First published in 1962; digitized in 1999.

Institutional PDF: www.iucr.org/__data/assets/pdf_file/0014/761/bragg_wl.pdf

Institutional transcription: www.iucr.org/what-we-do/publications/books/Fifty-Years-of-X-ray-Diffraction/w-l-bragg

Cited passage: printed p. 533, PDF p. 3, retrospective account of sodium chloride and potassium chloride analysis using Laue photographs in late 1912 and early 1913, followed by work with the spectrometer. This is a first-person retrospective, not the original structure-determination paper.

Awarded jointly to William Henry Bragg and William Lawrence Bragg for methods of determining crystal structures using X-rays. Bragg's law connects measured angles to lattice-plane spacings.^[ref]

By William Henry Bragg and William Lawrence Bragg. Published in Proceedings of the Royal Society of London, Series A 88(605), 428–438, 1 July 1913. Received 7 April and read 17 April 1913.

DOI: doi.org/10.1098/rspa.1913.0040

Institutional scan: chair.itp.ac.ru/biblio/papers/ClassicPapersSeminar/Bragg1913a.pdf

Cited passages: pp. 428–430, apparatus and alignment check; pp. 435–438, repeated orders, absorption comparison and structural inference.

By William Lawrence Bragg, credited as W. L. Bragg. Published in Proceedings of the Royal Society of London, Series A 89, 248–277 (1913). The first page records receipt on 21 June and reading on 26 June 1913. The communication credit to William Henry Bragg is distinct from authorship.

DOI: doi.org/10.1098/rspa.1913.0083

Inspected scan: scispace.com/pdf/the-structure-of-some-crystals-as-indicated-by-their-1ugl7pojiz.pdf

Cited passages: p. 248, authorship and communication credits; pp. 262–263, Figures 8–9 and Tables VII–IX, sodium chloride sections, orientations, thickness comparison and spot intensities; pp. 264–265, Figure 10, interpenetrating face-centered arrays and the remaining atomic-assignment uncertainty. The historical scattering-weight interpretation is not modern X-ray scattering theory.