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Bragg, Sir William Lawrence


(b. Adelaide, Australia, 31 March 1890; d. Ipswich. England, 1 July 1971),

X-ray crystallography, physics.

Bragg was the eldest son of the physicist Sir William Henry Bragg and Lady Gwendoline Bragg, granddaughter of Sir Charles Todd, the postmaster general and government astronomer of South Australia. Bragg was educated at St. Peter’s College, Adelaide, and at the University of Adelaide, where he studied mathematics. He continued his studies at Trinity College, Cambridge, where he was admitted in 1909; but after one year, at the suggestion of his father, he transferred to physics. After obtaining first class honors in the natural science tripos in 1912, he started research under J. J. Thomson. This work, however, was interrupted by the outbreak of World War I, when Bragg volunteered for service. After some time in a horse artillery battery, he was transferred to act as technical adviser on sound ranging at the Map Section, G.H.Q., where his knowledge of physics was partly responsible for the considerable success of the sound-ranging techniques. In 1915 he was jointly awarded the Nobel Prize for physics with his father for work on the X-ray determination of crystal structures.

After the war Bragg returned briefly to Trinity College as a lecturer, but in 1919 he was appointed Langworthy professor of physics at the University of Manchester, in succession to Rutherford. During this happy and successful period he was made a fellow of the Royal Society, and in 1921 married Alice Hopkinson, the daughter of a doctor, by whom he had four children. In 1937 Bragg moved for a year to the National Physical Laboratory as director, but after Rutherford’s premature death, he was invited to Cambridge as Cavendish professor of experimental physics. He stayed at Cambridge (with some interruptions for wartime liaison work with Canada and the United States) until 1954, when he moved to the Royal Institution, London, as Fullerian professor of chemistry and as director of the Davy-Faraday Research Laboratory–a post at one time held by his father. At the Royal Institution he sponsored and conducted crystallographic research and also devoted himself with energy and talent to another of his lifelong interests–the popularization and teaching of science, including the history of science. He retired in 1966 but maintained an active interest in both crystallography and scientific popularization until shortly before his death.

Bragg started his first important work as a result of the claim–made in 1912 by Friedrich, Knipping, and Laue–that they had observed the diffraction of X rays by a crystal. William Henry Bragg. who advocated a corpuscular theory of X rays. was greatly interested in Laue’s work. despite the fact that the observed effect was explained in terms of, and strongly supported Bark-la’s alternative wave theory of X radiation. Lawrence and his father discussed Laue’s findings in 1912, and William Henry developed the theory that the diffraction effect might be explicable as the shooting of corpuscles down avenues between lines of atoms in crystals.1 Bragg seems to have found this suggestion unconvincing, although he was careful not to contradict his father in public, and after further study of Laue’s paper, came to the conclusion that this was indeed a diffraction effect, but that in its application to ZnS Laue’s explanation was incorrect and unnecessarily complex. Part of the problem concerned Lauc’s suggestion that ZnS was a simple cubic system. As a result he had found a number of unexpected gaps in the diffraction pattern. He had explained that these gaps derived from the absence of particular wavelengths in the incident beam, or perhaps from fluorescence. Bragg suggested2 that ZnS should be seen as face-centered cubic, rather than as simple cubic. He was then able to show that as a result the diffraction pattern was entirely explicable as having arisen from the diffraction of white X radiation through a three-dimensional grating. No special assumptions about the characteristics of the incident beam were required.

In his paper Laue had calculated the conditions for diffracted intensity maxima for the simple cubic system where the incident beam was parallel to one side of the cell. The path differences of diffracted rays in the three dimensions were thus represented by the three expressions a cos θ1, a cos θ2 and a,(1–cosθ3), where a equals the length of the side of the unit cell: and intensity maxima were achieved when the following conditions were satisfied: , , a where α= cos θ1; β = cos θ2; γ = cos θ3; and

h1, h2, h3, and represented an integer equivalent to the order of the diffracted beam in each dimension. (See Figure 1.)

While Bragg concurred with Laue’s identification and treatment of the problem, he nonetheless, in an impressive display of physical insight, reconceptualized the effect as that of the reflection of X rays off crystal planes, and formulated this in the expression λ = 2d cos θ, which showed the relationship between angle of incidence θ, wavelength λ, and distance between parallel atomic planes d. (This expression in its more usual form nλ = 2d sin θ, where n is an integer corresponding to the order of refraction and θ corresponds to the glancing angle–[“the Bragg angle”]–became universally known in the community of crystallographers as “Bragg’s law.” See Figure 2.)

This reworking was of far-reaching significance, for when compared with Laue’s expression, Bragg’s law (and the notion of reflection) rendered the process of diffraction easier to visualize and simplified calculation–advantages that were particularly important in the early development of X-ray crystallography, although Laue’s expression

proved more appropriate for later quantitative work. It was thus immediately clear that the crystal “manufactured” its own monochromatic X rays. The notion of reflection also explained why Laue had found that diffracted spots were circular when the photographic plate was close to the crystal, but became elliptical when the plate was more distant. Moving in a cone from the source, the X rays, once reflected, tended to converge in one plane.

With this work, Bragg’s father abandoned the corpuscular theory, and father and son embarked on a brilliant period of intense collaboration, interrupted only by the outbreak of World War I. Although much of their work was published jointly, they brought rather different interests and skills to the collaboration. William Henry Bragg brought a deep concern with physical issues and great skill as an experimenter–most particularly in the form of the X-ray diffractometer. Lawrence Bragg brought a rapidly developing knowledge of and sensitivity for the crystalline state, and the powerful notion of reflection from atomic planes.

In a joint paper read in April l9l33 the Braggs described the ionization spectrometer and the observed relative intensities of the different “orders” of diffracted X rays. when these were reflected off “normal” crystal planes. They calculated the length of side of the elementary cube of NaCI but were unable to derive a final value for , because it was not clear whether the distance between reflecting planes represented that between two identical or successive planes.

This problem was solved in a preliminary but spectacular fashion in a paper read by Bragg in June l9l34. He devised a simple method for projecting and indexing reflections, which he used to show that there were systematic differences between such simple cubic structures as KCI, such face-centered cubic structures as KBr, and NaCI which appeared to be intermediate between the other two structures. He explained this by suggesting that the scattering power of atoms varied in proportion to atomic weight. Thus, in the case of KCI, the atoms were of approximately equal scattering power, and this was reflected in the simple cubic lattice to which both, as it were, contributed. This was not the case for KBr where the lattice was defined by the heavier Br atom. NaCI was an intermediate case, reflecting the greater but not predominant scattering power of the Cl atom.

Lawrence Bragg then calculated a figure proportional to the number of molecules in each scattering center, and found the value of KCl to be half that of the other molecules considered. This suggested strongly that in each of these other cases a single molecule was associated with each scattering center, while in the case of KCl an atom alone was so associated. With this knowledge the calculation of a tentative wavelength for X rays became possible.

In July 1913 the Braggs published the structure of diamond, showing the carbon atoms to be tetrahedral5, although this was largely the work of William Henry, and in November, Lawrence Bragg outlined further crystallographic work.6 The importance of accurate intensity measurements induced him to abandon photographic methods and concentrate on the diffractometer. The importance of comparing the relative intensities of the different orders of characteristic X rays in determining the space group of the crystal had been made clear in the paper described above. Now Lawrence Bragg showed that the further quantitative study of intensities could be used to determine the position of those atoms the positions of which were not fixed with reference to symmetry considerations. In this paper he resolved the structures of FeS and CaCO3–both with a single such parameter, and the first such structures to be solved. It may be suggested fairly that this set of papers constituted a “charter” for the later development of X-ray crystallography.

After World War I Lawrence Bragg continued this work. His general strategy was to develop the power of X-ray methods for crystal structure determination, whether by direct or indirect means. His first contribution was to publish a list of atomic radii7 which, however, were calculated from an incorrect baseline, and required later correction. The aim of this work was to set limits to possible atomic packing arrangements, and hence reduce the number of potential solutions of unknown structures with several parameters.8 His second venture, with James and Bosanquet,9 was more successful and involved work on absolute intensity measurements. They derived empirical f-curves–the ratio of the amplitude scattered by an atom at different angles to that scattered by a single classical electron–which were then used by Hartree in comparisons with theoretical f-curves derived from the Bohr model of the atom, and Schrodinger’s later wave mechanics. In a crystallographic context, the work made it possible to check C. G. Darwin’s prewar theory of the strength of reflections from perfect and mosaic crystals.

Bragg and his collaborators next turned to the determination of more difficult structures–the silicates–despite the many doubts about the possibility of solving structures with more than one or two parameters. In a few years. however, this work proved spectacularly successful, and it was shown that silicate structures depended on the ratio of silicon to oxygen atoms.10 To a considerable extent this work depended on Bragg’s almost intuitive sense of what constituted a plausible structure–a “good engineering job.” At the same time he also encouraged work on metals, although his personal contribution was limited to the theoretical analysis of order-disorder phenomena.11

In his later years Bragg became more involved with administration and less concerned with day-to-day scientific work, although his scientific powers were in no way diminished. His continuing commitment to the development of X-ray crystallography was clearest in his support for and participation in the work of that small group of crystallographers (notably M. F. Perutz) who started work on the structure of globular proteins in the late 1930’s and pushed on, despite great difficulties, to achieve spectacular success in the late 1950’s.12

Bragg is therefore associated with the entire history and development of X-ray crystallography, and his major contributions can be seen as spanning a number of fields. The work before 1914 was seminal for X-ray crystallography, but also constituted a major contribution to both physics (X-ray wavelengths) and inorganic chemistry (continuous networks of ions rather than matched pairs in NaCl). The later work on absolute intensities laid a sound methodological basis for the development of quantitative X-ray crystallography, and was important for debates on atomic structure. The successful study of silicates not only revolutionized the basis of mineralogy, but was used by Pauling in his work on structural chemistry. The work on metals required fundamental rethinking in metal chemistry, while X-ray crystallography, and hence Bragg’s work, contributed a vital element to the growth of molecular biology both directly and indirectly.

Bragg’s importance for science may thus be judged in several ways. First, he was able to bring together elements from diverse fields. (It cannot, perhaps, be emphasized too strongly that at the roots of X-ray crystallography lies a synthesis of both great power and imagination.) Secondly, he possessed physical insight to an unusually high degree. combined with the happy knack of being able to present his- ideas precisely but simply to both professional and lay audiences. Thirdly, his unusual degree of commitment and energy led him to press forward with the development of X-ray crystallography, where a less dedicated man might reasonably have considered the difficulties insuperable. Fourthly, Bragg was a great scientific organizer. He communicated his enthusiasm to those around him. whether in science or industry, and much work that does not bear his name can, as a result, be seen as having arisen from his inspiration.


1. W. H. Bragg. “X-rays and Crystals.” in Nature, 90 (1912),219.

2. W. L. Bragg. ’The Diffraction of Short Electromagnetic Waves by a Crystal “in Proceedings of the Cambridge Philosophical Society. Mathematical and Physical Sciences, 17 (1912), 43 -57.

3. W. H Bragg and W. L. Bragg, “The Reflection of X-rays by Crystals” in Proceedings of the Royal Satiety. 88A (1913). 428–438.

4. W. L. Bragg, “The Structure of Some Crystals as Indicated by Their Diffraction of X-rays” ibid., 89A (1913), 248–277; this calculation is also used in a paper submitted at the same time by W. HL Bragg; “The Reflection of X-rays by Crystals (II).” ibid. 246–248.

5. W. H. Bragg and W. L. Bragg, “The Structure of the Diamond.” ibid., 277.

6. W. L. Bragg, ’The Analysis of Crystals by the X-ray Spectrometer, “ibid.. 468–489.

7. W. L Bragg, “The Arrangement of Atoms in Crystals,” in Philosophical Magazine. 6th ser., 40 (1920). 169- 189.

8. The problem was that it was not possible to move from diffraction data to a structure, but only backwards, deducing diffraction patterns from a supposed structure. Trial-and-error methods were therefore used, and it was important to limit the range of possible trials, which otherwise became very large

9. W. L. Bragg, K. W. James, and C. H. Bosanquet. “Über die Streuung der Rontgenstrahlen dureh die Atome eines Kri-stalles,” in Zeitschrift für Physik,8 (1921),77–84.

10. See. for instance. W. L. Bragg and B. E. Warren. “The Structure of Diopside CaMg(SiO3)2,” in Zeiischrift fur Kristattographie. . . . 69 (1928). 168–193: and W. L. Bragg. “Atomic Arrangement in the Silicates.” in Transactions of the Faraday Society.25 (1929). 291–314.

11. W. L. Bragg and E. J. Williams, “The Effect of Thermal Agitation on Atomic Arrangements in Alloys.” in Proceedings of the Royal Society, 145 A (1934), 699–730; and W. L. Bragg and E. J. Williams. “The Effect of Thermal Agitation on Atomic Arrangements in Alloys (II),” ibid., 145 (1935), 540–566.

12. The first such structure was determined in 1957 by J. C. Kendreu, another of Bragg’s collaborators: J. C. Kendrew el al., “A Three-Dimensional Model of the Myoglobin Molecule,” in Nature,181 (1958), 662–666.


I. Original Works. There is no complete bibliography of Bragg’s published work, although when the biographical memoir of the Royal Society is published this should include the customary bibliography.

Bragg’s works include X-rays and Crystal Structure (London, 1915), written with W. H. Bragg; The Crystalline State, I, General Survey (London, 1933); Old Trades and New Knowledge (London, 1933); and Electricity (London. 1936). He was editor of The Crystalline State, II-IV (London, 1948, 1953, 1965). Later works were “The Development of X-ray Analysis,” in Proceedings of the Royal Society, 262A (1961), 145–158: “Personal Reminiscences,” in P. P. Ewald, ed Fifty Years of X-ray Diffraction (Utrecht, 1962). 531–539; The Crystalline State, vol. IV: Crystal Structures of Minerals (London, 1965), written with C. F. Claring-bull; “Manchester Days,” in Acta crystallographica26A (1970), 173–177; and The Development of X-ray Analysis D. C. Phillips and H. Lipson, eds. (London. 1975)

II. Secondary Literature. On Bragg and his work, see P. P. Ewald. ed.. Fifty Years of X-ray Diffraction (Utrecht. 1962), which contains a wealth of historical and biographical detail by and about crystallographers. including Bragg; and Acta crystallographica, 26A (1960). 171–196, with assessments and appreciations by H. Lipson, I. Naray-Szabo, M. F. Perutz, D. C. Phillips, and J. Thewlis.

By permission of the family, extensive archival material has been deposited at the Royal Institution. A catalogue is in preparation.

John Law

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"Bragg, Sir William Lawrence." Complete Dictionary of Scientific Biography. . 24 May. 2017 <>.

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Bragg, Sir William Lawrence

Sir William Lawrence Bragg, 1890–1971, English physicist, b. Adelaide, Australia, educated in Australia and at Trinity College, Cambridge; son of W. H. Bragg. He was professor of physics at Victoria Univ., Manchester, from 1919 to 1937. From 1938 to 1953 he was professor of experimental physics at Cambridge and director of the Cavendish Laboratory. In 1954 he was made head of the Royal Institution. He shared with his father the 1915 Nobel Prize in Physics for their studies, with the X-ray spectrometer, of X-ray spectra, X-ray diffraction, and of crystal structure. In 1941 he was knighted. Among his works are The Structure of Silicates (1930, 2d enl. ed. 1932) and Atomic Structure of Minerals (1937). With his father he wrote X Rays and Crystal Structure (1915, 5th ed. 1925).

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Bragg, Sir (William) Lawrence

Bragg, Sir (William) Lawrence (1890–1971) English physicist, b. Australia. He was director (1938–53) of the Cavendish Laboratory at Cambridge. With his father, Sir William Henry Bragg (1862–1942), he determined the mathematics involved in X-ray diffraction, showed how to compute X-ray wavelengths and studied crystal structure by X-ray diffraction. For these advances, they were jointly awarded the 1915 Nobel Prize in physics.

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