Quick Facts
Born:
June 28, 1902, Waltham, Massachusetts, U.S.
Died:
June 27, 1991, Arlington (aged 88)
Subjects Of Study:
amorphous solid
crystal

Bertram Eugene Warren (born June 28, 1902, Waltham, Massachusetts, U.S.—died June 27, 1991, Arlington) was an American crystallographer whose X-ray studies contributed to an understanding of both crystalline and noncrystalline materials and of the transition from the amorphous to the crystalline state.

Most of Warren’s academic and professional life was spent at the Massachusetts Institute of Technology, Cambridge; he received the Sc.D. degree there in 1928 and joined the faculty in 1930, serving successively as assistant, associate, and, finally, full professor of physics. With Sir Lawrence Bragg he conducted a study of diopside, a member of the pyroxene group of silicate minerals. Their X-ray analysis, a milestone in the understanding of the silicate minerals, provided an explanation of the observed variation in silicon-oxygen ratios of silicates. Warren later turned his attention to noncrystalline materials and the imperfections in crystals. He showed that carbon black was not completely amorphous but possessed randomly oriented two-dimensional layer structures and that the general physical properties of metals are largely determined by crystal imperfections.

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X-ray diffraction, phenomenon in which the atoms of a crystal, by virtue of their uniform spacing, cause an interference pattern of the waves present in an incident beam of X-rays. The atomic planes of the crystal act on the X-rays in exactly the same manner as does a uniformly ruled diffraction grating on a beam of light. A beam of X-rays contacts a crystal with an angle of incidence θ. It is reflected off the atoms of the crystal with the same angle θ. The X-rays reflect off atomic planes in the crystal that are a distance d apart. The X-rays reflecting off two different planes must interfere constructively to form an interference pattern; otherwise, the X-rays would interfere destructively and form no pattern. To interfere constructively, the difference in path length between the beams reflecting off two atomic planes must be a whole number (n) of wavelengths (λ), or nλ. This leads to the Bragg law nλ = 2d sin θ. By observing the interference pattern, the internal structure of the crystal can be deduced. See also Bragg law; Laue diffraction pattern.

The Editors of Encyclopaedia BritannicaThis article was most recently revised and updated by Erik Gregersen.