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A New Method Of X-Ray Crystal Analysis*
Published online by Cambridge University Press: 10 January 2013
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The beautiful methods of crystal analysis that have been developed by Laue and the Braggs are applicable only to individual crystals of appreciable size, reasonably free from twinning and distortion, and sufficiently developed to allow the determination of the direction of their axes. For the majority of substances, especially the elementary ones, such crystals cannot be found in nature or in ordinary technical products, and their growth is difficult and time-consuming.
The method described below is a modification of the Bragg method, and is applicable to all crystalline substances. The quantity of material required is preferably 0.005 c.c., but one tenth of this amount is sufficient. Extreme purity of material is not required, and a large admixture of (uncombined) foreign material, twenty or even fifty per cent, is allowable provided it is amorphous or of known crystalline structure.
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References
page 13 note 1 A brief description of this method was given before the American Physical Society in October, 1916, and published in this journal for January, 1917.
page 13 note 2 If the powder is fine, rotation is not necessary unless great precision is desired. With crystal grains 0.01 cm. in diameter, or less, the pattern generally appears quite uniform without rotation.
page 16 note 1 X-Rays and Crystal Structure, pp. 120 ff.
page 16 note 2 Nat. Acad. Proc., 2, 268, 1916Google Scholar.
page 16 note 3 Phys. Rev., 7, 599, 1916CrossRefGoogle Scholar; Nat. Acad. Proc., 8, 185, 1917Google Scholar.
page 17 note 1 Webster, and Clark, , Proc. Nat. Acad., 8, 185, 1917Google Scholar.
page 17 note 2 The general radiation of the same wave-length as the a line is included in these values.
page 17 note 3 See Duane, and Hunt, , Phy. Rev., 6, 619Google Scholar, and Hull, Phys. Rev., 7, 156Google Scholar.
page 17 note 4 A complete table of wave-lengths of series lines for all elements thus far investigated is given by Siegbahn, , Jahrb. Radioact, u. Electronik, 13, 300, 1916Google Scholar.
page 17 note 5 Hull, and Rice, , Phys. Rev., 8, 326, 1916Google Scholar.
page 17 note 6 L. c.
page 19 note 1 The absorption of the Si and O in zircon is negligible compared to that of the zirconium, so that crystal zircon is as efficient as metallic zirconium.
page 19 note 2 The ionization chamber contains two electrodes of equal length. The second electrode, the one farther from the crystal, was connected to the electrometer, and the pressure of methyl iodide in the chamber was such that the wave-lengths in the middle of the range investigated suffered 50 per cent absorption in passing through the first half of the chamber. The electrometer deflection is proportional to I 0e–μl (I—e–μl, where I 0 is the intensity on entering the chamber, l the length of either electrode and μ the coefficient of absorption of the methyl odide. This expression has a very flat maximum for e–μl = ½, so that for a considerable range on either side, the readings are proportional to I 0.
page 22 note 1 In order to shorten the table the simple cube spacings, which are much more numerous than the others, have not been tabulated beyond d/n =.1766.
page 24 note 1 The term “construction point” is used to denote the position of some definite point, which may be looked upon as the starting point of each lattice, with respect to the co-ordinate axes.
page 25 note 1 This formula is easily obtained from the fundamental equation
d =x1 cos α+y1 cos β+z1 cos γ—p,
by substituting for cos α cos γ, cos v, and their values in terms of h, k, l, λ, μ, and v given by the equations:
where cos α. cos β, cos γ are the direction cosines, and l′, m, n the direction ratios of the perpendicular p from the origin to the plane hkl.
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