. The Bell System technical journal . s a different quintet of equations for every conceivable triadof integral values of the indices h. One might infer that in Lauesexperiment the screen would be found completely covered with spotsdue to all the different triplets. However it turns out that only thespots for which all the integers are small stand out strongly enoughto be seen. Meanings for these integers must now be found; butbefore findmg them I will deduce two more equations out of thequintet. Squaring and adding the left-hand members of equations (6a, 6b, 6c),doing the same with the right-
. The Bell System technical journal . s a different quintet of equations for every conceivable triadof integral values of the indices h. One might infer that in Lauesexperiment the screen would be found completely covered with spotsdue to all the different triplets. However it turns out that only thespots for which all the integers are small stand out strongly enoughto be seen. Meanings for these integers must now be found; butbefore findmg them I will deduce two more equations out of thequintet. Squaring and adding the left-hand members of equations (6a, 6b, 6c),doing the same with the right-hand members, equating the sums and CONTEMPORARY ADVANCES IN PHYSICS 415 substituting from (6^, 6e), we obtain: 2 - 2(ati3, + a,i32 + a3/33) = ^, (//r + /^a + /^2-). (7) Now by the second of the theorems concerning direction-cosines, thequantity in parentheses on the left is none other than the cosine ofthe angle between the direction of advance of the primary beam, andthe direction of the scattered waves which go to form the spot or. Fig. 16—Diffraction-peaks obtained with a fixed crystal and a fixed collector, with a constant value of the angle of deflection $, by varying the wave-length.(Davisson and Germer.) diffraction-maximum of the indices hi, ho, hs. If we conceive thediffraction-beam as the path of a portion of the energy which camewith the primary stream and was deflected out of it, then this is theangle of deflection. Call it $. We have: 2a~ sin^ =T^V^7TI7+1?.2 2a (8)(9) As the reader will observe, there is no allusion here, explicit orimplicit, to the orientation of the crystal. This is therefore theappropriate equation for the powder method, in which crystalsturned every way are presented all together to the primary stream,and no one knows the orientation of any particular one—indeed theindividuals are often too small to be seen. Equation (9) describes a cone, having for its origin the mass ofassembled crystals, for its axis the direction of the primary bea
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