. The Bell System technical journal . crystallographic axis). Let Ni, N2, N3 be the components of the unit normal N to the a tomicplane in terms of the plate edges Pi, Po, P3, and Al, .Y2, .Y3 the componentsof the unit vector X along the incident beam. Then sin = AliVi + X2N2 + XgAs () (the inner product of these two vectors, which is thus equal to the cosineof the angle between the incident ray and the normal to the atomic planeor cos (90 - 6)). In matrix form this may also be written: Xc Ni,k-( = sin ei,;Where Xc is the matrix Al , A2 , A3 () ^See Bond, VV. L. The Mathema
. The Bell System technical journal . crystallographic axis). Let Ni, N2, N3 be the components of the unit normal N to the a tomicplane in terms of the plate edges Pi, Po, P3, and Al, .Y2, .Y3 the componentsof the unit vector X along the incident beam. Then sin = AliVi + X2N2 + XgAs () (the inner product of these two vectors, which is thus equal to the cosineof the angle between the incident ray and the normal to the atomic planeor cos (90 - 6)). In matrix form this may also be written: Xc Ni,k-( = sin ei,;Where Xc is the matrix Al , A2 , A3 () ^See Bond, VV. L. The Mathematics of the Physical Properties of Crystals, BellSys. Tech. Jour., Vol. XXII, No. 1. X-RAVS AXD ORIEXTATION OF OlART/. CRYSTALS 321 From Fig. we see that, for the beam entering as shown, the componentsof the unit vector X\ along the beam are 0 sin gicos gi so that equation () becomes sin d,,k.( = .¥•> sin gi + N^ cos ,!,i which has the solution gx^ 0 - b[ whereand sm t) = sin 6 cos sin~^ A^i () ()() ( Fig. —Position 2 for a plate of general orientation Again, with the plate rotated 90° around its normal (to position 2) sothat the entering beam is in the position shown by the unit vector X2 inFig. , the components of Xi are — cos gi sin gi 0 so thator sin 0 = N2 sin ^^2 — -Vi cos ^2 g2 = e + b[ ()() 322 BELL SYSTEM TECHNICAL JOURNAL whereand tan 02 = — A^2 sin 6 sin U = cos sin~^ N3 ()()
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