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Question

Please answer (a) 

(a) Use your knowledge of reciprocal space to write a general expression for the d-spacing of a set of hkl planes in the triclinic system. This equation should be written entirely in terms of real space parameters, abc a, ß and y. (b) Show that in the case of the hexagonal crystal system the general equation from 4 (a) reduces to: 1 4 (h² + hk + k²\ 12 + || d2 a2 (c) Similarly show that for the case of a tetragonal crystal the general form from 4 (a) reduces to: 4 (h² + k²\ 12 + d? a2 (d) Show that for a tetragonal crystal the angle ø between the plane (hkili) of spacing di and the plane (h2kzlı) of spacing d2 is given by:e h,h2 + k,k2 , 4l2 a2 cos o = (hi+k,(3+k3,号 + q?
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Transcribed Image Text:(a) Use your knowledge of reciprocal space to write a general expression for the d-spacing of a set of hkl planes in the triclinic system. This equation should be written entirely in terms of real space parameters, abc a, ß and y. (b) Show that in the case of the hexagonal crystal system the general equation from 4 (a) reduces to: 1 4 (h² + hk + k²\ 12 + || d2 a2 (c) Similarly show that for the case of a tetragonal crystal the general form from 4 (a) reduces to: 4 (h² + k²\ 12 + d? a2 (d) Show that for a tetragonal crystal the angle ø between the plane (hkili) of spacing di and the plane (h2kzlı) of spacing d2 is given by:e h,h2 + k,k2 , 4l2 a2 cos o = (hi+k,(3+k3,号 + q?
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