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# Π π π π π cos π π π n e e i n i n for n is

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π π π π π ) cos ( π π π n e e i n i n = = (for n is integer) For 0 ] 1 [ ) ( ) ( ) ( + + + + + + k h i l h i l k i e e e π π π hkl should not be mixed, under this condition: if h+k+l=even #, ) ( 4 2 2 + + = Ca O hkl f f F If h+k+l=odd #, ) ( 4 2 2 + = Ca O hkl f f F

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(c) a=2(r Ca2+ +r O2- )=2(1.0+1.4)= 4.8angstrom (5 points) (d) The first five planes are (111), (200), (220), (311), (222) (5 points) (e) (10 points) sinθ/λ Ca2+ O2- ± ² ³ ´ µ ¶± ¶² ¶³ ¶´ ¶µ ²± ± ±·² ±·³ ±·´ ±·µ ¸¹²º »²¼ 0 18 10 0.1 16.8 8 0.2 14 5.5 0.3 11.5 3.8 0.4 9.3 2.7 0.5 8.1 2.1 0.6 7.35 1.8 0.7 6.7 1.5 0.8 6.2 1.5 0.9 5.7 1.4 1 5.1 1.35 (f) (5 points for each line = 25 points) line hkl d(Å) θ(degrees) sinθ/λ f(Ca2+) f(O2-) |F|^2 p p-L factor multiplication Int% 1 111 2.77 16.14 32.28 0.1804 14.8 6 1239 8 23.11 229066.3 37.55298 2 200 2.4 18.72 37.44 0.2083 14 5.5 6084 6 16.71 609981.8 100 3 220 1.7 26.99 53.98 0.2946 11.5 3.8 3745 12 7.331 329455.1 54.01065 4 311 1.45 32.16 64.32 0.3455 10.2 3.2 784 24 4.954 93214.46 15.28152 5 222 1.39 33.77 67.54 0.3609 10 3 2704 8 4.461 96500.35 15.8202 ± ²± ³± ´± µ± ¶±± ¶²± ²± ·± ³± ¸± ´± ¹± µ± ²º»¼½º¾ ¾¿À (10 points)
(g) Diffraction pattern from Jade (see above) They are pretty well matched. [4]. The fluorite structure CaF 2 is face-centered cubic with atoms at the following locations: Ca: (0,0,0) + FCC translations F: ( ¼ , ¼ , ¼ ) + FCC translations; F: ( ¾ , ¾ , ¾ ) + FCC translations (a) How many CaF 2 molecules are there per unit cell? (b) Sketch the CaF 2 structure. (c) Find the spacing alone [111] of successive planes of (1) Ca atoms and (2) F atoms, in terms of the conventional cubic cell side a. (d) Based on information provided above, derive simplified expressions for the structure factor F in terms of h, k and l .

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• Fall '12
• p
• Diffraction, Neutron diffraction, X-ray scattering techniques, 4F

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