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# A 4 ca atoms 8 f atoms 5 points b 5 points c 5 points

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(a) 4 Ca atoms, 8 F atoms (5 points) (b) (5 points) (c) (5 points each = 15 points) (d) Structure alculation is based on the following atom position (5 points each = 15 points) Ca position F position F position 0 0 0 ¼ ¼ ¼ ¾ ¾ ¾ ½ ½ 0 ¾ ¾ ¼ 5/4 5/4 ¾ 0 ½ ½ ¼ ¾ ¾ ¾ 5/4 5/4 ½ 0 ½ ¾ ¼ ¾ 5/4 ¾ 5/4

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Follow the calculation ( 20points= formula 5 points, deduction 10 points, hkl evaluation 5 points) [5]. (a) 2 O atoms: (000), (1/2,1/2,1/2) 4 Cu atoms: (1/4,1/4,1/4), (3/4, 1/4, 3/4), (3/4, 3/4, 1/4), (1/4, 3/4, 3/4) ] 1 [ ] 1 [ ] [ ] 1 [ ) ( ) ( ) ( ) ( 2 ) ( ) 3 3 ( 2 ) 3 3 ( 2 ) 3 3 ( 2 ) ( 2 ) ( 8 1 ) ( 2 2 2 k l i l h i k h i l k h i Cu l k h i O l k h i l k h i l k h i l k h i Cu l k h i O j lw kv hu i j e e e e f e f e e e e f e f e f F j j j + + + + + + + + + + + + + + + + + = + + + + + + + = + + + + + = = + + π π π π π π π π π π π
(b) For 0 ] 1 [ ) ( 2 + + + l k h i O e f π h+k+l=even For 0 ] 1 [ ) ( ) ( ) ( ) ( 2 + + + + + + + + + k l i l h i k h i l k h i Cu e e e e f π π π π , hkl should not be mixed So for F hkl =0 hkl should be mixed and h+k+l=odd line F hkl 100 no mixed and h+k+l=1 odd 0 110 yes h+k+l=2 even = 2 2 O f F 111 yes unmixed hkl + = Cu if F 4 200 yes unmixed hkl and h+k+l=even + = Cu O f f F 4 2 2 210 no Mixed and h+k+l=3 odd 0 211 yes h+k+l=even = 2 2 O f F 220 Yes unmixed hkl and h+k+l=even + + = Cu O f f F 4 2 2 The first five planes are (110), (111), (200), (211), (220). (c) line d-spacing a 110 3.01 4.256783 111 2.47 4.278165 200 2.13 4.26 211 Too weak to reveal 220 1.5 4.242641 average 4.259397 Experimentally, a=4.259angstrom (d) line d a θ sinθ/λ f (Cu+) f (O2-) |F|^2 p p-L factor 1*2*3 Int% 110 3.01 4.256 14.82 29.65 0.166113 23 6 144 12 27.72 47912.8 4.5 111 2.47 4.278 18.17 36.34 0.202429 21.6 5.5 7464 8 17.84 1065719 100 200 2.13 4.26 21.19 42.39 0.234742 20 5 4900 6 12.67 372645 35

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211 1.73 26.29 52.58 0.287539 18 3 36 24 7.783 6724.76 0.63 220 1.5 4.242 30.89 61.79 0.333333 16 3 4900 12 5.406 317926 30 It’s almost identical to the last column. (e) Jade: Pretty well matched.
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• Fall '12
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• Diffraction, Neutron diffraction, X-ray scattering techniques, 4F

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