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THE FACE-CENTERED CUBE AND CUBICAL CLOSEPACKING E. DE BARRY BARNETT Sir John Cass Technical Institute, London, England
STUDENTS usuallv find great difficultyin understanding how the face-centered cube gives riie to close-packini but the derivation can easily be shown with almost startling clearness by the following simple model. Eichteen balls of about l-in. diameter are reauired " in anv four shardv contrasting colors. The choice of colhrs can be left to the individual teacher, but the writer has found the following convenient, and suitable for those with defective color vision: one black, five yellow, six red, six silver. Each ball must he drilled with four eaui-spaced equatorial holes, but the oetahedrally drilled bzhs of the Griffin skeletal models are very satisfactory, unused holes being left vacant. The four units shown in the diaeram are constructed. I n each the balls are in contact, a n d held in place by wooden pegs or Griffin "expendable bonds." The four units are then piled together in the order shown (2 on top of I, etc.) and in the aspect shown (this last is important). If the resulting model is inspected, the face-centered cubical arrangement is seen at once. If attention is now focused on the black ball it will be seen to be equatorially surrounded by six silver balls. Further, there are three red balls in north polar positions and three red balls in south polar positions. This gives
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the 12-fold coordination characteristic of close-packing. Since the red balls surrounding the north pole are not in eclipsed positions to the red balls surrounding the south pole (they are not in the "same longitude"), the closepacking is cubical and not hexagonal.
JOURNAL OF CHEMICAL EDUCATION
