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MessagePosté le: Jeu 29 Sep - 17:27 (2016)    Sujet du message: Close Packing In Crystals Pdf Free Répondre en citant




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Close Packing In Crystals Pdf Free

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Carl Friedrich Gauss proved that the highest average density that is, the greatest fraction of space occupied by spheres that can be achieved by a lattice packing is. Pandey, "Close-Packed Structures" International Union of Crystallography by University College Cardiff Press. External links[edit]. The difference to the next plane, the A plane, is again 6r2/3 in the z-direction and a shift in the x and y to match those x- and y-coordinates of the first A plane.[7]. The coordination number of hcp and fcc is 12 and their atomic packing factors (APFs) are equal to the number mentioned above, 0.74. ( r , r + 3 r , r ) , ( 3 r , r + 3 r , r ) , ( 5 r , r + 3 r , r ) , ( 7 r , r + 3 r , r ) , … . fcc = ABCABCA (every third layer is the same) hcp = ABABABA (every other layer is the same). In close-packing, the center-to-center spacing of spheres in the xy plane is a simple honeycomb-like tessellation with a pitch (distance between sphere centers) of one sphere diameter.

The hcp arrangement can be seen in the triangular orientation, but alternates two positions of spheres, in a triangular orthobicupola arrangement. [ 2 i + ( ( j + k ) mod 2 ) 3 [ j + 1 3 ( k mod 2 ) ] 2 6 3 k ] r {displaystyle {begin{bmatrix}2i+((j + k){bmod {2}}){sqrt {3}}left[j+{frac {1}{3}}(k{bmod {2}})right]{frac {2{sqrt {6}}}{3}}kend{bmatrix}}r} . Thus, this row will have coordinates like this:. The second row's coordinates follow the pattern first described above and are:. fcc arrangement seen on 4-fold axis direction . Since the new spheres touch two spheres, their centers form an equilateral triangle with those two neighbors' centers. The three spheres are all already touching each other, forming an equilateral triangle, and since they all touch the new sphere, the four centers form a regular tetrahedron.[6] All of the sides are equal to 2r because all of the sides are formed by two spheres touching.

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