This structure does not constitute a lattice because the surroundings of the

# This structure does not constitute a lattice because

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This structure does not constitute a lattice because the surroundings of the interior atoms and the corner are different. This type of structure is denser than the simple hexagonal structure. Some of the metals which possess the CPH/HCP structure are:
~ Page 51 of 79 ~ (a) Magnesium (b) Zinc (c) Cadmium (d) Titanium (e) Cobalt (f) Hafnium (g) Selenium (h) Tellurium (i) Thallium (j) Yttrium (k) Zirconium (l) Lithium (below -193 ˚C) (m) Sodium (below -233 ˚C) (n) Beryllium, etc. NUMBER OF ATOMS PER UNIT CELL The atoms that belong to the unit cell are called the basic atoms. Their numbers differ from one shape of arrangement to another. The number can be found from the following equation: N = N C + N I + N F where N: is the number of the basic atoms in the unit cell. N C : is the number of the atoms in the corner. N I : is the number of the atoms inside the cube. N F : is the number of the atoms in the center of the face. BODY-CENTRED CUBIC STRUCTURE (BCC) The unit cell of the BCC system has an atom at each corner and also one at the centre of each crystal or unit cell. Each atom at a corner of the unit cell is shared by 8 unit cells but the one atom at the centre of the unit cell entirely belongs to just that individual unit cell. Therefore, the number of atoms per unit cell is N = N C + N I + N F = (8 x ⅛) + 1 = 2 FACE-CENTERED CUBIC STRUCTURE (FCC) The unit cell of the FCC system has an atom at each corner and also one at the centre of each of the six faces. Each atom at a corner of the unit cell is shared by 8 unit cells and each face atom is shared by two cells. Hence the number of atoms per unit cell is N = N C + N I + N F = (8 x ⅛) + (6 x ½) = 4. CLOSE-PACKED HEXAGONAL STRUCTURE (CPH/HCP) Taking each segment of the structure as a separate cuboid, a corner atom is common to eight unit cells, so that there are (8 x ⅛) + 1 = 2 atoms per unit cell. Since there will be three (3) cuboids, 2 x 3 = 6.
~ Page 52 of 79 ~ The number of atoms belonging to each closed-packed hexagonal (CPH) unit cell is also calculated as follows: N = N C + N I + N F = (12 * 1/6) + 3 + (2 * ½) = 6. CO-ORDINATION NUMBER In a crystalline structure, every atom is surrounded by other atoms. Thus the number of atoms surrounding a central atom is fixed. The co-ordination number therefore shows the number of first neighbours of an atom , e.g. co- ordination number of carbon is 4 and that of hydrogen is 1. Co-ordination number for diamond cubic structure is 4. The co-ordination number, in simple cubic structure, is 6, as it has four nearest neighbours in the same plane plus one each exactly above and below of that corner atom. Similarly co-ordinate number of body centred cubic structure is 8 and for face centred cubic structure it is 4 + 4 + 4 = 12 and for hexagonal closed packed structure, co-ordination number is 12. Noncrystalline (Amorphous) Structures The noncrystalline solids materials do not have their basic particles arranged in a geometric patter.

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