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| S.No. | Properties | Diamond cube(dc) | Simple Cube(sc) | Body CenteredCube(bcc) | Face Centered Cube(fcc) | Hexa-gonalClose_pack structure | NaCl |
| 1 | Vol.of unit cell | a^3 | a^3 | a^3 | a^3 | (3/2) [√3(ca^2)] | a^3 |
| 2 | No. of atoms percell | 8 | 1 | 2 | 4 | 6 | 4 cations4 anions |
| 3 | No.of atoms per unit vol. | 8/ a^3 | 1/ a^3 | 2/ a^3 | 4/ a^3 | 4/ [√3(ca^2)] | 8/a^3 |
| 4 | No.of nearest neighbours | 4 | 6 | 8 | 12 | 12 | |
| 5 | Nearest neighbourDistance(2r) | a√3/4 | a/2 | a√3/2 | a√2/2 | a/2 | |
| 6 | Atomic radius | a√3/8 | a/2 | a√3/4 | a√2/4 | a/2 | |
| 7 | Atomic packingFactor | π√3/16=0.34 | π/6= 0.52 | π√3/8=0.68 | π √2/6=0.74 | π√2/6=0.74 | 0.67 |
| 8 | Examples | Ge, Si and Diamond | Polonium | Sodium,Iron,Chromium | Aluminium,Copper,Lead | Magnesium,Zinc,Cadmium | Ionic solids such as NaCl, AgCl,LiFMgO,CaO |
Water shows an anomaly in the range from 4°C to 0°C. With reduction in temperature at and below 4°C the density decreases instead of increasing. At 0°C, the Ice Temperature, it has the lightest density. This is because of the open-pack hexagonal structure of ice crystal. From 4°C to 0°C, the phase transition is occurring through out the volume of liquid and at 0°C the phase transition is complete. At this temperature the whole mass of water is fully transformed into a solid piece of ice. Therefore at 0°C we have the lightest density of Ice. It is this anomaly which helps the survival of fishes in frozen lakes. Nine-tenth of ice-berg is submerged and one-tenth of the ice-berg is visible. Therefore we say that the tip of the ice-berg is visible.
1.11.2 ALLOTROPIC FORMS OF CARBON
There are elements which exist as different crystalline allotropes such as Carbon. This most commonly found element exists as three crystalline allotropes namely Graphite, Diamond and Buckminstefullerene Crystal also known a buckeyball structure. The structure is shown in Figure 1.56 and Figure 1.57 and their properties are tabulated in Table (1.22).
1.11.2.1. DIAMOND CRYSTAL.
In Figure 1.56 we show the Diamond allotropic form of Carbon. As shown in Fig 1.56 A , Diamond is two interpenetrating FCC sub-lattices with one sub-lattice displaced with respect to the other along the diagonal of the cube by a quarter of diagonal length (a√3)/4 where ‘a’ the lattice parameter. Since Diamond unit cell is a cube, its lattice parameter is the side of a cube as shown in Figure 1.56 B. The basic unit cell of Diamond is cube of equal sides ‘a’ length. ‘a’ is the lattice constant of Diamond. Its value is 3.57 Angstrom. The basic unit cell is subdivided into 8 subcubes ABCDEFGH. ABCD comprise the upper 4 subcubes and EFGH comprise the lower 4 subcubes. In the Figure 1.56B , subcube E is hidden due to the perspective view. The subcube A, C, in the upper layer and F,H in the lower layer contain the tetrahedral structure of carbon atoms as shown in Figure 1.56D. As a result the basic UNIT CELL has 8 C atoms at the 8 corners of the cube, 6 C atoms on the six faces of the cube and 4 C atoms in the bodies of A, C , F, H subcube. The net result is that on looking at the PLAN VIEW of Diamond Unit Cell as shown in Figure 1.56C we see one C atom sharing its 4 valence electrons with 4 C atoms at its 4 corners. This kind of structure is repeated through out.
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