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Chemistry

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Published in: Chemistry
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Solids

Amiya B / Bhubaneswar

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Qualification: MSc

Teaches: Biology, Chemistry, Computer Science, C / C++, Python Programming

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  1. Regular arrangements of atoms within a crystalline solid Crystalline lattice of any solid is nature's way of aggregating the particles to minimize their energy We can represent the crystalline lattice with a small collection of atoms, ions or molecules Unit cell called the unit cell When the unit cell is repeated over and over - like the tiles of a floor - but in 3 dimensions, Crystalline Lattice the entire lattice is reproduced Consider the two-dimensional crystalline lattice shown in fig. The unit cell for this lattice is dark-colored square a point in space occupied by Each circle represents a lattice point an atom, ion or molecule Repeating the pattern in the square throuhgout the two-dimensional space generates the entire lattice. Many different unit cells exist, and we often classify unit cells by their symmetry We will focus primarily on cubic unit cells (also we will look at one hexagonal unit cell) Cubic unit cells are characterized by equal edge lengths and 900 angles at their corners consists of a cube with one atom at each corner edge length is twice the radius of the atoms (1=2r) It may seem like the unit cell contains 8 atoms, it actually contains only one Each corner atom is shared by 8 other unit cells In other words, any one unit cell actually contains only one-eighth of each of the eight simple cubic atoms at its corners, for a total of only one atom per unit cell 6 Coordination number any one atom touches only six others Packing efficiency the simple cubic unit cell contains a lot of empty space consists of a cube with one atom at each corner one atom in the very center of the cube Solid3 Crystalline Solids Cubic unit cells Fig. 3 cubic unit cells atoms do not touch along each edge of the cube, but instead along the diagonal line that runs from one corner, through the middle of the cube, to the opposite corner. Edge length = body-centered cubic center atom is not shared Contains two atoms per unit cell with any other neighboring cells 8 coordiantion number atom in the very center of the cube, which touches 8 atoms at the corners Packing efficiency Significantly higher than for the simple cubic unit cell Each atom in this structure strongly interacts with more atoms than each atom in the simple cubic unit cell is a cube with one atom at each corner one atom in the center of each cube face Like face-centered unit cell the atoms do not touch along each edge of the cube, instead atom touch alone the diagonal face The edge length in terms of the atomic radius face-centered cubic Contains 4 atoms per unit cell because the center atoms on each of the six faces are shared between two unit cells 12 Coordination number 74% Packing efficiency Any one atom strongly interacts with more atoms than in either the simple cubic unit cell or body-centered cubic unit cell Coordiantion number Packing efficiency A characteristic feature of any unit cell is the coordination number The number of atoms with which each atom is in direct contact is the number of atoms with which a particular atom can strongly interact A quantity closely related to the coordination number is the packing efficiency The percentage of the volume of the unit cell occupied by the spheres The higher the coordination number, the greater the packing efficiency.

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