(a) There are seven primitive crystal systems : Cubic , tetragonal orthorhombic , hexagonal, monoclinic triclinic and rhombonhedral. They differ in the arrangement of their crystallographic axes and angles.
(i) Cubic : The cubic unit cell is the smallest repeating unit when all angles are ` 90^(@)C` and all lengths are equal. As such each axis is defined by a Cartesian coordinate. Each is defined by a Cartesian coordinate . Each cubic cell has 8 atoms in each corner . of the cube , and that atom is shared with 8 neighboring cells. This is a unit cell with parameters a= b= ` alpha= beta = gamma = 90^(@)`
(ii) Tetragonal : Teragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors , so that the cube becomes a rectangular prism with a square base. This is a unit cell with parameters `a = b ne c , alpha = beta = gamma = 90^(@)`
(iii) Orthorhombic : Orthorhombic lattics result from stretching a cubic lattice along two of its orthogonal pairs by two different factors , resulting in a rectangular prism with a rectangular base ( a by b) and height (c), such that a ,b and c are distinct. All three bases intersect at ` 90^(@)` angles, so that three lattice vectors remain mutually orthogonal . This is a unit cell with parameters ` a ne b ne c , alpha = beta = gamma = 90^(@)`
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(iv) Hexagonal : this is a unit cell with parameters ` a = b ne c , alpha = beta = 90^(@) , gamma = 120^(@)` The hexagonal closest packed (hcp) has a coordination number of 12 and contains 6 atoms per unit cell.
( v) Monoclinic : In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic system. Thet form a rectangular prism with a parallelogram as its base. This is a unit cell with parameters ` a ne b ne c `
` alpha = gamma = 90^(@) = beta ne 90^(@)`
(vi) Triclinic : The triclinic is also called as anorthic crystal system. A crystal system is decribed by three basic vectors. In the triclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system . in addition, the angles betweeen these vectors must all be different and may include ` 90^(@)` . This is unit cell with parameters ` a ne b ne c `
` alpha ne beta ne sigma = 90^(@)`
The triclinic lattice is the least symmetric of the 14 three - dimensional Bravais lattices. it has (itself ) the minimum symmetry all lattices have, points of inversion at each lattice point and at 7 more points for each lattice point : at the midpoints of the edges and the faces, and at hte centre points . it is the only lattice type that itself has no mirror planes.
` (##SUR_CHE_XII_V02_MQP_O1_E01_038_S06.png" width="80%">
(vii) Rhombohedral : The unit cell is a rhombohedron ( which gives the name for the rhombohedral lattice system) . This is a unit cell with parameters a= b= c , ` alpha = beta = gamma ne 90^(@)` . In geometry , a rhombohedron is a three- dimensional figure like a cube, except that its faces are not squares but rhombi . it is a special case of a parallelpiped where all edges are the same length. It can be used to define the rhombohedral lattice system, a honeycomb with rhombohedral cells
` (##SUR_CHE_XII_V02_MQP_O1_E01_038_S07.png" width="80%">
