Crystal structure of the material :- the manner in which atoms, ions, or molecules are spatially.

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1 Crystal structure A crystalline material :- is one in which the atoms are situated in a repeating or periodic array over large atomic distances. Crystal structure of the material :- the manner in which atoms, ions, or molecules are spatially. Atomic hard sphere model:- atoms (or ions) are thought of as being solid sphere having well- define diameters. Lattice :- means a three dimensional array of points coinciding with atom positions ( or sphere centers). Unit cell :- the unit cell is a structure unit or building block that can describe the crystal structure. Repetition of the unit cell generates the entire crystal. The unit cell geometry Crystal system - The unit cell geometry is completely defined in terms of six parameters the three lengths a, b and c and the three angles. Page 1

2 Unit cell studies are useful for two reasons 1. It contains a small number of atoms and is therefore easy to study. 2. It can extract important information about the crystal structure la rftam fo. There are many types of unit cells that can take one of the seven main ones shown in Table (2-1) which are called crystal systems. Table (2-1) Crystal systems Page 2

3 But most importantly for the metal cubic system and hexagonal system of cells. Most metals (more than 90%) contain one of these two systems. Page 3

4 The most common types of crystal structure in solids Face centered cubic FCC Body centered cubic BCC Hexagonal close packed HCP Hexagonal system For each crystal structure mentioned above we will determine: - Position of atoms - Examples - The relation between the length (a) of cell and the radius of the atom R. - The coordination number CN. - Number of atoms / unit cell. - Atomic packing factor APF. Face Centered Cubic Structure (FCC) (Cubic System) - Atoms are located of the corners and on the centers of all the faces of cubic unit cell. - Cu, Al, Ag, Au have this crystal structure. - The relation between the length (a) and the radius of the atom R ( a= 2R ) - The coordination number CN = The number of closest neighbors to which an atom is bonded. CN (FCC)= 12 - Number of atoms per unit cell = 8x1/8 + 6 x 1/2= 4 atom/ unit cell. Page 4

5 - Atomic packing factor APF = Fraction of volume occupied hard spheres = 0.74 (maximum possible) Body Centered Cubic Structure (BCC) (Cubic System) - Atom at each corner and at center of cubic cell. - Cr, Na, Fe have this crystal structure. - Number of atoms per unit cell n = 8x1/8 + 1= 2 atom/ unit cell. - Relation between a and R is a = - The coordination number CN = 8 - Atomic packing factor APF = = 0.68 Hexagonal close packed (HCP) - Zn, Cd, Mg, etc. Hexagonal closest packed structures in all crystal systems. - Number of atoms per unit cell n = 1/2 + 3= 6 atom/ unit cell. - Relation between a and c (height) 2R, c =.a = 1.633a - The coordination number CN = 12 - Atomic packing factor APF = 0.74 Page 5

6 Density Computations A knowledge of the crystal structure of a metallic solid permits computation of its theoretical density through the relationship : Classify Solids 1. Single crystal :All unit cells interlock in the same way and have the same orientation. Page 6

7 2. Polycrystalline material :Comprised of many small crystals or grains. The grains have different crystallographic orientation. There exist atomic mismatch within the regions where grains meet. These regions are called grain boundaries. 3. suohproma : Disordered lack of a systemic atomic arrangement. Page 7