Interstitial sites in close packing Assignment Help

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Interstitial sites in close packing

         Even in the compact packing of the spheres, there is left some empty space between spheres. This empty space in the crystal lattice is known as site or void or hole. The types of voids are given as follows,

         (1) Trigonal void :  This site is formed when three spheres lie at the vertices of the equilateral triangle. Size of the trigonal site can be given by the following relation,

 

2217_trigonal void.png

         r = 0.155R

         r  = Radius of the spherical trigonal void

         R = Radius of closely packed spheres


         (2) Tetrahedral void : A tetrahedral void is developed when triangular voids (made by three spheres in one layer touching each other) have contact with one sphere either in the upper layer or in the lower layer.

 

2283_tetrahedral void.png

         Number of the tetrahedral voids is double the number of spheres in the crystal structure.

r/R = 0.225

         here, r is the radius of the tetrahedral void or the atom occupying tetrahedral void.

         R is the radius of the spheres forming the tetrahedral void.

         (3) Octahedral void : This type of void is surrounded by six closely packed spheres, that is it is formed by six spheres.

 

862_octahedral void.png

 

         The Number of the octahedral voids is equal to the number of the spheres.

r/R = 0.414

                 (4) Cubic void : This type of void is formed between 8 closely packed spheres which occupy all the eight cubes corners

 

1661_cubic void.png

 

                     r/R = 0.732

 

         The decreasing order of size of the specified voids is,

         Cubic > Octahedral > Tetrahedral > Trigonal

 

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