enclosed space is an \"octahedral hole\". C. Locating Lattice Holes in cubic Clo

Question

enclosed space is an "octahedral hole". C. Locating Lattice Holes in cubic Closest Packing Examine the model of the face-centered cubic unit cell, which also describes the structure of cubic closest packing. Locate the tetrahedral hole behind each corner sphere. Are these holes shared by any other unit cells? Can you find any other tetrahedral holes in this unit cell? How many complete tetrahedral holes are there in each unit cell? Notice the octahedral hole in the center of the unit cell. Along each edge of the face-centered unit cell there is a fraction of another hole. Place four unit cells together along this edge to complete the hole? How many spheres enclose the hole? What type of hole is this? How many edges in a cube? What fraction of this type of hole lies along each edge? Experiment 18, Page 8 of 10

Explanation / Answer

C. locating holes in cubic lattice

In an fcc unit cell

The tetrahedral hoes are shared between adjacent cells

There are tetrahderal holes located at the corners

There are 8 tetrahedral holes in all

Octahedral holes

The hole type if octahedral

there are 8 edges in cube

The fraction of this type of hole 0.524

Total octahedral holes = 4

number of spheres in fcc unit cell is  6

ratio of octahedral holes ot spheres 0.66

ratio of tetrahderal holes to sphere 1.33

For hexagonal close packed lattice

Number of spheres in a unit cell 6

number of tetrahedral holes 4

number of octahedral holes 6

Ionic crystals with hexagonal or cubic slosest packing,

coordination number for ion in tetrahedral holes 8

coordination number of ion in octahedral hole 8

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