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| Derivation of the Relationship Between Radius r of the Tetrahedral Void and the Radius R of the Atoms in the Close Packing |
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| A tetrahedral void may be represented in a cube as shown in the below figure. |
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| fig 2.12 - Tetrahedral void |
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| The three spheres form the triangular base, the fourth lies at the top and the sphere E occupies the tetrahedral void. |
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| Let the length of the side of the cube = a |
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| From right angled triangle ACB, face diagonal. |
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| As spheres A and B are actually touching each other face diagonal AB = 2R. |
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| Again from the right angled triangle ABD body diagonal |
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| But as shaded sphere touches other spheres evidently body diagonal |
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| AD = 2(R + r) |
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| Dividing equation (ii) by equation (i) we get |
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| r = 0.225 R |
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| Radius ratio of the tetrahedral void = 0.225 R |
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