the formula of a compound is A2B3 with hcp lattice. What frction of tetrahedral voids are occupied?

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Solution

In this A₂B₃ molecule:
Suppose, A form hcp lattice while B occupy tetrahedral voids.
Number of octahedral voids = Number of close-packed particles
Number of octahedral voids = A
So number of tetrahedral voids = 2A
Let the fraction of tetrahedral voids = A / x = B
A : B = 2 : 3
2A : A / x = 2 / 3
2x = 2 / 3
x = 4 / 3
So, fraction of tetrahedral voids = 4 / 3

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