In crystalline solids anions B are arranged in cubic close packing. Cations A are equally distributed between octahedral and tetrahedral voids. If all the octahedral voids are occupied, the formula for solid is.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
If all the octahedral voids are occupied in a cubic close-packed arrangement of anions B, it means that there are an equal number of cations A occupying those octahedral voids. In a cubic close-packed structure, the number of octahedral voids is equal to the number of anions. So, the formula for the solid can be represented as AB.
Since the cations A are also equally distributed between tetrahedral voids, it implies that the number of cations A occupying tetrahedral voids is half the number of anions B. Therefore, the final formula for the solid would be A2B.
Table of content
Formula for Crystalline Solid
Solution:
In the given crystalline solid with a face-centred cubic (FCC) structure, the anions B are arranged in cubic close packing. The FCC lattice has a total of four anions in its unit cell. Within this structure, there are both octahedral and tetrahedral voids present.
The number of octahedral voids is always half the number of tetrahedral voids. Since the cations A are distributed equally between the octahedral and tetrahedral voids, the number of cations in the octahedral voids is the same as the number in the tetrahedral voids.
Given that there are four octahedral voids in the FCC unit cell, there are also four tetrahedral voids. Therefore, the total number of cations in both the octahedral and tetrahedral voids is eight (4 from octahedral voids and 4 from tetrahedral voids).
The ratio of the number of cations to anions per unit cell is 8:4, which simplifies to 2:1. This indicates that there are two cations (A) for every one anion (B).
Based on this information, the formula for the compound is A2B, where A represents the cation and B represents the anion. Therefore, A2B is the formula for the compound.
Summary:
In crystalline solids anions B are arranged in cubic close packing. Cations A are equally distributed between octahedral and tetrahedral voids. If all the octahedral voids are occupied, the formula for solid is A2B.
The formula A2B is determined based on the ratio of cations to anions in the unit cell, which is 2:1. Therefore, A2B is the formula for the compound.
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