Consider an ionic solid M X with NaCl structure. Construct a new structure (Z) whose unit cell i

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Consider an ionic solid M X with NaCl structure. Construct a...

Consider an ionic solid $M X$ with $\mathrm{NaCl}$ structure. Construct a new structure $(Z)$ whose unit cell is constructed from the unit cell of $M X$ following the sequential instructions given below. Neglect the charge balance. (i) Remove all the anions $(X)$ except the central one (ii) Replace all the face centered cations ( $M$ ) by anions $(X)$ (iii) Remove all the corner cations $(M)$ (iv) Replace the central anion $(X)$ with cation $(M)$ The value of $\left(\frac{\text { number of anions }}{\text { number of cations }}\right)$ in $Z$ is __ .

Consider an ionic solid $M X$ with $\mathrm{NaCl}$ structure. Construct a new structure $(Z)$ whose unit cell is constructed from the unit cell of $M X$ following the sequential instructions given below. Neglect the charge balance.
(i) Remove all the anions $(X)$ except the central one
(ii) Replace all the face centered cations ( $M$ ) by anions $(X)$
(iii) Remove all the corner cations $(M)$
(iv) Replace the central anion $(X)$ with cation $(M)$ The value of $\left(\frac{\text { number of anions }}{\text { number of cations }}\right)$ in $Z$ is __ .

Key Concepts

NaCl Crystal Structure

The NaCl structure is a prototypical example of an ionic crystal structure where two different types of ions are arranged in a highly symmetric, interpenetrating lattice. In this structure, the ions adopt complementary positions such as those on the faces, corners, and center within a cubic unit cell. Understanding the distribution of ions in such structures is fundamental in solid state chemistry and crystallography as it provides insight into coordination, bonding, and the physical properties of ionic compounds.

Unit Cell and Fractional Occupancies

A unit cell is the smallest repeating entity in a crystal that, when repeated in three dimensions, constructs the entire lattice. Atoms or ions that reside at special positions in the unit cell—such as corners, faces, or the body center—contribute fractional amounts (e.g., 1/8 for corners, 1/2 for faces) to the overall composition. Mastery of these concepts is essential for determining the actual number and ratio of atoms or ions in complex structures.

Stoichiometry in Crystalline Solids

Determining the stoichiometry of a crystal involves summing the contributions of all atoms or ions based on their fractional positions within the unit cell. This precise counting is critical not only for understanding the chemical composition but also for predicting the properties of the material, as it reveals the ratios of different types of ions or atoms in the bulk structure.

Structural Modification via Ion Substitution and Removal

Modifying a crystal structure by substituting or removing specific ions is a common technique used to tailor material properties. Structural modification can alter the stoichiometry and symmetry of the original unit cell, leading to changes in physical characteristics. Understanding how such operations affect the arrangement and ratios of constituents is key in materials design and solid state chemistry.

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