Question

In \(\mathrm{CaF}_{2}\) structure, \(\mathrm{Ca}^{2}\) ions form ccp arrangement and F- ions occupy (a) half the tetrahedral voids (b) all tetrahedral voids (c) half the octahedral voids (d) all octahedral voids

Short answer

(b) F- ions occupy all tetrahedral voids.

Step-by-step solution

Understand the crystal structure

In the CaF2 structure, calcium ions (Ca²⁺) form a cubic close-packed (ccp) arrangement. This is also known as a face-centered cubic (fcc) structure. The ccp arrangement implies that Ca²⁺ ions form a lattice that creates octahedral and tetrahedral voids within the structure.

Determine the void occupancy by F- ions

In any ccp lattice, there are two tetrahedral voids for each atom in the lattice. For CaF2, there is 1 Ca²⁺ ion and 2 F⁻ ions per formula unit. Since there are 2 F⁻ ions per Ca²⁺ ion, and they occupy the tetrahedral voids, F⁻ ions occupy all tetrahedral voids present in the structure.

Verify the relationship between Ca²⁺ ions and F⁻ ions

A ccp lattice contains one Ca²⁺ ion and two F⁻ ions per formula unit. Since each Ca²⁺ in the ccp arrangement leads to the creation of two tetrahedral voids, and F⁻ ions fit into these voids, all tetrahedral voids are filled by F⁻ ions.

Key concepts

Cubic Close-Packed Arrangement

The cubic close-packed (ccp) arrangement is a way atoms are arranged in a crystal lattice, where each atom is surrounded by 12 nearest neighbors. This arrangement is also known as the face-centered cubic (fcc) structure because atoms are located at each of the corners and the centers of all the cube faces. It is one of the most efficient ways to pack spheres, maximizing space utilization.
The ccp arrangement is significant in determining the properties of a crystal, such as its density, stability, and how it interacts with light. In this arrangement, voids or empty spaces are created, which atoms or ions can occupy. These include both tetrahedral and octahedral voids that are essential in understanding the structure of compounds like \(\mathrm{CaF}_{2}\).
When discussing materials having ccp structures, we often infer characteristics like strength and compactness due to this efficient packing. Understanding this concept is essential for predicting and explaining the physical and chemical behavior of crystalline materials.

Tetrahedral Voids

Tetrahedral voids are small spaces within a crystal lattice formed when four atoms in a cubic close-packed arrangement surround an empty space, creating a shape that resembles a tetrahedron. Each ccp lattice point contributes to creating two tetrahedral voids. These voids play a crucial role in the structures of ionic compounds and their properties.
In ionic compounds, smaller ions often occupy these voids. For instance, in the calcium fluoride (\(\mathrm{CaF}_{2}\) structure, the smaller fluoride (\(\mathrm{F}^{-}\) ions occupy the tetrahedral voids within the ccp lattice of calcium ions. This allows the fluoride ions to be relatively comfortable in size and fit snugly within these small spaces.

• Tetrahedral voids are integral for determining how different ions and atoms can fit together in a packed structure.
• Understanding these voids helps in comprehending the ratio of different ions in any compound.
• The occupation of these voids affects the overall stability and interactions within the crystal structure.

Such knowledge is particularly useful when studying structures like \(\mathrm{CaF}_{2}\), as it helps understand why certain compounds form in the way they do.

Octahedral Voids

Octahedral voids are another type of space found within a crystal lattice. Unlike tetrahedral voids, they are larger and formed by six surrounding spheres in the lattice, creating an octahedron-like space. These larger voids can accommodate bigger ions compared to tetrahedral voids.
Every atom in a cubic close-packed structure creates one octahedral void, making them less numerous than tetrahedral voids. However, they are significant in many crystal structures due to their size.

• Octahedral voids are pivotal in determining the complex ionic arrangements in crystals.
• They accommodate larger ions and affect the coordination numbers and resulting properties of the materials.
• Understanding the distribution and occupation of these voids helps in predicting the density and structural integrity of the crystal.

Although not filled in the \(\mathrm{CaF}_{2}\) structure, octahedral voids are critical in other structures and essential in understanding crystal chemistry.

Calcium Fluoride Structure

The calcium fluoride (\(\mathrm{CaF}_{2}\) structure is an excellent example of how ions arrange in a crystal lattice to form a stable material. In \(\mathrm{CaF}_{2}\), calcium ions (\(\mathrm{Ca}^{2+}\) form a cubic close-packed (ccp) arrangement. This leaves room for the fluoride ions to occupy the tetrahedral voids entirely.
This particular arrangement means that for every calcium ion, there are two fluoride ions fitting snugly into the tetrahedral voids, maintaining electrical neutrality of the structure. Complete filling of these voids ensures that the compound is densely packed and stable.

• \(\mathrm{CaF}_{2}\) illustrates how smaller anions like fluoride can inhabit tetrahedral voids created by larger cations such as calcium.
• The arrangement allows for optimal packing and contributes to the material's properties including its hardness and how it conducts sound.
• The complete filling of tetrahedral voids is a clear example of ion packing efficiency in a crystalline material.

Understanding the \(\mathrm{CaF}_{2}\) structure helps one grasp the concept of ionic crystal formation and properties, making it a foundational concept in the study of materials science.