El mineral uraninita (UO2) adopta una estructura de fluorita [Figura 11.42(c)] en la que la long

Step 1: u000AIn the fluorite structure, each uranium atom is surrounded by eight oxygen atoms, formi

El mineral uraninita (UO2) adopta una estructura de fluorita...

$ \mathrm{El}$ mineral uraninita $\left(\mathrm{UO}_2\right)$ adopta una estructura de fluorita [Figura 11.42(c)] en la que la longitud de una arista de celda unitaria es de $5.468 \mathrm{~A}$. (a) ¿Los âtomos de uranio estarán representados por las esferas más grandes de la figura 11.42 (c) o por los más pequeños? Explique. (b) Calcule la densidad de la uraninita.

Key Concepts

Atomic Representation in Crystal Structures

In crystallographic diagrams, atoms are often represented by spheres of different sizes to indicate their relative atomic radii and roles within the structure. Distinguishing between larger and smaller spheres helps in identifying which species is likely to be the cation or anion based on their typical sizes. This concept is pivotal in interpreting structural models and understanding the spatial arrangement of atoms within the crystal.

Density Calculation in Crystals

Density in crystalline solids is calculated by dividing the total mass of the atoms within a unit cell by the volume of that unit cell. This method requires determining the number of formula units per cell, the atomic masses of the constituent atoms, and converting the unit cell dimensions into consistent volume units. Ensuring all these factors are correctly accounted for is critical in obtaining an accurate density.

Crystallographic Unit Cell

The unit cell is the smallest repeating unit in a crystal, defined by its lattice parameters such as the edge length. It contains a specific number of formula units arranged in a precise geometry. In the case of the fluorite structure, understanding how many atoms are contained in the unit cell is essential for further calculations, such as determining the density of the material.

Fluorite Structure

The fluorite structure is a common crystal arrangement typified by compounds like CaF?, where the cations (such as uranium in UO?) occupy a face?centered cubic (FCC) lattice and the anions (such as oxygen) fill all the tetrahedral sites. This structure highlights key coordination and symmetry properties that determine how the atoms are arranged within the crystal.

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