Below are shown three different crystallographic planes for...

Below are shown three different crystallographic planes for a unit cell of some hypothetical metal. The circles represent atoms: (a) To what crystal system does the unit cell belong? (b) What would this crystal structure be called? (c) If the density of this metal is $18.91 \mathrm{g} / \mathrm{cm}^{3}$ determine its atomic weight.

Below are shown three different crystallographic planes for a unit cell of some hypothetical metal. The circles represent atoms:
(a) To what crystal system does the unit cell belong?
(b) What would this crystal structure be called?
(c) If the density of this metal is $18.91 \mathrm{g} / \mathrm{cm}^{3}$ determine its atomic weight.

Key Concepts

Atomic Weight Determination

Atomic weight determination from crystallographic data involves using the material’s measured density along with the known unit cell geometry and the number of atoms per cell. By rearranging the density formula, one can solve for the atomic weight, making it a fundamental technique in materials characterization.

Density Calculation in Crystals

Density calculation in the context of crystal structures involves relating the mass of atoms within a unit cell to the cell’s volume. This is typically done using an equation that includes the number of atoms per cell, the atomic weight, Avogadro’s number, and the volume of the unit cell. A solid grasp of this concept is important for solving problems where density is a key parameter.

Crystal Systems

Crystal systems classify materials based on the symmetry and dimensions of their unit cells. This involves analyzing the edge lengths and angles between them to determine whether a cell belongs to systems like cubic, tetragonal, orthorhombic, etc. A clear understanding of crystal systems is crucial in interpreting the geometric arrangement of atoms and how it influences the material's properties.

Crystal Structures

Crystal structures refer to the organized, repeating arrangement of atoms within the unit cell of a crystalline solid. Common structures like face?centered cubic (FCC), body?centered cubic (BCC), and hexagonal close-packed (HCP) describe how atoms are arranged spatially. Recognizing the crystal structure is essential for predicting physical properties and behavior of materials.

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