Calculate the densities of Si and GaAs from the lattice...

Calculate the densities of Si and GaAs from the lattice constants (Appendix III), atomic weights, and Avogadro's number. Compare the results with densities given in Appendix III. The atomic weights of $\mathrm{Si}, \mathrm{Ga}$, and $\mathrm{As}$ are $28.1,69.7$, and 74.9, respectively.

Key Concepts

Crystal Structure and Unit Cell

The crystal structure refers to the orderly geometric arrangement of atoms in a crystalline material, and the unit cell is the smallest repeating unit that represents the entire crystal lattice. Understanding the crystal structure and the number of atoms per unit cell is crucial for calculating material properties, such as density, as it directly affects the mass contained in a given volume of the material.

Lattice Constants and Unit Cell Volume

The lattice constant is the physical dimension of the unit cell, and it is used to calculate the volume of the unit cell. In density calculations, knowing the unit cell volume allows for the determination of the mass per volume, as the volume defines the space occupied by the repeated structure in the crystal.

Atomic Weight and Avogadro’s Number Conversion

Atomic weights provide the mass of one mole of atoms, and Avogadro’s number is used to convert this molar mass to the mass of a single atom. This conversion is essential when calculating the mass contained in a unit cell by accounting for the individual mass of each atom contributing to that cell.

Density Calculation

Density is calculated by dividing the mass of the atoms within a unit cell by the volume of that cell. This fundamental concept in materials science connects the microscopic details of atomic arrangement with the macroscopic property of density, allowing for theoretical predictions of material density based on atomic weights and structural parameters.

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