The density of BCC iron is 7.882 g / cm^3 and the lattice parameter is 0.2866 nm when hydrogen

step 1 Let's consider iron, which has, actually, it's a density of 7 .87 grams per cubic centimeter, an

The density of BCC iron is 7.882 g / cm^3 and the lattice...

The density of BCC iron is $7.882 \mathrm{~g} / \mathrm{cm}^3$ and the lattice parameter is $0.2866 \mathrm{~nm}$ when hydrogen atoms are introduced at interstitial positions. Calculate (a) the atomic fraction of hydrogen atoms; and (b) number of unit cells on average that contain hydrogen atoms.

The density of BCC iron is $7.882 \mathrm{~g} / \mathrm{cm}^3$ and the lattice parameter is $0.2866 \mathrm{~nm}$ when hydrogen atoms are introduced at interstitial positions. Calculate
(a) the atomic fraction of hydrogen atoms; and
(b) number of unit cells on average that contain hydrogen atoms.

Key Concepts

Body-Centered Cubic (BCC) Structure

A BCC crystal structure is characterized by atoms at the eight corners of a cube and one atom at the center. This arrangement results in a specific effective number of atoms per unit cell, which is critical for calculations involving mass, density, and atomic fractions in materials science.

Lattice Parameter

The lattice parameter refers to the edge length of the unit cell in a crystal lattice. It is essential for calculating the unit cell's volume, which, combined with material density, enables the determination of the mass of atoms within the cell.

Unit Cell Volume and Density

By using the lattice parameter, one can calculate the volume of a single unit cell. When coupled with the material's density, this volume allows the computation of the mass contained in one unit cell, linking the microscopic crystal structure with macroscopic properties.

Atomic Fraction

The atomic fraction is a ratio that represents the number of atoms of a specific type divided by the total number of atoms present in the system. This concept is vital for quantifying the composition of multi-component systems, especially when impurities or interstitial atoms are introduced.

Interstitial Sites

Interstitial sites are the spaces between the regular lattice positions in a crystal. They can accommodate smaller atoms, such as hydrogen in many metals, altering the overall composition and properties of the material. Understanding which sites these atoms occupy is crucial for assessing how they influence the material's behavior.

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