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Density of Crystal Calculator

Compute density crystal using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.

Reviewed by Manoj Kumar, Mathematics Educator

Reviewed by Manoj Kumar, Mathematics Educator

Formula

density = (Z * M) / (Na * a^3)

Crystal density equals the product of atoms per unit cell (Z) and molar mass (M), divided by the product of Avogadro number (Na) and the cube of the edge length (a). The edge length must be converted from angstroms to centimeters before calculation.

Worked Examples

Example 1: Copper (FCC)

Problem:Calculate the density of copper with molar mass 63.55 g/mol, Z=4 (FCC), and edge length 3.61 angstroms.

Solution:density = (4 * 63.55) / (6.022e23 * (3.61e-8)^3)\ndensity = 254.2 / (6.022e23 * 4.707e-23)\ndensity = 254.2 / 28.34\ndensity = 8.97 g/cm\u00B3

Result:Density = 8.97 g/cm\u00B3

Example 2: Iron (BCC)

Problem:Calculate the density of iron with molar mass 55.85 g/mol, Z=2 (BCC), and edge length 2.87 angstroms.

Solution:density = (2 * 55.85) / (6.022e23 * (2.87e-8)^3)\ndensity = 111.7 / (6.022e23 * 2.364e-23)\ndensity = 111.7 / 14.23\ndensity = 7.85 g/cm\u00B3

Result:Density = 7.85 g/cm\u00B3

Frequently Asked Questions

What is crystal density and why does it matter?

Crystal density is the mass per unit volume of a crystalline solid, calculated from the arrangement of atoms within its unit cell. It is a fundamental property used in materials science to identify substances, predict mechanical strength, and evaluate purity. The density depends on the molar mass of the atoms, how many atoms occupy each unit cell, and the size of the unit cell. Experimentally measured densities can be compared to calculated values to detect defects or impurities in a crystal lattice.

How is crystal density different from bulk density?

Crystal density (also called theoretical or X-ray density) assumes a perfect, defect-free crystal with no voids or grain boundaries. Bulk density is the measured density of a real material sample, which may contain vacancies, dislocations, grain boundaries, and porosity. As a result, bulk density is typically lower than crystal density. The ratio of bulk to crystal density gives the relative density or packing quality of a material, which is important in ceramics, metallurgy, and pharmaceutical tablet manufacturing.

References

Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy