Science & Lab Tools
Cubic Cell Calculator
Calculate properties of cubic crystal cells including edge length, atomic radius, density, and atomic mass.
Enter values to see results
Related to Cubic Cell Calculator
The Cubic Cell Calculator is a specialized tool for crystallography that helps determine key properties of cubic crystal structures. It calculates atomic radius, density, and the number of atoms per unit cell based on the cell type, edge length, and atomic mass. The calculator supports three main types of cubic cells: simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC).
Calculation Methods
The calculator uses specific formulas for each cell type to determine atomic radius: - Simple Cubic (SC): r = a/2 - Body-Centered Cubic (BCC): r = (√3 × a)/4 - Face-Centered Cubic (FCC): r = (√2 × a)/4 where 'r' is the atomic radius and 'a' is the edge length.
Density Calculation
The density is calculated using the formula: ρ = (M × n)/(V × NA) where M is the atomic mass, n is the number of atoms per cell, V is the volume (a³), and NA is Avogadro's number (6.022 × 10²³).
The calculator provides three key results that help understand the structure and properties of cubic crystal systems. Each result has specific implications for material science and crystallography research.
Atomic Radius (pm)
The atomic radius is given in picometers (pm) and represents half the distance between adjacent atoms in the crystal structure. This value is crucial for understanding atomic packing and determining interatomic distances in the crystal.
Density (kg/m³)
The calculated density indicates how closely packed the atoms are in the crystal structure. Higher density values suggest more efficient atomic packing, which is typical of FCC structures compared to SC structures.
Atoms per Cell
This value shows how many atoms are present in one unit cell: 1 for SC, 2 for BCC, and 4 for FCC. This number is important for understanding the packing efficiency and structural characteristics of the crystal.
1. What is a cubic unit cell?
A cubic unit cell is the smallest repeating unit in a cubic crystal structure. It has equal edge lengths and 90° angles between all faces. The arrangement of atoms within this cell determines many of the material's physical properties.
2. How do the different cubic cell types differ?
Simple cubic (SC) has atoms only at the corners, body-centered cubic (BCC) has an additional atom at the center of the cube, and face-centered cubic (FCC) has atoms at the center of each face in addition to the corners.
3. Why is atomic radius important in crystallography?
Atomic radius helps determine how atoms are packed in a crystal structure, which affects properties like density, mechanical strength, and thermal conductivity. It's essential for understanding material behavior and designing new materials.
4. What affects the density of a cubic crystal?
The density of a cubic crystal depends on the atomic mass, the number of atoms per unit cell, and the cell's edge length. The type of cubic structure (SC, BCC, or FCC) directly affects the number of atoms per cell and thus the density.
5. What is the scientific source for this calculator?
This calculator is based on fundamental crystallographic principles from solid-state physics and materials science. The formulas and methods are derived from established crystallographic theory, particularly from works like "Introduction to Solid State Physics" by Charles Kittel and "Solid State Physics" by Neil W. Ashcroft and N. David Mermin. The calculations follow standard crystallographic conventions defined by the International Union of Crystallography (IUCr) for determining atomic positions, unit cell parameters, and crystal densities in cubic systems.