Curie Constant Calculator
Calculate Curie constant for paramagnetic materials and magnetic susceptibility analysis
Calculate Curie Constant
Atoms per unit cell
Unit cell edge length
Per atom magnetic moment
Curie Constant Results
Formula: C = (μ₀/3kB) × (N/a³) × μ²
Curie's Law: M = (C/T) × B (Magnetization proportional to C×B/T)
Magnetic Susceptibility: χ = C/T (at temperature T)
Paramagnetic Analysis
Example: Simple Cubic Lattice
Material Parameters
Lattice structure: Simple cubic
Lattice constant: a = 0.2 nm
Atoms per unit cell: N = 1
Magnetic moment per atom: μ = 2 μB
Calculation
C = (μ₀/3kB) × (N/a³) × μ²
C = (4π×10⁻⁷/3×1.381×10⁻²³) × (1/(0.2×10⁻⁹)³) × (2×9.274×10⁻²⁴)²
C ≈ 1.305 K⋅A/(T⋅m)
Physical Interpretation
At room temperature (300 K): χ = C/T = 4.35×10⁻³
This represents a moderately strong paramagnetic response
Material would show measurable magnetization in applied field
Curie's Law Fundamentals
Paramagnetism
Materials with unpaired electrons align with magnetic field
Temperature Dependence
Magnetic susceptibility χ = C/T decreases with temperature
Magnetic Moments
Atomic magnetic moments determine material response
Crystal Structure
Lattice geometry affects atomic density and coupling
Physical Constants
Applications
Magnetic susceptibility measurements
Material characterization and identification
Magnetic cooling and refrigeration
Electronic structure studies
Quantum magnetism research
Understanding the Curie Constant
What is the Curie Constant?
The Curie constant characterizes how a paramagnetic material responds to magnetic fields. It depends on the magnetic moments of atoms and their density in the crystal lattice. The Curie constant is fundamental to understanding magnetic susceptibility and its temperature dependence.
Curie's Law
- •Magnetization M = (C/T) × B
- •Magnetic susceptibility χ = C/T
- •Inversely proportional to temperature
- •Valid for paramagnetic materials at high T
Curie Constant Formula
C = (μ₀/3kB) × (N/a³) × μ²
- C: Curie constant [K⋅A/(T⋅m)]
- μ₀: Permeability of free space
- kB: Boltzmann constant
- N: Atoms per unit cell
- a: Lattice constant [m]
- μ: Magnetic moment per atom [J/T]
Note: The Curie constant is material-specific and depends on both atomic properties (magnetic moment) and crystal structure (lattice constant, coordination).
Physical Significance and Applications
Material Characterization
The Curie constant provides insight into the electronic structure of materials, including the number of unpaired electrons and their magnetic interactions. It's essential for identifying paramagnetic phases.
Temperature Dependence
Curie's law (χ = C/T) explains why paramagnetic susceptibility decreases with temperature. At higher temperatures, thermal energy competes with magnetic alignment, reducing the material's response to external fields.
Magnetic Cooling
Materials with high Curie constants are valuable for magnetic refrigeration. The strong temperature dependence of magnetic susceptibility enables adiabatic demagnetization cooling to achieve very low temperatures.