Crystal Structure and Metal Properties Calculator
α-iron, body-centred cubic with a = 2.8665 Å, has a theoretical density of 7.87422 g/cm³, matching the measured 7.874 g/cm³.
7.87422010378339 g/cm³
Full answer, then cut to fewer decimals (not rounded):
- 7.87422010378339 g/cm³
- 7.8742201037833 g/cm³
- 7.874220103783 g/cm³
- 7.87422010378 g/cm³
- 7.8742201037 g/cm³
- 7.874220103 g/cm³
- 7.87422010 g/cm³
- 7.8742201 g/cm³
- 7.874220 g/cm³
- 7.87422 g/cm³
- 7.8742 g/cm³
- 7.874 g/cm³
- 7.87 g/cm³
- 7.8 g/cm³
- Crystal structure
- BCC
- Atoms per unit cell
- 2
- Coordination number
- 8
- Atomic packing factor
- 0.6801747616
- Atomic radius
- 1.24123091 Å
- Measured density (CRC)
- 7.874 g/cm³
- Melting point
- 1538 °C
- Young’s modulus
- 211 GPa
- Thermal conductivity
- 80.4 W/(m·K)
Step-by-step solution
- ρ = nA ÷ (V_c Nₐ) with n = 2 atoms per BCC cell
- V_c = a³ = 2.8665³ = 23.55352098 ų
- ρ = 2 × 55.845 ÷ (23.55352098 × 10⁻²⁴ × 6.022 × 10²³) = 7.874220104 g/cm³
Crystal Structure and Metal Properties Formula
ρ = nA / (V_c Nₐ)
n atoms per cell (BCC 2, FCC 4, HCP 6), V_c cell volume; BCC r = √3a/4, FCC r = √2a/4
Worked Example
α-iron, body-centred cubic with a = 2.8665 Å:
- ρ = nA ÷ (V_c Nₐ) with n = 2 atoms per BCC cell
- V_c = a³ = 2.8665³ = 23.55352098 ų
- ρ = 2 × 55.845 ÷ (23.55352098 × 10⁻²⁴ × 6.022 × 10²³) = 7.874220104 g/cm³
Atoms per unit cell: 2 · Coordination number: 8 · Atomic packing factor: 0.6801747616 · Atomic radius: 1.24123091 Å · Measured density (CRC): 7.874 g/cm³ · Melting point: 1538 °C · Young’s modulus: 211 GPa · Thermal conductivity: 80.4 W/(m·K)
GATE tip
Iron changes from BCC to FCC at 912 °C; in the same unit-cell picture the density rises by about 1 %, which explains the contraction seen in dilatometry.
More Physical Metallurgy Calculators
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Bragg's Law Calculator
nλ = 2d sin θ, d = a/√(h² + k² + l²)
Cu Kα₁ λ = 1.5406 Å; cubic crystals
Example: The (110) peak of α-iron at 2θ = 44.67° with Cu Kα radiation: Interplanar spacing d = 2.02699 Å.
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Vacancy Concentration Calculator
n_v / N = exp(−Q_v / kT)
k = 8.617 × 10⁻⁵ eV/K; N = Nₐρ/A atoms per m³
Example: Copper (Q_v = 0.9 eV) at 1000 °C: Vacancy fraction n_v/N = 0.000273741.
-
ASTM Grain Size Calculator
N = 2^(G − 1) grains/in² at 100×
G = −6.6439 log₁₀ ℓ − 3.288 (ℓ in mm); grains per mm² = 2^(G + 2.954)
Example: A micrograph showing 64 grains per square inch at 100×: ASTM grain size number G = 7.
-
Nucleation Calculator
r* = 2γ/ΔG_v, ΔG* = 16πγ³/(3ΔG_v²)
ΔG_v = ΔH_f ΔT / T_m; heterogeneous S(θ) = (2 + cos θ)(1 − cos θ)²/4
Example: Copper solidifying with 200 K of undercooling: Critical radius r* = 1.27854 nm.
Frequently asked questions
Why do FCC and HCP have the same packing factor?
Both stack close-packed layers (ABCABC and ABAB), giving the maximum packing factor of 0.74.
Why does measured density differ slightly?
Vacancies, impurities and thermal expansion: the agreement is usually within 0.5 %.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Crystal Structure and Metal Properties Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/crystal-structure-calculator/
IEEE
Scientific Converters, "Crystal Structure and Metal Properties Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/crystal-structure-calculator/