An interactive laboratory for materials engineering: unit cell atomic packing, uniaxial dogbone tensile testing with necking, iron-carbon equilibrium Lever Rule phase fractions, and Charpy impact toughness.
286.4 pm
a = 4R / √323.48 ×10⁶ pm³
a³ unit cell domain68.02%
V_atoms / V_cell7.90 g/cm³
ρ = (n·M) / (Vc·NA)Continuous closed-form calculations evaluated in real-time from active instrument parameters.
286.4 pm
a = 4R / √368.02%
V_atoms / V_unit_cell8 atoms
ρ = 7.90 g/cm³2 shared
8 × 1/8 + 1Mecha Atelier Material Science laboratory provides real-time mathematical and structural evaluations across key physical metallurgy disciplines:
- FCC (Face-Centered Cubic): 4 atoms/unit cell, coordination number 12, APF = 0.74, a = 2·sqrt(2)·r. - BCC (Body-Centered Cubic): 2 atoms/unit cell, coordination number 8, APF = 0.68, a = 4·r / sqrt(3). - HCP (Hexagonal Close-Packed): 6 atoms/unit cell, coordination number 12, APF = 0.74, ideal c/a = 1.633.
Engineering stress σ = F / A_0 and engineering strain ε = ΔL / L_0. Hooke's Law in linear-elastic regime σ = E · ε. Plastic deformation past 0.2% yield offset transitions into strain hardening up to Ultimate Tensile Strength (UTS), followed by localized necking and ductile rupture.
Phase weight fractions are determined via tie-lines and the Lever Rule: W_alpha = (C_Fe3C - C_0) / (C_Fe3C - C_alpha). Eutectoid transformation occurs at 727°C and 0.76 wt% C, decomposing austenite (γ) into lamellar pearlite (ferrite α + cementite Fe3C).
Charpy V-notch energy absorption measures brittle vs ductile fracture transitions across temperature, characterizing the Ductile-to-Brittle Transition Temperature (DBTT) in BCC steels.