Cold working raises iron dislocation density from 10¹⁰ to 10¹⁵ m⁻². Shear modulus is 82 GPa and Burgers vector is $\mathbf b=(a_0/2)[111]$, a₀=0.2856 nm. Estimate stored energy in MJ/m³ (one decimal place).
The Burgers-vector magnitude is $b=\sqrt3a_0/2=2.4734\times10^{-10}$ m. Using the usual line-energy estimate Gb²/2, the extra stored energy density is $\Delta U=\tfrac12Gb^2(\rho_f-\rho_i)\simeq2.51\times10^6$ J/m³ =2.5 MJ/m³. Line-energy prefactors depend on the approximation; the source grading retains its broad 0.4–5.1 range.
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