Consider a sample of well-annealed copper. Find the Burger's vector given that the energy per unit line length is 1.4×10−9J/m, E=177GPa and ν=0.36. Assume α=0.5.
b (in nm):
To find the Burger's vector (b), we can use the formula:
b = (2E * γ) / (π * (1 - v) * α)
where:
E = Young's modulus
γ = energy per unit line length
v = Poisson's ratio
α = atomic volume
Given:
E = 177 GPa = 177 * 10^9 Pa
γ = 1.4 * 10^-9 J/m
v = 0.36
α = 0.5 (in this case, we assume it is given in units of nm^3)
Substituting the values into the formula:
b = (2 * 177 * 10^9 Pa * 1.4 * 10^-9 J/m) / (π * (1 - 0.36) * 0.5 nm^3)
Let's calculate it step by step:
b = (2 * 177 * 1.4) / (π * 0.64 * 0.5) * 10^9 nm
b = (494.4) / (1.0053) * 10^9 nm
b ≈ 491.7 * 10^9 nm
b ≈ 491.7 nm
Therefore, the Burger's vector is approximately 491.7 nm.