Bloch–Grüneisen formula - a formula describing the temperature dependence of that part of the electrical resistivity ρ of metals which is due to the scattering of conduction electrons by the thermal vibrations of the atoms of the crystal lattice:
Here m* and e0 is the effective mass and the charge of a conduction electron, n is the concentration of electrons, T is the temperature, θD is the Debye temperature, M is the mass of an atom of the metal, C is a constant ≈ 1—10 eV, d is the lattice constant, K0= 2π(3n/8π)1/3. The Bloch–Grüneisen formula was obtained independently in 1930 by the German physicist E. Grüneisen and the American physicist F. Bloch. For T<<θD it leads to the dependence ρ=T5, and for T<<θD to ρ≈T. The Bloch–Grüneisen formula, obtained without allowing for the anisotropy of the metal and for other mechanisms of electron scattering (for example, the scattering of electrons by impurities or by other electrons), serves for relatively rough estimates of ρ.