An approach to local band average for the temperature dependence of   lattice thermal expansion
  It has long been puzzling regarding the mechanism behind the nonlinearity of lattice thermal expansion at low temperatures despite modeling considerations from various perspectives in classical or quantum approximations. An analytical solution in terms of local bond average is presented herewith showing that the thermal expansion coefficient follows closely the specific heat of Debye approximation without the involvement of mode Gruneisen constant or the bulk modulus. Matching predictions to experimental observations using the Debye temperature and the atomic cohesive energy as input evidences that the current approach may represent the true situation of temperature induced lattice expansion though the exact form of phonon density of states need to be considered for further refinement. 
Chang Q. Sun