  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.
