static lattice model

السلام عليكم

اريد معلومات عن static lattice model التعريف واين النجاحات واماكن الفشل اذا ممكن بسرعه

Static Lattice Model :-


The Static lattice model describes the motion of the basis in a potential to be simple harmonic motion in an equilibrium position centered at the lattice point and the kinetic energy has to be equal zero, or much less than potential energy .

In this model has two assumptions
1) motion within such a field or potential is harmonic.
2) ions and atoms while defined a Bravias lattice.
3) electrons are responsible for thermal conduction.

Static lattice model success to find specific heat is proportional to T at low temperature.

But have many failures, We have grouped the major failures of the static lattice model into three broad categories :-
1) Failures to explain transport properties.

Temperature dependence of the electronic relaxation time
Failure of the Wiedmann -Franze Law
Superconductivity
Thermal conductivity
Transmission of sound

2)failures to explain the interaction of various types of radiation with the solid .

Reflectivity of ionic crystal
Inelastic scattering of light
scattering of X-ray
Scattering of neutron


3) Failures to explain equilibrium properties

melting
Equilibrium density and cohesive energy
Specific Heat
Thermal expansion

Conclusions

Static lattice model describes the motion of the basis in a potential to be simple harmonic motion, but in this model have many failures to explain some properties, for example in harmonic theory there is no thermal expansion because the phonon amplitude remains the same, in the static model no phonon collision then thermal conductivity equal to infinity