The same as indicated by @TeethWhitener: The phonon density of states gives the number of modes per unit frequency per unit volume of real space.dRic2 said:
Lattice specific heat refers to the amount of heat energy required to raise the temperature of a lattice structure by one unit. It is a measure of the thermal energy stored in the vibrations of the atoms within the lattice.
Lattice specific heat is typically measured using calorimetry, which involves measuring the change in temperature of a substance as heat is added or removed. The specific heat can then be calculated by dividing the amount of heat energy by the mass and temperature change.
The specific heat of a lattice structure is influenced by several factors, including the type of material, its crystal structure, and the temperature at which it is measured. Additionally, the presence of impurities or defects within the lattice can also affect its specific heat.
Lattice specific heat is directly related to thermal conductivity, as both properties are determined by the same factors such as crystal structure and temperature. A material with a higher specific heat will typically have a lower thermal conductivity, as it requires more energy to raise its temperature.
Understanding lattice specific heat is important in the study of materials and their thermal properties. It can help in the design and development of materials for specific applications, as well as in predicting their behavior under different temperature conditions. Additionally, it is a fundamental concept in thermodynamics and solid state physics.