In the Wikipedia article cited - http://en.wikipedia.org/wiki/Debye_model#Debye.27s_derivation - N is the number of atoms.hugonot said:Thanks, However, I know this references.
My problem is:
I have got specific temperature dependence C(T) for the solid compound.
I can estimate Debye temperature from the fit, but it will be only one value for the whole range of temperatures.
How can I estimate Debye temperature at specific temperature?
How can t be estimated from material dependent variables? I know the formula for TD http://en.wikipedia.org/wiki/Debye_model but what should I use as N and V?
If V stands for volume, what means N or rather how to calculate it?
Could you give me an example? I mixed up
Any temperature dependence in the Debye Temperature comes from temperature dependences in elastic constants (and due to thermal expansion). These changes are small: about 1 part in 1000 to 1000,000 per Kelvin.hugonot said:I guess is Debye temperature dependent on temperature? I.e TD(T)?
Does anybody know a theoretical formula for temperature dependence of Debye temperature?
What type of molecule, i.e. is this a mineral or alloy?hugonot said:
The Debye temperature formula is a mathematical equation used to calculate the characteristic temperature of a solid material. It is named after Peter Debye, a physicist who proposed the concept of a "Debye solid" in the early 20th century.
The Debye temperature formula is calculated by taking into account the density and elastic properties of a material. It is expressed as: ΘD = (h / kB) * (3N / 4πV)^(1/3) * (vs^3 / vl^3), where h is Planck's constant, kB is the Boltzmann constant, N is the number of atoms per unit volume, V is the volume of the unit cell, vs is the speed of sound in the solid, and vl is the speed of longitudinal sound waves.
The Debye temperature is a measure of the average energy or temperature of the lattice vibrations in a solid. It is used to describe the thermal and elastic properties of materials, and can also provide insights into the structural and electronic properties of a material.
The Debye temperature can vary greatly with different materials, depending on their density, elasticity, and crystal structure. Generally, metals tend to have higher Debye temperatures than non-metals, and materials with stronger bonds tend to have higher Debye temperatures than those with weaker bonds.
The Debye temperature formula is used in various fields such as materials science, condensed matter physics, and geophysics. It is utilized in the study of thermal and mechanical properties of materials, as well as in the design and development of new materials for specific applications. It also has applications in geophysics, where it is used to understand the thermal properties of Earth's interior and the behavior of materials under extreme conditions.