Specific Heat by Planck’s Photons instead of Debye’s Phonons?

Jan. 13, 2011 - PRLog -- Background

Historically, the theory of the heat capacity of a crystal lattice based on phonons was proposed by Einstein’s theory of characteristic vibrations in 1907. In 1912, Debye proposed specific heat by normal modes of crystal vibration. However, Raman in the 1950’s argued that normal vibration modes of the lattice cannot be the source of heat capacity because vibration cannot be sustained ‘ad infinitum’ in the presence of even the smallest amount of material damping

Raman argued the specific heat of a crystal was given by Einstein’s theory of characteristic vibration. But unlike Debye’s phonons based on the large number of normal modes of the crystal, Raman limited Einstein’s characteristic vibration theory to only those frequencies corresponding to the spectral lines in the far infrared (FIR). Although Raman’s interpretation of Einstein’s specific heat avoids unphysical normal modes of a crystal, Debye’s theory is widely accepted today for specific heat at the macroscale.

However, Debye’s theory of specific heat remains controversial. Specific heat is considered an intensive thermophysical property of a material independent of size or substance, and therefore macroscopic specific heat is routinely applied to the nanoscale. But interpretation of observations at the nanoscale based on macroscale specific heat has led to unphysical conclusions, e.g. the thermal conductivity of thin films is found to be reduced from bulk while nanofluids are found to have thermal conductivity above that given by standard mixing rules.

Avoidance of Unphysical Conclusions at the Nanoscale

Unlike Debye’s phonons having macroscopic specific heat at the nanoscale, specific heat by Planck’s photons vanishes, the consequence of which is that thin film conductivity remains at bulk as film thickness is reduced and nanofluids obey standard mixing rules. See http://www.nanoqed.org at "Zero Specific Heat" and QED induced Heat Transfer", 2010

Specific Heat by Photons

Specific heat in a crystal by photons finds basis in Planck’s derivation of blackbody radiation in an evacuated cavity except for the reduced speed of light in the crystal.  Unlike Debye’s phonons, Planck’s photons are consistent with QM in that the inexhaustible energy source for atomic vibrations is the thermal kT energy of the atom -  the source of all EM radiation.  QM stands for quantum mechanics, k for Boltzmann’s constant, T for absolute temperature, and EM for electromagnetic.

Discussion

In the 1950’s, lack of experimental FIR data did not allow Raman to support his argument that the specific heat of crystal is determined by averaging the specific heat for all FIR spectral lines using Einstein’s theory of characteristic vibrations. For the metals, the FIR spectra were not reported. Instead, experimental specific heats over the temperature range from 15 to 300 K were used to compute an effective average characteristic vibration frequency based on Einstein’s specific heat theory. For silver, aluminum, and lead, Raman’s average frequencies were 102, 163, and 35 cm-1.  

However, the average frequencies based on Planck specific heat for silver, aluminum, and lead were found to be significantly higher at 175, 222, and 333 cm-1, respectively. To explain this disparity, one must note that FIR spectra are not so simple to be represented by a number of discrete spectral lines. Typical FIR spectra show spectral lines superimposed on a broad background thereby holding in question Raman’s notion of computing specific heat by averaging the specific heats from discrete spectral lines. Lower average frequencies are expected in subsequent papers by computing the average Planck specific heat including the broadband background by integrating the normalized absorbance over the range of appropriate wavelengths. See http://www.nanoqed.org at "Specific Heat by Planck's Photons", 2011

Conclusions

1. The Planck specific heat of crystal lattice is consistent with QM in Planck’s formulation of blackbody radiation in an evacuated cavity provided the velocity of light is reduced by the refractive index of the crystal.

2. The Planck specific heat based on photons vanishes at the nanoscale but is consistent with Debye’s phonons at the macroscale.

3. Unphysical reductions in thermal conductivity of thin films and violations of standard mixing rules in nanofluids based on Debye’s phonons is avoided with Planck specific heat based on photons that maintains bulk conductivity in thin films and obeys mixing rules in nanofluids.  

4. Correlation of Planck specific heat with Raman’s experimental data requires higher average characteristic frequencies than for Raman’s method of summing discrete FIR spectral lines based on phonons in Einstein’s specific heat theory.

5. Planck specific heat is expected to correlate with experimental data if the average specific heat is computed based on the normalized absorbance given from the FIR spectra. Correlation of the specific heat of a crystal with experimental FIR spectra is an exciting possibility, but requires more study beyond the scope of this paper.

# # #

About QED Indcued EM Radiation: Classically, absorbed EM energy is conserved by an increase in temperature. But at the nanoscale, temperature increases are forbidden by quantum mechanics. QED radiation explains how absorbed EM energy is conserved at the nanoscale by the emission of nonthermal EM radiation