The quasi-low temperature behaviour of specific heat

A new mathematical approach to condensed matter physics, based on the finite temperature field theory, was recently proposed. The field theory is a scale-free formalism; thus, it denies absolute values of thermodynamic temperature and uses dimensionless thermal variables, which are obtained with the group velocities of sound and the interatomic distance. This formalism was previously applied to the specific heat of condensed matter and predicted its fourth power of temperature behaviour at sufficiently low temperatures, which was tested by experimental data for diamond lattice materials. The range of temperatures with the quartic law varies for different materials; therefore, it is called the quasi-low temperature regime. The quasi-low temperature behaviour of specific heat is verified here with experimental data for the fcc lattice materials, silver chloride and lithium iodide. The conjecture that the fourth order behaviour is universal for all condensed matter systems has also supported the data for glassy matter: vitreous silica. This law is long known to hold for the bcc solid helium-4. The characteristic temperatures of the threshold of the quasi-low temperature regime are found for the studied materials. The scaling in the specific heat of condensed matter is expressed by the dimensionless parameter, which is explored with the data for several glasses. The explanation of the correlation of the ‘boson peak’ temperature with the shear velocity is proposed. The critique of the Debye theory of specific heat and the Born–von Karman model of the lattice dynamics is given.

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A quantum field theory of thermal conductivity and specific heat in the low temperature glasses

Physics Letters A ◽

10.1016/s0375-9601(00)00043-8 ◽

2000 ◽

Vol 266 (2-3) ◽

pp. 198-208 ◽

Cited By ~ 8

Author(s):

Toyoyuki Kitamura ◽

Shozo Takeno

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Thermal Conductivity ◽

Low Temperature ◽

Specific Heat ◽

Quantum Field

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Atomic displacement parameters for garnets: a lattice-dynamical evaluation

Acta Crystallographica Section B Structural Science ◽

10.1107/s0108768195010925 ◽

1996 ◽

Vol 52 (2) ◽

pp. 239-250 ◽

Cited By ~ 9

Author(s):

T. Pilati ◽

F. Demartin ◽

C. M. Gramaccioli

Keyword(s):

Experimental Data ◽

Low Temperature ◽

Specific Heat ◽

Thermodynamic Functions ◽

Vibrational Spectra ◽

Atomic Displacement ◽

Atomic Charges ◽

Static Disorder ◽

Atomic Displacement Parameters ◽

Best Fit

Atomic displacement parameters (a.d.p.'s), together with vibrational spectra (Raman and IR) and thermodynamic functions, have been calculated for some minerals of the garnet group, such as pyrope (Mg3Al2Si3O12), grossular (Ca3Al2Si3O12), andradite (Ca3Fe2Si3O12) and almandine (Fe3A12Si3O12). For this purpose, a rigid-ion Born–von Karman model has been applied, using empirical atomic charges and valence force fields derived from a best fit to the vibrational spectra of a group of orthosilicates and oxides. Agreement with the experimental data is good, with the only exception of pyrope and almandine: for these minerals the calculated a.d.p.'s of the Mg2+ atom in the former and of the corresponding Fe2+ atom in the latter are too low. This result confirms the unusual behaviour of these atoms, for which dynamic disorder has been claimed. However, if the values of the specific heat and entropy are considered and compared with our calculations, this situation can be best explained assuming the transition to static disorder of the Mg2+ and Fe2+ atoms to occur at low temperature.

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LOW TEMPERATURE SPECIFIC HEAT OF INTERMETALLICS (Ti/Be)B2

Modern Physics Letters B ◽

10.1142/s021798490701302x ◽

2007 ◽

Vol 21 (14) ◽

pp. 885-891 ◽

Cited By ~ 7

Author(s):

NUPINDER KAUR ◽

N. K. GAUR ◽

R. K. SINGH

Keyword(s):

Experimental Data ◽

Thermal Properties ◽

Low Temperature ◽

Specific Heat ◽

Debye Temperature ◽

Cohesive Energy ◽

Specific Heats ◽

Molecular Force ◽

Low Temperature Specific Heat ◽

Rigid Ion Model

We have applied the Rigid Ion Model (RIM) to study the cohesive and thermal properties of binary intermetallic BeB 2 and TiB 2. The paper reports the calculated results on cohesive energy (ϕ), compressibility (β), molecular force constant (f), Restrahalen frequency (ν0), Debye temperature (Θ D ) and Gruneisen parameter (γ) for the temperature range 50 K ≤ T ≤ 300 K and the effect of van der Waal interaction on these properties are also shown. Our results on Debye temperature are closer to the experimental data. In addition, we have computed the specific heats for BeB 2 and TiB 2 and compared them with the available experimental data.

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DIFFUSION OF LIGHT ADATOMS ON SOLID SURFACES

Modern Physics Letters B ◽

10.1142/s0217984995000309 ◽

1995 ◽

Vol 09 (06) ◽

pp. 307-318

Author(s):

L. Y. CHEN ◽

S. C. YING

Keyword(s):

Experimental Data ◽

Low Temperature ◽

Theoretical Approach ◽

Temperature Regime ◽

Quantum Tunneling ◽

Entire Range ◽

Solid Surfaces ◽

Recent Experimental Data ◽

Thermally Activated ◽

Theoretical Results

We present a brief review of a theoretical approach to the diffusion of light adatoms that covers the entire range from the classical regime of thermally activated hopping to the low temperature regime of quantum tunneling between adjacent sites. We compare our theoretical results with recent experimental data for the system H/Ni(100). We also contrast our results with those obtained from the quantum transition state approach.

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Introduction. Cosmology meets condensed matter

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2008.0098 ◽

2008 ◽

Vol 366 (1877) ◽

pp. 2793-2802 ◽

Cited By ~ 4

Author(s):

T.W.B Kibble ◽

G.R Pickett

Keyword(s):

Field Theory ◽

Low Temperature ◽

Particle Physics ◽

Royal Society ◽

Condensed Matter ◽

Topological Defects ◽

European Science Foundation ◽

European Science ◽

The Subject ◽

Early Universe Cosmology

At first sight, low-temperature condensed-matter physics and early Universe cosmology seem worlds apart. Yet, in the last few years a remarkable synergy has developed between the two. It has emerged that, in terms of their mathematical description, there are surprisingly close parallels between them. This interplay has been the subject of a very successful European Science Foundation (ESF) programme entitled COSLAB (‘Cosmology in the Laboratory’) that ran from 2001 to 2006, itself built on an earlier ESF network called TOPDEF (‘Topological Defects: Non-equilibrium Field Theory in Particle Physics, Condensed Matter and Cosmology’). The articles presented in this issue of Philosophical Transactions A are based on talks given at the Royal Society Discussion Meeting ‘Cosmology meets condensed matter’, held on 28 and 29 January 2008. Many of the speakers had participated earlier in the COSLAB programme, but the strength of the field is illustrated by the presence also of quite a few new participants.

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The band structure of aluminium I. Determination from experimental data

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1957.0089 ◽

1957 ◽

Vol 240 (1222) ◽

pp. 340-353 ◽

Cited By ~ 84

Keyword(s):

Experimental Data ◽

Low Temperature ◽

Band Structure ◽

Fermi Surface ◽

Specific Heat ◽

Electron Energy ◽

Brillouin Zone ◽

Free Electron ◽

The Third ◽

Low Temperature Specific Heat

The band structure and particularly the shape of the Fermi surface are deduced mainly from the available experimental data on the de Haas-van Alphen and anomalous skin effects, and from the low-temperature specific heat. Since these data are rather incomplete, it is found necessary to use in conjunction with them a theoretical band-structure calculation, which, however, unavoidably contains rough approximations. Except near the surface of.the Brillouin zone, E (k) is found to be very close to the free-electron energy. The first zone is found to contain 3.6 × 10 -3 holes per atom around the zone comers. There is overflow of electrons into the second zone across all the zone faces, and these regions of the Fermi distribution are joined together near the centres of the zone edges; the third zone contains a very small number of electrons.

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The Nephelauxetic Effect — Calculation and Accuracy of the Interelectronic Repulsion Parameters

Zeitschrift für Naturforschung B ◽

10.1515/znb-1972-0102 ◽

1972 ◽

Vol 27 (1) ◽

pp. 1-6 ◽

Cited By ~ 4

Author(s):

E. König

Keyword(s):

Field Theory ◽

Experimental Data ◽

Low Temperature ◽

Sufficient Accuracy ◽

Ligand Field ◽

Electron Systems ◽

Ligand Field Theory ◽

Transition Energies ◽

Semi Empirical ◽

Complex Ion

Expressions are reviewed which may be used to determine 10 Dq and B from the spin-allowed bands in the optical spectra of d3 and d7 electron systems within octahedral and tetrahedral sym metry. Application to low-temperature single crystal spectra demonstrates that (i) the semi-empirical ligand field theory reproduces transition energies with sufficient accuracy; (ii) differences in the values of 10 Dq and B observed with different fitting methods may be attributed to the inaccuracy of experimental data; (iii) there are generally valid values of B35 and β35 for each complex ion.

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