New theoretical approach describing the pressure effect
on the melting temperature
Jozsef Garaia and Jiuhua Chena, b
a
Department of Mechanical and Materials Engineering, Florida International University, Miami, USA
b
CeSMEC, Florida International University, Miami, USA
The effect of the pressure on the melting temperature is an important physical phenomenon
with many technical and geophysical applications. Recent advances in diamond anvil cell
techniques allow experimentally determining the relationship to high pressures and temperatures;
however, the results have high uncertainty and the reported pressure-melting curves of different
laboratories are sometimes differs even 1000 degreesex. 1-4. The equations derived from theory,
like the Kraut-Kennedy5 and the Lindenmann6, 7 models, face with the same problem8 because
the initial parameters used in the equations have significant effect on the pressure-melting
temperature relationship. The correlation between the Debye temperature and the melting
temperature for materials with the same crystal structure is well established9. The Lindemann
melting criteria is proposed to explain this relationship10; however, the derived equations do not
give a universal description which fits to all substances.
In this study, rooting from theoretical considerations, a new interpretation is proposed to
explain the relationship between the Debye and the melting temperature. It has been proposed
from theory that the Debye temperature relates to phonon vibration with wavelength equal to the
smallest unit of the lattice. This hypothesis has been tested on highly symmetrical monoatomic
arrangements with positive result11. Based on theoretical consideration it has also been proposed
that melting occurs when the wavelength of the average thermal phonon vibration is in resonance
with the atomic sheets on the surface of the crystal. The self resonance results in the detachment
of the atomic/molecular layers from the surface and melting occurs12, 13. Since both the Debye
and the melting temperature relate to lattice parameters it is suggested that when pressure applied
the ratio of these parameters should remain the same. Thus the ratio of the average phonon
frequency corresponding to the Debye and to the melting temperatures should be the same
regardless of the pressure. This assumption allows calculating the melting curve from one
experiment if the equation of state is available. The experimental data of metals (Al and Pt), and
ceramic (MgO), is used to test the hypothesis. The parameters of the Birch Murnaghan14, 15 and
Garai16 EoS are determined from experiments by unrestricted fitting. The pressure melting
temperature curves can be calculated by using the thermodynamic parameters of the two EoSs.
The fit of the calculated curves against the experiments is excellent for Al and Pt and reasonable
for MgO indicating that the proposed pressure-melting temperature description of crystalline
solids is correct.
Using the derived relationship and the EoSs of MgSiO3 perovskite and epsilon iron the
melting temperatures at the core mantle boundary and at the outer-inner core are predicted for
these two minerals respectively.
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0
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[11] J. Garai, arXiv:physics/0703001v2 [physics.chem-ph]
[12] J. Garai, arXiv:cond-mat/0206425v5 [cond-mat.mtrl-sci]
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