Abstract
The Helmholtz free energy, A, of a rigid body is a function of temperature, and of the six homogeneous strain components. If the crystal is to be rigid, three inequalities must be satisfied for the derivatives of A with respect to the six strain components, for a regular (cubic) lattice. This enables one to limit the pressure-temperature range for which the crystal is stable. The violation of the condition c44>0, that the crystal resist shearing, is interpreted as leading to melting. From a knowledge of the forces between the molecules the phase integral, and therefore the free energy, may be calculated as a function of T, V, and the six strain components. The numerical calculations are carried out for a body-centered cubic lattice. The product of all the frequencies is calculated directly, so that the assumption that the Debye equation for the frequency distribution holds, is not necessary. The melting curve, pressure against temperature, is then determined.
Keywords
Helmholtz free energyShearing (physics)ThermodynamicsCrystal (programming language)Debye modelLattice (music)Phase transitionMelting pointCubic crystal systemCrystal structureMaterials scienceCondensed matter physicsPhysicsChemistryCrystallographyQuantum mechanics
Affiliated Institutions
Related Publications
Structural properties of NaCl and KCl under pressure
The pseudopotential method within the local-density approximation is used to investigate the static and structural properties of NaCl and KCl. Calculated values for the lattice ...
<i>Ab initio</i>lattice dynamics and phase transformations of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Zr</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>
Zirconia, $\mathrm{Zr}{\mathrm{O}}_{2}$, is one of the most important ceramic materials in modern technology. Its versatility is closely related to phase transformations. Althou...
X-ray Studies on the C<sub>12</sub>EO<sub>2</sub>/Water System
Binary mixtures of the poly(oxyethylene) surfactant C12EO2 and water have been investigated using optical microscopy and time-resolved X-ray diffraction during temperature scans...
Calculation of the Total Energy and Pressure of Compressed Cesium
The results of a self-consistent $X\ensuremath{\alpha}$ augmented-plane-wave calculation of the cohesive energy, pressure, and enthalpy of bcc and fcc cesium metal are presented...
Evolution of crystal structures in metallic elements
Crystal structures of metals are often treated as dense packing of atomic spheres. Face-centered cubic and hexagonal close-packed structures are favored in many metals. Long-per...
Publication Info
- Year
- 1939
- Type
- article
- Volume
- 7
- Issue
- 8
- Pages
- 591-603
- Citations
- 730
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
730
OpenAlex
Cite This
Max Born
(1939).
Thermodynamics of Crystals and Melting.
The Journal of Chemical Physics
, 7
(8)
, 591-603.
https://doi.org/10.1063/1.1750497
Identifiers
- DOI
- 10.1063/1.1750497