Thermal expansion

About: Thermal expansion is a research topic. Over the lifetime, 21040 publications have been published within this topic receiving 349407 citations. The topic is also known as: heat expansion.

On the Equation of State for Solids

Abstract: The problem of the thermodynamics of crystal lattices has been treated by rigorous methods recently in a series of papers by Born and collaborators. In particular, Bradburn succeeded in deriving the equation of state for a solid cubic crystal, consisting of identical atoms, under the assumption that the mutual potential energy of a pair of atoms satisfies a law of the form $\phi $ = - ar$^{-m}$ + br$^{-n}$. In the present paper a method is developed which makes it possible to determine the exponents m and n in the force law for a given element from measurements of the sublimation energy, the compressibility, the thermal expansion coefficient, and the dependence of these quantities on pressure and temperature. The method is applied to a large number of elements, and it is shown that the compression and the thermal expansion of these substances, as predicted by the theory, are in satisfactory agreement with the measured values of these quantities up to very high pressure and up to temperatures near the melting-point. The question whether melting is caused by the mechanical instability of the lattice is also investigated, and a certain rule connecting the two phenomena is found which is closely related to Lindemann's law.

Platinum—A thermal expansion reference material

Abstract: Platinum has a face-centered cubic crystal structure and does not have any phase changes between absolute zero and its melting point at 2045 K High-purity platinum can be readily obtained in rod and sheet form and thus provides an excellent thermal expansion standard Five investigations that used accurate and precise experimental techniques were used to establish analytical expressions for the coefficients of thermal expansion from 0 to 1800 K

Giant thermal expansion and α-precipitation pathways in Ti-alloys

Abstract: Ti-alloys represent the principal structural materials in both aerospace development and metallic biomaterials. Key to optimizing their mechanical and functional behaviour is in-depth know-how of their phases and the complex interplay of diffusive vs. displacive phase transformations to permit the tailoring of intricate microstructures across a wide spectrum of configurations. Here, we report on structural changes and phase transformations of Ti–Nb alloys during heating by in situ synchrotron diffraction. These materials exhibit anisotropic thermal expansion yielding some of the largest linear expansion coefficients (+ 163.9×10−6 to −95.1×10−6 °C−1) ever reported. Moreover, we describe two pathways leading to the precipitation of the α-phase mediated by diffusion-based orthorhombic structures, α″lean and α″iso. Via coupling the lattice parameters to composition both phases evolve into α through rejection of Nb. These findings have the potential to promote new microstructural design approaches for Ti–Nb alloys and β-stabilized Ti-alloys in general.

Thermodynamics and Equations of State of Iron to 350 GPa and 6000 K

Abstract: The equations of state for solid (with bcc, fcc, and hcp structures) and liquid phases of Fe were defined via simultaneous optimization of the heat capacity, bulk moduli, thermal expansion, and volume at room and higher temperatures. The calculated triple points at the phase diagram have the following parameters: bcc–fcc–hcp is located at 7.3 GPa and 820 K, bcc–fcc–liquid at 5.2 GPa and 1998 K, and fcc–hcp–liquid at 106.5 GPa and 3787 K. At conditions near the fcc–hcp–liquid triple point, the Clapeyron slope of the fcc–liquid curve is dT/dP = 12.8 K/GPa while the slope of the hcp–liquid curve is higher (dT/dP = 13.7 K/GPa). Therefore, the hcp–liquid curve overlaps the metastable fcc–liquid curve at pressures of about 160 GPa. At high-pressure conditions, the metastable bcc–hcp curve is located inside the fcc-Fe or liquid stability field. The density, adiabatic bulk modulus and P-wave velocity of liquid Fe calculated up to 328.9 GPa at adiabatic temperature conditions started from 5882 K (outer/inner core boundary) were compared to the PREM seismological model. We determined the density deficit of hcp-Fe at the inner core boundary (T = 5882 K and P = 328.9 GPa) to be 4.4%.

An X-ray diffraction and MAS NMR study of the thermal expansion properties of calcined siliceous ferrierite.

Abstract: Powder and single-crystal X-ray diffraction, combined with MAS NMR measurements, has been used to study the thermal expansion of siliceous zeolite ferrierite as it approaches a second-order displacive phase transition from a low-symmetry (Pnnm) to a high-symmetry (Immm) structure. Below the transition temperature, ferrierite exhibits positive thermal expansivity. However, above the transition temperature a significant change in thermal behavior is seen, and ferrierite becomes a negative thermal expansion material. Accurate variable-temperature single-crystal X-ray diffraction measurements confirm the transition temperature and allow the changes in average atomic position to be followed with temperature. The results from the single-crystal X-ray diffraction study can be correlated with 29Si MAS NMR chemical shifts for the low-temperature phase. At low temperatures the results show that the positive thermal expansivity is driven by an overall increase in Si−Si distances related to an increase in Si−O−Si bon...