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.

High Temperature Structure and Thermal Expansion of Some Metals as Determined by X‐Ray Diffraction Data. I. Platinum, Tantalum, Niobium, and Molybdenum

Abstract: The crystal structure and thermal expansion of platinum, tantalum, niobium, and molybdenum have been determined between 1100° and 2500°K. These metals were found to undergo a uniform thermal expansion over the temperature range of this investigation and to undergo no structural change. The permanent elongation of tantalum wires, produced by annealing at temperatures between 2473° and 2773°K, appears to be caused by reorientation of crystal grains in the specimen and to preferred direction of crystal growth during annealing, rather than to a change in crystal structure.Quadratic equations have been developed for the thermal expansion of platinum, tantalum, niobium, and molybdenum. These equations are represented, respectively, by Δa0/a0=7.543×10−6(T−291)+2.362×10−9(T−291)2,Δa0/a0=6.080×10−6(T−291)+7.50×10−10(T−291)2,Δa0/a0=7.591×10−6(T−291)+6.96×10−10(T−291)2, and Δa0/a0=0.987×10−3+2.40×10−6(T−273)+2.20×10−9(T−273)2.Values of the expansion coefficient α were computed for each of the metals by differentiati...

Control of biaxial strain in single-layer Molybdenite using local thermal expansion of the substrate

Abstract: Single-layer MoS2 is a direct-gap semiconductor whose electronic band structure strongly depends on the strain applied to its crystal lattice. While uniaxial strain can be easily applied in a controlled way, e.g., by bending of a flexible substrate with the atomically thin MoS2 layer on top, experimental realization of biaxial strain is more challenging. Here, we exploit the large mismatch between the thermal expansion coefficients of MoS2 and a silicone-based substrate to apply a controllable biaxial tensile strain by heating the substrate with a focused laser. The effect of this biaxial strain is directly observable in optical spectroscopy as a redshift of the MoS2 photoluminescence. We also demonstrate the potential of this method to engineer more complex strain patterns by employing highly absorptive features on the substrate to achieve non-uniform heat profiles. By comparison of the observed redshift to strain-dependent band structure calculations, we estimate the biaxial strain applied by the silicone-based substrate to be up to 0.2 percent, corresponding to a band gap modulation of 105 meV per percentage of biaxial tensile strain.

Thermal Expansion Behavior of NaZr2(PO4)3Type Compounds

Abstract: The thermal expansion of the skeletal framework was essentially zero for NaZr2(PO4)3-type compounds; the interstitialion, e.g., Na+, was primarily responsible for the total thermal expansion. The composition dependence of the thermal expansion is discussed in terms of the amounts, crystallographic sites, and ionic radii of the interstitial ions. The mechanism which results in low thermal expansion was clarified, particularly for KZr2(PO4)3, in which a larger ion is substituted for Na+, and NbZr(PO4)3, which does not contain Na+. Polycrystalline ceramics formed from these crystals might be useful as thermal-shock-resistant materials.

Mathiessen's Rule and Anisotropic Relaxation Times

Abstract: Departures from Matthiessen's rule were measured for dilute alloys of copper with gold, tin, or germanium, and of silver with gold or tin; and for strained copper and silver. The concentration of alloyed elements ranged from 0.01 to 1 at.%; residual resistivities per atomic percent impurity are estimated to be known within better than 1% accuracy and were compared with Linde's values. In evaluating the deviations, corrections were applied for the volume dependence of the residual resistivity due to thermal expansion and the ideal resistivity due to alloying. The results were interpreted on a simple two-band model as due to different anisotropies of the relaxation times associated with different scattering processes; the expected temperature dependence of the anisotropy of phonon scattering was taken into account. At temperatures where the residual resistivity dominates, deviations from Matthiessen's rule become comparable to or greater than the ideal resistivity, making experimental determination of the ideal resistivity in this region open to criticism.