Calculation of the linear coefficient of thermal expansion of multi-element, single-phase metal alloys from the first principles

One of the possible ways to calculate the coefficient of thermal expansion is a method based on determining the dependence of the total energy of the electron-ion system on the parameters of the crystal lattice at different temperatures. There is a relationship between the calculated values of the linear coefficients of thermal expansion and the melting point of the material. For metals and multi-element single-phase alloys, the dependence of the function V = α·Tmax on the parameter T/Tmax (α — the linear coefficients of thermal expansion, Tmax — melting point of the material) is obtained from the first principles, which has the same form for all single-phase multi-element metal alloys and is presented analytically. Using the method of pseudopotential and quasiharmonic approximation, the linear coefficients of thermal expansion of multi-element metal alloys are calculated. The temperature dependence of the coefficient of thermal expansion, after approximating the results of the computational experiment, is presented in analytical form. The results were compared with known tabular data. To confirm the reliability of the model, the calculation was performed for a number of pure metals. The consistency of the calculated and experimental data on the coefficient of thermal expansion of single-phase alloys calculated from the first principles is observed. There is a relationship between the calculated values of the linear coefficients of thermal expansion and the melting point of the material. For metals and multi-element single-phase alloys, the dependence of the function V = α·Tmax on the parameter T/ Tmax (α — the linear coefficients of thermal expansion, Tmax — melting point of the material) is obtained from the first principles, which has the same form for all single-phase multi-element metal alloys and is presented analytically. Keywords: Electron-ion system energy, interatomic interaction potential, force constants, quasiharmonic approximation, coefficient of thermal expansion.

Thermoelasticity in organic semiconductors determined with terahertz spectroscopy and quantum quasi-harmonic simulations

The thermomechanical response of organic semiconducting solids – an essential aspect to consider for the design of flexible electronics – was determined using terahertz vibrational spectroscopy and quantum quasiharmonic approximation simulations.

Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon

Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100 K to 1,500 K on a single crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmonicity and nuclear quantum effects, reproduced the measured shifts of individual phonons with temperature, whereas quasiharmonic shifts were mostly of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to predict the thermal expansion owing to a large cancellation of contributions from individual phonons.

SYNCHRONIZATION OF FRACTIONAL VAN-DER-POL OSCILLATOR

A model of self-oscillating system with a differential equation of motion of fractional order under the action of external harmonic signal is proposed. Solutions of equation of motion which correspond to the regime of steady-state synchronized oscillations and the regime of beats near the synchronization band are obtained in the quasiharmonic approximation. The amplitude frequency and phase-frequency characteristics of synchronization of fractional Van-der-Pol oscillator are analyzed. An analogy between the generator with a fractional feedback circuit and the generator with delayed feedback is established.