Quantitative Analysis Of Temperature Dependence Research Articles

Raman spectroscopic study of stronadelphite Sr5(PO4)3F at various temperatures

The Raman spectra of stronadelphite, Sr5(PO4)3F, were investigated in the temperature range of 80–1023 K at ambient pressure. No phase transition was observed though some vibrations merge or disappear during heating in this study. With increasing temperature the Raman shifts of all observed bands for Sr5(PO4)3F continuously decrease. The quantitative analysis of temperature dependences for the Raman active PO4 internal modes indicates that the ν3 and ν1 stretching vibrations have larger absolute temperature coefficients (from −1.18 × 10−2 to −1.46 × 10−2 cm−1 K−1) whereas the ν4 and ν2 bending vibrations show smaller absolute temperature coefficients (from −0.08 × 10−2 to −0.90 × 10−2 cm−1 K−1), which may be attributed to the structural evolution of PO4 tetrahedron in Sr5(PO4)3F at high temperature. The temperature and pressure dependence of the force constant for PO stretching modes in Sr5(PO4)3F were calculated. The isobaric mode Grüneisen parameters were determined as 0.046–0.365 with an average of 0.252, and the anharmonic mode parameters as −0.28 ∼ 1.55 with an average of 0.33. The nonzero anharmonic mode parameters indicate an intrinsic anharmonicity for stronadelphite Sr5(PO4)3F.

Raman spectroscopic study of MnAl2O4 galaxite at various pressures and temperatures

The vibrational properties of synthetic galaxite, MnAl2O4, were investigated at various pressures (0–29.7 GPa) and temperatures (80–973 K), respectively. The Raman frequencies of all observed bands for galaxite continuously increase with increasing pressure and decrease with increasing temperature, respectively. The quantitative analysis shows that the lowest frequency T2g mode has the smallest isothermal mode Gruneisen parameter. Combined with previous studies, the thermal Gruneisen parameter of galaxite is determined to be 1.23(5). The quantitative analysis of temperature dependences of Raman bands yields that the lowest frequency T2g mode has the largest isobaric mode Gruneisen parameter. The intrinsic anharmonic mode parameters are also calculated and nonzero, indicating an existence of intrinsic anharmonicity for MnAl2O4 spinel.

Quantitative Analysis of Temperature Dependence of Raman shift of monolayer WS2.

We report the temperature-dependent evolution of Raman spectra of monolayer WS2 directly CVD-grown on a gold foil and then transferred onto quartz substrates over a wide temperature range from 84 to 543 K. The nonlinear temperature dependence of Raman shifts for both and A1g modes has been observed. The first-order temperature coefficients of Raman shifts are obtained to be −0.0093 (cm−1/K) and −0.0122 (cm−1/K) for and A1g peaks, respectively. A physical model, including thermal expansion and three- and four-phonon anharmonic effects, is used quantitatively to analyze the observed nonlinear temperature dependence. Thermal expansion coefficient (TEC) of monolayer WS2 is extracted from the experimental data for the first time. It is found that thermal expansion coefficient of out-plane mode is larger than one of in-plane mode, and TECs of and A1g modes are temperature-dependent weakly and strongly, respectively. It is also found that the nonlinear temperature dependence of Raman shift of mode mainly originates from the anharmonic effect of three-phonon process, whereas one of A1g mode is mainly contributed by thermal expansion effect in high temperature region, revealing that thermal expansion effect cannot be ignored.

Phase transitions in molecular crystals of dicarboxylic acids

A comparative analysis of phase transitions in molecular crystals of saturated dicarboxylic acids with {COOH(CH2) n COOH} chains of different lengths has been performed by differential scanning calorimetry, which revealed a number of new effects related with specific features of the phase transitions. A quantitative analysis of temperature dependence of the heat capacity has been carried out in the context of the theory of smeared (Λ-shaped) first-order phase transitions.

Raman spectra and X-ray diffraction of tuite at various temperatures

High-temperature Raman spectra and thermal expansion of tuite, γ-Ca3(PO4)2, have been investigated. The effect of temperature on the Raman spectra of synthetic tuite was studied in the range from 80 to 973 K at atmospheric pressure. The Raman frequencies of all observed bands for tuite continuously decrease with increasing temperature. The quantitative analysis of temperature dependence of Raman bands indicates that the changes in Raman frequencies for stretching modes (ν3 and ν1) are faster than those for bending modes (ν4 and ν2) of PO4 in the present temperature range, which may be attributed to the structural evolution of PO4 tetrahedron in tuite at high temperature. The thermal expansion of tuite was examined by means of in situ X-ray diffraction measurements in the temperature range from 298 to 923 K. Unit cell parameters and volume were analyzed, and the thermal expansion coefficients were obtained as 3.67 (3), 1.18 (1), and 1.32 (3) × 10−5 K−1 for V, a, and c, respectively. Thermal expansion of tuite shows an axial anisotropy with a larger expansion coefficient along the c-axis. The isothermal and isobaric mode Gruneisen parameters and intrinsic anharmonicity of tuite have been calculated by using present high-temperature Raman spectra and thermal expansion coefficient combined with previous results of the isothermal bulk modulus and high-pressure Raman spectra.