Contribution To Thermal Expansion Research Articles

High-temperature heat capacity of an anharmonic crystal to orderλ4

The thermal-expansion contribution to the high-temperature heat capacity of an anharmonic crystal to $O({\ensuremath{\lambda}}^{4})$ is obtained. It is found that an additional term of $O({\ensuremath{\lambda}}^{4})$ contributes to the ${T}^{2}$ coefficient of heat capacity at constant volume. The heat capacity at constant pressure has also been calculated to the same order and the difference ${c}_{p}\ensuremath{-}{c}_{v}$ is shown to be consistent with that obtained from the exact thermodynamic identity.

Electron delocalization contribution to single crystal thermal expansion of a polydiacetylene

AbstractThe thermal expansion contribution due to temperature‐dependent π‐electron delocalization is evaluated from spectral measurements on a single crystal polydiacetylene (poly‐2,4‐hexadiyne‐1,6‐diol bisphenylurethane). The observed temperature independence of backbone associated vibrations (less than ±1 cm−1 change in νCC and νCC between 25 and 90°C) implies that thermal conformational fluctuations and equilibrium defect formation (which produce a negative thermal expansion coefficient) do not measurably affect π‐electron delocalization. The separation of equilibrium defects is either much longer than that of nonequilibrium defects or much longer than required to appreciably limit π‐electron delocalization in an effectively defect‐free polymer. Arguments presented indicate that, in the experimental temperature interval, the observed thermal expansion coefficient in the chain direction is over an order of magnitude larger than the delocalization‐associated contribution.

Effect of pressure on the knight shift in V 51 and β-Mn 55 metals

The pressure dependence of the Knight shift in vanadium and β-manganese has been measured up to 10 kbar. In vanadium ( ΔK K ) ( ΔV V ) is approximately −0.8, while in β-manganese the shift increases with pressure and ( ΔK K ) ( ΔV V ) amounts to −7.5 for zero pressure shifts of 0.58 and 0.4 per cent respectively. In β-manganese the pressure dependence of the quadrupole coupling constant has also been measured, which increases by 20 per cent at 10 kbar. Contributions from thermal expansion were separated. For the Knight shift, the experimental explicit temperature dependence is negligible in the range 200°–300°K, while for the quadrupole coupling constant, the explicit thermal contribution is orders of magnitude larger than the thermal expansion contribution.

Analysis of Debye-Waller—Factor and Mössbauer-Thermal-Shift Measurements. II. Thermal-Shift Data on Fe

Techniques developed in a previous paper are used to subtract the second-order Doppler contribution from measured thermal shifts on pure Fe and dilute Fe in various hosts. This allows the temperature dependence of the isomer shift arising from the electron density at the nucleus to be seen more clearly than was previously possible. It is shown that this temperature dependence cannot be accounted for by thermal expansion alone. In pure Fe a contribution related to the magnetization is clearly evident, as is theoretically expected. A contribution in addition to this and the thermal-expansion contribution is present, contrary to the conclusion generally drown from previous work. The additional contribution to the isomer shift is discussed in terms of two theories which have been used to explain the temperature dependence of hyperfine coupling constants.

The Effect of Anharmonic Vibration on the Debye-Waller Factor and the Diffuse Scattering of X-Rays

Contributions of anharmonic vibration to the Debye-Waller factor and the intensity of X -ray diffuse scattering were calculated for polyatomic crystal by the quantum statistics. Applying the anharmonic parameters which were obtained in the theory of specific heat, the contribution to the temperature factor and the intensity of diffuse scattering were estimated numerically for ionic crystals. From the comparison between the results of calculation and experiments, it was made clear that most parts of anharmonic effect arise from the thermal expansion, although cubic And quartic anharmonic contributions are noticeable for KCl at high tem-peratures. The effect of anharmonicity was investigated at absolute zero degree in ionic crystals.