Thermal dilatation

MSE.13. I. Prigogine et J. Philippot, Sur la theorie moleculaire de I helium hquide, II. Le coefficient de dilatation thermique de I hehum liquide (Molecular theory of liquid hehum, II. The coefficient of thermal dilatation of hquid hehum), Physica 19, 227—234 (1953). 

The magnet temperature variation AT is approximately proportional to the power dissipated by the magnet and therefore to the square of the magnet current I. The variation of AS is a function of AT which reflects the changes in magnet geometry due to thermal dilatations. The net result is... 

In analogy with the approach that has been described in the section on the low-temperature heat capacity, the high-temperature heat capacity of the LnXj compounds can be described as the sum of the lattice and excess contributions (eq. (1)). However, whereas at low temperature the lattice heat capacity mainly arises from harmonic vibrations, at high temperatures the effects of anharmonicity of the vibrations, of thermal dilation of the lattice and of thermally... 

Gildseth W, Habenschuss A, Spedding FH (1972) Precision measurements of densities and thermal dilation of water between 5.deg. and 80.deg. J. Chem. Eng. Data, 17 (4) pp... 

Eisenbach also discussed the significance of the WLF-parameters with respect to the fractional free volume at Tg and to the difference of thermal dilation coefficients of rubbery and glassy states. 

The Fermi liquid as well as the Hartree-Fock theory, however, can hardly account for the observed temperature dependence of the spin susceptibility obtained at constant volume - namely, corrected for thermal dilatation of the sample - which shows a monotonic but sizable growth as the temperature increases (Fig. 8) [53, 54, 58]. This variation turns out to be much faster than the one expected from the H-F theory, which only predicts a F (T) with a very slow temperature dependence that is spread out over on a temperature scale [58, 59]. 

There are only a few suitable methods for high-temperature density measurement. The reason is the corrosive nature of molten salts and the thermal dilatation of the materials used for measurement. Most convenient for molten salts are the methods of hydrostatic weighing and the maximum bubble pressure method. For more viscous liquids, such as some silicate melts, the falling body method is suitable. These three methods will be described in detail here. For further study the reader is referred to an excellent book by Mackenzie (1959). 

In general, the measurement of electrical conductivity is not an absolute method and the conductance cell used has to be calibrated using the molten salt with a known conductivity. When the calibration of the cell is done at ambient temperatures, the accurate resistance measurement requires correction for the change in the resistance cell capacity with temperature. The total accuracy of measurement is then affected by knowing the coefficient of thermal dilatation of the material used from which the cell was made. 

The Derivatograph, which was first described by Paulik et al. (35) in 1958, is a multifunction thermal analysis system which can record the TG, DTG, DTA, and T curves of a sample on a single chart. By means of accessory attachments, the TD (thermal dilation) and DTD (derivative of TD) (5) curves may be recorded as well as the evolved gas curves (see Chapter 8). 

This coefficient is due to two factors the variation of spontaneous polarisation in the crystalline phase (major effect) and the thermal dilatation of the polymers. 

In principle, the piezo/cantilever system can reach a force sensitivity of about 10 N. In practice, thermal dilations induce drift of surfaces with respect to each other, reducing the accuracy of the piezo displacement and the sensitivity. For this reason, the micas and the cantilever are closed in a sealed clean chamber, that is temperature-controlled in the range 15- 45°C with an accuracy of 0.05°C. In this way, thermal drifts are reduced to a few tenths of nm per minute and the contamination of mica and the sample is avoided. The resulting experimental force sensitivity is about 10 N. The force measurement is performed by progressively approaching or retracting the surfaces. When the equilibrium separation is reached, the piezo displacement and the transmitted wavelengths are recorded. A complete approach/retraction cycle takes typically 30 minutes. A review on the SFA technique can be found in [41]. 

The VTF equation was initially proposed in order to explain the viscosity of undercooled liquids. Other models using the free volume concept are connected to the above relationship. Free volume theories are based on the assumption that the mobile species move only when, locally, a suflSciently large void opens. These models are used for glasses which do not follow the Davies-Jones law linking the difference of thermal dilation and compressibility of the liquid state. 

For experimental details, high pressure apparatus and techniques, references to original articles can be found in the review by Bloch and Pavlovic (1969). Briefly, the most common methods used in following a magnetic transition are change in the mutual inductance sensed through a set of coils placed around the specimen in a transformer-like set up, magnetic susceptibility, electrical resistivity and in some cases thermal dilation. To a limited extent more sophisticated... 

Comparison between the two kinds of alumina and several concentrations of the filler was carried out from compressive strength, thermal dilatation, and thermal conductivity measurements. 

Zooming on a the time series, it is possible to observe daily oscillations due to thermal dilation and/or sea tides. In addition, during severe... 

Figure 2. Temporal evolution of three-dimensional displacements relevant to the RTS-1 (top) and RTS-2 (bottom) monitoring networks. Inset shows daily oscillations due to thermal dilation of the hull s structure and/or sea tides. Accelerations were observed mainly during adverse weather conditions.

Good agreement between theoretical and experimental results is obtained when thermal deformations together with differential thermal dilatation between the bearing aixl the shaft are considered. 

The magnetostriction and thermal dilatation coefficients of RjFej B (R = Y, Nd, Sm) compounds... 

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