Thermoelastic coefficients

Another anomalous property of some nickel—iron aHoys, which are caHed constant-modulus aHoys, is a positive thermoelastic coefficient which occurs in aHoys having 27—43 wt % nickel. The elastic moduH in these aHoys increase with temperature. UsuaHy, and with additions of chromium, molybdenum, titanium, or aluminum, the constant-modulus aHoys are used in precision weighing machines, measuring devices, and osciHating mechanisms (see Weighing AND proportioning). 

Kag] Young s modulus and thermoelastic coefficient Young s moduli of cementite and perlite as function of carbon and chromium concentration... 

Young s modulus E Thermoelastic coefficient TKE Compensation range of E Shear modulus G... 

Because the two states available to a polymer network can co-exist in a macroscopic sample, unique thermoelastic coefficients are observed. The coefficients of interest are those of force-temperature and of length-temperature. These are related to each other by the identity... 

Several common variables, grouped under the term thermoelastic coefficients, are defined finm the thermodynamie eoeffieients. 

This condition is deduced by introducing the heat capacity and thermoelastic coefficients by ... 

Therefore from the basic experimental data such as a state equation or thermoelastic coefficients, heat capacities etc., it is possible to obtain thermodynamic coefficients. A double integration of equation [2.25] will give a characteristic function, i.e. knowing the complete thermodynamics of the phase studied. 

For a seismometer which is not temperature compensated, the temperature sensitivity is typically dominated by the thermoelastic coefficient of the mainspring, as shown in Fig. 14 (left). The cantilever balances the mass M against the force of gravity go but as the temperature T changes the stiffness of the beam, represented as a spring constant K changes, and the apparent vertical acceleration x changes. 

Most copper alloys and steels have a thermoelastic coefficient on the order of P = -300 ppm/°C, the minus sign indicating that the mainspring relaxes with an increase in temperature. 

No thermoelastic inversion should appear in the force-temperature coefficient at constant elongation a, inasmuch as the effect of ordinary thermal expansion is eliminated by fixing a instead of the length L as the temperature is varied. As the elongation approaches unity, both the force and its temperature coeffi.cient df/dT)p,a must van-... 

Finally, we turn from solutions to the bulk state of amorphous polymers, specifically the thermoelastic properties of the rubbery state. The contrasting behavior of rubber, as compared with other solids, such as the temperature decrease upon adiabatic extension, the contraction upon heating under load, and the positive temperature coefficient of stress under constant elongation, had been observed in the nineteenth century by Gough and Joule. The latter was able to interpret these experiments in terms of the second law of thermodynamics, which revealed the connection between the different phenomena observed. One could conclude the primary effect to be a reduction of entropy... 

What are the main error sources in PAC experiments One of them may result from the calibration procedure. As happens with any comparative technique, the conditions of the calibration and experiment must be exactly the same or, more realistically, as similar as possible. As mentioned before, the calibration constant depends on the design of the calorimeter (its geometry and the operational parameters of its instruments) and on the thermoelastic properties of the solution, as shown by equation 13.5. The design of the calorimeter will normally remain constant between experiments. Regarding the adiabatic expansion coefficient (/), in most cases the solutions used are very dilute, so the thermoelastic properties of the solution will barely be affected by the small amount of solute present in both the calibration and experiment. The relevant thermoelastic properties will thus be those of the solvent. There are, however, a number of important applications where higher concentrations of one or more solutes have to be used. This happens, for instance, in studies of substituted phenol compounds, where one solute is a photoreactive radical precursor and the other is the phenolic substrate [297]. To meet the time constraint imposed by the transducer, the phenolic... 

Thermoelastic Effect A mechanical phenomenon that involves the thermal expansion coefficient is the thermoelastic effect, in which a material is heated or cooled due to mechanical deformation. The thermoelastic effect is represented by the following relation ... 

Values of the dipole moment ratio of PNS are obtained from dielectric measurements. From thermoelastic experiments, performed on polymer networks, the temperature coefficient of the unperturbed dimensions is determined. Analysis of these results using the RIS model is performed leading to the parameters given above. 

Values of the mean-square dipole moment, , of PDEI are determined as a function of temperature. The value of the dipole moment ratio is 0.697 at 303 K. Trifunctional model networks are prepared. From thermoelastic experiments performed on the networks over a temperature range 293 - 353 K, it is found that the value of the temperature coefficient of the unperturbed dimensions amounts to 1.05 0.17 K-1. The dipole moments and the temperature coefficients of both the dipole moments and the unperturbed dimensions are critically interpreted in terms of the RIS model, and are found to be in a reasonable agreement. 

The dipole moment ratio and the temperature coefficient of both the dipole moment and the unperturbed dimensions of the polyesters PDA and PDS are measured. The experimental value of dlln 0) / d Tshows an anomalous dependence on the elongation ratio of the networks at which the thermoelastic measurements are performed. Although the rotational states scheme gives a fairly good account of the polarity of the chains, it fails in reproducing the experimental values of d (In 0) / d T, the causes of this disagreement are discussed. 

These expressions show that a deformed polymer network is an extremely anisotropic body and possesses a negative thermal expansivity along the orientation axis of the order of the thermal expansivity of gases, about two orders higher than that of macromolecules incorporated in a crystalline lattice (see 2.2.3). In spite of the large anisotropy of the linear thermal expansivity, the volume coefficient of thermal expansion of a deformed network is the same as of the undeformed one. As one can see from Eqs. (50) and (51) Pn + 2(iL = a. Equation (50) shows also that the thermoelastic inversion of P must occur at Xim (sinv) 1 + (1/3) cxT. It coincides with F for isoenergetic chains [see Eq. (46)]. 

This conclusion permits comparison of the thermomechanical and thermoelastic results for various networks. The most reliable data are summarized in Table 2. The temperature coefficients of the unperturbed dimensions of chains d In intermolecular interactions of the configuration of the network chains. 

Kilian 103) has used the van der Waals approach for treating the thermoelastic results on bimodal networks. He came to a conclusion that thermoelasticity of bimodal networks could satisfactorily be described adopting the thermomechanical autonomy of the rubbery matrix and the rigid short segments. The decrease of fu/f was supposed to be related to the dependence of the total thermal expansion coefficient on extension of the rigid short segment component. He has also emphasized that calorimetric energy balance measurements are necessary for a direct proof of the proposed hypothesis. 

For most particulate composites the mismatch between the particles and the matrix is more important than the anisotropy of either component (though alumina/aluminium titanate composites provide a notable exception and are described below). The main features of the stresses can therefore be understood in terms of a simple elastic model assuming thermoelastic isotropy and consisting of a spherical particle in a concentric spherical shell of matrix with dimensions chosen to give the appropriate volume fractions. The particles are predicted to be under a uniform hydrostatic stress, ap after cooling. If the particles have a larger thermal expansion coefficient than the matrix, this stress is tensile, and vice versa. For small particle volume fractions the stress... 

Thermoelastic stresses are generated during a change from the deposition temperature to another temperature Tj. The difference between the thermal expansion coefficients of the film (f) and substrate (s) cause deformation to occur in the film plane. This is constant throughout the thickness of the film, such that ... 

In this relation, a and a, are the thermal expansion coefficients of the substrate and film. These depend on the temperature T. If the film is homogeneous and elastically isotropic, the in plane thermoelastic stress is expressed by ... 

Ej and are respectively Young s modulus and Poisson s coefficient for the film. Furthermore, assuming that the thermal expansion coefficients are independent of the temperature, the thermoelastic stress increases linearly with the film deposition temperature. 

Other types of damage may be produced through thermomechanical effects. For example, when being annealed at 450°C a CVD aluminum film on a Si substrate is subjected to compressive thermoelastic stresses owing to the considerable difference between the thermal expansion coefficients of aluminum (a = 23 x 10 °C 0 and the silicon substrate (a. = 3.5 x 10 °C 0-When cooling, the film may therefore contract by as much as 1%. Due to the combined action... 

Closed-form expressions based on composite theory are especially useful in correlating and predicting the thermoelastic properties (moduli and coefficients of linear thermal expansion) of multiphase materials [1,2]. An article by Tucker et al [3] with emphasis on the internally consistent combination of a set of judiciously chosen techniques to predict the thermoelastic properties of a wide variety of multiphase polymeric systems, and the review articles by Ahmed and Jones [4] and by Chow [5], provide concise descriptions of micromechanical models and are recommended to readers interested in relatively brief discussions of several popular models. 

Most micromechanical theories treat composites where the thermoelastic properties of the matrix and of each filler particle are assumed to be homogeneous and isotropic within each phase domain. Under this simplifying assumption, the elastic properties of the matrix phase and of the filler particles are each described by two independent quantities, usually the Young s modulus E and Poisson s ratio v. The thermal expansion behavior of each constituent of the composite is described by its linear thermal expansion coefficient (3. It is far more complicated to treat composites where the properties of some of the individual components (such as high-modulus aromatic polyamide fibers) are themselves inhomogeneous and/or anisotropic within the individual phase domains, at a level of theory that accounts for the internal inhomogeneities and/or anisotropies of these phase domains. Consequently, there are very few analytical models that can treat such very complicated but not uncommon systems truly adequately. 

Calorimetric data have shown that only half of the total water sorbed by elastin (about 0.6 g water / g dry protein) is really "bound", the remaining water being freezable ( 1). The volumetric data reported in the literature (15,16) refer therefore to an essentially heterophase system, so that the negative and very large coefficient of thermal expansion of the fully hydrated protein does not appear to be suitable for the Interpretation of the thermoelastic data and calculation of the... 

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