Primary expansion coefficient

The eigenvalues of that tensor are the three primary expansion coefficients and. ... 

If we used perturbation theory to estimate the expansion coefficients c etc., then all the singly excited coefficients would be zero by Brillouin s theorem. This led authors to make statements that HF calculations of primary properties are correct to second order of perturbation theory , because substitution of the perturbed wavefunction into... 

The total pyroelectric response at constant stress, p , is the sum of the primary pyroelectic response, given by p, and the secondary pyroelectric response, which is the product of the direct piezoelectric stress coefficient gs, and the thermal expansion coefficients ... 

Thermal expansion coefficients and the primary and secondary pyroelectric coefficients of animal bone. Nature 224, 798 (1969). 

During the primary processing, the thermal expansion coefficient of calcined coke changes, and that treatment at the range of 700°C to 900°C is effective. 

The glass-rubber transition temperature, commonly known as glass transition temperature (Tg), is a phase change reminiscent of a thermodynamic second-order transition. In the case of a second-order transition a plot of a primary quantity shows an abrupt change in slope, while a plot of a secondary quantity (such as expansion coefficient and specific heat) then shows a sudden jump. 

CVD also has a number of disadvantages. One of the primary disadvantages lies in the properties of the precursors. Ideally, the precursors need to be volatile at near-room temperatures. This is non-trivial for a number of elements in the periodic table, although the use of metal-organic precursors has eased this situation. CVD precursors can also be highly toxic (Ni(CO) ), explosive (B Hg), or corrosive (SiCl ). The byproducts of CVD reactions can also be hazardous (CO, H, or HP). Some of these precursors, especially the metal-organic precursors, can also be quite costly. The other major disadvantage is the fact that the films are usually deposited at elevated temperatures. This puts some restrictions on the kind of substrates that can be coated. More importantly, it leads to stresses in films deposited on materials with different thermal expansion coefficients, which can cause mechanical instabilities in the deposited films. 

In heat transfer studies, the primary variable is temperature, and it is desirable to express the net buoyancy force (Eq. 9-2) in terms of temperature differences. But this requires expressing the density difference in terms of a temperature difference, which requires a knowledge of a property that represents the variation of the density of a fluid with temperature atconstant pressure. The property that provides that information is the volume expansion coefficient /3, defined as (Fig. 9-4)... 

The primary requirement is to adjust the thermal expansion coefficients of the frit and enamel to that of the metal. For this purpose and for the necessary corrections, use is mostly made of additive factors. In view of the imperfections involved in such calculations, the main criterion is always the laboratory test the enamel is applied on a metal specimen and fired to assess the resulting coating quality. 

There are two possible approaches to the selection of materials from the standpoint of thermal shock resistance. The first is suitable for glass and fine dense ceramics and was discussed in Section II. 5. 2. With these materials, it is necessary to avoid formation of primary cracks which originate at the surface and propagate rapidly into the interior where they are the cause of extensive fracture. In this case, the favourable properties include high strength and high thermal conductivity, and low elasticity modulus and expansion coefficient values. 

Ultrasonic techniques are so numerous that a comprehensive discussion is not possible. Since an ultrasonic wave is an adiabatic pressure wave, in general both a temperature and a pressure perturbation of the system occurs. In most nonaqueous solvents, the temperature perturbation is of primary importance, because chemical equilibria are generally much more sensitive to temperature changes than to pressure changes. In aqueous solutions, however, the pressure perturbation is usually of primary importance, because the thermal-expansion coefficient of water is very small, so that the pressure wave is almost isothermal. A serious disadvantage of ultrasonic methods is that rather large volumes of solution are required for low-frequency measurements and relatively high concentrations (> 10" M) of reactants are required at all frequencies. Recent experimental innovations have alleviated these problems to some extent. The most common ultrasonic... 

Large mismatches between the expansion coefficients of the adhesive and the two adherends have been the primary cause of numerous failmes resulting in high... 

Materials typically expand when heated. The expansion is characterized by the linear or volumetric thermal expansion coefficient. The three primary types of materials expand differently. Polymers expand more than metals, and metals expand more than ceramics. For many materials thermal expansion is related to the melting temperature of the material, also a relation between the thermal expansion coefficient of polymers and their elastic modulus is given. 

A glass transition occurs for an amorphous polymer when the slope of a plot of specific volume changes abruptly with rise of temperature. The slope itself (the thermal expansion coefficient a), a = [llY] dV/dT, shows a step-change at Tg. A crystalline polymer also shows a transition at the same temperature, due to its amorphous phase. (It will be explained later that only semi-crystallinity may exist and there are almost always amorphous domains.) In the case of a crystalline polymer, however, a primary transition temperature, T, exists, signified by an abrupt change in volume. The specific volume of the crystalline polymer is always lower than that of the equivalent amorphous one because its more compact stmcture increases the density. 

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