Coefficient of the thermal expansion

If one of the principal coefficients is negative then the quadric is a hyperboloid of one sheet. If two of the principal coefficients are negative the quadric is a hyperboloid of two sheets (Nye, 1957). The quadric for the coefficient of the thermal expansion... 

The thermal properties of polycarbonate are not outstanding and the opportunities to improve it are remote. Addition of 30 wt% of carbon or glass fibers increases deflection temperature under load only by about 20°C to the maximum attainable value of 150°C but coefficient of the thermal expansion is drastically reduced which makes it suitable for many of its potential applications. 

The coefficient of the thermal expansion has been calculated from the thermal evolution of the lattice parameters and the cell volume as follows... 

Rigidity modulus, GPa Teusile streugth, MPa Temperature of the deformation, °C Impact viscosity, kJ/m Water consump- tion, weight % Coefficient of the thermal expansion (x.y)... 

The electronic configuration for an element s ground state (Table 4.1) is a shorthand representation giving the number of electrons (superscript) found in each of the allowed sublevels (s, p, d, f) above a noble gas core (indicated by brackets). In addition, values for the thermal conductivity, the electrical resistance, and the coefficient of linear thermal expansion are included. 

Coefficient of Linear Thermal Expansion. The coefficients of linear thermal expansion of polymers are higher than those for most rigid materials at ambient temperatures because of the supercooled-liquid nature of the polymeric state, and this applies to the cellular state as well. Variation of this property with density and temperature has been reported for polystyrene foams (202) and for foams in general (22). When cellular polymers are used as components of large stmctures, the coefficient of thermal expansion must be considered carefully because of its magnitude compared with those of most nonpolymeric stmctural materials (203). 

Thermal Expansion. Coefficients of linear thermal expansion and linear expansion during transformation are listed in Table 7. The expansion coefficient of a-plutonium is exceptionally high for a metal, whereas those of 5- and 5 -plutonium are negative. The net linear increase in heating a polycrystalline rod of plutonium from room temperature to just below the melting point is 5.5%. 

Thermal Expansion. The averaged value of the coefficient of linear thermal expansion of diamond over the range 20 to 100°C is 1.34 X 10 cm/cm/ C and 3.14 x 10 from 20 to 800°C. At room temperature the values for sihca glass and diamond ate 0.5 X 10 and 0.8 X 10 , respectively. The relatively low expansion combined with the low reactivity of diamonds, except for carbide formation, leads to some challenges in making strong bonds between diamond and other materials. 

Plastic products are often constrained from freely expanding or contracting by rigidly attaching them to another structure made of a material (plastic, metal, etc.) with a lower coefficient of linear thermal expansion. When such composite structures are heated, the plastic component is placed in a state of compression and may buckle, etc. When such composite structures are cooled, the plastic component is placed in a state of tension, which may cause the material to yield or crack. The precise level of stress in the plastic depends on the relative compliance of the component to which it is attached, and on assembly stress. 

To minimize the stresses induced by differential thermal expansion/contraction one must (1) employ fastening techniques that allow relative movement between the component parts of the composite structure, (2) minimize the difference in coefficient of linear thermal expansion between the materials... 

An influence on dimensions and tolerances involves the coefficient of linear thermal expansion or contraction. This CLTE value has to be determined at the product s operating temperature (Chapter 2, THERMAL EXPANSION AND CONTRACTION) Plas tics can provide all extremes in CLTEs. As an... 

When materials with different coefficients of linear thermal expansion (CLTE) are bolted, riveted, bonded, crimped, pressed, welded, or fastened together by any method that prevents relative movement between the products, there is the potential for thermal stress. Most plastics, such as the unfilled commodity TPs, may have ten times the expansion rates of many nonplastic materials. However there are plastics with practically no expansion. Details are reviewed in Chapter 2, THERMAL EXPANSION AND CONTRACTION. 

Like metals, plastics generally expand when heated and contract when cooled. Usually, for a given temperature change many TPs have a greater change than metals. The coefficient of linear thermal expansion (CLTE) is the ratio between the change of a... 

Figure 3 a presents the variation of the thermal expansion coefficients a for the inclusions (f), the matrix (m) and the composite (c) and the derived values for a s at the interphase (a.). Similarly, Fig. 3b gives the variation of the normalized to the unit-lengths thermal expansions of the constituents versus temperature T. 

The glass transition temperature of a dilute system, according to the free volume changes, is determined by the diluent volume fraction Vd, and changes of the thermal expansion coefficient, a, at Tg by using ... 

Thermally-Driven Buoyancy Flow. Thermal gradients can Induce appreciable flow velocities in fluids, as cool material is pulled downward by gravity while warmer fluid rises. This effect is Important in the solidification of crystals being grown for semiconductor applications, and might arise in some polymeric applications as well. To illustrate how easily such an effect can be added to the flow code, a body force term of pa(T-T ) has been added to the y-coraponent of the momentum equation, where here a is a coefficient of volumetric thermal expansion. 

The crystal quality of the InGaN QWs becomes poor mainly due to the lattice-constant mismatch and the difference of the thermal expansion coefficient between InN and GaN with increasing the In composition [4,5]. Therefore, in order to improve the external quantum efficiency (i/ext) of the InGaN-based LEDs and LDs, it is important to elucidate and optimize the effects of the various growth conditions for the InGaN active layer on the structural and optical properties. Recently, we reported a fabrication of efficient blue LEDs with InGaN/GaN triangular shaped QWs and obtained a substantial improvement of electrical and optical properties of the devices [6,7]. 

Here Q(t) denotes the heat input per unit volume accumulated up to time t, Cp is the specific heat per unit mass at constant pressure, Cv the specific heat per unit mass at constant volume, c is the sound velocity, oCp the coefficient of isobaric thermal expansion, and pg the equilibrium density. (4) The heat input Q(t) is the laser energy released by the absorbing molecule per unit volume. If the excitation is in the visible spectral range, the evolution of Q(t) follows the rhythm of the different chemically driven relaxation processes through which energy is... 

The coefficient of linear thermal expansion is almost constant, for most types of glass, for temperatures up to 400-600°C. The actual value depends on the chemical constitution of the glass. It then increases rapidly above a certain temperature, often called the... 

Several methods of measurement of the thermal expansion have been developed as a function of the material, dimension and shape of the sample, temperature range and requested accuracy. The measurement of the linear expansion coefficient a = 1/L (AL/A7) of a sample is done by recording the length change AL (in a definite direction) due to a temperature variation AT. 

The measure of the thermal expansion coefficient below room temperature is particularly difficult for low-expansion materials (see Section 3.9). Remember also how newly produced composite materials show extremely low-expansion coefficient of both sign. 

By applying the definition of the thermal expansion coefficient, given by Equation 9-39, we obtain... 

Here T0 is a reference temperature and if this is 273K the coefficient A] 103. The temperature may then be lowered until the melting point, Tm, is reached. At this point a crystalline solid is formed, the density of which will usually be within 10% of the liquid. The density can be described by a similar equation to Equation (3.28) but the coefficient is quite different, i.e. As 1015 The origin of the thermal expansion in a... 

Figure 13.14 The PPC traces of the thermal expansion coefficient a (deg-1) as a function of temperature for chymotrypsinogen and RNase A. The data show that both native (low-temperature region) proteins exhibit a strong negative temperature coefficient as well as a large positive curvature. (Permission to use the figure granted by MicroCal, LLC.)...

The membrane layout should be as symmetric as possible to achieve good temperature homogeneity over the membrane area and, as a consequence, low stress gradients. This includes also thermal stress owing to the mismatch of the thermal expansion coefficients of the layer materials. 

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