Expansion coefficient linear

The eigenvalues of this mabix have the form of Eq. (68), but this time the matrix elements are given by Eqs. (84) and (85). The symmetry arguments used to determine which nuclear modes couple the states, Eq. (81), now play a cracial role in the model. Thus the linear expansion coefficients are only nonzero if the products of symmebies of the electronic states at Qq and the relevant nuclear mode contain the totally symmebic inep. As a result, on-diagonal matrix elements are only nonzero for totally symmebic nuclear coordinates and, if the elecbonic states have different symmeby, the off-diagonal elements will only... 

Phase Temperature range, °C Linear expansion coefficient X 10 /K Transformation expansion, 100 AL/L... 

These techniques help in providing the following information specific heat, enthalpy changes, heat of transformation, crystallinity, melting behavior, evaporation, sublimation, glass transition, thermal decomposition, depolymerization, thermal stability, content analysis, chemical reactions/polymerization linear expansion, coefficient, and Young s modulus, etc. 

Phoenix, also, is a borosilicate glass made by the British Heat Resisting Glass Co. The linear expansion coefficient (50-450°Q is 3-24 X 10" . Tubing and rod are supplied in a wide range of sizes. The tubing is made with either standard wall or heavy wall. 

Laboratory glassware made from this glass is available. It is a borosilicate glass manufactured by Wood Bros. Glass Co. The linear expansion coefficient (0-400°Q is 3-2 x 10 . 

This is another borosilicate glass, and was developed to make strain-free seals with timgsten. It is made by the General Electric Co., and often described as GEC W.l, or simply as W.l. The linear expansion coefficient (20-350°C) is 3-75 x 10 . 

Made by Plowden Thompson Ltd. Dial 36 is a borosilicate glass for sealing to timgsten. The linear expansion coefficient (20-300°Q is 3-6 X 10 . 

BTH No. 12 is a lead glass for lamp and valve manufacture, made by the British Thomson-Houston Co. The linear expansion coefficient (50-400°Q is 9-1 X 10- . 

This is made by the General Electric Co., and is used for medical ampoules. It loses very little alkali to aqueous solutions. The linear expansion coefficient is 7-3 x 10 from 20 to 350°C. This is intermediate between the soft and hard glasses, and M.6. is sometimes used in graded seals. 

This glass, made by the General Electric Co., is similar to white neutral above, but is coloured amber by addition of iron and manganese. The linear expansion coefficient is 7-5 x 10" from 20 to 350°C. It is useful for ampoules when the contents need protection from ultra-violet radiation. 

Lemington H.26X., made by the General Electric Co., is a very hard borosilicate glass of high softening temperature. Tte Mg point is 780°C. It is used in high pressure mercury vapour lamps. The linear expansion coefficient is 4-6 x 10 from 20 to 580°C. Sodium and potassiiun are absent and alumina is present in quantity in this glass. 

A borosilicate glass for sealing to alloys of the Kovar type (p. Ill) l Clso seals to some electrical porcelains. It is made by the British phomson Houston Co., and is often referred to as BTH C,40 or as The linear expansion coefficient is 4-85 x 10 from 50 to... 

Pids is a soda glass for sealing to platinum, and is made by Plowden b Thompson Ltd. The linear expansion coefficient (20-300°C) is pi K 10-. ... 

Substrate material Price per unit area (arb. units) Dielectric permittivity of insulator Maximum working temperature (K) Resistivity of dielectric layer (fl-cm) Density (g/cm3) Linear expansion coefficient x i[Pg.490]

The measurement of the linear expansion coefficient can be carried out by several methods (see Chapter 13), for example, by means of an interferometric dilatometer [77], a capacitance dilatometer [78] or a SQUID dilatometer [74]. The latter can achieve resolutions as small as 2 x l(T14m. 

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. 

Several methods have been used to measure the linear expansion coefficient for T< 300K [1,2], These different techniques are ... 

Within the SCF-CI method a fixed set of molecular orbitals is used. This means that during the calculation (leading to slow convergence) the individual molecular orbitals remain unchanged. A method where the linear expansion coefficients and the LCAO coefficients are optimized simultaneously is the multi-configuration SCF (MCSCF). 

In the present variation-perturbation calculations the first order corrections were expanded in 600-term ECG basis defined in equations (15) and (16). The components of the polarizability were computed from equation (11) using the optimized The optimization was performed separately for each component and intemuclear distance. The values of aj, (co) are arithmetic sums of the plus and minus components (equation (12)) computed from two separate first-order corrections. For a given component v (either or ), and are expanded in the same basis but, because they are solutions to two different equations (equation (9)) they differ in the linear expansion coefficients. The computed components of the static polarizability an(/ ) and a R) are drawn in Fig. 2 and their numerical values at selected intemuclear distances are listed in Table 1. 

A standard type of variable used in the definition of an orbital is a set of linear expansion coefficients. Given the basis functions a gen-... 

For materials that are isotropic, that is, have the same properties in all directions, it can be shown that ay = 3ai. A material that has different properties in different directions is said to be anisotropic. Thus, a linear expansion coefficient, if no direction of measurement is explicitly stated, implies an isotropic material. Conversely, a volume thermal expansion coefficient implies an anisotropic material, and one should exercise caution when deriving linear thermal expansion coefficients from volume-based measurements. 

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