Expansion coefficient of metals

The reasoning we employed in the previous section is valid for insulating solids. Indeed, for metals, we know that a contribution is made by the free electrons to the partition function and therefore to the specific heat capacity at constant volume. We will now look at the situation for the expansion. 

We can think in the case of the electron gas subject to Fermi-Dirac statistics, but calculation shows that we obtain an identical result by using the simple model of the gas of electrons subject to three degrees of freedom of translation, in the case of the equal energy distribution model. If the metal includes electrons per atom, its molar internal energy will be  

By deriving this pressure in relation to the temperature, we find  

If we substitute this back into equation [1.170], we find an electron parameter of the Gruneisen constant y , (T,V) = 2/3 

the linear expansion coefficient of the metal will be the sum of two terms the contribution of the lattice T,(T,V)Cy and the contribution of the free electrons Yei T,V)Cy j. Hence, we can write  

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TABLE 20. Linear thermal expansion coefficients of metals and of corresponding sealing glasses... 

SeaUng glasses may be classified by reference to the expansion coefficients of metals (e.g. tungsten and molybdenum) and alloys (Ni-Fe-Co, Ni-Fe-Cr, and other alloys) with which they are used. Hence sealing... 

There is a considerable mismatch between the thermal expansion coefficients of metals and those of organic polymers. The metal particles can sometimes shrink away from the surrounding polymer as the temperature falls from the moulding temperature. Improved bonding between metal and polymers would be beneficial. It is possible to obtain filled plastics with thermal conductivities up to 95% of those of metals, simply by using high aspect ratio aluminium flakes. 

Thermal expansion mismatch between the reinforcement and the matrix is an important consideration. Thermal mismatch is something that is difficult to avoid ia any composite, however, the overall thermal expansion characteristics of a composite can be controlled by controlling the proportion of reinforcement and matrix and the distribution of the reinforcement ia the matrix. Many models have been proposed to predict the coefficients of thermal expansion of composites, determine these coefficients experimentally, and analy2e the general thermal expansion characteristics of metal-matrix composites (29-33). 

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%. 

Cordierite [12182-53-5] Mg Al Si O g, is a ceramic made from talc (25%), kaolin (65%), and Al O (10%). It has the lowest thermal expansion coefficient of any commercial ceramic and thus tremendous thermal shock resistance. It has traditionally been used for kiln furniture and mote recently for automotive exhaust catalyst substrates. In the latter, the cordierite taw materials ate mixed as a wet paste, extmded into the honeycomb shape, then dried and fired. The finished part is coated with transition-metal catalysts in a separate process. 

The expansion coefficient of a solid can be estimated with the aid of an approximate thermodynamic equation of state for solids which equates the thermal expansion coefficient with the quantity where yis the Griineisen dimensionless ratio, C, is the specific heat of the solid, p is the density of the material, and B is the bulk modulus. For fee metals the average value of the Griineisen constant is near 2.3. However, there is a tendency for this constant to increase with atomic number. 

Under thermal cycling conditions, the principal source of stress within the oxide scale is the temperature change . Christl et have noted that, when cooling 2.25%Cr-l%Mo steel from 600°C in air, compressive stresses build up in the haematite, whilst tensile stresses build up in the magnetite and spinel layers. This arises because the thermal expansion coefficients of the individual oxide layers increase in the order a metal < a spinel < a magnetite < a haematite . ... 

Although the oxidation of nickel has been extensively studied it is only recently that the process has been clearly understood. The relative simplicity of the system in which only a single-phase layer of oxide, NiO, forms has encouraged research, and a further simplification is that the expansion coefficients of the oxide and metal are similar, (17.1 and 17.6 xlO" °C respectively,) so that the effects of thermal cycles can be largely neglected. 

Casting Casting around steel parts, which are first hot dipped in aluminium or in aluminium-silicon alloy (the Al-Fin process), gives good bonding but requires careful design because of the different thermal-expansion coefficients of the two metals. 

For the cathode seal material, there is a criterion that the thermal expansion coefficient of the metal component must be lower than that of the a-alumina header. A nickel-cobalt-iron alloy (NiloK) with a... 

An X-ray atomic orbital (XAO) [77] method has also been adopted to refine electronic states directly. The method is applicable mainly to analyse the electron-density distribution in ionic solids of transition or rare earth metals, given that it is based on an atomic orbital assumption, neglecting molecular orbitals. The expansion coefficients of each atomic orbital are calculated with a perturbation theory and the coefficients of each orbital are refined to fit the observed structure factors keeping the orthonormal relationships among them. This model is somewhat similar to the valence orbital model (VOM), earlier introduced by Figgis et al. [78] to study transition metal complexes, within the Ligand field theory approach. The VOM could be applied in such complexes, within the assumption that the metal and the... 

For most metal-reinforced nanocomposites the thermal expansion coefficient of the metal phase will be larger than that of the matrix, reversing the expected stress fields compared to SiC-reinforced alumina. Thus while the tensile radial stresses surrounding occluded particles may induce transgranular cracking, the compressive hoop stresses may inhibit crack propagation if the particles are located at grain boundaries. Macrostresses in sub-micron Ni... 

In forsterite ceramics the mineral forsterite (Mg2Si04) crystallizes. They have excellent low-dielectric-loss characteristics but a high thermal expansion coefficient which imparts poor thermal shock resistance. During the 1960s they were manufactured for parts of rather specialized high-power devices constructed from titanium and forsterite and for which the operating temperature precluded the use of a glass-metal construction. The close match between the thermal expansion coefficients of titanium and forsterite made this possible. Today alumina-metal constructions have completely replaced those based on titanium-forsterite and the ceramic is now manufactured only to meet the occasional special request. 

A parallel-plate capacitor at 25 °C comprises a slab of dielectric of area 10 4 m2 and thickness 1 mm carrying metal electrodes over the two major surfaces. If the relative permittivity, temperature coefficient of permittivity and linear expansion coefficient of the dielectric are respectively 2000, — 12MK 1 and 8MK 1, estimate the change in capacitance which accompanies a temperature change of + 5 °C around 25 °C. [Answer — 0.035 pF]... 

Unfortunately, expansion coefficients of plastics and metals can be quite different. For this reason it is suggested that electrodes are kept in closed glass tubes in a thermostat bath when not in use, at the temperature at which they will be employed. If this is not done, there is a... 

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