Thermal expansion coefficients anisotropic

Alterations by moisture exposure are fair. Shrinkage and coefficient of thermal expansion are anisotropic with values typical of crystalline polymers. Creep resistance is good. 

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. 

Here, / is assumed to be independent of direction within the fiber, but for highly anisotropic fibers such as carbon and Kevlar , allowances must be made for their variation in thermal expansion coefficient with direction. The thermal expansion coefficient perpendicular to the fiber axis, U2, can also be derived ... 

The approach to the critical point, from above or below, is accompanied by spectacular changes in optical, thermal, and mechanical properties. These include critical opalescence (a bright milky shimmering flash, as incident light refracts through intense density fluctuations) and infinite values of heat capacity, thermal expansion coefficient aP, isothermal compressibility /3r, and other properties. Truly, such a confused state of matter finds itself at a critical juncture as it transforms spontaneously from a uniform and isotropic form to a symmetry-broken (nonuniform and anisotropically separated) pair of distinct phases as (Tc, Pc) is approached from above. Similarly, as (Tc, Pc) is approached from below along the L + G coexistence line, the densities and other phase properties are forced to become identical, erasing what appears to be a fundamental physical distinction between liquid and gas at all lower temperatures and pressures. 

Some kind of thermal shock loading is inevitable during service of FMs. In addition, most FMs have anisotropic thermal-expansion coefficients due to their unique architectures. In 2004, Koh and co-workers investigated the thermal shock resistance of Si3N4/BN FMs [29], They observed their excellent thermal shock resistance by measuring the retention of the flexural strength after thermal shock test, as shown in Fig. 1.17. The monolithic Si3N4 exhibited... 

The possibility of negative thermal-expansion coefficient (TEC) values along a direction of strong coupling in layered or chain structures (the so-called membrane effect") was suggested for the first time by Lifshitz [4] for strongly anisotropic compounds. In the phonon spectra of such compounds... 

Anisotropic polymer filaments could be produced by in-situ photopolymerization of oriented acrylate monomers. Ordering of the monomers was achieved by an elongational flow prior to the polymerization process. The produced polymers showed a high elastic modulus and a low thermal expansion coefficient in the direction of the orientation. 

It has been demonstrated that molecular orientation can be achieved starting with a low molecular weight species which is oriented in an elongational flow and subsequently cured under UV-irradiation. The orientation of the monomer is frozen-in by the ultra-fast process of polymerization and crosslinking. Both extrusion and stretching can be carried out at relatively low temperatures and pressures. Polymer filaments produced in this way are definitely anisotropic as is evidenced by their birefringence and by a strong increase of the tensile modulus and a decrease of the thermal expansion coefficient in the axial direction. 

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. 

Although not explicitly stated, the discussion so far is only strictly true for isotropic, e.g., cubic, polycrystalline materials. Crystals that are noncubic and consequently are anisotropic in their thermal expansion coefficients behave quite differently. In some cases, a crystal can actually shrink in one direction as it expands in another. When a polycrystal is made up of such crystals, the average thermal expansion can be very small, indeed. Cordierite and lithium-aluminosilicate (LAS) (see Fig. 4.4) are good examples of this class of materials. As discussed in greater detail in Chap. 13, this anisotropy in thermal expansion, which has been exploited to fabricate very low-a materials, can result in the buildup of large thermal residual stresses that can be quite detrimental to the strength and integrity of ceramic parts. 

Table 13.2 Thermal expansion coefficients for some ceramic crystals with anisotropic thermal expansion behavior...

TABLE 34.10 Thermal Expansion Coefficients for Some Anisotropic Crystals (ppm/°C) ... 

The almost perfect orientation of p-aramid fibers is reflected in the anisotropic behavior of its thermal expansion coefficient. The linear expansion coefficient for these materials is negative (Table 13.2). Because the volumetric thermal expansion coefficient is not affected by orientation, the radial coefficient must increase as fiber orientation increases. The negative expansion coefficient of these materials has opened a whole field of applications in electronics (see section 13.8.4.2). 

II. 1.2b. 1.Thermal Expansion Thermal expansion of unidirectional SiC/RBSN composite is mainly a function of constituents volume fractions and measurement direction relative to the fiber, and is not affected by constituents porosity. Measurement of linear thermal expansion with temperature in nitrogen for the 1-D SiC/RBSN composites parallel and perpendicular to the fibers indicates a small amount of anisotropy (Fig. 5). This is attributed to small difference in thermal expansion coefficients of SiC fibers (4.2 x 10 ) and RBSN matrix (3.8 x 10 ) as well as anisotropic thermal expansion of carbon coating on SiC fibers. In the fiber direction, linear thermal expansion is controlled by the SiC fiber, and in the direction perpendicular to the fiber, it is controlled by the RBSN matrix. 

A different approach to the prediction of thermal expansion coefficients was taken by Schapery (1968), who calculated upper and lower bounds for both isotropic and anisotropic composites. The method is applicable to systems containing an arbitrary number of constituents and an arbitrary phase geometry. In some cases, the bounds coincide, and exact solutions may be found in other cases, approximations only may be derived. In a simple two-component system, Schapery obtained the following expression for the volumetric expansion coefficient of the composite ... 

The thermal expansion coefficients are related to the crystal structure and to the type and strength of the bond. Many ceramics have low to medium expansion coefficients, as can be seen in Table 4.10. The coefficients may or may not depend strongly on temperature. In many cases the thermal expansion is anisotropic and can have negative values in certain temperature regions. 

If the anisotropic expansions of the unit cells are considered, CZP behaves in an opposite way to Sro 5Zr2(P04)3 (SZP). Increasing the temperature of CZP leads to c axis expansion and a axis contraction, while in the case of SZP the c axis contracts and the a axis expands. The use of a suitable CZP/SZP solid solution with composition (Ca,Sr)o 5Zr2(P04)3 leads to almost constant a and c axis lengths as the temperature is increased with a resultant thermal expansion coefficient of almost zero (Table 12.28). 

The thermal expansion of anisotropic fibers is usually characterized by two coefficients of thermal expansion (CTEs), the longitudinal CTE, oi, and the radial CTE, a,. The direct measurement of ai is straightforward but that of a is difficult since the gauge length is the fiber diameter. Further, the use of one single a, CTE to depict the transverse thermal expansion of carbon fibers is only appropriate for those fibers which have a transverse microtexture with axial symmetry, an assumption that is clearly not correct for all fibers. 

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