Thermal contraction negative

The radial (compressive) stress, qo, is caused by the matrix shrinkage and differential thermal contraction of the constituents upon cooling from the processing temperature. It should be noted that q a, z) is compressive (i.e. negative) when the fiber has a lower Poisson ratio than the matrix (vf < Vm) as is the normal case for most fiber composites. It follows that q (a,z) acts in synergy with the compressive radial stress, 0, as opposed to the case of the fiber pull-out test where the two radial stresses counterbalance, to be demonstrated in Section 4.3. Combining Eqs. (4.11), (4.12), (4,18) and (4.29), and for the boundary conditions at the debonded region... 

Negative thermal expansion coefficients along the chain axes have been observed experimentally on many crystalline polymer lattices7,16 -18). Hence, the thermal contraction along the chain axis seems to be a general phenomenon in crystalline polymers. As a result of this conclusion, we are immediately faced with the question... 

There are an increasing number of perovskite phases known that show a contraction as the temperature increases, at least over a certain temperature range. This effect is usually known, somewhat circuitously, as negative thermal expansion (NTE). Thermal contraction is not the result of a single mechanism. Here two examples are given. 

Xu et al. (1999) also discovered that the thermal contraction of the c-axis of p-eucryptite is inhibited as the crystal is cooled below room temperature. By contrast, c continues to increase until it is saturated near 20°C. This yields average CTE values, from 20 to 298 K for ordered crystals, of+ 18.1 X 10 K along the a-sxes and +109.5 X 10" K along the c-axis. Curiously, in the disordered crystals over the same temperature range, both axes are negative, —10.4 X 10 for a and —85.3 X 10 K for c. Xu et al. (1999) attribute the inhibition of -axes contraction with cooling below room temperature to strengthening localization of Li ions. 

In table 5 the lattice parameters, a, of the cubic p-RH2+jr phases are presented as a function of x at several temperatures. The static and thermal lattice expansions have been added when available. We note the well-known general contraction (negative Aa/Ax-values) of the dihydride lattice with increasing x, which is an expression of the strong ionic character of its interaction with the excess H atoms on O sites an example is given in fig. 9 for the case of YH2+ (, where the break in the a(x)-curve at x=0.10 H/Y indicates the limit of the pure p-phase. 

For YbBi2 the thermal contraction and the variation of lattice constant with temperature has also been measured by Kasaya et al. (1985). Again, a negative expansion coefficient has been found at low temperatures, similar to SmBe. 

This is the integral relative thermal contraction of the isotropic fiber and the matrix within Ti and T2 when cooling down, this value is negative. 

Most materials expand when heated. However, many fibers contract when heated. This fiber behavior is called thermal contract, or negative thermal expansion. 

We note first that not all amorphous substances actually exhibit a negative a in the experimentally probed temperature range. In such cases, it is likely that the contraction coming from those interactions in these materials is simply weaker than the regular, anharmonic lattice thermal expansion. Other contributions to the Griineisen parameter will be discussed later as well. 

The contraction of solids on heating seems anomalous because it offends the intuitive concept that atoms will need more room to move as the vibrational amplitudes of the atoms increase. However, this argument is incomplete. Figure 11.9 plots schematically the variation of A with V at two temperatures, for both positive and negative thermal expansion. The volumes marked explicitly on the E-axis give the minima of each A vs. V isotherm. These are the equilibrium volumes at temperatures T and T2 respectively (J2 > 7j) and zero pressure. 

Gibbs energy minimization has also predicted negative isobaric expansion coefficients for certain crystalline zeolite framework structures, which subsequently were confirmed experimentally [6], Many solids show negative thermal expansion at very low temperatures, including even some alkali halides (Barron and White (Further reading)). Many other solids on heating expand in some directions and contract in others. 

Usefiil zero thermal expansion composites are made by combining materials that show the unusual property of negative thermal expansion (i.e. contraction) with normal (positive) expansion materials. Examples of phosphates showing negative thermal expansion are the diphosphate-divanadate solid solutions ZrP2- V Oy and the microporous aluminophosphate AIPO-17 which shows a particularly large effect. ... 

The thermal expansion curves of the individual Si02 modifications are plotted in Fig. 2, which also illustrates the discontinuous change in the specimen size occurring at the inversion temperature. The high-temperature quartz exhibits a quite rare anomaly, namely a negative coefficient of expansion in all crystallographic directions. On its expansion curve, tridymite likewise exhibits a peak followed by contraction. 

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