Thermal expansion negative

Negative thermal expansion materials, J. Chem. Soc., Dalton Trans. 1999, 3317-3326. 

Negative thermal expansion (NTE) is a property of materials in which they become smaller with increasing temperature. It is a comparatively rare property and the general trend is for substances to 

It is useful to relate the expansivity to the volume dependence of the entropy. This is readily seen by manipulating the expression for the isobaric expansivity, a, 

In most solids vibrations parallel to bond directions decrease in frequency as the volume increases and the entropy (eq. (11.14)) increases with volume (dS/dV)T and the thermal expansion are positive. Negative thermal expansion is usually associated with more open structures where coordination numbers are low and vibrations perpendicular to bond directions can dominate the change in entropy with volume and thus the derivative (dS/dV)T. 

Around 400 K there is a phase transition to a disordered but still cubic structure associated with the terminal oxygen atom in a WO4 tetrahedron which can migrate to another tetrahedron, thereby reversing the direction in which a pair of tetrahedra point. Nevertheless the same general atomic mechanisms are responsible for the negative thermal expansion up to the decomposition temperature. 

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. 

Configurational averaging - solid solutions and grossly non-stoichiometric oxides 

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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. 

Figure 11.9 Schematic variation of Helmholtz energy A with volume V for (a) positive and (b) negative thermal expansion.

Woodcock, D.A. and Lightfoot, P. (1999) Negative thermal expansion in the siliceous zeolites chabazite and ITQ-4 a neutron power diffraction smdy. Chem. Mater., 11, 2508-2514. 

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... 

These expressions show that a deformed polymer network is an extremely anisotropic body and possesses a negative thermal expansivity along the orientation axis of the order of the thermal expansivity of gases, about two orders higher than that of macromolecules incorporated in a crystalline lattice (see 2.2.3). In spite of the large anisotropy of the linear thermal expansivity, the volume coefficient of thermal expansion of a deformed network is the same as of the undeformed one. As one can see from Eqs. (50) and (51) Pn + 2(iL = a. Equation (50) shows also that the thermoelastic inversion of P must occur at Xim (sinv) 1 + (1/3) cxT. It coincides with F for isoenergetic chains [see Eq. (46)]. 

Negative Thermal Expansivity of Drawn Crystalline Polymers... 

Dilatometric studies have demonstrated the negative thermal expansivity for many oriented crystalline polymers 64,170 176). The results of these experimental studies may be summarized as follows. Cold-drawing of PE below Tm 172) and solid-state extrusion under elevated pressure 170 1711 lead to a monotonous decrease of the positive thermal expansion coefficient with increasing draw ratio. At a certain degree of orientation, dependent on temperature, PM becomes negative with Pi < Pell (Fig. 16). This is the second way of reaching negative expansivity applied, e.g. to POM (w = 63 % Tdr = 423 K) 173>. 

According to Eq. (110) Px must only be positive, As has been pointed out above, Eq. (106) allows a negative thermal expansivity. Therefore, the analysis of the structural models of oriented crystalline polymers seems to predict the anisotropy of thermal expansivity more correctly. 

The anticorrelation between entropy and volume for liquid water has been attributed to the formation of an open hydrogen-bonded network, in which a decrease in orientational entropy is accompanied by a volume increase (Debenedetti, 2003). This network is transient and short-ranged in liquid water (rather than being permanent and long-ranged in ice), and is the microscopic basis for water s negative thermal expansion. This open hydrogen-bonded network has a profound influence on the thermodynamics of liquid water (Debenedetti, 2003). 

Chapman, K. W., Chupas, P. J., Kepert, C. J., Compositional dependence of negative thermal expansion in the Prussian... 

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