Phase transition anomalous

Manoharan PT, Ramasamy S, Thangadurai P. 2004. Pb-207 MAS NMR and conductivity identified anomalous phase transition in nanostructured PbF2- Eur PhysJB 57 425-432. 

The above-mentioned phase transitions conform to the Le Chatelier principle, the sample volume decreasing under high pressure. They are not basically different Irom those observed in the static method, under conditions of thermodynamic equilibrium. There is, however, a class of anomalous phase transitions, which occur only in dynamic experiments and in which the shock compression gives rise to lower densities. The first of such phases was obtained in 1965 by shock treatment of the turbostratic BN [224] the new phase differed from both the graphite-Uke (/i-BN) like (c-BN) polymorphs of boron nitride and was named E-BN (E standing for the explosion phase ). Later, it appeared that the lattice parameters of E-BN are nearly identical to one of the phases of fullerene Ceo [225, 226], viz. a = 11.14, ft = 8.06, c = 7.40 A for E-BN, cf. a= 11.16, = 8.17, c = 7.58 A for Qo, with similar densities of 2.50 g/cm. Thus, the BN-fullerene was obtained by explosion (though not recognized as such) some 25 years before the carbon fuUerene was identified. Later on. 

Table 10.6 Anomalous phase transitions effected by shock waves...

Frustration caused by competing exchange interactions may also play a role in this anomalous phase transition. Indeed, competing exchange is common to many RT2Si2 intermetallics where R=Ce,Np (see sect. 2.3) or U (for work on UNi2Si2, see Lin... 

Fig. 44. - Left The dependence of the degree of disorder, Q on temperature, T, for (a) ideal limiting phase transitions of the l and 11" order, (b) diffuse phase transition of the and II " order and (c) an approximate function — the degree of assignment of ZO) ands Z(H). Right the approximation of phase transitions using two stepwise Dirac function designated as L and their thermal change dUdT. (A) Anomalous phase transitions with a stepwise change at the transformation point. To (where the exponent factor n equals unity and the multipfication constant has values -1, -2 and oo). (B) Diffuse phase transition with a continuous change at tlic point, T with the same multiplication constant but having the exponent factor 1/3. ...

The well defined change in compressibility of the fee alloy at 2.5 GPa clearly indicates the expected behavior of a second-order phase transition. The anomalously high value of the compressibility for the pressure-sensitive fee alloy is demonstrated in the comparison of compressibilities of various ferromagnetic iron alloys in Table 5.1. The fee Ni alloy, as well as the Invar alloy, have compressibilities that are far in excess of the normal values for the... 

The semiconducting properties of the compounds of the SbSI type (see Table XXVIII) were predicted by Mooser and Pearson in 1958 228). They were first confirmed for SbSI, for which photoconductivity was found in 1960 243). The breakthrough was the observation of fer-roelectricity in this material 117) and other SbSI type compounds 244 see Table XXIX), in addition to phase transitions 184), nonlinear optical behavior 156), piezoelectric behavior 44), and electromechanical 183) and other properties. These photoconductors exhibit abnormally large temperature-coefficients for their band gaps they are strongly piezoelectric. Some are ferroelectric (see Table XXIX). They have anomalous electrooptic and optomechanical properties, namely, elongation or contraction under illumination. As already mentioned, these fields cannot be treated in any detail in this review for those interested in ferroelectricity, review articles 224, 352) are mentioned. The heat capacity of SbSI has been measured from - 180 to -l- 40°C and, from these data, the excess entropy of the ferro-paraelectric transition... 

The fact that the order parameter vanishes above does not mean that Nature does not have an inkling of things to come well below (or above) T. Such indicators are indeed found in many instances in terms of the behaviour of certain vibrational modes. As early as 1940, Raman and Nedungadi discovered that the a-) transition of quartz was accompanied by a decrease in the frequency of a totally symmetric optic mode as the temperature approached the phase transition temperature from below. Historically, this is the first observation of a soft mode. Operationally, a soft mode is a collective excitation whose frequency decreases anomalously as the transition point is reached. In Fig. 4.4, we show the temperature dependence of the soft-mode frequency. While in a second-order transition the soft-mode frequency goes to zero at T, in a first-order transition the change of phase occurs before the mode frequency is able to go to zero. 

Equations (7.31a, b) imply that the melting curve slopes forward in the usual case (e.g., Fig. 2.9 for C02) where the density of the solid exceeds that of the liquid (psoiid > PiiquidX but this curve tilts backward in the anomalous case of water (Fig. 7.1), where psoiid < Piiquid (ice cubes float ). The relationships (7.31a, b) can also be paraphrased and generalized to any phase transition a in the statement... 

In the present article, we have dealt only with the phase transition of NIPA gels. Hence, it is not clear at present whether the anomalous phenomena observed on NIPA gels are universal features of the discontinuous transitions of gels or not. According to the theory of coherent-phase equilibria, it depends on the values of the elastic constants whether the phase-coexistence structure is... 

Fukai Y, Kazama S. NMR studies of anomalous diffusion of hydrogen and phase transition in vanadium-hydrogen alloys . Acta Metall., (1977), 25, 59-70. 

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