Specific heat transition state

Although there have been few data collected, postshock temperatures are very sensitive to the models which specify y and its volume dependence, in the case of the Gruneisen equation of state (Boslough, 1988 Raikes and Ahrens, 1979a Raikes and Ahrens, 1979b). In contrast, the absolute values of shock temperatures are sensitive to the phase transition energy Ejp of Eq. (4.55), whereas the slope of the versus pressure curve is sensitive to the specific heat (see, e.g.. Fig. 4.28). 

Transition region or state in which an amorphous polymer changed from (or to) a viscous or rubbery condition to (or from) a hard and relatively brittle one. Transition occurs over a narrow temperature region similar to solidification of a glassy state. This transformation causes hardness, brittleness, thermal expansibility, specific heat and other properties to change dramatically. 

The transition from a ferromagnetic to a paramagnetic state is normally considered to be a classic second-order phase transition that is, there are no discontinuous changes in volume V or entropy S, but there are discontinuous changes in the volumetric thermal expansion compressibility k, and specific heat Cp. The relation among the variables changing at the transition is given by the Ehrenfest relations. 

Generally, a phase transition is triggered by an external stress which most commonly is a change in temperature or pressure. Properties that can change discontinuously include volume, density, specific heat, elasticity, compressibility, viscosity, color, electric conductivity, magnetism and solubility. As a rule, albeit not always, phase transitions involve structural changes. Therefore, a phase transition in the solid state normally involves a change from one to another modification. 

Even when complete miscibility is possible in the solid state, ordered structures will be favored at suitable compositions if the atoms have different sizes. For example copper atoms are smaller than gold atoms (radii 127.8 and 144.2 pm) copper and gold form mixed crystals of any composition, but ordered alloys are formed with the compositions AuCu and AuCu3 (Fig. 15.1). The degree of order is temperature dependent with increasing temperatures the order decreases continuously. Therefore, there is no phase transition with a well-defined transition temperature. This can be seen in the temperature dependence of the specific heat (Fig. 15.2). Because of the form of the curve, this kind of order-disorder transformation is also called a A type transformation it is observed in many solid-state transformations. 

An anomalous behaviour is found also for 4He, as can be observed from Fig. 2.9 the 4He specific heat shows a sharp maximum around 2.2K, corresponding to the transition to the superfluid state (He II). The characteristic shape of the C-T curve has baptized this transition with the name of A-transition . 

We notice from Fig. 3.4(b) that the lattice specific heat cph is not modified by the superconducting transition cph = /3T3 with the same of the normal state. 

We can conclude that the new behaviour of the superconducting material is due to a new state for the electrons in fact, at the critical temperature, there is a jump of the electronic specific heat. In no external magnetic field, it is a second-order transition, which does not involve latent heat. 

Soon after Dennison had deduced from the specific-heat curve that ordinary hydrogen gas consists of a mixture of two types of molecule, the so-called ortho and para hydrogen, a similar state of affairs in the case of iodine gas was demonstrated by direct experiment by R. W. Wood and F. W. Loomis.1 In brief, these experimenters found that the iodine bands observed in fluorescence stimulated by white light differ from those in the fluorescence excited by the green mercury line X 5461, which happens to coincide with one of the iodine absorption lines. Half of the lines are missing in the latter case, only those being present which are due to transitions in which the rotational quantum number of the upper state is an even integer. In other words, in the fluorescence spectrum excited by X 5461 only those lines appear which are due to what we may provisionally call the ortho type of iodine molecule. 

The orbitals of the d states in clusters of the 3d, 4d, and 5d transition elements (or in the bulk metals) are fairly localized on the atoms as compared with the sp valence states of comparable energy. Consequently, the d states are not much perturbed by the cluster potential, and the d orbitals of one atom do not strongly overlap with the d orbitals of other atoms. Intraatomic d-d correlations tend to give a fixed integral number of d electrons in each atomic d-shell. However, the small interatomic d-d overlap terms and s-d hybridization induce intraatomic charge fluctuations in each d shell. In fact, a d orbital contribution to the conductivity of the metals and to the low temperature electronic specific heat is obtained only by starting with an extended description of the d electrons.7... 

It may of course be unnecessary to consider all these terms and the equation is much simplified in the absence of magnetism and multiple electronic states. In the case of Ti, it is possible to deduce values of the Debye temperature and the electronic specific heat for each structure the pressure term is also available and lambda transitions do not seem to be present. Kaufman and Bernstein (1970) therefore used Eq. (6.2), which yields the results shown in Fig. 6.1(c). 

Other phases are then characterised relative to this ground state, using the best approximation to Eq. (6.1) that is appropriate to the available data. For instance, if die electronic specific heats are reasonably similar, there are no lambda transitions and T 6o, then the entropy difference between two phases can be expressed just as a function of the difference in their Debye temperatures (Domb 1958) ... 

Sato, M., Fujishita, H. and Hoshino, S., Specific Heat Anomaly of BaPb1.xBixOa at the Superconducting Transition. J. Phys. C Solid State Phys. 16 L417 (1983). 

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