Position disorder phase transition

The Ag (100) surface is of special scientific interest, since it reveals an order-disorder phase transition which is predicted to be second order, similar to tire two dimensional Ising model in magnetism [37]. In fact, tire steep intensity increase observed for potentials positive to - 0.76 V against Ag/AgCl for tire (1,0) reflection, which is forbidden by symmetry for tire clean Ag(lOO) surface, can be associated witli tire development of an ordered (V2 x V2)R45°-Br lattice, where tire bromine is located in tire fourfold hollow sites of tire underlying fee (100) surface tills stmcture is depicted in tlie lower right inset in figure C2.10.1 [15]. 

The formation and dissolution of 2D Me UPD phases can involve positive and negative 2D nucleation and growth steps, respectively. 2D nucleation and growth represent a first order phase transition where an expanded overlayer is transformed into a condensed one (or vice versa) by a discontinuous change of r. Additionally, higher order (order-disorder) phase transitions, characterized by 7" = constant, but with a discontinuity in its partial derivative (dr / dE), may also take place within 2D Meads overlayers in the UPD range. However, clear experimental evidence for higher order phase transitions in Me UPD overlayers does not yet exist. 

Figure 2 shows the schematic structure in the paraelectric (T > Tn) and an-tiferroelectric (T < Tn) phases, hi the paraelectric phase the time-averaged position of the H atoms hes in the middle of an O - H...0 bond, whereas in the antiferroelectric phase, the protons locahze close to one or the other O atom. Prior to the recent NMR work [20-25], the largely accepted model of the phase transition was that the phase transition involved only the ordering of the H atoms in the O - H...0 bonds, and no changes in the electronic structure of the C4 moieties were considered to take place. The NMR results show that, in addition to the order/disorder motion of the H atoms, the transition also involves a change in the electronic charge distribution and symmetry of the C4 squares. 

Fig. 8 Temperature dependence of the four NMR peaks of squaric acid [20]. Note how the four peaks coalesce to one above the phase transition, but that the average of the peak positions does not stay constant, as required for a pure order/disorder transition. It increases around the transition temperature, emphasizing an additional displacive component, coexisting with the order/disorder one...

If we want to calculate the entropy of a liquid, a gas, or a solid phase other than the most stable phase at T =0, we have to add in the entropy of all phase transitions between T = 0 and the temperature of interest (Fig. 7.11). Those entropies of transition are calculated from Eq. 5 or 6. For instance, if we wanted the entropy of water at 25°C, we would measure the heat capacity of ice from T = 0 (or as close to it as we can get), up to T = 273.15 K, determine the entropy of fusion at that temperature from the enthalpy of fusion, then measure the heat capacity of liquid water from T = 273.15 K up to T = 298.15 K. Table 7.3 gives selected values of the standard molar entropy, 5m°, the molar entropy of the pure substance at 1 bar. Note that all the values in the table refer to 298 K. They are all positive, which is consistent with all substances being more disordered at 298 K than at T = 0. 

Entropy, denoted by S, is a state function that measures molecular disorder, or randomness. The entropy of a system (reactants plus products) increases (AS is positive) for the following processes phase transitions that convert a solid to a liquid or a liquid to a gas reactions that increase the number of gaseous molecules dissolution of molecular solids and certain salts in water raising the temperature of a substance expansion of a gas at constant temperature. 

Chapters 13 and 14 use thermodynamics to describe and predict phase equilibria. Chapter 13 limits the discussion to pure substances. Distinctions are made between first-order and continuous phase transitions, and examples are given of different types of continuous transitions, including the (liquid + gas) critical phase transition, order-disorder transitions involving position disorder, rotational disorder, and magnetic effects the helium normal-superfluid transition and conductor-superconductor transitions. Modem theories of phase transitions are described that show the parallel properties of the different types of continuous transitions, and demonstrate how these properties can be described with a general set of critical exponents. This discussion is an attempt to present to chemists the exciting advances made in the area of theories of phase transitions that is often relegated to physics tests. 

---