Dipole phase transitions

Stigter and Dill [98] studied phospholipid monolayers at the n-heptane-water interface and were able to treat the second and third virial coefficients (see Eq. XV-1) in terms of electrostatic, including dipole, interactions. At higher film pressures, Pethica and co-workers [99] observed quasi-first-order phase transitions, that is, a much flatter plateau region than shown in Fig. XV-6. 

The appearance of spontaneous polarization in the case of LuTaO is related to volumetric irregularities and ordering of the Li+ - Ta5+ dipoles, as is in the case of the similar niobium-containing compound Li4Nb04F. It can be assumed that the main difference between the two compounds is that the irregularities and the Li+ - Ta5+ dipoles are thermally more stable compared to the niobium-containing system. This increased stability of the dipoles leads to the reversible phase transition at 660°C. 

MS2 Study of magnetic dipole and electric quadrupole interactions, two Ni sites differing in angle between H and EFG axis phase transitions in NiS2.oo NiS 1 96... 

Thus, in a study on the properties of dipole systems, most promise is shown by the representation of chain interactions, which, first, reflects the tendency toward ordering of dipole moments along the axes of chains with a small interchain to intrachain interaction ratio. Second, this type of representation makes it possible to use, with great accuracy, analytical equations summing the interactions of all the dipoles on the lattice. Third, there are grounds for the use of the generalized approximation of an interchain self-consistent field presented in Refs. 62 and 63 to describe the orientational phase transitions. 

The description of phase transitions in a two-dimensional dipole system with exact inclusion of long-range dipole interaction and the arbitrary barriers AUv of local potentials was presented in Ref. 56 in the self-consistent-field approximation. The characteristics of these transitions were found to be dependent on AU9 and the number n of local potential wells. At =2, Tc varies from Pj /2 to Pj as AU9... 

A theoretical treatment of the effect caused by the competition between the sine-like angular-dependent component of the adsorption potential and dipole lateral interaction demonstrated that the values 6 are the same in the ground state and at the phase transition temperature.81 Study of the structure and dynamics for the CO monolayer adsorbed on the NaCl(lOO) surface using the molecular dynamics method has also led to the inference that angles 0j are practically equalized in a wide temperature range.82 That is why the following consideration of orientational structures and excitations in a system of adsorbed molecules will imply, for the sake of simplicity, the constant value of the inclination angle ty =0(see Fig. 2.14) which is due to the adsorption potential u pj,q>j). 

An inference of fundamental importance follows from Eqs. (2.3.9) and (2.3.11) When long axes of nonpolar molecules deviate from the surface-normal direction slightly enough, their azimuthal orientational behavior is accounted for by much the same Hamiltonian as that for a two-dimensional dipole system. Indeed, at sin<9 1 the main nonlocal contribution to Eq. (2.3.9) is provided by a term quadratic in which contains the interaction tensor V 2 (r) of much the same structure as dipole-dipole interaction tensor 2B3 > 0, B4 < 0, only differing in values 2B3 and B4. For dipole-dipole interactions, 2B3 = D = flic (p is the dipole moment) and B4 = -3D, whereas, e.g., purely quadrupole-quadrupole interactions are characterized by 2B3 = 3U, B4 = - SU (see Table 2.2). Evidently, it is for this reason that the dipole model applied to the system CO/NaCl(100), with rather small values 0(6 25°), provided an adequate picture for the ground-state orientational structure.81 A contradiction arose only in the estimation of the temperature Tc of the observed orientational phase transition For the experimental value Tc = 25 K to be reproduced, the dipole moment should have been set n = 1.3D, which is ten times as large as the corresponding value n in a gas phase. Section 2.4 will be devoted to a detailed consideration of orientational states and excitation spectra of a model system on a square lattice described by relations (2.3.9)-(2.3.11). 

Carbon Monoxide. There are close similarities between carbon monoxide and nitrogen. The molecules are isoelectronic, and the bond lengths and dissociation energies are quite comparable. The phase diagrams of the two compounds show the same trends in the moderate pressure range with a variety of phase transitions between essentially alike crystal structures [333], when allowance is made for the lack of the inversion center and the presence of a weak electric dipole moment in carbon monoxide. However, the behavior and stability at higher... 

The ground-state energy terms of this form contribute to the potential energy of the Hamiltonian from Eq. 6, where they act as effective ferroelectric interactions between neighboring PO4 dipoles, thus being responsible for phase transition in KDP and DKDP. In the case of KDP (H atom and Ro = 2.50 A) calculated values of parameters h and I are = llOmeV and = 0.22 A, while in the case of DKDP (D atom and Ro-o = 2.52 A), they are = 58 meV and P = I = 0.22 A. 

However, it seems that possibilities of this model to explain some of the experimental results were not fully explored. Also, this model shows some weaknesses. First, it predicts a value of Tc in DKDP (310 K) that is higher than the experimental value (229 K). Second, the calculated rate of the proton transfer in the PE phase is too low to explain the width of the CP in the neutron scattering spectra of KDP [62]. Third, and most important, because the model assumes that dipoles of PO4 groups lie along the c-axis, it cannot to explain static and dynamic properties of the transverse polarization fluctuations, whose importance in the phase transition mechanism has been supported by several experimental results [8,20,28,31-33]. 

In Figure 2 the ir-A and AV-A plots for SODS on O.OIM NaCl sub-solutions having different pH values are shown. In all cases, phase transitions from liquid-expanded to liquid-condensed state are evident ( ). Acidification of the subsolution Increases the transition pressure but the transition is less pronounced at the lowest pH studied. This is also accompanied by an expansion of the condensed part of the curve. Small negative surface potentials are observed over most areas. The highest potential is obtained for film spread on the pH 2.2 subsolution. For small areas, the surface potential attains a positive value. This may be related to reorientation of the dipole moments of the molecules which occur once a threshold surface concentration is exceeded (O. Mlnglns and Pethlca (7) studied the monolayer properties of SODS on various sodium chloride solutions (0.1, 0.01 and O.OOIM) at 9.5 C, and they showed that the monolayer is only stable on the more concentrated salt solutions (0.1 and O.OIM). In this work, no noticeable... 

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