Two different adsorption phenomena are studied using, in particular, Monte Carlo techniques: (i) Lattice gas models with competing interactions of ANNNI-type are shown to describe various uniaxial commensurate and incommensurate structures as observed in chemisorbed overlayers such as H on Fe(110) and O2 on Pd(110).

(ii) At interfaces of multi-state models (Potts, spin-i Ising models) nonboundary states are adsorbed preferably; critical properties of this “wetting” phenomenon are investigated.

We propose a simple modification of the Fisher droplet model which, unlike classical nucleation theory, reproduces very well some Monte Carlo equilibrium cluster distributions P1 for the three-dimensional Ising or lattice gas model. It then follows that p1(h) /p1(h=0) = A exp(− η l) where η ∝hl/Y, y≃0.45, when the magnetic field h is small enough, as suggested from the consideration of an effective cluster size ly , while η seems rather proportional to h at larger values of the field, as implied by some exact results.

The elastic energy of a solid solution of atoms of different sizes can be written as a Fourier sum with coefficients as a function of position in reciprocal space. Each coefficient is made up of three components. The first one is an energy associated with taking atoms of the pure elements and placing them randomly on the average lattice o f the alloy. The second one is an elastic gradient energy associated with composition fluctuations and which is proportional to the second derivative of the dispersion curve. The third is the relaxation energy concerned with the motion of atoms away from the average lattice to more comfortable positions. Because of the contribution of the elastic gradient energy, it is shown that the shape of the phonon dispersion curve can affect precipitation or ordering in a solid solution.

Finite-size scaling is applied to the Hamiltonian version of the asymmetric Z3-Potts model. Results for the phase boundary of the commensurate region and for the corresponding critical index ν are presented. It is argued that there is no Lifshitz point, the incommensurate phase extending down to small values of the asymmetry parameter.

We utilize a modern continuum mechanics framework to reconsider an old problem for fluid interfaces, also addressed by Maxwell and van der Waals. We prove that their results need not be valid necessarily. This conclusion is arrived at as a consequence of questioning the existence of thermodynamic potentials and the validity of usual thermodynamic ,relations within unstable (spinodal) regions. One central result is that Maxwell's equal area rule needs not be valid and certain statistical models are shown to be internally inconsistent. Precise conditions for the validity of Maxwell's rule and the variational theory of van der Waals are established in terms of the coefficients defining the interfacial stress. Finally, a generalized continuum thermodynamics framework is developed which provides an alternative derivation of van der Waals variational theory and properly extends it to dynamic situations. However, other possibilities exist which allow a thermodynamics of fluid interfaces not necessarily restricted by the conditions of Maxwell and van der Waals. The results of the paper could be viewed as a convincing argument to utilize this framework (with the necessary modifications) to interpret more complex phenomena of phase transformations.

In the framework of regular solution model, we test the validity of some usual approximations (QC, CVM) of entropy in (disordered) binary alloys by Monte Carlo simulation. The validity range of these approximations are explored both in alternant and nonalternant lattice with ferro- and antiferromagnetic coupling. The CVM tetrahedron approximation is also analysed on a structure containing only tetrahedra : the 120 polytope [8] in 3d curved space.

Over the past decade, a great deal of effort has gone into understanding the properties of spin glasses [1,2]. However, because these are rather unique systems which show simultaneously apparent phase transition as well as metastable or glassy behavior, progress has been slow. Though it was initially believed that spin glasses could be treated as if they had a true equilibrium phase transition, we now recognize that this cannot be the whole story. Recently, it has become clear that spin glasses are very complex systems, in which irreversible and time dependent effects play an important role. We now know that one must go beyond the regime of validity of equilibrium thermodynamics. In this paper, we will discuss the mountinq evidence, both experimental and theoretical, for why nonequilibrium approaches are essential in order to understand spin glasses.

The studied transformation is associated with the decomposition reaction of brucite-type hydroxides into the corresponding oxide. It is shown, by various techniques (X-ray and neutron diffraction, Raman Spectroscopy, proton conductivity) that some modifications take place in the hydroxide structure before its transformation into the oxide structure,i.e., at a temperature lower than the transformation temperature. A mechanism is proposed to account for the experimental data.

Phase diagrams, for systems undergoing one or several incommensurate and lock-in transitions, are discussed in the framework of the Landau theory of phase transitions. It is shown that their essential features can be deduced from the explicit forms of the free-energy density ø and the k-dispersion of the coefficient α(→k)of the quadratic contribution of the order-parameter components in ø. Two families of phase diagrams are distinguished depending on symmetry considerations.

In recent years a separate branch of electron microscopy, which can conveniently be termed “Solid State Electron Microscopy” has evolved into a discipline of its own, which makes use of a set of techniques such as

- diffraction contrast electron microscopy

- high resolution transmission electron microscopy

- selected area electron diffraction

- convergent beam electron diffraction

- optical diffraction of high resolution electron micrographs

and which allows to provide information on a wide variety of solid state phenomena. With the availability of microscopes with a resolution equal to interatomic distances its field of application has recently been extended greatly.

The techniques for measurement and analysis of the absolute intensity from concentrated alloys have now improved to the point where reliable analysis for local order and displacements can be performed in reasonable times, for both clustering and ordering. Coupling the results with computer simulation provides information on the details of chemical fluctuations and, as well, tests of modern theories of transformations. In some cases, the results have been confirmed via direct imaging (FIM, HRTEM). The role of this information in our understanding of phase transformations is reviewed, and suggestions for future studies are given.

Atomic structures of G.P. zones and solute clusters in Al-Cu and Cu-Be alloys are studied by the atom resolution electron microscope images. The images of plate-like G.P. zones appear as dotted images with various brightnesses along (200) lattice planes. The solute clusters are also observed along (111) lattice planes.

Nine crystal structures, taken from literature, are compared with each other and with the room temperature structure of Rb2ZnBr4. Compared are the modulation functions and some pronounced local distortions. It appears that the ten structures have strikingly similar cooperative rotations of the anion tetrahedra.

High-resolution electron microscope observations were carried out on the cation-deficient spinel compounds Ga2/3Cr2S4 and InCr5/3S4. X-ray analysis of both compounds indicates that there exist 1/3 vacancy per formula unit in 8a positions. It was also found that the vacancy ordering occurs in Ga2/3Cr2S4 below about 1100°C, as well as in InCr5/3S4. Lattice images of vacancy ordered and disordered structures were obtained. In some electron micrographs of ordered InCr5/3 S4, several domains of disordered region were observed in between the matrix of the ordered structure. In a [110] image, characteristic lattice defects were observed on the (110) plane.

Crystalline 9-hydroxyphenalenone is monoclinic between 145 K and the melting point at 475 K. The space group is P21 below 255 K, P21/c between 255 K and 380 K, and I2/c above 385 K. A model for the 255 K transition involves inplane rotations of about 40° for one quarter of the molecules. Further rotation and translation takes place at the 380–385 K phase transitions. All three phases are expected to be ferroelastic, but at present only the unit cell of the room temperature phase has been reversibly reoriented. The spontaneous strain decreases from 0.24 at 145 K through 0.18 at room temperature to 0.14 at 430 K, assuming a tetragonal prototype. Domain walls are temperature dependent with orientation (1.86, 0, 1) and (1, 0, −1.86) at 298 K. Ferroelastic transformation proceeds by a slip process, approximately in the molecular planes. A prototype common to all three phases can be derived with space group P41. Macroscopically, the transformation is accompanied by a remarkable change of shape; if unfractured, the crystals exhibit shape memory.

The process of the phase transformation of evaporated films of TiO0.5 has been demonstrated by in situ annealing using an electron microscope. Single crystals of the δ-phase, whose structure is identified with Andersson's hexagonal model, precipitate during annealing. Crystal structure images in cooperation with the calculated images reveal that the inner parts of the δ-phase crystal have various thickness. The transition structures I and II having ordered vacancies of titanium and oxygen respectively also appear on annealing. The difference in the distortion of their lattices from the parent rock-salt type lattice suggests that the effective atomic volume of titanium is larger than that of oxygen in the crystal of the transition structure. The observed transformations, α-phase → δ ;phase → transition structure, are explained by consideration of the structural relationships among these phases.

The domain structure and the commensurate - incommensurate transition of some niobates, with general formula A2BNb5O15 where A = Ba, Sr or Pb and B = Na or K, are examined by using electron microscopy and electron diffraction methods. A model of the commensurate phase at room temperature is proposed and the natureof the incommensurate phase is discussed.

It is shown that the detailed investigation of an irreversible SPT implies the combination of X-ray, neutron and electron diffraction data. This diffraction analysis is applied to K Al F4 and Rb Al F4. There is a good agreement between the three diffraction techniques in the case of Rb Al F4 where the SPT is reversible. On the other hand, for K Al F4 room temperature quadratic phase, electron diffraction exhibits exta spots which are not evidenced by X-ray and neutron diffraction. Finally the assumption of an orthorombic lattice from neutron scattering for the low temperature phase is consistant with electron diffraction results.

The displacement of a particular atom in a modulated crystallographic structure can be described in terms of a Fourier Series. In the harmonic single wave vector approximation, the structure factor can be written as a function of the atomic displacement vectors. Such expressions are however not valid in the multi-wave-vector case. We propose a general description for the modulation of displacement where each scattering center (atom) is distributed on several sites whose population is modulated. In the paper, we will show that approach is well suited for computing. We have developed a general least squares program which has been applied to the modulated phase of αU(T < 43 K) [2].

X-ray and electron diffraction studies have shown that NbTe4 and TaTe4 exhibit a deformation modulated structure. The distortion can be described by a modulation vector which also has components Pernendicular to the chain axis (c-axis). The modulation is commensurate along the c-axis of the basic tetragonal structure in the case of TaTe4 and incommensurate for NbTe4. Two main sets of satellite reflections could be distinguished in electron diffraction, which are in a first-second order relationship, as established by X-ray structure refinement. Additional reflections in the NbTe4 electron diffraction pattern appear upon cooling down to liquid nitrogen temperature, although no changes of the incommensurability with temperature were observed. Physical measurements showed a metallic behaviour for both comnounds with ptype dominance above 60K. No evidence was found for the occurrence of a Peierls-transition to an insulating or semiconducting state, nor did the temperature denendence of the electric and magnetic quantities show an anomalous behaviour.

A deformation model is proposed in which nart of the transition-metal-atoms undergo displacements along the chain axis in order to form pairs and triplets.

This distortion is associated with a relaxation of the chalcogen squares.