QENS and FTIR studies on binding states of benzene molecules adsorbed in zeolite HZSM-5 at room temperature

Fourier-transform infrared (FTIR) spectroscopy and quasi-elastic neutron scattering (QENS) were employed for monitoring of the binding states of benzene molecules, adsorbed in HZSM-5 zeolite at 300 K and for loadings of 0.6 to 7 molecules per unit cell. While the in-plane combination C-C and C-H stretching bands of adsorbed benzene remained una.ected, a splitting was observed in the out-of-plane C-H bending vibrational bands, a feature reported for the transformation of benzene from liquid to solid phase. Also, the intensity ratio of the in-plane C-C stretching band (ν19 of adsorbed benzene at 1479 cm-1 and the bands in the region ) 3100-3035 cm-1 due to fundamentals and combination C-C and C-H stretching vibrations indicated a trend observed typically for a condensed phase of benzene. No shift was observed in the frequency of the above-mentioned IR bands when zeolite samples exchanged with Na+ or Ca2+ were employed. QENS results suggest that the benzene molecules occluded in zeolitic pores (~3 molecules per unit cell) undergo a 6-fold rotation but their translation motion is too slow. Also, a high residence time of 16.5 ps was observed for the benzene entrapped in HZSM-5, compared to a time of ~2.5 ps reported for the liquid and ~19 ps for the solid state of benzene. These results reveal again the compression of the benzene molecules on adsorption in zeolitic pores. It is suggested that the benzene molecules confined in cavities experience a strong intermolecular interaction, giving rise eventually to their clustered state depending on the loading. In the clustered state, benzene molecules are packed with their plane parallel to zeolitic walls and interact with each other through p-electron clouds. No electronic bonding is envisaged between these clusters and the framework or the extra-framework zeolitic sites

Three-Dimensional Elastic Compatibility: Twinning in Martensites

We show how the St.Venant compatibility relations for strain in three dimensions lead to twinning for the cubic to tetragonal transition in martensitic materials within a Ginzburg-Landau model in terms of the six components of the symmetric strain tensor. The compatibility constraints generate an anisotropic long-range interaction in the order parameter (deviatoric strain) components. In contrast to two dimensions, the free energy is characterized by a "landscape" of competing metastable states. We find a variety of textures, which result from the elastic frustration due to the effects of compatibility. Our results are also applicable to structural phase transitions in improper ferroelastics such as ferroelectrics and magnetoelastics, where strain acts as a secondary order parameter

Intermediate states at structural phase transition: Model with a one-component order parameter coupled to strains

We study a Ginzburg-Landau model of structural phase transition in two dimensions, in which a single order parameter is coupled to the tetragonal and dilational strains. Such elastic coupling terms in the free energy much affect the phase transition behavior particularly near the tricriticality. A characteristic feature is appearance of intermediate states, where the ordered and disordered regions coexist on mesoscopic scales in nearly steady states in a temperature window. The window width increases with increasing the strength of the dilational coupling. It arises from freezing of phase ordering in inhomogeneous strains. No impurity mechanism is involved. We present a simple theory of the intermediate states to produce phase diagrams consistent with simulation results.Comment: 16 pages, 14 figure

Droplet Fluctuations in the Morphology and Kinetics of Martensites

We derive a coarse grained, free-energy functional which describes droplet configurations arising on nucleation of a product crystal within a parent. This involves a new `slow' vacancy mode that lives at the parent-product interface. A mode-coupling theory suggests that a {\it slow} quench from the parent phase produces an equilibrium product, while a {\it fast} quench produces a metastable martensite. In two dimensions, the martensite nuclei grow as `lens-shaped' strips having alternating twin domains, with well-defined front velocities. Several empirically known structural and kinetic relations drop out naturally from our theory.Comment: 4 pages, REVTEX, and 3 .eps figures, compressed and uuencoded, Submitted to Phys. Rev. Let

Disorder-Driven Pretransitional Tweed in Martensitic Transformations

Defying the conventional wisdom regarding first--order transitions, {\it solid--solid displacive transformations} are often accompanied by pronounced pretransitional phenomena. Generally, these phenomena are indicative of some mesoscopic lattice deformation that ``anticipates'' the upcoming phase transition. Among these precursive effects is the observation of the so-called ``tweed'' pattern in transmission electron microscopy in a wide variety of materials. We have investigated the tweed deformation in a two dimensional model system, and found that it arises because the compositional disorder intrinsic to any alloy conspires with the natural geometric constraints of the lattice to produce a frustrated, glassy phase. The predicted phase diagram and glassy behavior have been verified by numerical simulations, and diffraction patterns of simulated systems are found to compare well with experimental data. Analytically comparing to alternative models of strain-disorder coupling, we show that the present model best accounts for experimental observations.Comment: 43 pages in TeX, plus figures. Most figures supplied separately in uuencoded format. Three other figures available via anonymous ftp

Tweed in Martensites: A Potential New Spin Glass

We've been studying the ``tweed'' precursors above the martensitic transition in shape--memory alloys. These characteristic cross--hatched modulations occur for hundreds of degrees above the first--order shape--changing transition. Our two--dimensional model for this transition, in the limit of infinite elastic anisotropy, can be mapped onto a spin--glass Hamiltonian in a random field. We suggest that the tweed precursors are a direct analogy of the spin--glass phase. The tweed is intermediate between the high--temperature cubic phase and the low--temperature martensitic phase in the same way as the spin--glass phase can be intermediate between ferromagnet and antiferromagnet.Comment: 18 pages and four figures (included

Nucleation in Systems with Elastic Forces

Systems with long-range interactions when quenced into a metastable state near the pseudo-spinodal exhibit nucleation processes that are quite different from the classical nucleation seen near the coexistence curve. In systems with long-range elastic forces the description of the nucleation process can be quite subtle due to the presence of bulk/interface elastic compatibility constraints. We analyze the nucleation process in a simple 2d model with elastic forces and show that the nucleation process generates critical droplets with a different structure than the stable phase. This has implications for nucleation in many crystal-crystal transitions and the structure of the final state

Random Field Models for Relaxor Ferroelectric Behavior

Heat bath Monte Carlo simulations have been used to study a four-state clock model with a type of random field on simple cubic lattices. The model has the standard nonrandom two-spin exchange term with coupling energy $J$ and a random field which consists of adding an energy $D$ to one of the four spin states, chosen randomly at each site. This Ashkin-Teller-like model does not separate; the two random-field Ising model components are coupled. When $D / J = 3$, the ground states of the model remain fully aligned. When $D / J \ge 4$, a different type of ground state is found, in which the occupation of two of the four spin states is close to 50%, and the other two are nearly absent. This means that one of the Ising components is almost completely ordered, while the other one has only short-range correlations. A large peak in the structure factor $S (k)$ appears at small $k$ for temperatures well above the transition to long-range order, and the appearance of this peak is associated with slow, "glassy" dynamics. The phase transition into the state where one Ising component is long-range ordered appears to be first order, but the latent heat is very small.Comment: 7 pages + 12 eps figures, to appear in Phys Rev

Modelling avalanches in martensites

Solids subject to continuous changes of temperature or mechanical load often exhibit discontinuous avalanche-like responses. For instance, avalanche dynamics have been observed during plastic deformation, fracture, domain switching in ferroic materials or martensitic transformations. The statistical analysis of avalanches reveals a very complex scenario with a distinctive lack of characteristic scales. Much effort has been devoted in the last decades to understand the origin and ubiquity of scale-free behaviour in solids and many other systems. This chapter reviews some efforts to understand the characteristics of avalanches in martensites through mathematical modelling.Comment: Chapter in the book "Avalanches in Functional Materials and Geophysics", edited by E. K. H. Salje, A. Saxena, and A. Planes. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-45612-6_

Simulations of cubic-tetragonal ferroelastics

We study domain patterns in cubic-tetragonal ferroelastics by solving numerically equations of motion derived from a Landau model of the phase transition, including dissipative stresses. Our system sizes, of up to 256^3 points, are large enough to reveal many structures observed experimentally. Most patterns found at late stages in the relaxation are multiply banded; all three tetragonal variants appear, but inequivalently. Two of the variants form broad primary bands; the third intrudes into the others to form narrow secondary bands with the hosts. On colliding with walls between the primary variants, the third either terminates or forms a chevron. The multipy banded patterns, with the two domain sizes, the chevrons and the terminations, are seen in the microscopy of zirconia and other cubic-tetragonal ferroelastics. We examine also transient structures obtained much earlier in the relaxation; these show the above features and others also observed in experiment.Comment: 7 pages, 6 colour figures not embedded in text. Major revisions in conten