A Simple Visual Demonstration of Phase Diagram Concepts for an Introductory Materials Science Course Using Colored Solvents

A simple and effective demonstration to help students comprehend phase diagrams and understand phase equilibria and transformations is created using common chemical solvents available in the laboratory. Common misconceptions surrounding phase diagram operations, such as components versus phases, reversibility of phase transformations, and the lever rule are addressed. Three different binary liquid mixtures of varying compatibility create contrastive phase equilibrium cases, where colorful dyes selectively dissolved in each of corresponding phases allow for quick and unambiguous perceptions of solubility limit and phase transformations. Direct feedback and test scores from a group of students show evidence of the effectiveness of the visual and active teaching tool.

Phase diagram with an enhanced spin-glass region of the mixed Ising–XY magnet LiHo{x}Er{1-x}F{4}

We present the experimental phase diagram of LiHoxEr1-xF4, a dilution series of dipolar-coupled model magnets. The phase diagram was determined using a combination of ac susceptibility and neutron scattering. Three unique phases in addition to the Ising ferromagnet LiHoF4 and the XY antiferromagnet LiErF4 have been identified. Below x = 0.86, an embedded spin-glass phase is observed, where a spin glass exists within the ferromagnetic structure. Below x = 0.57, an Ising spin glass is observed consisting of frozen needlelike clusters. For x ∼ 0.3–0.1, an antiferromagnetically coupled spin glass occurs. A reduction of TC(x) for the ferromagnet is observed which disobeys the mean-field predictions that worked for LiHoxY1-xF4.

Magnetic phase diagram of superantiferromagnetic TbCu2 nanoparticles

The structural state and static and dynamic magnetic properties of TbCu2 nanoparticles are reported produced by mechanical milling under inert atmosphere. The core magnetic structure retains the bulk antiferromagnetic arrangement. The overall interpretation is based on a superantiferromagnetic behavior which at low temperatures coexists with a canting of surface moments and mismatch of antiferromagnetic sublattices of the nanoparticles.

Stretching single-domain proteins: Phase diagram and kinetics of force-induced unfolding

Single-molecule force spectroscopy reveals unfolding of domains in titin on stretching. We provide a theoretical framework for these experiments by computing the phase diagrams for force-induced unfolding of single-domain proteins using lattice models. The results show that two-state folders (at zero force) unravel cooperatively, whereas stretching of non-two-state folders occurs through intermediates. The stretching rates of individual molecules show great variations reflecting the heterogeneity of force-induced unfolding pathways. The approach to the stretched state occurs in a stepwise “quantized” manner. Unfolding dynamics and forces required to stretch proteins depend sensitively on topology. The unfolding rates increase exponentially with force f till an optimum value, which is determined by the barrier to unfolding when f = 0. A mapping of these results to proteins shows qualitative agreement with force-induced unfolding of Ig-like domains in titin. We show that single-molecule force spectroscopy can be used to map the folding free energy landscape of proteins in the absence of denaturants.

Phase diagram of a polydisperse soft-spheres model for liquids and colloids

The phase diagram of soft spheres with size dispersion is studied by means of an optimized Monte Carlo algorithm which allows us to equilibrate below the kinetic glass transition for all size distributions. The system ubiquitously undergoes a first-order freezing transition. While for a small size dispersion the frozen phase has a crystalline structure, large density inhomogeneities appear in the highly disperse systems. Studying the interplay between the equilibrium phase diagram and the kinetic glass transition, we argue that the experimentally found terminal polydispersity of colloids is a purely kinetic phenomenon.

A study of ternary phase diagrams of tungsten and tantalum.

"Materials Laboratory, Contract no. AF 33(616)-5678, Project no. 7351."

Phase diagram of the three-band half-filled Cu-O two-leg ladder

We determine the phase diagram of the half-filled two-leg ladder both at weak and strong coupling, taking into account the Cu d(x)(2)-y(2) and the O p(x) and p(y) orbitals. At weak coupling, renormalization group flows are interpreted with the use of bosonization. Two different models with and without outer oxygen orbitals are examined. For physical parameters, and in the absence of the outer oxygen orbitals, the D-Mott phase arises; a dimerized phase appears when the outer oxygen atoms are included. We show that the circulating current phase that preserves translational symmetry does not appear at weak coupling. In the opposite strong-coupling atomic limit the model is purely electrostatic and the ground states may be found by simple energy minimization. The phase diagram so obtained is compared to the weak-coupling one.

Phase diagram of the bosonic double-exchange model

The phase diagram of the simplest approximation to double-exchange systems, the bosonic double-exchange model with antiferromagnetic (AFM) superexchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions, and variational mean-field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segmentlike ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase transition, only short-range ordering would be found in neutron scattering. Researchers looking for a quantum critical point in manganites should be wary of this possibility. Finite-size scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.

Phase diagram and influence of defects in the double perovskites

The phase diagram of the double perovskites of the type Sr_(2-x)La_(x)FeMoO_(6) is analyzed, with and without disorder due to antisites. In addition to an homogeneous half metallic ferrimagnetic phase in the absence of doping and disorder, we find antiferromagnetic phases at large dopings, and other ferrimagnetic phases with lower saturation magnetization, in the presence of disorder.

Monte Carlo determination of the phase diagram of the double-exchange model

We study the phase diagram of the double exchange model, with antiferromagnetic interactions, in a cubic lattice both at zero and finite temperature. There is a rich variety of magnetic phases, combined with regions where phase separation takes place. We identify phases, intrinsic to the cubic lattice, which are stable for realistic values of the interactions and dopings. Some of these phases break chiral symmetry, leading to unusual features.

The phase diagram of the mercury-indium alloy system

The mercury-indium phase diagram has been investigated over the whole composition range from -78°C to the melting point of indium, using thermal analysis, X-ray and superconductivity techniques. This is believed to be the first application of superconductivity measurements to phase diagram investigations. A compound, HgIn, of very limited range of composition, melts congruently at -19.3°C; and gives rise to eutectics at 61.5 at. % indium and -31°C, and at 34.7% indium and -37.2°C. The β phase extends from 2.5 to 19.1 % indium and has a maximum melting point of -14.2°C at 14.2% indium. It forms a peritectic or eutectic at a temperature indistinguishable from the melting point of pure mercury with a solid solution in mercury containing some, but less than 0.3%, indium. A transition from face-centred tetragonal to face-centred cubic in the indium-rich solid solutions at about 93% indium gives rise to a peritectic at 108°C. The solubility of mercury in this face-centred cubic phase falls from about 22% at-31°C to 13% at -78°C. © 1963.

The effect of Al2O3 on liquidus temperatures of fayalite slags

The effect of alumina on the liquidus temperatures of fayalite slags at iron saturation has been investigated experimentally. Equilibrated synthetic slags were quenched, and the samples were subsequently examined using optical microscopy and electron probe microanalysis (EPMA). The isotherms in the fayalite primary field and boundary lines were determined, and the results were presented in the form of pseudo-ternary phase diagrams of FeO-CaO-SiO2 with 0, 2, 4, and 6 wt pet Al2O3 in the slag. The experimental results show that the alumina addition expands the fayalite primary phase field and decreases the liquidus temperatures in the fayalite primary phase field.