Fractional Change In Density Research Articles

Solid-liquid transition in polydisperse Lennard-Jones systems

We study melting of a face-centered crystalline solid consisting of polydisperse Lennard-Jones spheres with Gaussian polydispersity in size. The phase diagram reproduces the existence of a nearly temperature invariant terminal polydispersity (δ(t) =/~ 0.11), with no signature of reentrant melting. The absence of reentrant melting can be attributed to the influence of the attractive part of the potential upon melting. We find that at terminal polydispersity the fractional density change approaches zero, which seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction the system undergoes a sharp transition from crystalline solid to the disordered amorphous or fluid state with increasing polydispersity. This has been quantified by second- and third-order rotational invariant bond orientational order, as well as by the average inherent structure energy. The translational order parameter also indicates a similar sharp structural change at δ =/~ 0.09 in case of T(*) = 1.0, φ = 0.58. The free energy calculation further supports the sharp nature of the transition. The third-order rotationally invariant bond order shows that with increasing polydispersity, the local cluster favors a more icosahedral arrangement and the system loses its local crystalline symmetry. Interestingly, the value of structure factor S(k) of the amorphous phase at δ =/~ 0.10 (just beyond the solid-liquid transition density at T(*) = 1) becomes 2.75, which is below the value of 2.85 required for freezing given by the empirical Hansen-Verlet rule of crystallization, well known in the theory of freezing.

Crystallization of a Yukawa fluid via a modified weighted density approximation with a solid reference state

We investigate the freezing behavior of particles interacting with a Yukawa potential using extensions of the Denton and Ashcroft modified weighted density approximation (MWDA) model of density functional theory [A. R. Denton and N. W. Ashcroft, Phys. Rev. A 39, 470 (1989)]. An attempt is made to incorporate properties of the static solid into the fluid-based MWDA model via our previous model for the crystallization of inverse nth-power fluids [D. C. Wang and A. P. Gast, J. Chem. Phys. 110, 2522 (1999)], as well as a model that includes the Einstein vibrations of the localized particles. Both extensions yield improvements over the MWDA model in terms of coexisting densities and the ability to stabilize a body-centered cubic solid compared with computer simulation data. The fractional change in density upon freezing also compares favorably with results from available simulation studies and those for the inverse nth-power system. Reasons for the differences in results obtained for freezing properties of the Yukawa system among computer simulation data, theoretical approaches, and experimental studies are discussed.

Properties of crystallizing soft sphere systems

In this paper, we explore the similar behaviour of the Yukawa and power law systems at crystallization. This is done within the context of our density functional theory model, the modified weighted density approximation with a static solid reference state. Some issues we probe include the stable solid crystalline structure at equilibrium, the fractional change in density upon crystallization, the Lindemann ratio of the equilibrium solid and the magnitude of the first peak of the structure factor at freezing. We find many similarities between these two classes of potentials. We also compare our findings with computer simulation and experimental results. While the theoretical and simulation results in general agree, there exists some discrepancies between these results for the Yukawa system and the experimental findings for colloidal suspensions.

Equilibrium and Shear Induced Nonequilibrium Phase Behavior of PMMA Microgel Spheres

Polymethylmethacrylate (PMMA) spheres suspended in benzyl alcohol are found to swell to more than two times that of their dry radius and have been observed to undergo an equilibrium phase transition from liquid to crystalline structure with increasing concentration. The width of the coexistence region is found to be narrower by nearly half compared to simulation results for hard sphere systems. Comparison of the measured freezing point and fractional density change upon melting with those calculated from soft sphere simulations are consistent with a purely repulsive interparticle potential on the order of 1/r20. Analysis of powder pattern scattering profiles from samples in the crystallized region of the equilibrium phase diagram indicates crystallites made up of a registered random stacking of hexagonal close packed planes, similar to that found in monodisperse suspensions of hard spheres. With the application of oscillatory shear, nonequilibrium microstructures similar to those found in model hard sphere systems have been observed in these suspensions.

Solid-fluid equilibrium in a nonlinear hard sphere triatomic model of propane

We describe a study of the phase diagram of a nonlinear triatomic molecule with hard sphere interactions between the sites using isobaric ensemble Monte Carlo simulations. The model is constructed so as to serve as a hard sphere interaction site model of propane. Several different crystal structures were used to initialize the solid phase simulations. An apparently optimum crystal geometry was located by allowing the Monte Carlo simulation cell shape to fluctuate. The fluid phase was found to be stable over a range of volume fractions, which is 35% greater than for a system of hard spheres with the same molecular volume. The fractional density change on freezing is about 4%. When the free energy for the model is used in a generalized van der Waals theory of solid–fluid equilibrium it predicts low values of the triple point temperature and fractional density change on freezing which are qualitatively similar to those for propane.

Analytic embedded-atom potentials for fcc metals: Application to liquid and solid copper.

A simple analytic embedded-atom model that includes more than nearest neighbors is presented. Parameters for Cu, Ag, Au, Ni, Pd, and Pt have been obtained. The model has been applied to study the thermodynamic properties of copper with molecular dynamics. The calculated fractional density change on melting, heat of fusion, linear coefficients of thermal expansion, and heat capacities above room temperature are in good agreement with experimental results.

Theory of freezing in simple systems.

The transition parameters for the freezing of two one-component liquids into crystalline solids are evaluated by two theoretical approaches. The first system considered is liquid sodium which crystallizes into a body-centered-cubic (bcc) lattice; the second system is the freezing of adhesive hard spheres into a face-centered-cubic (fcc) lattice. Two related theoretical techniques are used in this evaluation: One is based upon a recently developed bifurcation analysis; the other is based upon the theory of freezing developed by Ramakrishnan and Yussouff. For liquid sodium, where experimental information is available, the predictions of the two theories agree well with experiment and each other. The adhesive-hard-sphere system, which displays a triple point and can be used to fit some liquids accurately, shows a temperature dependence of the freezing parameters which is similar to Lennard-Jones systems. At very low temperature, the fractional density change on freezing shows a dramatic increase as a function of temperature indicating the importance of all the contributions due to the triplet direction correlation function. Also, we consider the freezing of a one-component liquid into a simple-cubic (sc) lattice by bifurcation analysis and show that this transition is highly unfavorable, independent of interatomic potential choice. The bifurcation diagrams for the three lattices considered are compared and found to be strikingly different. Finally, a new stability analysis of the bifurcation diagrams is presented.

The modern theory of crystallization and the Hansen-Verlet rule

A cluster expansion of an order parameter distribution function is introduced into the recent theory of crystallization of classical fluids. This allows us to demonstrate the purely geometric origin of the empirical Hansen-Verlet rule of crystallization (max. S(k) ⋍ 2·85 or c(k ⋍ 0·65 with S(k) = (1 - c(k)-1). Using moment expansions (whose convergence is assumed), we find that the minimum value for which bifurcation into a crystalline solution of the same thermodynamic potential as the coexisting fluid solution is possible within our perturbation scheme corresponds to c(k) = 0·69 for a f.c.c. structure and to 0·59 for a b.c.c. structure with k equal to the smallest reciprocal lattice vector of the corresponding cubic structure. To this end we have considered the limit where the fractional density change and the fluid's compressibility vanish in such a way that their ratio remains constant in order to guarantee the first order character of the transition. This limit allows us to work out the theory without any input data.

Molecular field theory of nematics: density functional approach. I. Bulk effects

The molecular field theory of nematics is rephrased in density functional language. The free energy in the nematic state is expressed as a functional expansion around the isotropic state in powers of the nematic order parameters Pl and the fractional density change eta at the isotropic-nematic transition. The crucial quantities in the expansion are spherical harmonics of the direct correlation functions in the isotropic state. Sensible approximations to these direct correlation functions lead to other well known formulations of nematic field theory. An exact (in the authors' approximation) result for eta is obtained in terms of the potential parameters Ul and the order parameters Pl at the phase transition. The authors discuss the relationship of their approach to other microscopic theories of nematics. The theory can be extended to discuss inhomogeneous systems.

Estitnation of Liquid Metals Density

AbstractA simple relation is reported for estimating DM, the density of liquid metals at their melting point, i.e. DM = K.D293, where K is a constant with a value of 0.914 and D293 is the density of the polycrystalline metal at 293 K. The following equation has been developed for the estimation of the temperature dependence of density Λ under the assumption that the fractional change in density between O K and the absolute boiling temperature, TB, is the same for all elements.Λ = K·D293/(TB/A)− TM where A is a constant with a value of 0.218 and TM is the absolute melting temperature. The validity of the above equation has been checked in 52 metals and values of DM and Λ are obtained for 18 further metals for which experimental data do not exist. Resume Une relation simple est etablie afin d'estimer DF la densite des metaux liquides a leur point de fusion,' i.e. DF = K·D293, ou K est une constance egale a 0.914 et D293 est la densite du metal polycristallin a 293°K. Toutelois, l'equation suivante a ete dev...

A simple relationship between the temperature dependence of the density of liquid metals and their boiling temperatures

For elemental metals, other than those in Groups VIII and IIB, there exists a simple rela-tionship between the temperature dependence of the liquid density, Λ [=(δD/δT)p], and the boiling temperature,TB. It is shown that the fractional change in density between 0 K andTB appears to be constant;i .e ., ATB/d00 =-0.23. D00 is a scale factor defined by Doo =DM- ΛTm, whereDm is the density of the liquid at the absolute melting temperature, TM. This relationship has been used to estimate A for eight high melting point elements for which no experimental data exist.

Density of He II in Superfluid Flow

The density of He II in supercritical, superfluid flow has been measured by a sensitive capacitance technique in the temperature range from 1.3 to 1.8 K. The average density of the liquid decreased with increasing superfluid velocity. The largest fractional density change observed was $\frac{\ensuremath{\Delta}\overline{\ensuremath{\rho}}}{\ensuremath{\rho}}=\ensuremath{-}9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ at a velocity of 7.75 cm/sec. The results can be accounted for adequately by the two-fluid, thermohydrodynamic equations of motion utilizing the expressions for the nonlinear, superfluid dissipation force and the mutual friction force.

The Mechanism of Cavity Growth in Copper during High-Temperature Fatigue

During the fatigue of copper at elevated temperatures cavities form on grain boundaries and cause a decrease in density. The fractional change in density is directly proportional to time for tests in which the plastic strain amplitude remains constant. In constant-stress tests, when the stress is sufficient to cause appreciable hardening, the fractional change in density is approximately proportional to (time)⅔. For the majority of the tests the activation energy of the growth process is 24.2 kcal.mole−1; this and other evidence suggests that growth depends on a grain-boundary diffusion mechanism as well as on the migration of vacancies created by fatigue. The results are interpreted on the basis of a model in which defects absorbed by grain-boundary migration contribute to cavity growth.

The Mechanism of Cavitation in Copper during Creep

Abstract During creep of copper, cavities form on grain boundaries and cause a decrease in density. The fractional change in density during creep is proportional to (time)1.5, in reasonable agreement with previous work. Cavities are nucleated continuously during creep, the number present being proportional to (time)0.5. The results suggest that an individual cavity increases its volume at a constant rate in keeping with a growth mechanism that involves diffusion of vacancies along the grain boundary to the cavity surface. When tensile creep specimens are compressed slowly at 400° C or at room temperature the density increases by similar amounts, suggesting that sintering does not occur by reversed grain-boundary sliding. The cavities formed by creep become stabilized by the diffusion of gas into them.

The mechanism of cavitation in magnesium during creep

Abstract During the creep of magnesium, cavities form on some grain boundaries, limiting the ductility of the material and causing its density to decrease. It is shown that cavitation is eliminated if a hydrostatic pressure is superimposed which is equal to the creep stress. If the hydrostatic pressure is applied after cavities are already present in the material, continuing creep results in negligible density change and existing cavities do not continue to grow. When hydrostatic pressure is applied throughout the early stages of creep and is then removed, the subsequent cavitation develops at a rate which is unaffected by the prior deformation. The fractional change in density during creep is approximately proportional to the duration of creep to the power of 2·5 increasing to about 4 immediately prior to fracture. This rate of change of density is greater than can be accounted for by the growth of a constant number of cavities by vacancy condensation and suggests a progressive creation of nuclei. The number of cavities is observed to increase with strain and the change in density during creep is interpreted in terms of a continuous formation of cavities which grow exclusively by condensation of vacancies which diffuse from grain boundaries approximately perpendicular to the applied stress.

Effect of deformation on the position of X-ray diffraction lines from gold

Abstract X-ray measurements have been made on gold deformed by 75% in compression. The probability of (deformation) stacking faults is less than 0.0015, a value obtained from the shift in positions of the Debye-Scherrer lines. Any change in lattice parameter corresponding to the fractional change in density (1.2 × 10−4) observed by Clarebrough et al. (1962) is masked by a large macroscopic strain (4.7 × 10−4, tensile) in the surface of the specimen.