Criticality in multicomponent spherical models : results and cautions

To enable the study of criticality in multicomponent fluids, the standard spherical model is generalized to describe an \ns-species hard core lattice gas. On introducing \ns spherical constraints, the free energy may be expressed generally in terms of an \ns\times\ns matrix describing the species interactions. For binary systems, thermodynamic properties have simple expressions, while all the pair correlation functions are combinations of just two eigenmodes. When only hard-core and short-range overall attractive interactions are present, a choice of variables relates the behavior to that of one-component systems. Criticality occurs on a locus terminating a coexistence surface; however, except at some special points, an unexpected ``demagnetization effect'' suppresses the normal divergence of susceptibilities at criticality and distorts two-phase coexistence. This effect, unphysical for fluids, arises from a general lack of symmetry and from the vectorial and multicomponent character of the spherical model. Its origin can be understood via a mean-field treatment of an XY spin system below criticality.Comment: 4 figure

Shape relaxation of epitaxial mesa for finite-size strain-engineering

Silicon-Germanium (Si$_{1-x}$Ge$_x$) layers are commonly used as stressors in the gate of MOSFET devices. They are expected to introduce a beneficial stress in the drift and channel regions to enhance the electron mobility. When reducing the gate lateral size, one of the major issues is the stress relaxation which results in a significant decrease in the electron mobility. We report a new morphological evolution of a strained epitaxial SiGe nanolayer on a silicon gate (mesa) driven by strain inhomogeneity due to finite-size effects. Unlike the self-induced instability of strained films, this evolution arises here due to the elastic inhomogeneity originating from the free frontiers. We analyze the growth dynamics within the thermodynamic surface diffusion framework accounting for elasticity and capillarity, the former being solved in two dimensions thanks to the Airy formalism. The resulting dynamical equation is solved with a decomposition on eigenmodes, and reveals different developments depending upon the mesa geometric parameters. Mass transfer occurs towards the relaxed areas and creates a beading at the nanolayers free surface with either a W or V shape as a function of time and geometry. The evolution is then controlled by the proportions of the structure as well as its scale.Comment: 10 pages, 5 figure

How Multivalency controls Ionic Criticality

To understand how multivalency influences the reduced critical temperatures, Tce (z), and densities, roce (z), of z : 1 ionic fluids, we study equisized hard-sphere models with z = 1-3. Following Debye, Hueckel and Bjerrum, association into ion clusters is treated with, also, ionic solvation and excluded volume. In good accord with simulations but contradicting integral-equation and field theories, Tce falls when z increases while roce rises steeply: that 80-90% of the ions are bound in clusters near T_c serves to explain these trends. For z \neq 1 interphase Galvani potentials arise and are evaluated.Comment: 4 pages, 4 figure

Charge and Density Fluctuations Lock Horns : Ionic Criticality with Power-Law Forces

How do charge and density fluctuations compete in ionic fluids near gas-liquid criticality when quantum mechanical effects play a role ? To gain some insight, long-range $\Phi^{{\mathcal{L}}}_{\pm \pm} / r^{d+\sigma}$ interactions (with $\sigma>0$), that encompass van der Waals forces (when $\sigma = d = 3$), have been incorporated in exactly soluble, $d$-dimensional 1:1 ionic spherical models with charges $\pm q_0$ and hard-core repulsions. In accord with previous work, when $d>\min \{\sigma, 2\}$ (and $q_0$ is not too large), the Coulomb interactions do not alter the ($q_0 = 0$) critical universality class that is characterized by density correlations at criticality decaying as $1/r^{d-2+\eta}$ with $\eta = \max \{0, 2-\sigma\}$. But screening is now algebraic, the charge-charge correlations decaying, in general, only as $1/r^{d+\sigma+4}$; thus $\sigma = 3$ faithfully mimics known \textit{non}critical $d=3$ quantal effects. But in the \textit{absence} of full ($+, -$) ion symmetry, density and charge fluctuations mix via a transparent mechanism: then the screening \textit{at criticality} is \textit{weaker} by a factor $r^{4-2\eta}$. Furthermore, the otherwise valid Stillinger-Lovett sum rule fails \textit{at} criticality whenever $\eta =0$ (as, e.g., when $\sigma>2$) although it remains valid if $\eta >0$ (as for $\sigma<2$ or in real $d \leq 3$ Ising-type systems).Comment: 8 pages, in press in J. Phys. A, Letters to the Edito

Physique statistique des fluides coulombiens classiques et quantiques au voisinage d'une paroi

We study the equilibrium statistical properties (such as density profiles and correlations) of classical and quantum Coulomb fluids near a wall : the latter is impenetrable, compelling effective interactions, and may have electrostatic properties such as dielectric response (with image charges) and/or influence (with a given potential drop between two conducting plates). For classical systems, statistics is dealt with by Mayer expansions, which are made convergent in the thermodynamic limit thanks to partial resummations introducing the screening effect in a systematic way. Thus we have to handle a Debye-Huckel inhomogeneous equation. In the weak-coupling limit, considering properly the possible short distance divergence of the interaction between a particle and the wall, we exhibit the response of charged systems to an external electrostatic field. The results may explain the effective attraction observed for like-charge particles near a wall. For quantum systems, quantum statistics and dynamics are taken into account in a formalism based on path integral and Mayer expansions. The density profiles and correlations are derived for a weakly-degenerated and weakly-coupled plasma near a wall without electrostatic properties. The quantum properties linked to the vanishing of wave functions on the wall appear to be appreciable far away from the wall, over a few classical screening lengths.Cette thèse concerne l'étude analytique des propriétés statistiques d'équilibre (telles que les profils de densité et fonctions de corrélation) des fluides coulombiens classiques et quantiques. au voisinage d'une paroi : celle-ci est impénétrable, contraignant les interactions effectives, et peut présenter des propriétés électrostatiques de réponse (de type diélectrique, avec des charges images) et/ou d'influence (avec une différence de potentiel appliquée entre deux plaques). Pour les systèmes classiques, le traitement statistique est mené en utilisant des développements en graphes de Mayer rendus convergents à la limite thermodynamique grâce à des ressommations partielles : cette technique introduit en fait systématiquement l'effet d'écran. On est alors amené à résoudre une équation de Debye-Hückel inhomogène. Dans la limite de faible couplage, considérant les éventuelles divergence à courte distance et longue portée de l'interaction d'une particule avec la paroi, nous exhibons le comportement des systèmes chargés soumis à un champ électrostatique extérieur. Nous apportons des éléments d'explication de l'attraction observée expérimentalement entre deux charges de même signe en solution au voisinage d'une paroi. Pour les systèmes quantiques, un formalisme basé sur l'intégrale de chemin et inspiré des développements classiques permet de traiter la statistique et la dynamique quantiques des particules. Dans le cadre des plasmas faiblement dégénérés et faiblement couplés, nous obtenons les expressions des profils de densité et de la décroissance algébrique des corrélations le long d'une paroi sans propriété électrostatique. Nous montrons que l'effet d'annulation des fonctions d'onde sur la paroi peut se manifester assez profondément sur quelques longueurs d'écran classiques loin de la paroi

Classical and quantum algebraic screening in a Coulomb plasma near a wall: A solvable model

http://arxiv.org/abs/cond-mat/0311048 ou https://www.irphe.univ-mrs.fr/~jnaqua/Articles/jstatphys99.pdfThe static position correlation in a quantum Coulomb plasma near a wall is studied by means of a model where two quantum charges are embedded in a classical plasma at equilibrium. Three kinds of walls are considered: a wall without electrostatic properties, a dielectric, and an ideal conductor. At large separations y along the wall, the correlation exactly decays as 1/y(3), though no algebraic tail exists for classical charges near an ideal conductor. This tail originates from thermal statistical and purely quantum fluctuations of polarization clouds which are deformed by the geometric constraint due to the wall and by the charges induced by influence inside a wall with electrical properties. The coefficient of the 1/y(3) tail can be calculated explicitly in a weak-coupling and low-delocalization regime. Then classical, diffraction, and purely quantum contributions are disentangled

Dipolar effective interaction in a fluid of charged spheres near a dielectric plate

https://www.irphe.univ-mrs.fr/~jnaqua/Articles/Static correlations in a classical fluid of charged spheres at equilibrium are studied in the vicinity of an insulating wall characterized by its dielectric constant. It is well known that the deformations of screening clouds induced by the presence of the wall result into an effective f(alphaalpha)(')(x,x('))/y(3) interaction in the pair distribution function between two charges e(alpha) and e(alpha)(') located at distances x and x(') from the wall and separated by a large distance y along the wall. We investigate the structure of f(alphaalpha)(')(x,x(')). The method is based on systematic resummations in the Mayer diagrammatics, which are valid both in the bulk and in an inhomogeneous situation. The screened potential phi arising in the formalism happens to coincide with the linearized mean-field approximation for the immersion free energy of two external unit charges. phi is shown to decay as a repulsive f(phi)(x,x('))/y(3) interaction, whatever the density profiles may be. f(phi)(x,x(')) takes a factorized dipolar structure f(phi)(x,x('))=(D) over bar (phi)(x)(D) over bar (phi)(x(')) for distances x and x(') larger than the maximum of the closest approach distances b(alpha)'s to the wall for every species alpha. Moreover, we devise a reorganization of resummed diagrammatics, which is adequate for the determination of the large-distance behavior of correlations, and we prove that, when all species have the same approach distance b to the wall, f(alphaalpha)(')(x,x(');b)=D-alpha(x)D-alpha(')(x(')). In this case, the leading tail of the effective electrostatic interaction between two like charges at the same distance x from a single wall is repulsive. Results are independent of charge magnitudes, of excluded-volume sphere sizes, and of the existence of a surface charge on the wall. It holds whether charges are concentrated at sphere centers or uniformly spread over their surfaces. Comparison is made with an experiment about dilute colloids where the linearized mean-field approximation proves to be relevant. At equilibrium attraction between like charges in confined geometry might arise from purely electrostatic charge-charge interactions only through correlation effects not taken into account in the latter approximation

Quantum Coulomb screening in the vicinity of a wall

The 1999 International Conference on Strongly Coupled Coulomb Systems, Palais du Grand Large, Saint-Malo, France, September 4-10, 1999The static position correlation in a quantum Coulomb plasma is studied at large distances in the vicinity of a wall. Three kinds of walls are considered: a wall without electrostatic properties, a dielectric, and a conductor. At large separations y along the wall, the correlation exactly decays as 1/y(3), though no algebraic tail exists for classical charges near a conductor. This tail originates from thermal statistical and intrinsic quantum fluctuations of screening clouds which are deformed by, geometric constraint due to the wall and by the charges induced by influence inside a wall with electrical properties. The coefficient of the 1/y(3) tail can be calculated explicitly in a weak-coupling and low-degeneracy limit. Then, classical, diffraction and purely quantum contributions are disentangle