Equilibrium crystal shapes in the Potts model

The three-dimensional $q$-state Potts model, forced into coexistence by fixing the density of one state, is studied for $q=2$, 3, 4, and 6. As a function of temperature and number of states, we studied the resulting equilibrium droplet shapes. A theoretical discussion is given of the interface properties at large values of $q$. We found a roughening transition for each of the numbers of states we studied, at temperatures that decrease with increasing $q$, but increase when measured as a fraction of the melting temperature. We also found equilibrium shapes closely approaching a sphere near the melting point, even though the three-dimensional Potts model with three or more states does not have a phase transition with a diverging length scale at the melting point.Comment: 6 pages, 3 figures, submitted to PR

Using the Wigner-Ibach Surmise to Analyze Terrace-Width Distributions: History, User's Guide, and Advances

A history is given of the applications of the simple expression generalized from the surmise by Wigner and also by Ibach to extract the strength of the interaction between steps on a vicinal surface, via the terrace width distribution (TWD). A concise guide for use with experiments and a summary of some recent extensions are provided.Comment: 11 pages, 4 figures, reformatted (with revtex) version of refereed paper for special issue of Applied Physics A entitled "From Surface Science to Device Physics", in honor of the retirements of Prof. H. Ibach and Prof. H. L\"ut

The trajectories of neutral polarizable particles in an inhomogeneous electric field

The trajectories of neutral polarizable particles are curved by an inhomogeneous electric field. This provides a variety of methods for measuring the polarizability (α) of neutrals. Amongst these methods, field electron microscopy seems to have been impaired so far by a lack of precision, despite its broad potentialities. The three-dimensional properties of the trajectories of polarizable particles are examined in this paper in order to determine their importance and their influence on the measurement methods. It is first shown, as a general property, that by introducing a dimensionless parameter λ and by using a scaling law, nearly all experimental situations can be analysed. In the particular case of the field electron or field ion microscope a three-dimensional calculation of the trajectories is made. The results show major differences with those of the previously existing two-dimensional theories. The velocity distribution of the particles is also considered and is found to have a non negligible influence. New graphs of fairly general validity are drawn that can be used to measure α with a field electron microscope. As an example a more correct value of the polarizability of Pb is determined (α = 9.7 ± 2.9 Å3)

Un microscope à électrons de champ pour la mesure de l'émission par les faces individuelles

A field emission microscope including a Faraday cage with a movable hole in the image screen is described. Thus, emission currents from single crystal faces are measured without deformation of the electron trajectories.On décrit un microscope à électrons de champ comportant un cylindre de Faraday dont l'ouverture d'entrée est mobile dans le plan de l'écran. On peut ainsi mesurer le courant d'émission de chaque face d'un monocristal sans déformation des trajectoires électroniques

THE ANISOTROPY OF THE SURFACE ENERGY OF NICKEL MEASURED BY T.E.M. OF FIELD EMITTERS

La pointe de nickel d'un microscope à émission de champ est amenée à prendre une forme stationnaire en ultra-vide. Cette forme est ensuite examinée par transfert de la pointe dans un microscope électronique à transmission. On montre que la calotte au sommet d'une pointe bulbeuse coïncide avec la forme d'équilibre d'un cristal isolé de nickel. L'anisotropie de l'énergie de surface du nickel est déterminée en fonction de l'orientation cirstalline.The stationary form of a clean nickel tip is produced in a field electron microscope (FEM) under ultra-high vacuum. The shape of the tip is then visualized in a transmission electron microscope (TEM). It is shown that the cap around the apex of a bulbous tip closely approximates the equilibrium shape of an isolated nickel crystal. The anisotropy of the surface energy (γ) of nickel is measured as a function of the crystallographic orientation

Une méthode améliorée de mesure de la polarisabilité des atomes libres à l'aide du microscope électronique de champ

The trajectories of neutral atoms are curved near the tip of a field electron microscope, due to their polarization in the inhomogeneous electric field. This phenomenon has permitted a rough measurement of the polarizability of atoms (Drechsler an Müller). We have now generalized the theory and modified the method of measurement in order to improve the precision and to simplify the application. It is found that the trajectories depend on one parameter which includes the polarizability (α), the mass, the initial velocity of the particle and the electric field strength at the tip apex. α can be determined if one measures the two times which are necessary to obtain the same degree of coverage on one face of the tip by adsorption of the beam atoms with and without field. The degree of coverage is monitored by measuring the field electron current emitted from this face. As an example, the method is used to measure the polarizability of Pb ; the result is : α = 19,5 ± 6 Å3 which is in agreement with theoretical estimations.Les trajectoires des atomes neutres sont courbées près de la pointe d'un microscope électronique de champ, à cause de leur polarisation par le champ électrique inhomogène. Ce phénomène a permis de déterminer la polarisabilité α des atomes du jet (Drechsler et Müller). Nous avons généralisé la théorie et modifié la méthode de mesure pour améliorer la précision et simplifier l'utilisation. On trouve que la forme des trajectoires dépend uniquement d'un paramètre qui inclut la polarisabilité (α) la masse, la vitesse initiale et le champ électrique au sommet de la pointe. On peut déterminer la polarisabilité si l'on mesure les deux temps nécessaires pour déposer sur une face de la pointe, à l'aide d'un jet de flux constant, le même degré de recouvrement avec et sans champ. La méthode a été appliquée à l'atome de plomb ; on a obtenu : α = 19,5 ± 6 Å3, ce qui est en accord avec les estimations théoriques

A Reflection Electron Microscopy Investigation of the Divergence of the Mean Correlated Difference of Step Displacements on a Si(111) Vicinal Surface

A Si(111) vicinal (misorientation $\approx 0.6$) is studied by in situ Reflection Electron Microscopy at 1173 K. A statistical study is done of the distances between pairs of $m^{\rm th}$ neighbours in a step train. The mean correlated difference of the step displacements from their mean positions $G(m)=$ is determined as a function of $m$. Evidence is given for the roughness of the surface. A logarithmic behaviour of $G(m)$ versus $m$ is demonstrated unambiguously up to $m=7$. Quantitative agreement is found with the theoretical predictions of Villain, Grempel and Lapujoulade. For more distant pairs of steps a different behaviour is demonstrated: $G(m)$ increases faster than Log$(m)$, a fact already found by another author