The Solid-on-Solid Surface Width Around the Roughening Transition

We investigate the surface width $W$ of solid-on-solid surfaces in the vicinity of the roughening temperature $T_r$. Above $T_r$, $W^2$ is expected to diverge with the system size $L$ like $\ln L$. However, close to $T_r$ a clean $\ln{L}$ behavior can only be seen on extremely large lattices. Starting from the Kosterlitz-Thouless renormalization group, we derive an improved formula that describes the small $L$ behavior on both sides of $T_r$. For the Discrete Gaussian model, we used the valleys-to-mountains-reflections cluster algorithm in order to simulate the fluctuating solid-on-solid surface. The base plane above which the surface is defined is an $L \times L$ square lattice. In the simulation we took $8\leq L\leq 256$. The improved formula fits the numerical results very well. {}From the analysis, we estimate the roughening temperature to be $T_r = 0.755(3)$.Comment: 9 pages, LaTeX (no figures), FSU-SCRI-93-67, CERN-TH.6893/9

Theory of vapor phase nucleation in binary mixtures of water and sulfuric acid.

An expression for the nucleation rate of a binary vapor mixture of H2O and H2SO4 at 25°C is derived which explicitly considers the contribution of H2SO4 hydrates to the droplet growth process. The continuum approximation used in earlier binary rate treatments has been abandoned in favor of treating the droplet composition in a discrete fashion. Rates of nucleation are calculated for a H2O–H2SO4 vapor mixture at 50%, 200%, and 300% relative humidities for various H2SO4 vapor activities. A finite nucleation rate is predicted with a relative humidity of 50% and a monomer H2SO4 vapor activity of 10−3. This translates to a vapor pressure of monomer H2SO4 of 3.6×10−7 mm Hg or 0.5 ppb of pure H2SO4 at 1 atm. At higher relative humidities (i.e., 300%), a finite nucleation rate is predicted for monomer H2SO4 concentrations of ∼0.04 ppt. This represents a vapor pressure of 3.2×10−11 mm Hg for monomer H2SO4

Logarithmic Corrections in the 2D XY Model

Using two sets of high-precision Monte Carlo data for the two-dimensional XY model in the Villain formulation on square $L \times L$ lattices, the scaling behavior of the susceptibility $\chi$ and correlation length $\xi$ at the Kosterlitz-Thouless phase transition is analyzed with emphasis on multiplicative logarithmic corrections $(ln L)^{-2r}$ in the finite-size scaling region and $(ln \xi)^{-2r}$ in the high-temperature phase near criticality, respectively. By analyzing the susceptibility at criticality on lattices of size up to $512^2$ we obtain $r = -0.0270(10)$, in agreement with recent work of Kenna and Irving on the the finite-size scaling of Lee-Yang zeros in the cosine formulation of the XY model. By studying susceptibilities and correlation lengths up to $\xi \approx 140$ in the high-temperature phase, however, we arrive at quite a different estimate of $r = 0.0560(17)$, which is in good agreement with recent analyses of thermodynamic Monte Carlo data and high-temperature series expansions of the cosine formulation.Comment: 13 pages, LaTeX + 8 postscript figures. See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm

Precision volume measurement system.

A new precision volume measurement system based on a Kansas City Plant (KCP) design was built to support the volume measurement needs of the Gas Transfer Systems (GTS) department at Sandia National Labs (SNL) in California. An engineering study was undertaken to verify or refute KCP's claims of 0.5% accuracy. The study assesses the accuracy and precision of the system. The system uses the ideal gas law and precise pressure measurements (of low-pressure helium) in a temperature and computer controlled environment to ratio a known volume to an unknown volume

Monte Carlo simulations of the solid-liquid transition in hard spheres and colloid-polymer mixtures

Monte Carlo simulations at constant pressure are performed to study coexistence and interfacial properties of the liquid-solid transition in hard spheres and in colloid-polymer mixtures. The latter system is described as a one-component Asakura-Oosawa (AO) model where the polymer's degrees of freedom are incorporated via an attractive part in the effective potential for the colloid-colloid interactions. For the considered AO model, the polymer reservoir packing fraction is eta_p^r=0.1 and the colloid-polymer size ratio is q=sigma_p/\sigma=0.15 (with sigma_p and sigma the diameter of polymers and colloids, respectively). Inhomogeneous solid-liquid systems are prepared by placing the solid fcc phase in the middle of a rectangular simulation box creating two interfaces with the adjoined bulk liquid. By analyzing the growth of the crystalline region at various pressures and for different system sizes, the coexistence pressure p_co is obtained, yielding p_co=11.576 k_BT/sigma^3 for the hard sphere system and p_co=8.0 k_BT/sigma^3 for the AO model (with k_B the Boltzmann constant and T the temperature). Several order parameters are introduced to distinguish between solid and liquid phases and to describe the interfacial properties. From the capillary-wave broadening of the solid-liquid interface, the interfacial stiffness is obtained for the (100) crystalline plane, giving the values gamma=0.49 k_BT/sigma^2 for the hard-sphere system and gamma=0.95 k_BT/sigma^2 for the AO model.Comment: 11 pages, 13 figure

High Precision Renormalization Group Study of the Roughening Transition

We confirm the Kosterlitz-Thouless scenario of the roughening transition for three different Solid-On-Solid models: the Discrete Gaussian model, the Absolute-Value-Solid-On-Solid model and the dual transform of the XY model with standard (cosine) action. The method is based on a matching of the renormalization group flow of the candidate models with the flow of a bona fide KT model, the exactly solvable BCSOS model. The Monte Carlo simulations are performed using efficient cluster algorithms. We obtain high precision estimates for the critical couplings and other non-universal quantities. For the XY model with cosine action our critical coupling estimate is $\beta_R^{XY}=1.1197(5)$. For the roughening coupling of the Discrete Gaussian and the Absolute-Value-Solid-On-Solid model we find $K_R^{DG}=0.6645(6)$ and $K_R^{ASOS}=0.8061(3)$, respectively.Comment: 46 pages, PostScript file (compressed and uuencoded), preprints CERN-TH.7182/94, HU-RI-2/94, and MS-TPI-94-

Glassy Roughness of a Crystalline Surface Upon a Disordered Substrate

The discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is studied by Monte Carlo simulations. A continuous transition is found from a phase with a thermally-induced roughness to a glassy one in which the roughness is driven by the disorder. The behavior of the height-height correlations is consistent with the one-step replica symmetry broken solution of the variational approximation. The results differ from the renormalization group predictions and from recent simulations of a 2D vortex-glass model which belongs to the same universality class.Comment: 12 pages (RevTeX) & 3 figures (PS) uuencode

Longitudinal and transverse dissipation in a simple model for the vortex lattice with screening

Transport properties of the vortex lattice in high temperature superconductors are studied using numerical simulations in the case in which the non-local interactions between vortex lines are dismissed. The results obtained for the longitudinal and transverse resistivities in the presence of quenched disorder are compared with the results of experimental measurements and other numerical simulations where the full interaction is considered. This work shows that the dependence on temperature of the resistivities is well described by the model without interactions, thus indicating that many of the transport characteristics of the vortex structure in real materials are mainly a consequence of the topological configuration of the vortex structure only. In addition, for highly anisotropic samples, a regime is obtained where longitudinal coherence is lost at temperatures where transverse coherence is still finite. I discuss the possibility of observing this regime in real samples.Comment: 9 pages, 7 figures included using epsf.st

Effect of ions on sulfuric acid-water binary particle formation : 2. Experimental data and comparison with QC-normalized classical nucleation theory

We report comprehensive, demonstrably contaminant-free measurements of binary particle formation rates by sulfuric acid and water for neutral and ion-induced pathways conducted in the European Organization for Nuclear Research Cosmics Leaving Outdoor Droplets chamber. The recently developed Atmospheric Pressure interface-time of flight-mass spectrometer was used to detect contaminants in charged clusters and to identify runs free of any contaminants. Four parameters were varied to cover ambient conditions: sulfuric acid concentration (10(5) to 10(9)molcm(-3)), relative humidity (11% to 58%), temperature (207K to 299K), and total ion concentration (0 to 6800ionscm(-3)). Formation rates were directly measured with novel instruments at sizes close to the critical cluster size (mobility size of 1.3nm to 3.2nm). We compare our results with predictions from Classical Nucleation Theory normalized by Quantum Chemical calculation (QC-normalized CNT), which is described in a companion paper. The formation rates predicted by the QC-normalized CNT were extended from critical cluster sizes to measured sizes using the UHMA2 sectional particle microphysics model. Our results show, for the first time, good agreement between predicted and measured particle formation rates for the binary (neutral and ion-induced) sulfuric acid-water system. Formation rates increase with RH, sulfuric acid, and ion concentrations and decrease with temperature at fixed RH and sulfuric acid concentration. Under atmospheric conditions, neutral particle formation dominates at low temperatures, while ion-induced particle formation dominates at higher temperatures. The good agreement between the theory and our comprehensive data set gives confidence in using the QC-normalized CNT as a powerful tool to study neutral and ion-induced binary particle formation in atmospheric modeling.Peer reviewe