Getting rid of fool's gold: Pyrite, also called fool's gold, is an iron sulfide mineral that is very commonly found in rock but is almost nonexistent in sediments today. Pyrite oxidizes quickly and is a major source of sulfur to the ocean, but it is also a proxy for the oxygen content historically in Earth's atmosphere. Gu et al. conducted a set of detailed observations of the pyrite oxidation process in a shale unit. The authors found that erosion tied to fracturing is just as important as the oxygen content for the dissolution process. They developed a model that helps determine the conditions in Earth's past for which pyrite might have been stable and the role of microorganisms in the oxidation process. Science , this issue p. eabb8092

Scaling of surface fluctuations of polycrystalline CdTe/Si(100) films grown by hot-wall epitaxy are studied. The growth exponent of surface roughness and the dynamic exponent of the autocorrelation function in the mound growth regime agree with the values of the Kardar-Parisi-Zhang (KPZ) class. The scaled distributions of heights, local roughness, and extremal heights show remarkable collapse with those of the KPZ class, giving an experimental observation of KPZ distributions in $2+1$ dimensions. Deviations from KPZ values in the long-time estimates of dynamic and roughness exponents are explained by spurious effects of multipeaked coalescing mounds and by effects of grain shapes. Thus, this scheme for investigating universality classes of growing films advances over the simple comparison of scaling exponents.

We integrate numerically the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ and $2+1$ dimensions using a Euler discretization scheme and the replacement of ${\left(\nabla h\right)}^2$ by exponentially decreasing functions of that quantity to suppress instabilities. When applied to the equation in $1+1$ dimensions, the method of instability control provides values of scaling amplitudes consistent with exactly known results, in contrast to the deviations generated by the original scheme. In $2+1$ dimensions, we spanned a range of the model parameters where transients with Edwards-Wilkinson or random growth are not observed, in box sizes $8\le L\le 128$. We obtain a roughness exponent of $0.37\le \alpha \le 0.40$ and steady state height distributions with skewness $S=0.25\pm 0.01$ and kurtosis $Q=0.15\pm 0.1$. These estimates are obtained after extrapolations to the large $L$ limit, which is necessary due to significant finite-size effects in the estimates of effective exponents and height distributions. On the other hand, the steady state roughness distributions show weak scaling corrections and evidence of stretched exponential tails. These results confirm previous estimates from lattice models, showing their reliability as representatives of the KPZ class.

In surfaces with grainy features, the local roughness w shows a crossover at a characteristic length rc, with roughness exponent changing from $\alpha${}1$\approx${}1 to a smaller $\alpha${}2. The grain shape, the choice of w or height-height correlation function (HHCF) C, and the procedure to calculate root-mean-square averages are shown to have remarkable effects on $\alpha${}1. With grains of pyramidal shape, $\alpha${}1 can be as low as 0.71, which is much lower than the previous prediction 0.85 for rounded grains. The same crossover is observed in the HHCF, but with initial exponent $\chi${}1$\approx${}0.5 for flat grains, while for some conical grains it may increase to $\chi${}1$\approx${}0.7. The universality class of the growth process determines the exponents $\alpha${}2=$\chi${}2 after the crossover, but has no effect on the initial exponents $\alpha${}1 and $\chi${}1, supporting the geometric interpretation of their values. For all grain shapes and different definitions of surface roughness or HHCF, we still observe that the crossover length rc is an accurate estimate of the grain size. The exponents obtained in several recent experimental works on different materials are explained by those models, with some surface images qualitatively similar to our model films.

The scaling of island and monomer density, capture zone distributions (CZDs), and island size distributions (ISDs) in reversible submonolayer growth was studied using the Clarke-Vvedensky model. An approach based on rate-equation results for irreversible aggregation (IA) models is extended to predict several scaling regimes in square and triangular lattices, in agreement with simulation results. Consistently with previous works, a regime I with fractal islands is observed at low temperatures, corresponding to IA with critical island size $i=1$, and a crossover to a second regime appears as the temperature is increased to $\epsilon R^{2/3}\sim 1$, where $\epsilon$ is the single bond detachment probability and $R$ is the diffusion-to-deposition ratio. In the square (triangular) lattice, a regime with scaling similar to IA with $i=3$ ($i=2$) is observed after that crossover. In the triangular lattice, a subsequent crossover to an IA regime with $i=3$ is observed, which is explained by the recurrence properties of random walks in two-dimensional lattices, which is beyond the mean-field approaches. At high temperatures, a crossover to a fully reversible regime is observed, characterized by a large density of small islands, a small density of very large islands, and total island and monomer densities increasing with temperature, in contrast to IA models. CZDs and ISDs with Gaussian right tails appear in all regimes for $R\sim {10}^7$ or larger, including the fully reversible regime, where the CZDs are bimodal. This shows that the Pimpinelli-Einstein approach for IA explains the main mechanisms for the large islands to compete for free adatom aggregation in the reversible model, and may be the reason for its successful application to a variety of materials and growth conditions.

We study roughness scaling of the outer surface and the internal porous structure of deposits generated with the three-dimensional bidisperse ballistic deposition (BBD), in which particles of two sizes are randomly deposited. Systematic extrapolation of roughness and dynamical exponents and the comparison of roughness distributions indicate that the top surface has Kardar-Parisi-Zhang (KPZ) scaling for any ratio $F$ of the flux between large and small particles. A scaling theory predicts the characteristic time of the crossover from random to correlated growth in BBD and provides relations between the amplitudes of roughness scaling and $F$ in the KPZ regime. The porosity of the deposits monotonically increases with $F$ and scales as $F^{1∕2}$ for small $F$, which is also explained by the scaling approach and illustrates the possibility of connecting surface growth rules and bulk properties. The suppression of relaxation mechanisms in BBD enhances the connectivity of the deposits when compared to other ballisticlike models, so that they percolate down to $F\approx 0.05$. The fractal dimension of the internal surface of the percolating deposits is $D_F\approx 2.9$, which is very close to the values in other ballistic-like models and suggests universality among these systems.