Exponential Temperature Dependence Research Articles

Layer-by-layer growth, apparent instability, and mound coarsening in thin film deposition controlled by thermally activated surface diffusion

Thin film deposition from vapor with adsorbate diffusion and Ehrlich-Schwoebel (ES) barriers at step edges is studied by kinetic Monte Carlo (KMC) simulations and scaling approaches. Mound coarsening with slope selection is shown at the largest thicknesses, where roughness (W) and correlation length (ξ) scale in time with exponents β≈n≈0.25, consistently with theoretical works but contrasting with previous simulations that systematically showed temperature-dependent exponents. At a given film thickness, we show that the mounded morphology is independent of the ES barrier, so that interlayer transport is suppressed, while the temperature increase of W and ξ is consistent with intralayer transport limited by adatom detachment from flat terrace borders. Initial layer-by-layer (LBL) growth occurs above a characteristic temperature that increases with the activation energies of terrace diffusion and of ES barrier, but weakly depends on the external flux. Subsequently, as the surface roughness is near the atom/molecule size, there is rapid roughening where, counterintuitively, larger effective growth exponents (β>0.5, suggesting unstable growth) are correlated with longer LBL regimes. Similar LBL-rough transitions were reported in organic film deposition and the model application to diindenoperylene films suggests a large ES barrier ∼0.4eV. In the mound coarsening regime, W/ξ and θ1/2/Wξ converge to constant values dependent on surface diffusion coefficients (θ is the film thickness). This convergence suggests mound coarsening with slope selection in SnTe films whose effective β is anomalously large, showing how film morphology can be interpreted beyond exponent measurements.

Unveiling nodeless unconventional superconductivity proximate to honeycomb-vacancy ordering in the Ir-Sb binary system

Vacancies in solid-state physics are underexplored in materials with strong electron-electron correlations. Recent research on the Ir-Sb binary system revealed an extended buckled-honeycomb vacancy (BHV) order. Superconductivity arises by suppressing BHV ordering through high-pressure growth with excess Ir atoms or Rh substitution, yet the superconducting pairing nature remains unknown. To explore this, we conducted muon spin rotation experiments on Ir1−δSb (synthesized at 5.5 GPa, Tc = 4.2 K) and ambient pressure synthesized optimally Rh-doped Ir1−xRhxSb (x=0.3, Tc = 2.7 K). The exponential temperature dependence of the superfluid density suggests a fully gapped superconducting state exists in both samples. The ratio of Tc to the superfluid density resembles that of unconventional superconductors. A significant increase in the superfluid density in the high-pressure synthesized sample correlates with Tc, indicating that unconventional superconductivity is intrinsic to the Ir-Sb binary system. These findings, along with the dome-shaped phase diagram, highlight IrSb as the first unconventional superconducting parent phase with ordered vacancies, requiring further theoretical investigations.

Variable‐Range Hopping Conduction in Amorphous, Non‐Stoichiometric Gallium Oxide

AbstractAmorphous, non‐stoichiometric gallium oxide (a‐GaOx, x < 1.5) is a promising material for many electronic devices, such as resistive switching memories, neuromorphic circuits and photodetectors. So far, all respective measurements are interpreted with the explicit or implicit assumption of n‐type band transport above the conduction band mobility edge. In this study, the experimental and theoretical results consistently show for the first time that for an O/Ga ratio x of 0.8 to 1.0 the dominating electron transport mechanism is, however, variable‐range hopping (VRH) between localized states, even at room temperature and above. The measured conductivity exhibits the characteristic exponential temperature dependence on T−1/4, in remarkable agreement with Mott's iconic law for VRH. Localized states near the Fermi level are confirmed by photoelectron spectroscopy and density of states (DOS) calculations. The experimental conductivity data is reproduced quantitatively by kinetic Monte Carlo (KMC) simulations of the VRH mechanism, based on the ab‐initio DOS. High electric field strengths F cause elevated electron temperatures and an exponential increase of the conductivity with F1/2. Novel results concerning surface oxidation, magnetoresistance, Hall effect, thermopower and electron diffusion are also reported. The findings lead to a new understanding of a‐GaOx devices, also with regard to metal|a‐GaOx Schottky barriers.

Structural properties, dielectric relaxation, and impedance spectroscopy of NASICON type Na3+xZr2−xPrxSi2PO12${\rm Na}_{3+x} {\rm Zr}_{2-x} {\rm Pr}_{x} {\rm Si}_2 {\rm PO}_{12}$ ceramics

AbstractWe investigate the dielectric and impedance spectroscopic investigation of Pr‐doped NASICON type () samples as a function of temperature and frequency. The Rietveld refinement of X‐ray diffraction patterns confirms the monoclinic phase having C2/c space groups for all the samples. The scanning electron microscopy shows the granular‐like structure and energy dispersive X‐ray analysis confirms the desired compositions. The temperature (90–400 K) and frequency (20 Hz–2 MHz) dependence of electric permittivity are explained using Maxwell–Wagner–Sillars (MWS) polarization and space charge polarization mechanisms. The dielectric relaxation shows nearly equal activation energy for all the samples with a non‐Debye type of relaxation in the measured temperature range. The complex impedance analysis shows the presence of broad grain and grain boundary relaxation peaks. The stretched exponent analysis of electric modulus using the Kohlrausch–Williams–Watts (KWW) function further confirms the non‐Debye type of relaxation. Moreover, scaling analysis of the electric modulus shows a similar type of relaxation for all the samples. The ac conductivity data are fitted using modified power law, where the temperature dependence of exponent () confirms the correlated barrier hopping (CBH) type conduction for all the samples. Our results indicate that the Pr‐doped NASICON samples are potential candidates for charge storage devices due to their large electric permittivity.

Correlating the Segmental Relaxation Time of Polystyrene.

A previous related paper dealing with the density relaxation of polystyrene (PS) has shown that the equilibrium relaxation time (τeq) has a purely exponential temperature dependence (ETD) below ≈100 °C. Such an ETD is now also confirmed based upon available dielectric spectra data for PS. By combining the ETD behavior of τeq (or aT) at low temperatures with a VFTH behavior at higher temperatures (based mainly on available recoverable shear compliance data), a composite correlation for τeq (or aT) is developed, which is continuous with continuous slope at a crossover temperature that is found to be 99.22 °C, where τeq = 92.15 s. This composite representation is shown to describe (without any adjustable parameters) available independent data for the segmental relaxation time over a finite range both above and below Tcrossover (i.e., the glass transition temperature).

Structural dynamics of a model of amorphous silicon

We perform extensive simulations and systematic statistical analyses on the structural dynamics of a model of amorphous silicon. The simulations follow the dynamics introduced by Wooten, Winer and Weaire: the energy is obtained with the Keating potential, and the dynamics consists of bond transpositions proposed at random locations and accepted with the Metropolis acceptance ratio. The structural quantities we track are the variations in time of the lateral lengths (Lx, Ly, Lz) of the cuboid simulation cell. We transform these quantities into the volume V and two aspect ratios B1 and B2. Our analysis reveals that at short times, the mean squared displacement (MSD) for all of them exhibits normal diffusion. At longer times, they cross over to anomalous diffusion (AD), with a temperature-dependent anomalous exponent α<1. We analyze our findings in the light of two standard models in statistical physics that feature anomalous dynamics, viz., continuous time random walker (CTRW) and fractional Brownian motion (fBm). We obtain the distribution of waiting times, and find that the data are consistent with a stretched-exponential decay. We also show that the three quantities, V, B1 and B2 exhibit negative velocity autocorrelation functions. These observations together suggest that the dynamics of the material belong to the fBm class.

Direct Numerical Analysis of Dynamic Facilitation in Glass-Forming Liquids.

We propose a computational strategy to quantify the temperature evolution of the timescales and length scales over which dynamic facilitation affects the relaxation dynamics of glass-forming liquids at low temperatures, which requires no assumption about the nature of the dynamics. In two glass models, we find that dynamic facilitation depends strongly on temperature, leading to a subdiffusive spreading of relaxation events which we characterize using a temperature-dependent dynamic exponent. We also establish that this temperature evolution represents a major contribution to the increase of the structural relaxation time.

Quantum scaling for the metal–insulator transition in a two-dimensional electron system

The quantum phase transition observed experimentally in two-dimensional (2D) electron systems has been a subject of theoretical and experimental studies for almost 30 years. We suggest Gaussian approximation to the mean-field theory of the second-order phase transition to explain the experimental data. Our approach explains self-consistently the universal value of the critical exponent 3/2 (found after scaling measured resistivities on both sides of the transition as a function of temperature) as the result of the divergence of the correlation length when the electron density approaches the critical value. We also provide numerical evidence for the stretched exponential temperature dependence of the metallic phase’s resistivities in a wide range of temperatures and show that it leads to correct qualitative results. Finally, we interpret the phase diagram on the density-temperature plane exhibiting the quantum critical point, quantum critical trajectory and two crossover lines. Our research presents a theoretical description of the seminal experimental results.

Electrical properties and conduction mechanisms of Ba0.75Sr0.25Ti1-xZrxO3 ceramics synthesized by sol-gel route

A series of Ba0.75Sr0.25Ti1-xZrxO3 (x = 0, 0.01, 0.03, 0.05, and 0.1) ceramics were synthesized via a facile sol-gel route. The confirmation of a tetragonal structure was achieved through Rietveld refinement of the powder X-ray diffraction (XRD), and the finding was subsequently corroborated by Raman spectroscopy. The Scanning electron microscopy (SEM) confirmed the roughly cubical-shaped grains and average grain size is 0.31 μm for x = 0 and 0.70 μm for x = 0.05. The electrical properties such as dielectric constant, dielectric loss and ac/dc conductivity were investigated as a function of temperature and frequency. The Jonscher's universal power law (JPL) and Arrhenius equation have been used for the analysis of conductivity. The electrical conductivity variation at intermediate frequencies was explained using JPL. The Super-linear power law (SPL) explains the electrical response at higher frequencies. The temperature-dependent frequency exponents ‘s1’ and ‘s2’ were employed to predict the quantum mechanical tunneling (QMT), non-overlapping small polarons hopping (NSPT), and correlated barrier hopping (CBH) conduction mechanisms.

Structural and ionic conduction study of Sm–Pr co-doped ceria electrolyte materials for LT-SOFC applications

Samarium praseodymium (Sm–Pr) co-doped ceria was synthesized by the co-precipitation technique as an electrolyte for low-temperature solid oxide fuel cell (LT-SOFC) applications. The structural, morphological, compositional, and electrical characterization of the synthesized samples were evaluated via x-ray diffraction (XRD), x-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), energy-dispersive x-ray spectroscopy (EDX) and impedance spectroscopy. The generation of a single-phase fluorite structure of co-doped ceria without any secondary phases has been verified by XRD analysis, exhibiting the successful incorporation of Sm and Pr ions into the ceria lattice. Vegard's law is utilized for Pr redox behavior explaining the variation in lattice constant values. SEM pictures show that the co-doped ceria powder has a homogeneous and well-dispersed microstructure, and has enhanced particle size. The impedance spectroscopy results indicate that Sm–Pr co-doped ceria has much higher ionic conductivity than single-doped ceria. The highest amount of ionic conductivity (σionic) for the composition Ce0.80Sm0.10Pr0.10O2−δ recorded as 2.12×10−2S/cm at 500°C, and 6.19×10−2S/cm at 750°C with the lowest activation energy Ea=0.48eV, which has been not reported earlier. Sm and Pr are chosen as dopants because of their capacity to generate oxygen vacancies and improve ceria's ionic conductivity. This study contributes to the enhancement in the ionic conductivity of co-doped ceria by co-precipitation technique and the temperature-dependent frequency exponent factor "s" is also explored to comprehend the conduction mechanism of the prepared samples.

Approaching the Curie temperature of ferromagnetic (Ga,Mn)P prepared by ion implantation and pulsed laser melting

This work aims to estimate the Curie temperature and critical exponents in the critical regime of III-V ferromagnetic semiconductor (FS) (Ga,Mn)P film using various methods, including Arrott and Kouvel-Fisher plots, as well as electrical transport measurements. The (Ga,Mn)P film was prepared by implanting Mn ions into an intrinsic (001) GaP wafer, followed by pulsed laser melting (PLM). The magnetic properties of the (Ga,Mn)P layer were systematically investigated. The study investigated the accuracy of four different methods in determining the critical behaviors for the magnetic properties close to TC. The results suggest that the critical exponents are similar to those of the mean-field model, as indicated by the modified Arrot plots and temperature dependent effective critical exponents. However, the accuracy of the temperature-dependent resistance Rxx(T) method and Kouvel-Fisher (K-F) analysis is limited due to the Gaussian distribution of Mn ions in the film.

Glass spectrum, excess wing phenomenon, and master curves in molecular glass formers: A multi-method approach.

The relaxation spectra of glass formers solely displaying an α-peak and excess wing contribution collected by various methods are reanalyzed to pin down their different spectral evolution. We show that master curve construction encompassing both α-peak and emerging excess wing works for depolarized light scattering (DLS) and nuclear magnetic resonance (NMR) relaxometry. It reveals the self-part of the slow dynamics' spectrum. Master curves are to be understood as a result of a more extensive scaling covering all temperatures instead of strict frequency-temperature superposition. DLS and NMR display identical relaxation spectra; yet, comparing different systems, we do not find a generic structural relaxation at variance with recent claims. Dielectric spectroscopy (DS) spectra show particularities, which render master curve construction obsolete. The DS α-peak is enhanced or suppressed with respect to that of DLS or NMR, yet, not correlated to the polarity of the liquid. Attempting to single out the excess wing from the overall spectrum discloses a stronger exponential temperature dependence of its amplitude compared to that below Tg and a link between its exponent and that of the fast dynamics' spectrum. Yet, such a decomposition of α-peak and excess wing appears to be unphysical. Among many different glasses, the amplitude of the excess wing power-law spectrum is found to be identical at Tg, interpreted as a relaxation analog to the Lindemann criterion.

Water-vapor absorption database using dual comb spectroscopy from 300 to 1300 K part I: Pure H2O, 6600 to 7650 cm-1

We present broadband dual frequency comb laser measurements of pure H2O absorption (natural isotopic abundance of 99.7 % H216O) from 6600 to 7650 cm−1 (1307–1515 nm) with a spectral point spacing of 0.0068 cm−1. Twenty-nine absorption spectra were collected at temperatures between 300 and 1300 K (±0.81 % average uncertainty) and pressures ranging from 0.5 to 16 Torr (±0.27 %) with an average residual absorbance noise of 7.4E-4 across the spectrum for all measurements. We fit measurements using a quadratic speed-dependent Voigt profile to determine 17,030 absorption parameters for 5986 transitions found in HITRAN2020. The measured parameters include line strength, line center, self-broadening, and self-shift, along with their power-law temperature-dependence exponents, and speed-dependent self-width parameters. A second version of the retrieved parameters with fits that do not include speed-dependence is also presented. We explore various trends to enable parameter extrapolation for weak transitions that were not covered in this work. We measured line parameters for an additional 614 features not presently catalogued in the HITRAN2020 database. In aggregate, these updates improved RMS absorbance error by a factor of 2.6 on average, and the remaining residual is predominantly spectral noise. This updated database improves high-temperature spectroscopic knowledge across the 6600–7650 cm−1 region of H2O absorption. An accompanying paper (Part II) describes similar measurements and a new database for air-broadened H2O absorption.

Cooling and instabilities in colliding radiative flows with toroidal magnetic fields

ABSTRACT We report on the results of a simulation-based study of colliding magnetized plasma flows. Our set-up mimics pulsed power laboratory astrophysical experiments but, with an appropriate frame change, is relevant to astrophysical jets with internal velocity variations. We track the evolution of the interaction region where the two flows collide. Cooling via radiative losses is included in the calculation. We systematically vary plasma beta (βm) in the flows, the strength of the cooling (Λ0), and the exponent (α) of temperature dependence of the cooling function. We find that for strong magnetic fields a counter-propagating jet called a ‘spine’ is driven by pressure from shocked toroidal fields. The spines eventually become unstable and break apart. We demonstrate how formation and evolution of the spines depend on initial flow parameters and provide a simple analytical model that captures the basic features of the flow.

Thermophysical properties and rapid solidification mechanism of liquid Zr&lt;sub&gt;60&lt;/sub&gt;Ni&lt;sub&gt;25&lt;/sub&gt;Al&lt;sub&gt;15&lt;/sub&gt; alloy under electrostatic levitation condition

In this study, the thermophysical properties and rapid solidification mechanism of highly undercooled liquid Zr&lt;sub&gt;60&lt;/sub&gt;Ni&lt;sub&gt;25&lt;/sub&gt;Al&lt;sub&gt;15&lt;/sub&gt; alloy are investigated through the electrostatic levitation technique. The maximum undercooling of this alloy reaches 316 K (0.25&lt;i&gt;T&lt;/i&gt;&lt;sub&gt;L&lt;/sub&gt;). Both density and surface tension display a linear relationship with temperature, while viscosity is related to temperature exponentially. When alloy undercooling is less than 259 K, two significant recalescence events are observed during solidification, corresponding to the formation of pseudobinary (Zr&lt;sub&gt;6&lt;/sub&gt;Al&lt;sub&gt;2&lt;/sub&gt;Ni + Zr&lt;sub&gt;5&lt;/sub&gt;Ni&lt;sub&gt;4&lt;/sub&gt;Al) eutectic and ternary (Zr&lt;sub&gt;6&lt;/sub&gt;Al&lt;sub&gt;2&lt;/sub&gt;Ni + Zr&lt;sub&gt;5&lt;/sub&gt;Ni&lt;sub&gt;4&lt;/sub&gt;Al + Zr&lt;sub&gt;2&lt;/sub&gt;Ni) eutectic. The growth velocity of the binary eutectic phase gradually increases with further undercooling and reaches a maximum undercooling value of 259 K. In contrast, once undercooling exceeds 259 K, a single recalescence event occurs, leading to the independent nucleation of all three compound phases from alloy melt and the rapid growth of a ternary anomalous eutectic structure. Notably, the growth velocity of the ternary eutectic phase exhibits a gradual decline with further undercooling. This diminishing trend of the growth velocity suggests that further undercooling might entirely suppress crystal growth dynamically at a threshold of 385 K. With classical nucleation theory and the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model, the onsets of crystallization for the three phases are calculated, thereby constructing a time–temperature-transformation (TTT) diagram. This diagram elucidates the competitive nucleation among the three phases in the undercooled melt. Both theoretical and experimental evidence reveal that Zr&lt;sub&gt;6&lt;/sub&gt;Al&lt;sub&gt;2&lt;/sub&gt;Ni phase is primarily nucleated at lower undercooling levels, whereas under higher cooling condition, it is possible for all three phases to nucleate simultaneously.

Liquid−vapor order parameter and coexistence-curve diameter of nitrogen, ethylene, and sulfur hexafluoride: From the triple point to the critical scaling regime

Analytic closed-form expressions are obtained for the liquid and vapor saturation densities defining the coexistence curve. The densities are modeled with broken power laws and Weibull distributions. Specifically, the coexistence curves of nitrogen, ethene and sulfur hexafluoride are derived, without the use of perturbative expansions, based on high-precision data extending from the triple point into the critical regime. The analytic continuation of the vapor branch below the triple point decays exponentially at low temperature. The order parameter and coexistence-curve diameter of the fluids are assembled from the regressed liquid and vapor branches of the coexistence curve, and the critical power-law scaling of these quantities is examined. The scaling exponents of the order parameter and the reduced diameter are regressed and compared with the calculated critical exponents of the 3D Ising universality class. Index functions representing the Log−Log slopes (temperature-dependent effective exponents) of the liquid and vapor densities, order parameter and diameter are used to determine the onset of the ideal power-law scaling regime and to illustrate the slope evolution of these quantities in the subcritical regime.

Self and N[formula omitted] collisional broadening of far-infrared methane lines at low-temperature with application to Titan

We report the measurement of broadening coefficients of pure rotational lines of methane at different pressure and temperature conditions. A total of 27 far-infrared spectra were recorded at the AILES beamline of the SOLEIL synchrotron at room-temperature, 200K and 120K, in a range of 10 to 800mbar. Self and N2 broadening coefficients and temperature dependence exponents of methane pure rotational lines have been measured in the 73–136cm−1 spectral range using multi-spectrum non-linear least squares fitting of Voigt profiles. These coefficients were used to model spectra of Titan that were compared to a selection of equatorial Cassini/CIRS spectra, showing a good agreement for a stratospheric methane mole fraction of (1.17 ± 0.08)%.

Finite-Temperature Avalanches in 2D Disordered Ising Models

We study the qualitative and quantitative properties of the Barkhausen noise emerging at finite temperatures in random Ising models. The random-bond Ising Model is studied with a Wolff cluster Monte-Carlo algorithm to monitor the avalanches generated by an external driving magnetic field. Satisfactory power-law distributions are found which expand over five decades, with a temperature-dependent critical exponent which matches the existing experimental measurements. We also focus on a Ising system in which a finite fraction of defects is quenched. Also the presence of defects proves able to induce a critical response to a slowly oscillating magnetic field, though in this case the critical exponent associated with the distributions obtained with different defect fractions and temperatures seems to belong to the same universality class, with a critical exponent close to 1.

Investigation on electrical transport and dielectric relaxation mechanism in TbCrO3 perovskite orthochromite

Herein, the TbCrO3 (TCO) chromite was synthesized by the sol-gel auto-combustion route and sintered at 900 °C. The Rietveld analysis of the room temperature powder X-ray diffraction profile confirmed the single-phase formation of the material crystallized in the orthorhombic phase of the perovskite structure with Pbnm space group symmetry. The surface morphology, the elemental composition, and the chemical states of the compound were investigated by field emission scanning electron microscopy, energy dispersive X-ray analysis, and X-ray photoelectron spectroscopy, respectively. The electronic density of states, band structure, and electron density were analyzed by Density Functional Theory. The electrical transport and dielectric relaxation mechanism were investigated using complex impedance spectroscopy over the experimental frequency and temperature ranging from 40-1.2x106Hz and 138−273 K, respectively. Two semicircular arcs in the impedance complex plane plots were modeled to an equivalent circuit configured by RG∥QG+RGB∥QGB which were attributed to the contributions of the highly resistive grain boundaries and relatively conducting grains in the material. The electrical conductivity as a function of frequency followed Jonscher’s universal power law behavior and an increasing nature of the temperature-dependent frequency exponent suggested small polaron hopping as the electrical conduction mechanism of the material. The least capacitive response of the TCO system was investigated by the complex electrical modulus formalism and the frequency-dependent imaginary modulus spectra were modeled by the Kohlrausch–Williams–Watts function, which resolved the thermally activated peaks of bulk and interface effects to the dielectric relaxation mechanism. The dielectric constant exhibited Maxwell-Wagner interfacial polarization effects and the dielectric loss factor showed frequency dispersion at all temperatures.

How do silicate weathering rates in shales respond to climate and erosion?

Mineral weathering, a major control on long term atmospheric CO2, can be limited by processes such as reaction kinetics, supply of fresh mineral, or water throughput in the weathering zone. In these cases, weathering fluxes increase with temperature, erosion, and runoff, respectively, and we refer to the regimes as kinetically limited (KL), erosive transport limited (ETL), and runoff limited (RL). Larger watersheds can exhibit mixtures of these behaviors in a transition regime (TR). To understand these weathering regimes, we focused on the lithology (shale) that is one of the most widespread lithologies exposed on continents globally. We identified and analyzed 142 shale watersheds across the United States, spanning a diverse range of climatic (mean annual temperature (MAT): 3–17 °C; mean annual precipitation (MAP): 220–1975 mm yr−1; potential evapotranspiration (PET): 908–2059 mm yr−1), topographic (mean catchment elevation: 78–2346 m; mean catchment slope: 0.4–28°), and hydrologic (annual runoff (q): 0.002–1.3 m yr−1) conditions. For these sites, we calculated silica fluxes (i.e., FSiO2) using SiO2 concentrations and river discharge measurements. We observed that when the humidity index (HI; MAP/PET) is <0.55, FSiO2 increases with MAP and q; however, when HI > 0.55 FSiO2, does not increase with MAP nor q. We posit that sites with HI < 0.55 are RL. The river chemistry for the RL sites is consistent with equilibrium between smectite and kaolinite. Fitting the data for sites with HI > 0.55 to an exponential temperature dependence, we find that the sensitivity of weathering to temperature is consistent with an apparent activation energy, Ea, of 56 ± 8 kJ mol−1. If sites with HI > 0.55 but average slopes <10°are removed, the value increases to 92 ± 10 kJ mol−1. This value is consistent with the Ea measured experimentally for the dissolution of the common shale clay, chlorite. To extrapolate from our measurements, we use geospatial-based definitions to classify HUC12 watersheds across the United States. This reveals that 48%, 37%, 9%, and 7% of US shale watersheds are RL, ETL, TR, and KL, respectively. Globally, we estimate that silicates weathering in shales consume 2.6 × 1012 mol CO2 yr−1, which is 22% of the total CO2 sequestered by silicate weathering.