Nucleation Rate Research Articles

Approximating Nucleation Rates of Glass Ceramics Using In-Situ X-ray Diffraction

Glass ceramics are ideal for applications ranging from the culinary to defense industries. The properties of glass ceramics are a strong function of their microstructure, which in turn is controlled by constitutive nucleation and growth treatments. Nucleation has been extensively studied but remains an experimental and theoretical challenge. Traditional isothermal methods for measuring nucleation rates require time-consuming measurements and careful statistics, leading to only a few material systems with nucleation data available, approximately one-hundred glass systems were studied in half a century. To overcome these challenges, we present a new non-isothermal technique utilizing in-situ X-Ray Diffraction (XRD) with data analyzed through a modified Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation. Three homogenous nucleated glass systems were analyzed: Li2O•2SiO2 (lithium disilicate), Na2O•2CaO•3SiO2 (combeite), and Li2Oׅ•2B2O3 (lithium diborate). This method utilizes crystallized fractions through XRD, allowing resolution far beyond microscopy techniques. It was thus possible to compare the evolution of the crystallized volume fractions by X-ray diffraction with optical microscopy from literature. This method was successful in reproducing the experimental nucleation curve from the temporal development of the number density and crystal size within four orders of magnitude, while also achieving the correct peak position, leading to a new method to rapidly approximate the nucleation rate of complex glass-ceramics.

Crystallographic Reorientation Induced by Gradient Solid-Electrolyte Interphase for Highly Stable Zinc Anode.

Oriented zinc (Zn) electrodeposition is critical for the long-term performance of aqueous Zn metal batteries. However, the intricate interfacial reactions between the Zn anode and electrolytes hinder a comprehensive understanding of Zn metal deposition. Here, the reaction pathways of Zn deposition and report the preferential formation of Zn single-crystalline nuclei followed by dense Zn(002) deposition is elucidated, which is induced by a gradient solid-electrolyte interphase (SEI). The gradient SEI composed of abundant B-O and C species facilitates faster Zn2+ nucleation rate and smaller nucleus size, promoting the formation of Zn single-crystalline nuclei. Additionally, the homogeneity and mechanical stability of SEI ensure the crystallographic reorientation of Zn anodes from Zn(101) to (002) planes, efficiently inhibiting dendrite growth and metal corrosion during the Zn2+ stripping/plating process. These advantages significantly enhance the stability of the Zn anode, as demonstrated by the prolonged cycling lifespan of symmetric Zn batteries and exceptional reversibility (>99.5%) over 5000 cycles in Zn//Cu asymmetric batteries. Notably, this strategy also enables the stable operation of anode-free Zn//I2 batteries with a long lifespan of 3000 cycles. This work advances the understanding of Zn electrochemical behaviors, encompassing Zn nucleation, growth, and Zn2+ stripping/plating.

Site-Specific Stochastic Rates and Energetics of Ag Nucleation on Highly Ordered Pyrolytic Graphite.

Nucleation is a fundamentally important step in electrochemical phase transition reactions, e.g., in electrodeposition, which is pertinent for emerging battery technology, nanoparticle synthesis, and many industrial processes. Surface defects have been suggested to enhance nucleation rates. However, directly quantifying the nucleation rates at specific surface sites is challenging due to the ensemble averaging effect in bulk measurements. Herein, we report the measurement of rates and energetics of electronucleation across the model surface of highly oriented pyrolytic graphite (HOPG). Specifically, scanning electrochemical cell microscopy (SECCM) is used to confine the nucleation spatially in the nanoscale cell, allowing one nucleation event to be measured at one time. The scanning capability further allows the mapping of Ag nucleation at the step edge vs basal plane. A stochastic model is developed to extract the nucleation rate and energetics from voltammetric experiments. We observed a ∼57 mV difference in the median nucleation overpotential between the step edge and basal plane, corresponding to a ∼12 kJ mol-1 difference in the nucleation energy barrier. The voltammetric method to measure the nucleation rate explored here can be extended to understand the heterogeneity of nucleation rates in other electrochemical nucleation systems, e.g., metal anode batteries.

Crystallization dynamics of MAPbI3 perovskite solar cells via solvent engineering methods

Perovskite materials have attracted interest in solar cells due to ease of processing from salts. However, the complex crystal formation of perovskite from solvents is poorly understood. Solvent engineering approach to determine the crystallization dynamics and orientation of MAPbI3 films using grazing incidence wide angle x-ray scattering (GIWAXS) and micro diffraction measurements were studied. The study further probes the effect of moisture, PTAA and PEDOTS: PSS hole transport layers on the stability of MAPbI3 films. Precursor solutions were prepared by dissolving MAI and PbI2 in pure DMF and mixture of DMF: DMSO in 4:1 v/v. Chlorobenzene and Ethyl acetate were used as antisolvent. Films prepared from DMF: DMSO mixture showed no PbI2 signature while those prepared from DMF only, showed PbI2 signature at q= 0.9 A-1. This was attributed to solvent engineering of DMF/DMSO that leads to the formation of MAI/PbI2/DMSO intermediate that delays the crystallization and promotes vertical growth of films. q= 0.9 A-1 signal was associated with high volatility of DMF which led to faster but discrepant nucleation and crystallization rate. Microdiffraction results showed insignificant influence of antisolvent on the perovskite structure. Humidity has a strong influence on the stability of MAPbI3 films. PbI2 intensity in the GIWAXS maps increased with increasing humidity while MAPbI3 intensity decreased. This implied increased degradation of MAPbI3 film with humidity due to recombination of charge carriers. A band gap of 1.57 eV, efficiency of 8.5% and Et of 26 meV were obtained. Films with good crystallization are desirable in solar cells.

How CO2 gas accelerates water nucleation at low temperature.

We conducted homogeneous nucleation experiments for dilute binary H2O-CO2 mixtures in Ar-N2 carrier gas with different CO2/H2O ratios at temperatures of 57 and 75K and total pressures of ∼40 and 70Pa, respectively. Direct experimental information on the number and type of molecules in the clusters and on the cluster number concentration is obtained by mass spectrometric detection of nucleating clusters that form in the uniform region of Laval expansions. Only homo-molecular water clusters are observed in the mass spectra. However, as the CO2/H2O ratio increases, a significant increase in the nucleation rate is observed. A simple kinetic model suggests that this acceleration of nucleation is due to the formation of short-lived, transient hetero-molecular H2O-CO2 dimers. Comparison with homogeneous binary nucleation of toluene-CO2 and unary nucleation of H2O shows that nucleation becomes more efficient in systems with stronger intermolecular interactions and a larger number of degrees of freedom. Such studies at the molecular level will improve our understanding of homogeneous nucleation mechanisms in atmospheric and industrial processes.

Non-equilibrium condensation flow characteristics of wet steam considering condensation shock effect in the steam turbine

A non-equilibrium condensation flow occurs in steam turbines, accompanied by condensation shock. At present, there are limited studies on the influence of condensation shock on the flow and condensation characteristics of wet steam, and the unsteady influence of condensation shock on the flow field of wet steam always have been ignored. In this paper, the unsteady flow characteristics of condensation were presented by considering the condensation shock effect. First, the condensation flow models and corresponding source terms were programmed and loaded with UDS (user-defined scalar) and UDF (user-defined function), respectively, and the governing equations were discretized using a high-resolution calculation method. The calculated results agreed well with the reported experimental results. Based on the models, the non-equilibrium condensation flow characteristics with inlet and outlet pressures in Laval nozzle considering the condensation shock effect were analyzed. Finally, during the unsteady phase change process, the effects of back pressure and saturation of the inlet on the liquid phase parameters were examined considering the condensation shock effect in the Dykas cascade. The results show that a decrease in the back pressure and an increase in the inlet pressure improve the condensation shock intensity in Laval nozzle. With the increase of condensation shock intensity, the nucleation rate increases. Moreover, in Dykas cascade, with the increase of back pressure from 48.8 kPa to 73.2 kPa, the maximum wetness decreases from 4.8 % to 2.1 %, whereas with the increase of relative saturation from 0.58 to 0.88, the maximum wetness increases from 2.4 % to 3.6 %. The results obtained in this paper are of significance to accurately analyze the actual situation of non-equilibrium condensation flow of wet steam and to develop methods for reducing wet steam loss in turbine stage.

Analysis of the Ni-5%at.W Alloy Substrate Texture Evolution at Different Strain Levels Using the EBSD Technique.

In this paper, the texture evolution of the Ni-5%W alloy baseband with different strain variables (εvM = 3.9, 4.9, and 5.1) during rolling and annealing was studied using the electron back scattering diffraction (EBSD) technique. The results indicate that after high-temperature annealing at 1150 °C, all three strain levels of the alloy substrates can achieve a strong cubic texture, with a content exceeding 99% (<10°). However, the texture evolution trajectory is significantly influenced by the strain level. When the content of cubic texture in the alloy substrates under strain levels of 3.9 and 5.1 is the same, significant temperature differences exist. Additionally, the different strain levels result in varying nucleation rates and growth rates of cubic texture in the Ni-5%W alloy substrates. The study reveals that in the alloy substrates under strain levels of 3.9 and 4.9, recrystallized cubic grain nuclei grow within a layered structure, resulting in larger grain sizes and lower nucleation rates. In contrast, in the alloy substrates under a strain level of 5.1, recrystallized cubic grain nuclei form from small equiaxed grains, leading to higher nucleation rates but smaller grain sizes, competing with random orientations. In the later stages of nucleation, recrystallized grains in the alloy substrates under a strain level of 5.1 exhibit a significant size advantage, rapidly growing by engulfing randomly oriented grains. Compared to the alloy substrates with lower strain levels, the recrystallized cubic grains in the alloy substrates under a strain level of 5.1 have higher nucleation rates and faster growth rates.

Optimization of Inclusion and Microstructure of As‐Cast Nonquenched and Tempered Steel F38MnVS with Trace Ce

Various techniques, such as optical microscopy, high‐temperature confocal laser scanning microscopy, scanning electron microscopy, electron backscatter diffraction, and thermodynamic calculations, are employed to analyze the optimization mechanism of Ce on the inclusions and microstructures in F38MnVS as‐cast samples. The results show that the addition of Ce inhibits MnS precipitation at the grain boundaries and significantly reduces the diameters and aspect ratios of the inclusions. After Ce treatment, a new type of composite inclusion appears in the steel. The modification of the inclusions by Ce promotes the optimization of the as‐cast microstructure during solidification, which mainly exhibits austenite grain refinement and polygonal ferrite formation in the grains. Based on the misfit degree theory, the refinement of the austenite grains is because of the nucleation of austenite grains facilitated by Ce2O2S and CeAlO3. The increased nucleation of the intragranular polygonal ferrite is mainly attributed to Ce2O2S, Ce2S3, CeAlO3, and VC, which can promote the nucleation of α‐Fe. Simultaneously, the addition of Ce reduces the phase transition temperature, increases the driving force of the phase transition, and increases the nucleation rate. This study's results can provide a reference for the application of Ce treatment in the preparation of nonquenched tempered steel for automobiles.

Effect of creep fracture mode transition of P91 steel welded joints on long-term creep fracture life

The formation mechanism of the two fracture behaviors and their effects on the creep life of P91 steel welded joints during creep were investigated, and the morphology and microstructure of the two fractures were characterized by SEM and EBSD, and the results were as follows: the change of fracture modes was affected by the creep strain rate and cavity nucleation rate in the joint. When the applied stress is large, the creep strain rate of BM is higher, and brittle fracture occurs at BM; when the applied stress is low, the cavity nucleation rate of FGHAZ is higher, and brittle fracture occurs at FGHAZ, known as type IV cracking. The occurrence of type IV cracking will reduce the accuracy of creep life prediction methods, and life prediction considering fracture mode can effectively improve the prediction accuracy.

Anthropogenic Extremely Low Volatility Organics (ELVOCs) Govern the Growth of Molecular Clusters Over the Southern Great Plains During the Springtime

AbstractNew particle formation (NPF) often drives cloud condensation nuclei concentrations and the processes governing nucleation of molecular clusters vary substantially in different regions. The growth of these clusters from ∼2 to &gt;10 nm diameters is often driven by the availability of extremely low volatility organic vapors (ELVOCs). Although the pathways to ELVOC formation from the oxidation of biogenic terpenes are better understood, the mechanistic pathways for ELVOC formation from oxidation of anthropogenic organics are less well understood. We integrate measurements and detailed regional model simulations to understand the processes governing NPF and secondary organic aerosol formation at the Southern Great Plain (SGP) observatory in Oklahoma and compare these with a site within the Bankhead National Forest (BNF) in Alabama, southeast USA. During our two simulated NPF event days, nucleation rates are predicted to be at least an order of magnitude higher at SGP compared to BNF largely due to lower sulfuric acid (H2SO4) concentrations at BNF. Among the different nucleation mechanisms in WRF‐Chem, we find that the dimethylamine (DMA) + H2SO4 nucleation mechanism dominates at SGP. We find that anthropogenic ELVOCs are critical for explaining the growth of particles observed at SGP. Treating organic particles as semisolid, with strong diffusion limitations for organic vapor uptake in the particle phase, brings model predictions into closer agreement with observations. We also simulate two non‐NPF event days observed at the SGP site and show that low‐level clouds reduce photochemical activity with corresponding reductions in H2SO4 and anthropogenic ELVOC concentrations, thereby explaining the lack of NPF.

Growing a single suspended perfect protein crystal in a fully noncontact manner

Nucleation is a fundamental process that determines the structure, morphology, and properties of crystalline materials, and is difficult to control because it is unpredictable. Here, we demonstrate a new method to control the protein crystal nucleation using a magnetic force, where we manipulate the movement and coalescence of nucleation precursors by adding paramagnetic salt into the crystallization solution to constrain the number and position of nucleation. We found that protein nucleation could be significantly affected by the magnetic force that the gradient magnetic fields generate. When the magnetization force is sufficiently enough, nucleation can be confined to the crystallization solution with no interface contact; therefore, only one crystal nucleus appears, which results in noncontact suspension growth of a single crystal in the crystallization solution system. Under these situations, the nucleation rate significantly decreases due to the coalescence of the dense liquid phase, and the crystal growth rate also decreases due to the suppression of convection, which increases the crystal quality. Our findings provide a new method for the noncontact control of crystal nucleation and demonstrate that externally applied physical environments can be used to affect the liquid-liquid phase separation process.

Simultaneous recovery of ammonium sulfate and ice from aqueous solution using eutectic freeze crystallization process

This study investigated the feasibility of eutectic freeze crystallization (EFC) process for ammonium sulfate (AS) salt recovery from 41 wt% AS solution. The EFC experiments were conducted using a 1 L double-jacketed crystallizer coupled with a recirculating chiller under varying freezing time, seed mass and seed size. The EFC process demonstrated successful AS salt recovery and water purification with the highest ice purity attained at 96.28 %. The construction of a binary AS-water phase diagram allowed the determination of the eutectic temperature, which was found to be −19.06 °C at 40 wt% of AS solution. The results indicated that the increase in freezing time enhanced the AS nucleation rate, growth rate, yield and mean product crystal size. The introduction of seeding not only provided well-controlled crystal nucleation and growth during EFC process, but also promoted the formation of larger, well-structured crystals and reduced agglomeration. Overall, the EFC process is a viable and promising option for recovering AS from wastewater, which offers high potential towards achieving zero liquid discharge goal, i.e. a sustainable and efficient approach in managing industrial effluent rich in ammonium and sulfate contaminants.

Seed-Assisted Hydrothermal Synthesis of Monodispersed Au@C Core–Shell Nanostructures for Enhancing Thermal Diffusivity of Water-Based Nanofluids

Au@C core–shell nanostructures (Au@C-NS) were synthesized through a low-temperature seed-assisted hydrothermal approach using glucose as carbon source. The material characterization and chemical analysis confirm that the synthesis method allows to obtain uniform core–shell nanostructures constituted by a crystalline metal core and an amorphous carbon shell. Depending on the synthesis conditions, their average size ranges from 146 nm to 342 nm with relative standard deviation as low as 7 %. It is proposed that the characteristic monodispersity results due to a high nucleation rate of the carbon phase at the liquid–solid interface. The obtained monodisperse Au@C-NS were used to prepare water-based nanofluids with superior heat transport properties. The thermal lens analysis shows that the thermal diffusivity of Au@C nanofluids is 9.5 % and 31.3 % higher than their Au nanofluids counterparts and pure water, respectively, at particle concentration of 285 × 1011 ml−1. Phonon-related interactions at the metal cores and carbon shells interfaces are proposed as the heat transport mechanism behind the thermal diffusivity enhancement of the Au@C water-based nanofluids.

Preparation of C-S-H seeds from waste glass powder and its effect on early performance of cement paste

This study investigates the hydrothermal synthesis of calcium silicate hydrate (C-S-H) seeds using nano-size glass powder (NGP) derived from siliceous raw materials and CaO as the calcareous precursor. The influence of varying NGP concentrations on the particle size, microstructure, and phase composition of the C-S-H seeds was systematically analyzed. The synthesized C-S-H seeds were subsequently employed as additives to evaluate their effects on the early hydration process and compressive strength development of cement paste. The results indicate that increasing the NGP concentration from 0.2 mol/L to 0.8 mol/L leads to an exponential increase in the median particle size of the C-S-H seeds from 147 nm to 1328 nm and a corresponding morphological transformation from flocculent to granular structures. Additionally, the purity of the C-S-H sample decreased from 74.8% to 54.5% as the NGP concentration increased. The addition of C-S-H seeds can increase the 12h compressive strength of cement pastes by 15.5%–53.5%. This improvement is due to the accelerated early hydration kinetics induced by the C-S-H seeds, which act as nucleation sites, thereby increasing the nucleation and growth rates by 31.4% and 53.2%, respectively.

Flow-based nonperturbative simulation of first-order phase transitions

We present a flow-based method for simulating and calculating nucleation rates of first-order phase transitions in scalar field theory on a lattice. Motivated by recent advancements in machine learning tools, particularly normalizing flows for lattice field theory, we propose the “partitioning flow-based Markov chain Monte Carlo (PFMCMC) sampling” method to address two challenges encountered in normalizing flow applications for lattice field theory: the “mode-collapse” and “rare-event sampling” problems. Using a (2+1)-dimensional real scalar model as an example, we demonstrate the effectiveness of our PFMCMC method in modeling highly hierarchical order parameter probability distributions and simulating critical bubble configurations. These simulations are then used to facilitate the calculation of nucleation rates. We anticipate the application of this method to (3+1)-dimensional theories for studying realistic cosmological phase transitions.

Modeling of the perovskite nickelate SmNiO3 nucleation from amorphous thin films: A Volmer's thermodynamical approach

We present a thermodynamical model based on Volmer's nucleation theory adapted to the case of the perovskite nickelate SmNiO3 crystallization (SNO) from an amorphous (aSNO) thin film. This amorphous phase is synthesized via reactive magnetron sputtering and then subsequently annealed in air at temperatures between 725 and 925 K to crystallize it. This model allows to predict the theoretical nucleation rate of the crystallized perovskite phase according to the annealing temperature, the type of the nucleation (homogeneous and heterogeneous mechanisms) and to estimate some physical and thermodynamical data related to this transformation. A theoretical evaluation of the nucleation rate shows that the optimum temperature for crystallization is close to 800 K for which the nucleation rate can reach 1021 m-3.s-1 if considering both homogeneous and heterogeneous nucleation mechanisms. As the annealing temperature moves away from 800 K, the theoretical nucleation rate drops drastically, as observed experimentally by X-ray Diffraction (XRD) when we annealed 200 nm thick aSNO films. The good agreement between the presented model and the experimental crystallization results allows us to numerically evaluate some physical parameters not yet reported to date in the literature for SNO perovskites such as the surface energy between the amorphous and the crystallized SNO phases, the strain energy when the crystallization occurs and the enthalpy associated with crystallization.

Nucleation and phase transition of decagonal quasicrystals.

In this work, we study the nucleation of quasicrystals from liquid or periodic crystals by developing an efficient order-order phase transition algorithm, namely, the nullspace-preserving saddle search method. In particular, we focus on nucleation and phase transitions of the decagonal quasicrystal (DQC) based on the Lifshitz-Petrich model. We present the nucleation path of DQC from the liquid and demonstrate one- and two-stage transition paths between DQC and periodic crystals. We provide a perspective of the group-subgroup phase transition and nucleation rates to understand the nucleation and phase transition mechanisms involving DQC. These results reveal the one-step and multi-step modes of symmetry breaking or recovery in the phase transition from DQC, where the multi-step modes are more probable.

An analysis of the synthesis, crystal structure, optical, spectroscopic, mechanical, self-focusing, and third-order nonlinear optical properties of Kojic acid single crystals

A single, excellent crystal of Kojic acid (KA) was developed utilising the traditional approach of gradual evaporation in a solution-growing procedure. A variety of characterisation techniques were utilised to evaluate the characteristics of the crystals generated. Single crystal x-ray diffraction (SXRD) was utilised to identify the crystal structure. The crystalline arrangement of the KA crystal was confirmed using a powder x-ray diffraction (PXRD) analysis. Experiments with UV–vis spectrometers revealed that the KA crystal has a lower wavelength at which it blocks UV light but has outstanding light transmission throughout the visible spectrum. The KA single crystal has an energy band gap (Eg) of 2.5 eV. The Z-scan method was used to examine the third order susceptibility, nonlinear refraction, and nonlinear absorption coefficient of the synthesised KA crystal. The dielectric characteristics and AC conductivity were examined, with a particular emphasis on their connection to resistance at room temperature. The presence of appreciable levels of kojic acid was confirmed by energy-dispersive spectrometry. The crystal’s thermal behaviour was investigated using differential thermal analysis (DTA) and thermogravimetric (TG) methods. The nucleation parameters and controlled nucleation rate were calculated using normal theoretical research methods.

Global modeling of aerosol nucleation with a semi-explicit chemical mechanism for highly oxygenated organic molecules (HOMs)

Abstract. New particle formation (NPF) involving organic compounds has been identified as an important process affecting aerosol particle number concentrations in the global atmosphere. Laboratory studies have shown that highly oxygenated organic molecules (HOMs) can make a substantial contribution to NPF, but there is a lack of global model studies of NPF with detailed HOM chemistry. Here, we incorporate a state-of-the-art biogenic HOM chemistry scheme with 96 chemical reactions to a global chemistry–climate model and quantify the contribution to global aerosols through HOM-driven NPF. The updated model captures the frequency of NPF events observed at continental surface sites (normalized mean bias changes from −96 % to −15 %) and shows reasonable agreement with measured rates of NPF and sub-20 nm particle growth. Sensitivity simulations show that compared to turning off the organic nucleation rate, turning off organic initial growth results in a more substantial decrease in aerosol number concentrations. Globally, organics contribute around 45 % of the annual mean vertically integrated nucleation rate (at 1.7 nm) and 25 % of the vertically averaged growth rate. The inclusion of HOM-related processes leads to a 39 % increase in the global annual mean aerosol number burden and a 33 % increase in cloud condensation nuclei (CCN) burden at 0.5 % supersaturation compared to a simulation with only inorganic nucleation. Our work predicts a greater contribution of organic nucleation to NPF than previous studies due to the semi-explicit HOM mechanism and an updated inorganic NPF scheme. The large contribution of biogenic HOMs to NPF on a global scale could make aerosol sensitive to changes in biogenic emissions.

Nucleation of multi-species crystals: methane cleatrate hydrates, a playground for classical force models

Nucleation and growth of methane clathrate hydrates is an exceptional playground to study crystallisation of multi-component, host-guest crystallites when one of the species forming the crystal, the guest, has a higher concentration in the solid than in the liquid phase. This adds problems related to the transport of the low concentration species, here methane. A key aspect in the modelling of clathrates is the water model employed in the simulation. In previous articles, we compared an all-atom force model, TIP4P/Ewald, with a coarse grain one, which is highly appreciated for its computational efficiency. Here, we perform a complementary analysis considering three all-atoms water models: TIP4P/Ewald, TIP4P/ice and TIP5P. A key difference between these models is that the former predicts a much lower freezing temperature. Intuitively, one expects that to lower freezing temperatures of water correspond to lower water/methane–methane gas–clathrate coexistence ones, which determines the degree of supercooling and the degree of supersaturation. Hence, in the simulation conditions, 250 K (500 atm, and fixed methane molar fraction), one expects computational samples made of TIP4P-ice and TIP5P, with a similar freezing temperature ( T f ∼ 273 K), to be more supersaturated with respect to the case of TIP4P-Ew ( T f ∼ 245 K), and crystallisation to be faster. Surprisingly, we find that while the nucleation rate is consistent with this prediction, growth rate with TIP4P-ice and TIP5P is much slower than with TIP4P-Ew. The latter was attributed to the slower reorientation of water molecules in strong supercooled conditions, resulting in a lower growth rate. This suggests that the freezing temperature is not a suitable parameter to evaluate the adequacy of a water model.