Stable Solid Phase Research Articles

Efficient wide-range calculation of free energies in solids and liquids using reversible-scaling molecular dynamics

We elaborate a novel and efficient method to obtain multiphase Helmholtz free energies from molecular dynamics (MD) simulations over wide ranges of volume and temperature in materials that can be described by temperature-independent ion forces, with both higher accuracy and order-of-magnitude cost savings compared to direct thermodynamic-integration techniques. Our method leverages and significantly extends the technique of reversible-scaling molecular dynamics (RSMD) proposed by de Koning et al. [Phys. Rev. Lett. 83, 3973 (1999)], which allows a free-energy difference in a given phase at constant volume to be calculated as a function of temperature from a single MD simulation. In mechanically stable solid phases, our approach carefully combines quasiharmonic lattice dynamics at low temperatures with an accurate and fully isolated RSMD simulation of the anharmonic vibrational free energy at high temperatures to produce a seamless free energy from zero temperature to above melt along constant-volume isochores. In the liquid, we combine a unique calculation of the free energy along a high-temperature reference isotherm with isochoric RSMD simulations from that temperature to below melt. In metastable solid phases that are mechanically unstable at low temperature, we use two-phase MD melt simulations together with the liquid free energy to obtain the solid free energy along the solidus melt line and then perform isochoric RSMD simulations to temperatures above and below that point. While our free-energy method is general, we have specifically adapted it here to the case of metals in which the ion forces are well described by model generalized pseudopotential theory (MGPT) multi-ion interatomic potentials, and additive electron-thermal free-energy contributions can be included. Then using refined Ta6.8$x$ MGPT potentials, we have converged total free energies and their components to very high and unprecedented sub-milli-Rydberg (mRy) numerical accuracy in the stable-bcc, liquid, and metastable-fcc phases of tantalum for volumes ranging from up to 26% expansion to nearly twofold compression and for temperatures to 25 000 K. In turn, we have successfully used the free energies so obtained to calculate physically accurate thermodynamic properties and gain new insight into their behavior, including sensitive thermodynamic derivatives, bcc and fcc melt curves, and a multiphase equation of state for tantalum (Ta) over the same temperature range and for pressures as high as 600 GPa. We show that the anharmonic free-energy component in the bcc solid, although only 1--5 mRy in magnitude for Ta, can have a significant (15%--20%) effect on thermal expansivity, the Gr\uneisen parameter, and melt temperatures. We further show that the electron-thermal free-energy component can similarly impact the specific heat and thermal expansivity in both the solid and the liquid, while only minimally affecting (to$\ensuremath{\le}3$%) the bcc and fcc melt curves.

Thermodynamic evaluation of the Np–Zr system using CALPHAD and ab initio methods

A new thermodynamic description of Np–Zr alloys is developed using the CALPHAD (CALculation of PHAse Diagrams) method based on available experimental information on phase equilibria, supplemented by ab initio energetics for end members that are not available in the standard CALPHAD unary database. The present thermodynamic description shows improvements compared to previous models in the predicted phase diagram when comparing to assessed reliable experimental data. Ab initio Density Functional Theory (DFT) calculations are also performed on all known stable solid phases of Np–Zr alloys and the end member Np and Zr metals. Comparing to the formation energetics predicted from the CALPHAD models of both this work and a previous study we find that DFT with the Generalized Gradient Approximation (GGA) to the exchange-correlation potential overestimates the formation enthalpies of Np and Np–Zr by about 0.15eV/atom, and the so-called DFT+U approach with a Ueff of near 0.65eV can reduce this error by about 0.07–0.10eV. Our comprehensive comparison between existing CALPHAD, ab initio and experimental results for Np–Zr indicates a need for further experiments on the phase equilibrium.

Z methodology for phase diagram studies: platinum and tantalum as examples

The Z methodology is a novel technique for phase diagram studies. It combines the direct Z method for the computation of melting curves and the inverse Z method for the calculation of solid-solid phase boundaries. In the direct Z method, the solid phases along the melting curve are determined by comparing the solid-liquid equilibrium boundaries of candidate crystal structures. The inverse Z method involves quenching the liquid into the most stable solid phase at various temperatures and pressures to locate a solid-solid boundary. The direct and inverse Z methods in conjunction with the VASP ab initio molecular dynamics package are used to investigate the phase diagrams of tantalum and platinum. We compare our results to the most recent experimental data.

Effects of organic/inorganic amendments on trace elements dispersion by leachates from sulfide-containing tailings of the São Domingos mine, Portugal. Time evaluation

Greenhouse pot experiments were conducted over 13months to evaluate the effect of two amendment mixture doses (30 and 75Mg/ha) on the geochemical dispersion of trace elements by leaching hazardous mine wastes from the São Domingos mine. Mineralogical evolution of these materials was also evaluated. Amendment mixtures containing solid wastes from agriculture (plant remains+strawberry substrate and rockwool used for the strawberry crop) and from distillation of Ceratonia siliqua L. and Arbutus unedo L. fruits were used to improve the chemical characteristics of leachates from sulfide mine wastes. Sulfide mine wastes had acidic characteristics, as well as high electrical conductivity and total element concentrations (g/kg; Al: 54.8–61.2; Fe: 104.0–110.0; Pb: 9.0–13.8; S: 63.6–68.0; As: ≈1). These features contributed to the large capacity for leaching of hazardous elements during, at least, the first four months of incubation. In the seventh month of incubation, there was a significant decrease in the leachate concentration of the majority of hazardous elements. The addition of amendments minimised trace element dispersion in leachate percolation during the first seven months (25 to 99% reduction compared to control, depending on the element and sampling period). However, the leachate characteristics were not influenced by amendment doses and no significant differences were observed in leachate composition (control and amended treatments) after 13months. Amendment application led to differences between the solid phases of the efflorescent salts formed on the surface of the control and the amended treatments. The efflorescent salts contained very soluble aluminium sulfates, together with alunite–jarosite-group solid phases in amended samples, and copiapite-group solid phases in control. In the core materials (5 to 10cm in depth), the mineralogy was similar in both control and amended samples. The presence of various stable solid phases from alunite–jarosite-group, such as jarosite and beudantite (mainly in deeper materials), can explain the low concentrations of trace elements in the leachates after thirteen months.

Quantum Monte Carlo study of the dynamic structure factor in the gas and crystal phase of hard-sphere bosons

We investigate the dynamic structure factor of a system of Bose particles at zero temperature using quantum Monte Carlo methods. Interactions are modeled using a hard-sphere potential of size $a$ and simulations are performed for values of the gas parameter $n{a}^{3}$ ranging from the dilute regime up to densities $n$ where the thermodynamically stable phase is a solid. With increasing density, we observe a crossover of the dispersion of elementary excitations from a Bogoliubov-type spectrum to a phonon-maxon-roton curve and the emergence of a broad multiphonon contribution accompanying the single-quasiparticle peak. In particular, for $n{a}^{3}=0.2138$, which corresponds to superfluid ${}^{4}$He at equilibrium density, the extracted spectrum turns out to be in good agreement with the experimental energy-momentum dispersion relation in the roton region and for higher momenta. The behavior of the spectral function at the same density in the stable solid and metastable gas phase above the freezing point is also discussed.

Two highly stable and selective solid phase microextraction fibers coated with crown ether functionalized ionic liquids by different sol–gel reaction approaches

In this work, two novel crown ether functionalized ionic liquid (FIL)-based solid phase microextraction (SPME) fibers were prepared by sol–gel technology using the synthesized 1-(trimethoxysily)propyl 3-(6′-oxo-benzo-15-crown-5 hexyl) imidazolium bis(trifluoromethanesulphonyl)imide ([TMSP(Benzo15C5)HIM][N(SO2CF3)2]) and 1-allyl-3-(6′-oxo-benzo-15-crown-5 hexyl) imidazolium bis(trifluoromethanesulphonyl)imide ([A(Benzo15C5)HIM][N(SO2CF3)2]) as selective stationary phases. Owing to the introduction of trimethoxysilypropyl to the imidazole cation, the [TMSP(Benzo15C5)HIM][N(SO2CF3)2] could be chemically bonded to the formed sol–gel silica substrate through the hydrolysis and polycondensation reaction. Similarly, the [A(Benzo15C5)HIM][N(SO2CF3)2] was able to participate in the formation of the organic–inorganic copolymer coatings through the free radical crosslinking reaction. These two fibers were determined to have “bubble-like” surface characteristics analogous to a previously prepared [A(Benzo15C5)HIM][PF6]-based fiber. Their thermal stabilities were much higher than that of the [A(Benzo15C5)HIM][PF6]-based coating. They were capable of withstanding temperatures as high as 400°C without evident loss of the crown ether FILs. They also had strong solvent, acid and alkali resistance, good coating preparation reproducibility and high selectivity for medium polar to polar compounds. The high selectivity of these two fibers could be attributed to the strong ion-dipole, hydrogen bonding and π–π interactions provided by the synergetic effect of ILs and benzo-15-crown-5 functionalities. Moreover, the selectivity of these two fibers was rather different although the structures of these two crown ether FILs were very similar. This is maybe because the relative contents of the crown ether FILs chemically bonded to the organic–inorganic copolymer coatings were quite different when prepared by different sol–gel reaction approaches.

The Viedma Deracemization of Racemic Conglomerate Mixtures as a Paradigm of Spontaneous Mirror Symmetry Breaking in Aggregation and Polymerization

Simulations of a chemical kinetics model, based on the free-energy relationships of classical primary nucleation theory, show that the deracemization phenomenon in systems of achiral or fast racemizing compounds yielding enantiopure crystals as the more stable solid phase is a true spontaneous mirror symmetry breaking process (SMSB). That is, the achievement of a stationary chiral state is more stable than the racemic one. The model translates the free-energy relationships determined by the existence of a critical size cluster to a chemical kinetics model, in which the consideration of forward and backward reaction rate constants avoids the misuse of network parameters that violate thermodynamic constraints (microreversibility principle), which would lead to apparent in silico SMSB. The model provides qualitative agreement for deracemizations by mechanical attrition of visible crystals, as well as for those obtained under temperature gradients. The analysis of the effect of the system parameters to obtain a SMSB scenario shows that the network possesses the principal characteristics of SMSB networks: 1) an enantioselective autocatalytic stage, corresponding to the non-linear kinetics of enantioselective (homochiral) cluster-to-cluster growth, and 2) the mutual inhibition step originating in the backward flow of chiral clusters towards smaller achiral clusters, or even to a racemizing monomer. The application of such a SMSB kinetic model to enantioselective polymerizations and to chiral biopolymers is discussed.

Solution‐Mediated Phase Transformation of a Hydrate to its Anhydrous Form of Donepezil Hydrochloride

AbstractThe solubility of form I (hydrate) and form III (anhydrous form) of donepezil hydrochloride (DHCl) in methanol/isopropyl ether mixtures was determined at different temperatures by a synthetic method with laser monitoring observation. The experimental data were correlated with the modified Apelblat equation. Dissolution enthalpy and entropy were predicted by this equation. The mechanisms involved in solution‐mediated transformation of a hydrate (form I) to its anhydrous form (form III) was investigated and characterized by in situ and offline measurement technologies, such as focused‐beam reflectance measurement (FBRM), powder X‐ray diffraction (PXRD), differential scanning calorimetry analysis (DSC), and moisture analyzer. The transformation involves nucleation of the metastable solid (form I), dissolution of the metastable solid, self‐recognition of the molecular units to nucleate a more stable solid phase (form III), and growth of the stable phase. The results indicate that the rate of transformation increases with increasing temperature and driving force.

Nucleation of a Stable Solid from Melt in the Presence of Multiple Metastable Intermediate Phases: Wetting, Ostwald’s Step Rule, and Vanishing Polymorphs

In many systems, nucleation of a stable solid may occur in the presence of other (often more than one) metastable phases. These may be polymorphic solids or even liquid phases. Sometimes, the metastable phase might have a lower free energy minimum than the liquid but higher than the stable-solid-phase minimum and have characteristics in between the parent liquid and the globally stable solid phase. In such cases, nucleation of the solid phase from the melt may be facilitated by the metastable phase because the latter can "wet" the interface between the parent and the daughter phases, even though there may be no signature of the existence of metastable phase in the thermodynamic properties of the parent liquid and the stable solid phase. Straightforward application of classical nucleation theory (CNT) is flawed here as it overestimates the nucleation barrier because surface tension is overestimated (by neglecting the metastable phases of intermediate order) while the thermodynamic free energy gap between daughter and parent phases remains unchanged. In this work, we discuss a density functional theory (DFT)-based statistical mechanical approach to explore and quantify such facilitation. We construct a simple order-parameter-dependent free energy surface that we then use in DFT to calculate (i) the order parameter profile, (ii) the overall nucleation free energy barrier, and (iii) the surface tension between the parent liquid and the metastable solid and also parent liquid and stable solid phases. The theory indeed finds that the nucleation free energy barrier can decrease significantly in the presence of wetting. This approach can provide a microscopic explanation of the Ostwald step rule and the well-known phenomenon of "disappearing polymorphs" that depends on temperature and other thermodynamic conditions. Theory reveals a diverse scenario for phase transformation kinetics, some of which may be explored via modern nanoscopic synthetic methods.

Free energy barriers for homogeneous crystal nucleation in a eutectic system of binary hard spheres

In this study, the free energy barriers for homogeneous crystal nucleation in a system that exhibits a eutectic point are computed using Monte Carlo simulations. The system studied is a binary hard sphere mixture with a diameter ratio of 0.85 between the smaller and larger hard spheres. The simulations of crystal nucleation are performed for the entire range of fluid compositions. The free energy barrier is found to be the highest near the eutectic point and is nearly five times that for the pure fluid, which slows down the nucleation rate by a factor of 10(-31). These free energy barriers are some of highest ever computed using simulations. For most of the conditions studied, the composition of the critical nucleus corresponds to either one of the two thermodynamically stable solid phases. However, near the eutectic point, the nucleation barrier is lowest for the formation of the metastable random hexagonal closed packed (rhcp) solid phase with composition lying in the two-phase region of the phase diagram. The fluid to solid phase transition is hypothesized to proceed via formation of a metastable rhcp phase followed by a phase separation into respective stable fcc solid phases.

Growth of Highly Oriented Deuterium Crystals in Silicon Nanochannels

The structure of solid deuterium confined in 9 nm wide tubular silicon nanochannels has been studied by means of elastic neutron scattering techniques. As a result we report the formation of fcc D(2) as the stable solid phase in confinement in contrast to the hcp bulk structure. Further, a preferred alignment of D(2) nanocrystals with respect to the surrounding crystalline silicon matrix is discussed in terms of heteroepitaxial growth of solid D(2) on crystalline pore walls.

A non-perturbative approach to freezing of superfuid 4He in density functional theory

Freezing of various classical liquids is successfully described by density functional theory (DFT). On the other hand, so far no report has been published that DFT describes the freezing of superfuid 4He correctly. In fact, DFT gives too stable solid phase and the superfuid phase does not exist at finite positive pressures within a second order perturbation. In this paper we try a non-perturbative version of DFT, that is modified weighted density approximation (MWDA) to go beyond second order perturbation for the freezing of superfuid 4He. Via an exact zero temperature quantum Monte-Carlo (QMC) method we have computed the equation of state and the compressibility of superfuid 4He. By utilizing a recently introduced analytic continuation method (the GIFT method), we have obtained also density response functions at different densities from QMC imaginary time correlation functions. Contrary to second order perturbation, by employing these QMC data as DFT input we find a too stable superfuid phase, preventing freezing around the experimentally observed freezing pressure. We find the same pathological behavior by using another model energy functional of superfuid 4He (Orsay-Trento model). We conclude that the straightforward MWDA calculation gives such a poor result when liquid-gas transition is present.

Density Functional Theory and Bose Statistics for the Freezing of Superfluid 4He

Density functional theory so far has experienced pathological results in the description of the freezing of superfluid 4He, even with the use of accurate inputs, namely the density response function, χ(q), and the equation of state of the superfluid. In fact, while the second order approximation of Ramakrishnan-Yussouff type gives a too much stable solid phase (Likos et al. in Phys. Rev. B 55:8867, 1997; Minoguchi and Galli in J. Law Temp. Phys. 162:160, 2011), a non-perturbative treatment called modified weighted density approximation (MWDA) gives, on the other hand, a too stable superfluid phase (Minoguchi et al. in J. Phys. Conf. Ser. 2012). We have preliminarily performed a MWDA calculation for a specific Gaussian distortion α=0.387 A−2 of liquid 4He. By using χ(q) and the equation of state of a system of liquid 4He in which Bose statistics has been suppressed, we have found that the calculation provides a lower energy. This indicates that the solid may be better described by a distorted normal liquid. The input data has been obtained via Path Integral Monte Carlo simulations of a system of distinguishable 4He atoms. The χ(q) has been obtained from the dynamic structure factors extracted, via the Genetic Inversion via Falsification of Theories (GIFT) method (Vitali et al. in Phys. Rev. B 82:174510, 2010) from imaginary time density–density correlation functions.

Solidification Behaviour of Ti–Cu–Fe–Co–Ni High Entropy Alloys

For the first time, we report here that the development of the novel Ti–Cu–Fe–Co–Ni high entropy alloys (HEAs) via vacuum arc melting technique using non consumable tungsten electrode under high purity Ar atmosphere on a water-cooled copper hearth. Ti–Cu–Fe–Co–Ni multicomponent alloys with varying Ti/Cu (x) molar ratio (x = 1/3, 3/7, 3/5, 9/11, 1, 11/9 and 3/2) have been prepared through the tailoring of microstructure to get understanding of the phase formation and the microstructural evolution of these multicomponent HEAs. X-ray diffraction and scanning electron microscopy coupled with energy dispersive spectroscopic results confirm the presence of (Cu)ss, (Co)ss and (β-Ti)ss dendrites with ultrafine eutectic between cubic (Cu)ss and Laves phase (Ti2Co type). The solidification pathways of novel alloys are critically discussed as follows. For x = 9/11, 1, 11/9 and 3/2; firstly, (β-Ti)ss dendrite is formed from the liquid, followed by the liquid phase separation between the cobalt-rich solid solution (Co)ss and copper-rich solid solution (Cu)ss and finally, the remaining liquid undergoes eutectic reaction between copper solid solution (Cu)ss and the Laves phase (Ti2Co Type), whereas for x = 1/3, 3/7 and 3/5; (β-Ti)ss dendrite is formed first from the liquid and then remaining liquid undergoes the liquid phase separation resulting two different dendrites of (Cu)ss and (Co)ss phases. Detailed thermodynamic calculations have been carried to rationalize the formation of stable solid solution phases of these newly developed multicomponent Ti–Cu–Fe–Co–Ni HEAs.

Heavy metal removal by biomineralization of urease producing bacteria isolated from soil

Microorganisms can mediate the formation of minerals by a biomineralization process. This offers an efficient way to sequester inorganic pollutants, including heavy metals within relatively stable solid phases, and the main mechanisms involved in mineral precipitation by microorganisms were investigated in this study. Biomineralization of nickel, copper, lead, cobalt, zinc and cadmium, by six metal-resistant bacterial strains, were investigated using microcosm experiments. These bacteria were isolated from nursery garden soil and characterized for their potential application in bioremediation. These bacteria produced the enzyme urease which can hydrolyze urea. Due to this enzymatic reaction, soil pH increased and carbonate was produced, which results in mineralization of the soluble heavy metal ions present in soil water and their ultimate conversion to carbonates. The selected bacteria showed high removal rates, ranging from 88% to 99% of heavy metals following incubation for 48 h. Scanning electron microscopy and X-ray diffraction analyses revealed that bioaccumulated heavy metals ions were deposited around the cell envelope as rhombohedral, sphere and needle shaped crystalline carbonate minerals when the pH was 8–9. This study demonstrated that indigenous bacteria can survive heavy metal toxicity from soil and wastewater and sequester soluble heavy metals into biominerals and these bacteria can play important role in heavy metal bioremediation.

Superfluidity of metastable glassy bulkpara-hydrogen at low temperature

Molecular para-hydrogen has been proposed theoretically as a possible candidate for superfluidity, but the eventual superfluid transition is hindered by its crystallization. In this work, we study a metastable non crystalline phase of bulk p-H2 by means of the Path Integral Monte Carlo method in order to investigate at which temperature this system can support superfluidity. By choosing accurately the initial configuration and using a non commensurate simulation box, we have been able to frustrate the formation of the crystal in the simulated system and to calculate the temperature dependence of the one-body density matrix and of the superfluid fraction. We observe a transition to a superfluid phase at temperatures around 1 K. The limit of zero temperature is also studied using the diffusion Monte Carlo method. Results for the energy, condensate fraction, and structure of the metastable liquid phase at T=0 are reported and compared with the ones obtained for the stable solid phase.

Effects of predetermined nuclei and limited transformation on polymorphic crystallization in a model polymer

AbstractFormation of different polymorphic structures plays important role in crystallization of some polymers, like polypropylene, polycaproamide, poly(vinylidene difluoride), and others. Physical properties of such materials depend on phase structure, that is, fractions of different polymorphs. Basing on the model of many‐phase transitions (Ziabicki, J Chem Phys 2005, 123, 174103; Ziabicki and Misztal‐Faraj, J Mater Res, 2011, 26, 1585) a model system consisting of an amorphous phase, stable solid phase, and metastable polymorphic phase was analyzed. Two effects in the kinetics of polymorphic crystallization have been analyzed: effect of the presence of universal and/or selective predetermined nuclei and limited crystallizability resulting from molecular constraints in high‐molecular systems. Conditions in which different phase compositions (i.e., different proportions of individual phases) have been discussed. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Formation of the joint of dissimilar metals in the solid phase by the method of vacuum hot rolling

On the basis of the experimental data and physical principles, we formulate the principal conditions of getting stable solid-phase joints of dissimilar materials as a result of their simultaneous vacuum hot rolling, namely, the possibility of sliding of one metal over the other, the motion of metals must obey the Bernoulli equation for incompressible liquids, the possibility of mass transfer of the atoms of dissimilar metals through their common boundary, the continuity of the flow or the second-by-second equality of the masses of rolled metal, and the equality of powers acquired by the metals.

Crystal structure and phase behavior of the tolyl glycerol ethers. From the conglomerate former to the chirality-driven nanogelator

According to differential scanning calorimetry data ortho-, meta-, and para-tolyl glycerol ethers 1–3 form thermodynamically most stable crystal phases during solution crystallization. For all members of the series the crystal phases formed during melt crystallization have different thermodynamic characteristics from those of the stable ones. Binary melting diagrams were constructed for the stable solid phases; on this basis it was found that 1 is prone to spontaneous resolution, and 2 and 3 form stable solid racemic compounds, the Gibbs energy of formation for which are found to be −2.70 and −2.43 kJ mol−1. Solution grown single crystals of 1–3 were investigated by an X-ray diffraction method. The principal supramolecular crystal formative motifs were revealed: 1D columns for 1 and scal-2, 2D bilayers having developed a 2D system of intermolecular hydrogen bonds (IMHB) for rac-2 and rac-3, and 2D bilayer having 1D spiral IMHB organization for scal-3. The possible reasons preventing the solid racemic compound formation in the case of 1, and the spontaneous resolution manifestation in the cases of 2 and 3 are disclosed. It was demonstrated that, from the whole family of tolyl glycerol ethers, only scal-3 samples are capable of supramolecular gels formation. This property is connected with the peculiarities of the scalemic 3 crystal packing.

Formation and stabilization of single-crystalline metastable AuGe phases in Genanowires

We use in situ observations by variable temperature transmission electron microscopy onAuGe alloy drops at the tips of Ge nanowires (NWs) with systematically varyingcomposition to demonstrate the controlled formation of metastable solid phases integratedin NWs. The process, which operates in the regime of vapor–liquid–solid growth, involves asize-dependent depression of the alloy liquidus at the nanoscale that leads to extremely Ge-richAuGe melts at low temperatures. During slow cooling, these liquid AuGe alloy drops showpronounced departures from equilibrium, i.e., a frustrated phase separation of Ge into theadjacent solid NW, and ultimately crystallize as single-crystalline segments of metastableγ-AuGe. Our findings demonstrate a general avenue for synthesizing NW heterostructurescontaining stable and metastable solid phases, applicable to a wide range of materials ofwhich NWs form by the vapor–liquid–solid method.