Molecular dynamics simulation of viscosity in supercooled liquid and glassy AgCu alloy

The viscosity of the model AgCu alloy is simulated by several methods using (i) correlation functions through the Green–Kubo formalism, (ii) a non-equilibrium molecular dynamics approach and (iii) creep tests under constant stress. Temperature dependences of the shear viscosity and the diffusion coefficient show the breakdown of the Stokes–Einstein relation well above the glass-transition temperature T_g. This observation is interpreted as a manifestation of the development of heterogeneities in the supercooled liquid approaching T_g. Based on a generalized Einstein formula for the viscosity of liquid, a temperature dependence of heterogeneity degree of supercooled liquid is estimated. Using the dependence of the deformation rate on external stress, the activation volume is evaluated to be four atomic volumes in liquid state. However, below the mode-coupling temperature T_c the activation volume increases by several times.     

Molecular dynamics investigations of glassforming binary Lennard-Jones systems with different anharmonicities

Dynamical properties of three glassforming binary Lennard-Jones systems with different anharmonicities of the interaction potential have been studied by molecular dynamics simulations. The onset temperature of slow dynamics T_A, the Mode Coupling theory critical temperature T_C and the Vogel–Fulcher–Tamman temperature T_VFT have been determined for the three models. A good agreement is found with most of the predictions of the Mode Coupling Theory. However, a detailed analysis of the master curve obtained from the superposition of the intermediate scattering functions reveals a significative temperature dependence of the stretched exponent β over a wide temperature range from the liquid state to the glass transition. It is shown that both fragility and stretched exponent β unambigously correlate with anharmonicity of the interaction potential.     

Structural investigation of amorphous and liquid Ge0.175Te0.825 by neutron scattering

The angular distribution of intensities of 1.003 Å neutrons scattered by an alloy of Ge_0.175Te_0.825 both in the amorphous and in the liquid state have been measured. The bulk amorphous sample, prepared by water quenching of the melt, has been examined at room temperature and just above the crystallization temperature T_x. The liquid sample has been examined at 400, 600 and 800°C. The analysis of the structure factors obtained from the corrected and scaled intensities indicates that the structural features of the amorphous sample are similar to those which would be expected if it were possible to cool the alloy to room temperature, while maintaining it in the liquid state. The analysis of the radical distribution functions, from Fourier inversion of the structure factors, indicates that a change of the coordination number n₁ from 2.43 to 3.25 occurs in passing from the amorphous to the liquid state at 400°C. This result has been interpreted in terms of coordination models. In the liquid state, it has been found that a model with fourfold coordinated Ge and threefold coordinated Te is consistent with n₁=3.25. The internal consistency of this model for the liquid state allows us to make a reasonable choice between the possibility of a 3 or 4 fold coordination for Ge in the glass. We conclude that a model based on four-fold coordinated Ge and twofold coordinated Te seems an appropriate representation for the coordination of the amorphous material.     

Structure of liquids and glasses in the Ge–Se binary system

A summary is given of the partial structure factors that have been measured for liquids and glasses in the Ge–Se binary system by using diffraction methods. Information is presented on the pair correlation functions describing the atomic species and use is made of the Bhatia–Thornton formalism to separate those pair correlation functions describing the system topology from those that describe the chemical ordering. The information made available by the measured Bhatia–Thornton partial structure factors on the thermodynamic properties of Ge–Se mixtures is briefly summarized. The properties of the network structures formed in liquid and glassy Ge–Se compounds are investigated as a function of composition, temperature and pressure. For GeSe₂ at ambient pressure it is shown that the so-called first sharp diffraction peak, which appears in the measured diffraction patterns at a small scattering wavevector value of ≈1 Å⁻¹ and which is associated primarily with Ge–Ge correlations, does account for discernable features of the observed intermediate range order in both the liquid and glassy phase. The first sharp diffraction peak in the measured Ge–Ge partial structure factor for both phases is described by comparable parameters suggesting communality in the underlying intermediate range order which survives the glass transition. Homopolar bonds are found to be a feature in the structure of liquid GeSe and both liquid and glassy GeSe₂ with Ge–Ge and Se–Se distances in the ranges 2.33(3)–2.42(2) and 2.30(2)–2.34(2) Å, respectively.     

Fast X-ray scattering measurements on high temperature levitated liquids

We describe a new high temperature environment based on aerodynamic levitation and CO₂ laser heating designed for high energy X-ray diffraction at the ID11 beamline at ESRF. The use of two lasers simultaneously provides a homogeneous temperature and makes it possible to explore the supercooled state with a high degree of control (about 500 °C below the melting point in this work) and to work very close to T_g. The scattered beam is measured over a relatively wide Q-range of 0.5–19 Å^?1 with the ESRF Frelon 2D CDD camera. Using 1-min measurements we obtained good quality structure factors at various temperatures in the liquid and supercooled state of CaAl₂O₄. We also performed time-resolved measurements using an acquisition time of 100 ms and we obtained good statistics even at large Q. The Al–O and Ca–O bond lengths and coordination numbers derived from the calculated pair distribution functions are in good agreement with our previous X-ray and neutron works.     

Relationship between viscous dynamics and the configurational thermal expansion coefficient of glass-forming liquids

We propose a model to describe the relationship between the viscosity of a glass-forming liquid and its configurational contribution to liquid state thermal expansion. The viscosity of the glass-forming liquids is expressed in terms of three standard parameters: the glass transition temperature (T_g), the liquid fragility index (m), and the extrapolated infinite temperature viscosity (η_∞), which are obtained by fitting of the Mauro–Yue–Ellison–Gupta–Allan (MYEGA) expression to measured viscosity data. The model is tested with experimental data for 41 different glass-forming systems. A good correlation is observed between our model viscosity parameter,h(T_g, m, η_∞), and the configurational coefficient of thermal expansion (i.e., the configurational CTE). Within a given class of glass compositions, the model offers the ability to predict trends in configurational CTE with changes in viscosity parameters. Since viscosity is governed by glass network topology, the model also suggests the role of topological constraints in governing changes in configurational CTE.     

Diffusion in bulk-metallic glass-forming Pd–Cu–Ni–P alloys: From the glass to the equilibrium melt

Since the discovery of bulk-metallic glasses there has been considerable research effort on these systems, in particular with respect to mass transport. Now the undercooled melt between the melting temperature and the caloric glass transition temperature, which has not been accessible before due to the rapid onset of crystallization, can be investigated and theories can be tested. Here we report on radiotracer diffusion measurements in metallic bulk-glass-forming Pd–Cu–Ni–P alloys. Serial sectioning was performed by grinding and ion-beam sputtering. The time, temperature as well as the mass dependence, expressed in terms of the isotope effect E, of Co-diffusion were investigated. In the glassy state as well as in the deeply supercooled state below the critical temperature T_c, where the mode coupling theory predicts a freezing-in of liquid-like motion, the experimentally determined very small isotope effects indicate a highly collective hopping mechanism involving some ten atoms. Below T_c the temperature dependence shows Arrhenius-type behavior with an effective activation enthalpy of 3.2 eV. Above T_c the onset of liquid-like motion is evidenced by a gradual drop of the effective activation energy and by the validity of the Stokes–Einstein equation, which is found to break down below T_c. This strongly supports the mode coupling scenario. The Stokes–Einstein equation is presently tested for other constituents of the alloy. The Co isotope effect measurements, which have never been carried out near T_c in any material, show atomic transport up to the equilibrium melt to be far away from the hydrodynamic regime of uncorrelated binary collisions.     

Modified perturbed hard-sphere equation of state for alkali metal alloys

A modified perturbed hard-sphere equation of state has been applied to calculate the liquid density of alkali metal alloys. Two scaling parameters ε and σ are sufficient to calculate the temperature-dependent parameters of equation of state a(T) and b(T) that are universal functions of the reduced temperature. Calculations cover a broad range of temperature from melting point close to critical point. In this work, we have extended the present correlation to mixtures of any number of components. The predicted results for the liquid density of K–Cs and Na–K alloys over the whole range of concentrations are in good agreement with experimental data. From 220 data points examined for molten alloys deviations are within about 5%.     

The Debye–Waller factor approaching the glass-transition temperature in phosphate glasses

The temperature dependence of the mean square displacement, 〈u²〉, calculated by elastic neutron scattering for two phosphate glasses, (AgI)_x(AgPO₃)_1−x with x = 0.3, 0.55, is analysed. The studied samples are probed in a wide range of temperatures going from a few tens of K up to the glass transition temperature and well into the undercooled liquid state. In the low temperature regime a solid like behaviour appears, showing a linear temperature dependence of the Debye–Waller factor, while around T_g the onset of a pronounced increase of 〈u²〉 is observed. The temperature dependence of the normalized elastic intensity and the drawn out Debye–Waller factor are fitted and analyzed by the theoretical previsions of Mode Coupling Theory finding a good agreement.     

Structural properties and evolution in the solidification process of Cu–Ag alloys

The atomic structures of liquid Cu–Ag alloys (Cu₈₀Ag₂₀, Cu₆₀Ag₄₀, Cu₄₀Ag₆₀ and Cu₂₀Ag₈₀) have been investigated in the solidification process by means of X-ray diffraction. The results show that the liquid structures of Cu–Ag alloys, which are micro-homogeneous and similar with their solid state, display quite stable changes on a large-scale range indicated by the correlation radius r_c, although the short-range order structures change obviously around their liquidus (liquid–solid transformation). This is different from the results of the In₃₀Sn₇₀ alloy we previously reported, which shows an abrupt structure changes around its liquidus. In addition, the Gaussian peaks decomposition of the radial distribution functions (RDF(r)) was also performed to shed light on the element distribution and structure evolution in the whole solidification process especially around the liquidus.     

Formation and structural characteristics of Pd–Ag/SiO2 and Pd–Cu/SiO2 catalysts synthesized by cogelation

Pd–Ag/SiO₂ and Pd–Cu/SiO₂ xerogel catalysts have been synthesized by cogelation of tetraethoxysilane (TEOS) and chelates of either Pd and Ag or Pd and Cu with 3-(2-aminoethylamino)propyltrimethoxysilane (EDAS). After an extensive study of the influences of synthesis operating variables over structural characteristics of gels, highly dispersed bimetallic Pd–Ag/SiO₂ and Pd–Cu/SiO₂ xerogel catalysts were obtained. These samples are then composed of completely accessible Pd–Ag and Pd–Cu alloy crystallites with sizes of 2–3.5 nm located inside silica particles exhibiting a monodisperse microporous distribution. It appears also that the metal complex acts as a nucleation agent in the formation of silica particles.     

Structure of chalcogenide glasses by neutron diffraction

The purpose of this work is to study the change in the structure of the Ge–Se network upon doping with Ag. We report here a neutron diffraction study on two glasses of the system Ag_x(Ge_0.25Se_0.75)_100−x with different silver contents (x = 15 and 25 at.%) and for two different temperatures (10 and 300 K). The total structure factor S(Q) for the two samples has been measured by neutron diffraction using the two-axis diffractometer dedicated to structural studies of amorphous materials, D4, at the Institut Laue Langevin. We have derived the corresponding radial distribution functions for each sample and each temperature, which gives us an insight about the composition and temperature dependence of the correlation distances and coordination numbers in the short-range. Our results are compatible with the presence of both GeSe_4/2 tetrahedra and Se–Se bonds. The Ag atoms are linked to Se in a triangular environment. Numerical simulations allowing the identification of the main peaks in the total pair correlation functions have complemented the neutron diffraction measurements.     

Structural investigation of an amorphous Si24Nb76 alloy produced by mechanical alloying using reverse Monte Carlo simulations

The atomic structure of an amorphous Si₂₄Nb₇₆ alloy produced by mechanical alloying was investigated by using one X-ray total structure factor S(K) as input data for reverse Monte Carlo (RMC) simulations. The partial S_Si–Si(K), S_Si–Nb(K), S_Nb–Nb(K) structure factors and G_Si–Si(r), G_Si–Nb(r), G_Nb–Nb(r) pair probability functions were obtained from the RMC simulations. The structural parameters (interatomic distances and co-ordination numbers) for the first neighbors were extracted and compared with those found in the Nb₃Si compound. It was observed some resemblance between these phases.     

Pressure-volume-temperature relations in liquid and glassy selenium

The PVT properties of amorphous selenium are studied experimentally and theoretically in the temperature range 0–70°C and for pressures up to 200 MPa. PVT surfaces are determined for the metastable liquid and for a glass formed by a pressurization and cooling procedure. Its liquid—glass intersection line $\text{T}{}_{\mathrm{<mtext>g</mtext>}}{}^2\text{(P)}$ is compared with the glass transition line T_g (P), here obtained by pressurizing the liquid isothermally at a rate of 2 MPa/min. Analytical expressions based on the PVT data are compared with the predictions of the Simha-Somcynsky hole theory originally formulated for open chainmolecular fluids. The agreement for the liquid, although satisfactory, is not as good as for amorphous organic polymers thus far studied, possibly because selenium contains both open-chain and Se₈ ring molecules. The theoretical scaling parameters for the best fit to experiment are compared with those obtained for polymers. A very high characteristic pressure and thus cohesive energy density are noted. The theoretical hole fraction is found to be nearly constant along the $\text{T}{}_{\mathrm{<mtext>g</mtext>}}{}^2\text{(P)}$ line for low pressures. For the glass, a theoretical equation of state obtained from that for the liquid by freezing the hole fraction, compares favorably with experiment. The Prigogine-Defray ratio ΔκΔC_p/TV(Δα)² at atmospheric pressure, calculated using literature values of ΔC_p, is found to be about 2.0.     

Theory of fluidity of liquids, glass transition, and melting

This is a presentation of a rigorous theory of fluidity of liquids, glass transition and melting of solids in the frame of an asymmetric double well potential model. Potential wells are doubled time to time by the local density fluctuations caused by the thermal longitudinal waves. The average frequency of doubling of potential wells is equal to the frequency of the most energetic waves which obey a law similar to Wein’s displacement law in black body radiation. Based on the equilibrium thermodynamic theory of fluctuations and the displacement law, a law of linear pre-diffusion mean-square displacement of particles in a solid is derived: the mean-square displacement of molecules within their potential wells increases linearly with temperature. It is shown that when this is broken-down (where the mean-square displacement at a certain temperature rapidly changes its slope as a function of temperature) glass devitrifies and crystal melts, and all possible solid-liquid transitions of a substance occur at the same critical mean-square displacement: any solid (not only crystals) transforms into liquid when the mean-square displacement, as a fraction of the average intermolecular distance, acquires a certain universal critical value - the same for different substances. It is proved that molecules in a liquid perform specific Brownian motion. The average jump distance is a function of temperature and it is much smaller than the nearest intermolecular distances. At a certain temperature, shown to be the Kauzmann temperature, the average jump distance of Brownian motion becomes equal to zero: the super-cooled liquid undergoes glass transition. The transition was proven to be a phase transition of the fourth order: the free energy of the system and its first, second and third derivatives are all continuous functions, but its fourth derivative with respect to temperature is discontinuous. Molecular mobility, diffusion and viscosity are obtained as functions of temperature.     

X-ray diffraction measurement of liquid As2Se3 by using third-generation synchrotron radiation

X-ray diffraction (XD) measurements of liquid As₂Se₃ were carried out in the temperature range up to 1600 °C where the temperature is well beyond the semiconductor to metal (SC–M) transition temperature around 1000 °C. The measurements were done by using third-generation synchrotron radiation at SPring-8 and the obtained structure factors have been much improved compared to previous in house XD measurements with regard to the momentum transfer range and the data statistics. The deduced pair distribution functions show that with increasing temperature, the position of the first peak does not change within the errorbar and the coordination number gradually decreases up to 1600 °C irrespective of the SC–M transition. These results coincide with those of the first-principle molecular dynamics simulation.     

Magnetic properties of liquid 3d transition metal–Si alloys

The magnetic susceptibility has been measured for liquid transition metal–Si alloys (TM_1−cSi_c, TM = Ni, Co, Fe, Mn) as a function of temperature. The magnetic susceptibilities of liquid Ni_1−cSi_c with c ⩾ 0.3, liquid Co_1−cSi_c with c ⩾ 0.4 and liquid Fe_1−cSi_c with c ⩾ 0.6 were found to be almost independent of temperature, which suggests that the Ni, Co and Fe ions on the Si side are in the non-magnetic state. Liquid Ni_1−cSi_c with c ⩽ 0.2, liquid Co_1−cSi_c with c ⩽ 0.3 and liquid Fe_1−cSi_c with c ⩽ 0.5 show the Curie–Weiss behavior with a reasonable value of effective Bohr magnetic number. Liquid Mn_1−cSi_c with c ⩽ 0.2 and c ⩾ 0.6 were found to be in their non-magnetic state. However, the Curie–Weiss behavior was observed for liquid Mn_1−cSi_c with c = 0.3, 0.4 and 0.5. The magnetic susceptibility of their liquid alloys in the non-magnetic state has been studied by using Anderson model. The density of 3d states at the Fermi level can be estimated from the data of magnetic susceptibility.     

Radial distribution studies of glassy tellurium-silicon alloys

X-ray investigations of glassy tellurium-silicon alloys (Si content 10–40 at%) are described. Alloys with 13 to 27 at% Si were obtained in bulk form, non-crystalline samples with 10, 30, 33, 36 and 40 at% Si were obtained by rapid quenching from the melt by the splat-cooling technique. The interference functions and the radial distribution functions of all alloys show a great similarity. However, the positions of the maxima of the pair distribution function decrease continuously with growing Si content and lead to values which are similar to atomic distances in crystalline Te and Si₂Te₃. The areas of the first two peaks of the RDF, F₁ (rougnly 2) and F₂ (roughly 12), are compared with calculated areas derived from different structural models which are based on the short-range order in crystalline Te with a chain structure and in Si₂Te₃ with a tetrahedron configuration. An interstitial model with Si atoms in holes of Te chains and a random substitution model, where the Te atoms and the Si atoms have the same short-range order, both show a concentration dependence of the areas F₁ contrary to the experimental values. A structural model which assumes the tetrahedron configuration of Si₂Te₃ for Si atoms (coordination number N_Si = 4) and a coordination number N_Te = 2 for Te atoms can describe the short-range order of glassy TeSi alloys in the whole investigated concentration range with 10–40 at% Si.     

High pressure effects on liquid viscosity and glass transition behaviour,polyamorphic phase transitions and structural properties of glasses and liquids

Since the pioneering work of Bridgman it has been known that pressure affects the glass transition of polymers and liquid state viscosities. Usually the T_g and viscosity both increase as a function of pressure as expected from ‘free volume’ theories. However, H₂O provided a notable exception in that the viscosity passes through a minimum at low temperature. It was thought that this might be linked to the anomalous thermal expansion behavior. However further research on geologically important aluminosilicate liquids revealed that they could show anomalous viscosity decreases with increasing pressure and this behavior is given a structural interpretation as five-fold coordinated Si⁴⁺ and Al³⁺ species are formed. Also the existence of polyamorphism or density-driven liquid–liquid phase transitions in certain systems can lead to anomalies in the T_g or η vs. P relations. This may be the case for H₂O, for example. Current research is focusing on investigating structural changes in liquids and glasses at high pressure as the rich variety of behavior is becoming recognized. Both experimental studies and computer simulations are important as the underlying phenomonology is linked to changes in the glass or liquid structure as a function of densification.     

Structural behavior of amorphous and liquid metallic alloys at elevated temperatures

The thermal behavior of the short-range order of Pd₄₀Cu₃₀Ni₁₀P₂₀ bulk metallic glasses has been investigated in situ by means of high-temperature X-ray synchrotron diffraction. The dependence of the X-ray structure factor S(q) of the glassy state on temperature follows the Debye theory up to the glass transition. Above the glass transition temperature T_g, the temperature dependence of S(q) is altered toward a continuous development of structural changes in the liquid state with temperature. The behavior of the structure factor during heating and cooling through the glass transition gives experimental evidence for melting the glass, and for freezing the liquid, respectively at the caloric glass temperature.