Viscous and thermodynamic behaviour of glass-forming organic liquids

The free energy difference (ΔG) between an undercooled liquid and its corresponding equilibrium solid has been evaluated on the basis of a method involving Taylor series expansion of ΔG around its value at the equilibrium melting temperature. The resultant expression is shown to be capable of correctly estimating ΔG at temperatures as low as the glass transition temperature. The method is then enlarged to obtain the configurational entropy and used in conjunction with the Adam and Gibbs model to derive a novel expression for the viscosity of undercooled liquids. Most commonly used expressions for the temperature dependence of viscosity are shown to be approximations of the equation obtained in this study.     

Thermodynamic behaviour of undercooled melts

The Gibbs free energy difference (ΔG) between the undercooled liquid and the equilibrium solid phases has been studied for the various kinds of glass forming melts such as metallic, molecular and oxides melts using the hole theory of liquids and an excellent agreement is found between calculated and experimental values of ΔG. The study is made for non-glass forming melts also. The temperature dependence of enthalpy difference (ΔH) and entropy difference (ΔS) between the two phases, liquid and solid, has also been studied. The Kauzmann temperature (T ₀) has been estimated using the expression for ΔS and a linear relation is found between the reduced glass transition temperature (T _g/T _m) and (T ₀)/T _m). The residual entropy (ΔS _R) has been estimated for glass forming melts and an attempt is made to correlate ΔS _R,T _g,T ₀, andT _m which play a very important role in the study of glass forming melts.     

Crystallization of glassforming melts under hydrostatic pressure and shear stress: Part I Crystallization catalysis under hydrostatic pressure: possibilities and limitations

This is the first part of a thorough study of the kinetics of melt crystallization under applied static pressure, P, and under shear stress. The thermodynamic and kinetic consequences of increased external pressure on nucleation rate, non-steady-state time lag, rate of crystal growth and overall crystallization kinetics in undercooled melts are analysed. Two types of undercooled liquids (with either positive or negative volume dilatation upon crystallization) are considered. Particular attention is given to the effect of pressure on the specific interface energy, σ, at the crystal/melt phase boundary. Using an appropriate thermodynamic model it is shown that for one-component systems, (∂σ/∂p)<0 is to be expected as a rule. Thus an additional decrease of the thermodynamic barrier of nucleation in pressurized melts is to be expected. However, it is also shown that the increase of melt viscosity with pressure in most cases reduces the effect of this decrease. Thus increased pressure has a limited effect as a nucleation catalyst. The possibilities in this respect are analysed and conditions under which static pressure may lead to enhanced crystallization are outlined. This revised version was published online in November 2006 with corrections to the Cover Date.     

Thermodynamic Functions of Undercooled Fe–P Melts

The approaches to calculating the thermodynamic properties of undercooled melts are critically evaluated. It is shown by the example of the eutectic Fe–P alloy that the rough estimates relying on various models of melt structure, primarily on the hole theory, provide inadequate results. Based on the concept of associated solutions and the thermodynamic functions of the constituent components found by solving the inverse problem of chemical thermodynamics, a procedure is proposed for analyzing the thermodynamic behavior of undercooled melts, in particular, near the glass transition. The thermodynamic quantities calculated by this procedure coincide with experimental data to within the measurement accuracy. The procedure is used to calculate the thermodynamic properties and viscosity of Fe–P melts between the glass-transition temperature (650 K) and 1873 K. The results are in perfect agreement with experimental data.     

The Structure-Thermodynamic State and the Mechanism of Crystallization of Gallium-Based Melts

Quantitative analysis of the structure factors and curves of radial distribution of atoms obtained as a result of X-ray study in a wide temperature range reveals a fundamental difference in the structure of melts of normal close-packed metals and semimetals (Ga, Bi). The results of calculation of the temperature dependence of the configurational component of entropy of semimetals confirm the presence of a covalent component of cluster type in the microheterogeneous structure of melts. The melting-crystallization processes, studied using the method of acoustic emission, exhibit a stepwise pattern for semimetals which is due to the incoherence of the metal and covalent components of the structure. The process of crystallization of gallium- and bismuth-based eutectic alloys is complicated by the presence of quasi-eutectic microsegregation, which affects both the structure parameters and configurational component of entropy.     

Temperature dependence of viscosity and density of the melts of quasibinary systems formed by copper chalcogenides

The temperature and concentration dependence of the kinematic viscosity and density of melts of quasi-binary systems formed of copper chalcogenides is investigated. The temperature dependence of the investigated properties is analyzed on the basis of the activated complex theory and of the fundamental equation of A.I. Bachinskii. It is shown that the postmelting effect is observed in all of the investigated melts, which is associated with the structural changes occurring on heating the melts. These changes consist in the transformation of a structurally inhomogeneous liquid into a homogeneous Newtonian liquid due to the thermal decay of clusters. It is also shown that the concentration dependence of viscosity exhibits a smooth behavior, and that of density exhibits a strictly additive behavior, which favors intermolecular interaction. The notions of this interaction follow from the treatment of the diagrams of state of appropriate quasi-binary systems and thermodynamic analysis.     

Fragility of superheated melts in Al–RE (Ce, Nd, Pr) alloy system

The fragility of superheated melt M, characterized by the temperature dependence of the viscosity scaled by the viscosity at the liquidus temperature, has been proposed by Bian et al. recently. In this work, the values of M of Al–RE(Ce, Nd, Pr) melts were calculated based on the viscosities measured in the range of less than 250 K above their liquidus temperatures. It was found that M has a good negative correlation with the glass-forming ability (GFA) in Al–RE binary alloy system. Although the previous study found that M could reflect the GFA in Al–Co–Ce alloy system, there is no good relationship between M and GFA in the alloy system including Al–RE and Al–Co–Ce alloys simultaneously. The relationship between fragility of superheated melts and glass-forming behavior in different Al-based alloy systems was elaborated.     

Viscous behaviour and glass formation in Fe78B13Si9 amorphous alloy

Using a rotational viscometer, the viscosity of molten Fe₇₈B₁₃Si₉ alloy was measured over the temperature range 1165–1350 °C. The temperature dependence of the viscosity of liquid alloy is adequately described by the Arrhenius equation. However, this expression cannot be directly extended to the undercooled liquid temperature region. In this paper a proper equation derived from the free volume theory is proposed to describe the viscosity-temperature behaviour of Fe₇₈B₁₃Si₉ alloy in the temperature range of the undercooled liquid and above its melting point. Furthermore, the isothermal time-temperature-transformation curve for crystallization is constructed based on the assumption of homogeneous nucleation and crystal growth, together with the temperature dependence of the viscosity. The critical cooling rate required to form a glass of Fe₇₈B₁₃Si₉ alloy was calculated to be approximately 10⁵° Cs^–1.     

Comments on ‘Solidification modes and microstructure of Fe–Cr alloys solidified at different undercoolings’

The critical growth velocity for a planar solidification front in undercooled alloy melts is discussed on the basis of the absolute stability theory to reexamine the interpretation of a current analysis of the solidification modes in undercooled bulk Fe–Cr alloys contributed by Xuezhi Zhang. Theoretically, it is possible to produce a planar front in the solidification of undercooled bulk melts. But practically, it is imopssible for the undercooled bulk Fe–Cr melts to produce a planar front in the solidification. The dendritic growth theories as well as the calculations due to Zhang have been analyzed.     

Free volume theories of the glass transition and the special case of metallic glasses

Theories based on the concepts of free volume and the existence of holes in liquids are briefly reviewed. Available experimental data on the changes in specific heat and thermal expansion at the glass transition temperature and the temperature dependence of viscosity near transition have been utilized to evaluate the hole formation energy and critical hole size in palladium-, platinum- and gold-based metallic glasses. It has been found that in conformity with theoretical predictions, transport in metallic glasses occurs by the movement of highly ionized atoms. A linear relationship exists between the hole formation energy and glass transition temperature of metallic glasses. It is suggested that a high energy of hole formation is a necessary criterion for easy vitrification of metallic melts. The behaviour of vacancies in crystalline metals is compared with the behaviour of holes in metallic glasses.On leave from the Department of Metallurgical Engineering, Banaras Hindu University, Varanasi-5, India     

Surface Tension and Viscosity of Quasicrystal-Forming Ti–Zr–Ni Alloys

Recent X-ray scattering measurements show that icosahedral short-range order in Ti–Zr–Ni alloys is responsible for a change in phase selection from the stable C14 Laves phase to the quasicrystalline icosahedral phase, and that icosahedral short-range order increases at deeper undercoolings. This change in short-range order should be reflected in changes in the thermophysical properties of the melt. The surface tension and viscosity of quasicrystal-forming Ti–Zr–Ni alloys were measured over a range of temperature, including both stable and undercooled liquids, by an electrostatic levitation (ESL) technique. ESL is a containerless technique which allows processing of samples without contact, greatly reducing contamination and increasing access to the metastable undercooled liquid. The measured viscosity is typical of glass-forming alloys of similar composition to the quasicrystal-forming alloys studied here; however, the surface tension shows an anomaly at deep undercoolings.     

The entropy theory of glass formation after 40 years

It is argued that an equilibrium theory of the glass transition is required before a full understanding of the glass transition, as observed kinetically, can be obtained. The lattice model provides a basis for such a theory and predicts that vitrification occurs as the configurational entropy S_c approaches zero. Comparison with nine different classes of polymer experiments shows semiquantitative agreement in each case. An important aspect of glass formation in polymers is that the crystal phase is not ubiquitous so that amorphous polymer material exists necessarily at low temperatures. A low-temperature equilibrium theory for these materials is required. Using equilibrium theory as a base, a kinetic theory is developed and an equation for the relaxation function is derived which predicts the proper temperature dependence of the viscosity and shows stretched exponential-like behavior for the relaxation.     

Highly collective atomic transport mechanism in high-entropy glass-forming metallic liquids

Quasielastic neutron scattering(QENS) has been used to study the atomic relaxation process and microscopic transport mechanism in high-entropy glass-forming metallic(HE-GFM) liquids. Self-intermediate scattering functions obtained from the QENS data show unusually large stretching, which indicates highly heterogeneous atomic dynamics in HE-GFM liquids. In these liquids, a group of atoms over a length scale of about 21 ? diffuses collectively even well above the melting temperature. However, the temperature dependence of diffusion process in one of the HE-GFM liquid is Arrhenius, but in the other HE-GFM liquid it is non-Arrhenius. Although the glass-forming ability of these HE-GFM liquids is very poor, the diffusion coefficients obtained from the QENS data indicate the long range atomic transport process is much slower than that of the best metallic glass-forming liquids at their melting temperatures.     

A New Thermodynamic Calculation Method for Binary Alloys：Part I：Statistical Calculation of Excess Functions

The improved form of calculation formula for the activities of the components in binary liquids and solid alloys has been derived based on the free volume theory considering excess entropy and Miedemaˊs model for calculating the formation heat of binary alloys.A calculation method of excess thermodynamic functions for binary alloys,the formulas of intregral molar excess properties and partial molar excess properties for solid ordered or disordered binary alloys have been developed.The calculated results are in good agreement with the experimental values.     

Study of viscosity of mono-, di-, and trialkylamines

Viscosities of several mono-, di-, and trialkylamines have been measured in the temperature range 298 to 333 K. It is observed that viscosities are highly dependent on shape, size, and association through H-bond or through dipole. Following the transition state theory, energy, Gibbs free energy, and entropy of activation of viscous flow have been calculated. The values of expansion energy for these liquids have also been calculated using free volume theory, and subsequently amines have been classified as volume-restrained or energy-restrained liquids. The group contribution method of Van Velzen, Cardozo, and Langenkamp for estimating viscosity has been examined with the present and literature data, and the new group contribution increments N _i and B _i for amines have been evaluated.     

Nucleation of crystals in deeply undercooled alloy melts

The CALPHAD approach coupled with modelling of solid-liquid interfacial energy has been used to calculate the driving force for nucleation in undercooled melts. Thermodynamic parameters needed in nucleation have been evaluated using simplified formulae or numerical methods from assessed phase diagrams. Various models for the interfacial energy and its temperature dependence have been used. Phase selection on solidification and devitrification of glasses as well as the range of amorphous phase formation have been predicted in the Al-Ce and Fe-B systems and compared with those experimentally determined. Furthermore, the formation of quasicrystals in the Al-Mn and the competition with other compounds has been investigated.     

Metastable phase diagrams of Cu-based alloy systems with a miscibility gap in undercooled state

Some Cu-based alloy systems with a large positive enthalpy of mixing display a eutectic or peritectic phase diagram under equilibrium conditions, but show a metastable liquid miscibility gap in the undercooled state. When the melt is undercooled below certain temperature beyond the critical liquid-phase separation temperature, it separates into two liquids with different compositions. The compositions of the two liquids change successively upon the metastable phase diagram before solidification occurs. The shape and position of the metastable miscibility gap are dependent of the alloy components and their interaction features. This study reviews the metastable phase diagrams of Cu-based alloy systems, which are derived from experiments and thermodynamic calculations.     

Viscosity measurement using drop coalescence in microgravity

We present in here validation studies of a new method for application in microgravity environment which measures the viscosity of highly viscous undercooled liquids using drop coalescence. The method has the advantage of avoiding heterogeneous nucleation at container walls caused by crystallization of undercooled liquids during processing. Homogeneous nucleation can also be avoided due to the rapidity of the measurement using this method. The technique relies on measurements from experiments conducted in near zero gravity environment as well as highly accurate analytical formulation for the coalescence process. The viscosity of the liquid is determined by allowing the computed free surface shape relaxation time to be adjusted in response to the measured free surface velocity for two coalescing drops. Results are presented from two sets of validation experiments for the method which were conducted on board aircraft flying parabolic trajectories. In these tests the viscosity of a highly viscous liquid, namely glycerin, was determined at different temperatures using the drop coalescence method described in here. The experiments measured the free surface velocity of two glycerin drops coalescing under the action of surface tension alone in low gravity environment using high speed photography. The liquid viscosity was determined by adjusting the computed free surface velocity values to the measured experimental data. The results of these experiments were found to agree reasonably well with the known viscosity for the test liquid used.     

Modelling the behaviour of gas bubbles in an epoxy resin: Evaluating the input parameters for a diffusion model using a free-volume approach

Models based on a mass-diffusion theory successfully represent the growth and collapse of gas bubbles in an epoxy resin. A quantitative evaluation of the steady-state diffusion equations requires values for the diffusion coefficient and the solubility of the mobile species within the resin precursor. These parameters are affected by changes in temperature and/or pressure, and they are generally not measured as part of a processing schedule. Models have been evaluated that predict the temperature dependence of the gas diffusion coefficient in the resin. A free volume approach describes the viscosity of the resin successfully at temperatures of up to 100 K above the glass-transition temperature. At higher temperatures, a thermal-energy-barrier approach is more appropriate. A direct correlation between the viscosity of the resin and the gas diffusion coefficient is proposed which is considered to be applicable to any gas/resin system where specific component interactions are negligible and the solute concentration is sufficiently low that it does not affect the free volume of the medium.