Critical Free Volume Research Articles

Modeling and analysis of chip segmentation in micro-cutting of Zr-based bulk metallic glass (BMG)

Bulk metallic glasses (BMG) exhibit an amorphous structure and possess excellent properties, such as high hardness (∼8 GPa), high elastic and strain limit (∼2 %), and wear/corrosion resistance. Chip formation behavior of BMG during machining is distinct from the crystalline materials, and is not very well understood. Hence, this paper presents experimental and analytical investigations to explore the underlying chip formation mechanism in the micro-cutting of BMG. The experimental study was carried out by analyzing the chip morphology, force signature, and hardness of the workpiece. BMG machining yields segmented chips due to the shear localization. The shear localization is clearly observed in terms of periodic primary shear bands and multiple secondary shear bands. The machined surface also shows work softening due to machining-induced deformation. It has been observed that free volume and the shear zone temperature affect the shear localization, which is reflected in the chip segmentation. A shear localization model has been developed, which includes the effects of new surface creation energy, shear energy, and friction energy. Based on a bifurcation analysis, critical free volume and temperature flow coefficients have been calculated. Based on the critical free volume and temperature flow coefficients, four distinct regimes of shear localization have been identified. The shear localization dampens out if the free volume coefficient is less than the critical free volume flow coefficient. Substantial shear localization is observed if the free volume flow coefficient exceeds the critical value. This study shows that free volume generation primarily drives the chip segmentation and shear localization, and the temperature effects play a secondary role.

An analysis of radical diffusion in ionic liquids in terms of free volume theory.

The Heisenberg spin exchange-dipole-dipole separation method was used to measure the translational diffusion coefficients of the 14N-labeled perdeuterated 2,2,6,6-tetramethyl-4-oxopiperidine-1-oxyl (14N-pDTEMPONE) nitroxide spin probe as a function of temperature in two methylimidazolium ionic liquid series, one based on the tetrafluoroborate (BF4) anion and another one on the bis(trifluoromethane)sulfonimide (TFSI, Tf2N) anion. The obtained translational diffusion coefficients of 14N-pDTEMPONE were analyzed in terms of the Cohen-Turnbull free volume theory. It was found that the Cohen-Turnbull theory describes, exceptionally well, the translational diffusion of 14N-pDTEMPONE in all the ionic liquids in the measured temperature range. In addition, the Cohen-Turnbull theory was applied to the viscosity and self-diffusion coefficients of the cation and anion-taken from literature-in the same ionic liquids. The critical free volume for the self-diffusion of the cation and anion in a given ionic liquid is the same, which suggests that the diffusion of each ionic pair is coordinated. The critical free volumes for the 14N-pDTEMPONE diffusion, self-diffusion, and viscosity for a given cation were about 20% greater in the TFSI based ionic liquids than in the BF4 based ionic liquids. It appears that the ratio of the critical free volumes for a given cation between the two series correlates with the ratio of their densities.

Free volume correlation with ac conductivity and thermo-mechanical properties of poly (ethylene oxide)-silica nanocomposites

Poly(ethylene oxide), PEO, based nanocomposites are shown to have higher ionic conductivity compared to pure PEO. In order to investigate the exclusive role of free volume structure of amorphous region of PEO on its electrical conductivity, PEO-silica nanoparticles composite films have been prepared with different silica loadings. The free volume fraction of polymer composites measured using positron annihilation lifetime spectroscopy (PALS) was observed to increase nonlinearly with the increase in loading of silica. The increase in free volume on silica loading has been attributed to PEO-silica interphase as well as newly created amorphous PEO. At higher loading, positron annihilation from regions near silica particles has been confirmed by coincidence Doppler broadening measurements. Thermal analysis of polymer nanocomposites shows a decrease in crystallinity and crystallite melting temperature with the increase in silica loading. The PEO-silica nanocomposite films showed enhanced ac conductivity as well as mechanical properties (higher Young’s modulus and ductility). The observed changes in free volume structure and semicrystalline morphology of PEO matrix are attributed to the physical confinement imposed by presence of silica nanoparticles in PEO matrix. The present study shows that free volume measured using PALS has a direct relation with ac conductivity which is observed to increase drastically after a critical free volume fraction.

Influence of Dilute Hf Additions on Precipitation and Martensitic Transformation in Ni-Ti-Pd Alloys

The effect of Hf (0–1 at.%) additions in a Ni-Ti-Pd alloy on P-phase precipitation and martensitic transformations was studied. The addition of hafnium resulted in the refinement of precipitates with an increase in number density. The overlapping strain fields created due to the decrease in inter-precipitate spacing are suspected to reduce the matrix volume to be less than the critical free volume size needed for the martensitic transformation over the temperature range studied (183–573 K). Hafnium was also found to delay the aging time to achieve peak hardness, suggesting a reduction in growth and coarsening kinetics.

Deformation and failure of bulk metallic glasses under different initial temperatures

Based on the coupled thermo-mechanical model, a constitutive model for bulk metallic glasses (BMGs), which is generalized to the multi-axial stress state and considers the effects of free volume, heat and hydrostatic stress, has been modified in the present paper. Besides, a failure criterion of critical free volume concentration is introduced based on the coalescence mechanism of free volume. The constitutive model as well as the failure criterion is implemented into the LS-DYNA commercial software by user material subroutine (UMAT). Then FEM simulations for different initial material temperatures are conducted and the evolutions of material parameter as well as corresponding macroscopic mechanical behaviour of material are analyzed. Relative analysis shows that the initial material temperature significantly affects the deformation and failure of material.

On the mechanism of deformation and failure in bulk metallic glasses

Based on the coupled thermo-mechanical model, a constitutive model for bulk metallic glasses (BMGs), which considers the effects of free volume, temperature and hydrostatic stress, has been further deduced and generalized to the multi-axial stress status in the present manuscript. Besides, a failure criterion of critical free volume concentration is introduced from the coalescence mechanism of free volume. Then the constitutive model and the failure criterion are implemented into LS-DYNA commercial software through the user material subroutine (UMAT). Integrated with the related test data, FEM simulations for different deformation scenarios are conducted. The evolutions of different material parameters and the corresponding mechanical behaviors of BMGs are analyzed, and especially the effects of strain rate, initial temperature and hydrostatic stress as well as the initial free volume concentration on the deformation and failure of BMGs are discussed in detail. It demonstrates that the multi-axial-stress-status constitutive model and the failure criterion are able to describe the mechanical behaviors of BMGs at different initial temperatures (below and within the supercooled liquid region) and strain rates universally.

Influence of free volume and medium-range order on the deformation response of rapidly solidified and bulk Zr-based (Zr52Ti6Al10Cu18Ni14) metallic glass

Free volume and medium-range order (MRO) present in rapidly solidified ribbons (RSRs) and bulk metallic glasses (BMGs) of Zr52Ti6Al10Cu18Ni14 have been probed by high resolution electron microscopy, fluctuation microscopy, positron annihilation and differential scanning calorimetry. In the as-solidified condition, RSRs showed higher free volume and lower MRO in comparison to BMGs. Within BMGs, the central regions showed higher MRO and lower free volume than the peripheral regions. Uniform deformation of BMGs and RSRs modified their structures, where in, free volume increased in the former and reduced in the latter. These changes in structures led to work hardening in RSRs and work softening in BMGs. Such behaviour could be explained by invoking a concept of critical free volume in the glass phase. For samples (in as-solidified condition) having free volume higher than the critical value, free volume decreased with deformation and showed work-hardening behaviour. In contrast, the work softening behaviour was noticed in samples having free volume lower than the critical free volume.

Free volume in ionic liquids: a connection of experimentally accessible observables from PALS and PVT experiments with the molecular structure from XRD data

In the current work, free volume concepts, primarily applied to glass formers in the literature, were transferred to ionic liquids (ILs). A series of 1-butyl-3-methylimidazolium ([C4MIM](+)) based ILs was investigated by Positron Annihilation Lifetime Spectroscopy (PALS). The phase transition and dynamic properties of the ILs [C4MIM][X] with [X](-) = [Cl](-), [BF4](-), [PF6](-), [OTf](-), [NTf2](-) and [B(hfip)4](-) were reported recently (Yu et al., Phys. Chem. Chem. Phys., 2012, 14, 6856-6868). In this subsequent work, attention was paid to the connection of the free volume from PALS (here the mean hole volume, <v(h)>) with the molecular structure, represented by volumes derived from X-ray diffraction (XRD) data. These were the scaled molecular volume Vm,scaled and the van der Waals volume V(vdw). Linear correlations of <v(h)> at the "knee" temperature (<v(h)>(T(k))) with V(m,scaled) and V(vdw) gave good results for the [C4MIM](+) series. Further relationships between volumes from XRD data with the occupied volume Vocc determined from PALS/PVT (Pressure Volume Temperature) measurements and from Sanchez-Lacombe Equation of State (SL-EOS) fits were elaborated (V(occ)(SL-EOS) ≈ 1.63 V(vdw), R(2) = 0.981 and V(occ)(SL-EOS) ≈ 1.12 V(m,scaled), R(2) = 0.980). Finally, the usability of V(m,scaled) was justified in terms of the Cohen-Turnbull (CT) free volume theory. Empirical CT type plots of viscosity and electrical conductivity showed a systematic increase in the critical free volume with molecular size. Such correlations allow descriptions of IL properties with the easily accessible quantity V(m,scaled) within the context of the free volume.

Critical Free Volume Concentration of Shear Banding Instability in Metallic Glasses

We present a model which predicts the critical free volume concentration of shear banding instability in metallic glasses (MGs). From the stability map, this model demonstrates that the prediction of shear band thickness is valid only for a short time after shear instability, and the diffusion of defects should be included in the mature shear band in MGs. The results agree well with the experimental observations and simulations.

On factors influencing the ductile-to-brittle transition in a bulk metallic glass

An experimental study to ascertain the ductile-to-brittle transition (DBT) in a bulk metallic glass (BMG) was conducted. Results of the impact toughness tests conducted at various temperatures on as-cast and structurally relaxed Zr-based BMG show a sharp DBT. The DBT temperature was found to be sensitive to the free-volume content in the alloy. Possible factors that result in the DBT were critically examined. It was found that the postulate of a critical free volume required for the amorphous alloy to exhibit good toughness cannot rationalize the experimental trends. Likewise, the Poisson’s ratio–toughness correlations, which suggest a critical Poisson’s ratio above which all glasses are tough, were found not to hold good. Viscoplasticity theories, developed using the concept of shear transformation zones and which describe the temperature and strain rate dependence of the crack-tip plasticity in BMGs, appear to be capable of capturing the essence of the experiments. Our results highlight the need for a more generalized theory to understand the origins of toughness in BMGs.

Nucleation kinetics, micro-crystallization and surface morphology studies of the nonlinear optical single-crystal l-lysinium trifluoroacetate

The organic nonlinear optical crystal of amino-carboxyl acid family, l-lysinium trifluoroacetate (abbreviated as LLTF) was successfully grown from its aqueous solution by the temperature-lowering technique. Its growth morphology was investigated based on the X-ray single-crystal diffraction data and the growth habits were studied using the micro-crystallization method. The metastable zonewidth and induction period were determined for the aqueous solution growth of LLTF. The surface free energy values were calculated from the experimental data. Nucleation kinetics and fundamental growth parameters such as critical radius, critical free energy and volume free energy change were also evaluated. Crystals of LLTF were obtained by the optimized nucleation parameters.

Dielectric analysis of chlorinated polyvinyl chloride stabilized with di‐n‐octyltin maleate

AbstractDielectric relaxation of chlorinated polyvinyl chloride stabilized with di‐n‐octyltin maleate has been studied in the frequency range 1 kHz–1 MHz at various temperatures between 300 and 450 K. A clear dielectric relaxation band (α‐type) associated with dipolar polarization has been observed in the studied range. The stabilizer molecules increase the segmental mobility of the polymer, and specific interaction occurs between both the CCl and CO polar groups. The temperature dependence of the relaxation process was analyzed by combining the critical free volume expression by Cohen and Turnbull with the Williams‐Landel‐Ferry (WLF) model of the thermal expansion of free and occupied volumes. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Amorphous and crystalline phase interaction during the Brill transition in nylon 66

A prominent α' process in specifically treated nylon 66 and microcomposite samples is identified by dynamic mechanical analysis and proposed to be an amorphous phase counterpart of the Brill transition identified by synchrotron wide-angle X-ray diffraction (WAXD). It is suggested that this α' process, which marks a critical free volume change and an onset of segmental chain movement in the amorphous phase, precedes and prompts the Brill transition in the crystalline phase.

Nucleation thermodynamical studies on nonlinear optical l-alanine single crystals

Nucleation parameters such as critical radius, critical free energy and volume free energy change have been evaluated for l-alanine single crystals. The interfacial energy of the solution at various temperatures has been estimated from existing solubility data. Metastable zone width and induction period measurements have been carried out experimentally. The thermal strength of the grown crystals has also been determined from differential scanning calorimetry (DSC).

Crystallization kinetics and high-resolution X-ray diffraction analysis on nonlinear optical l-threonine single crystals

Crystallization parameters such as critical radius, critical free energy and volume free energy change have been evaluated for l-threonine single crystals using homogeneous nucleation theory. Metastable zone width and induction period measurements have been carried out experimentally. Interfacial energy values for the aqueous solution of l-threonine were also calculated from the solubility data. Optimization of growth parameters has been tried for bulk crystal growth and it has been discussed in detail. The crystalline quality of the bulk samples grown at different pH values have been tested by high-resolution X-ray diffraction analysis.

Pair Correlation Functions and the Self-Diffusion Coefficient of Lennard-Jones Liquid in the Modified Free Volume Theory of Diffusion

In this paper, we apply the Matteoli-Mansoori empirical formula for the pair correlation function of simple fluids obeying the Lennard-Jones potential to calculate reduced self-diffusion coefficients on the basis of the modified free volume theory. The self-diffusion coefficient thus computed as functions of temperature and density is compared with the molecular dynamics simulation data and the self-diffusion coefficient obtained by the modified free volume theory implemented with the Monte Carlo simulation method for the pair correlation function. We show that the Matteoli-Mansoori empirical formula yields sufficiently accurate self-diffusion coefficients in the supercritical regime, provided that the minimum free volume activating diffusion is estimated with the classical turning point of binary collision at the mean relative kinetic energy 3k(B)T/2, where k(B) is the Boltzmann constant and T is the temperature. In the subcritical regime, the empirical formula yields qualitatively correct, but lower values for the self-diffusion coefficients compared with computer simulation values and those from the modified free volume theory implemented with the Monte Carlo simulations for the pair correlation function. However, with a slightly modified critical free volume, the results can be made quite acceptable.

Modified Free Volume Theory of Self-Diffusion and Molecular Theory of Shear Viscosity of Liquid Carbon Dioxide

In previous work on the density fluctuation theory of transport coefficients of liquids, it was necessary to use empirical self-diffusion coefficients to calculate the transport coefficients (e.g., shear viscosity of carbon dioxide). In this work, the necessity of empirical input of the self-diffusion coefficients in the calculation of shear viscosity is removed, and the theory is thus made a self-contained molecular theory of transport coefficients of liquids, albeit it contains an empirical parameter in the subcritical regime. The required self-diffusion coefficients of liquid carbon dioxide are calculated by using the modified free volume theory for which the generic van der Waals equation of state and Monte Carlo simulations are combined to accurately compute the mean free volume by means of statistical mechanics. They have been computed as a function of density along four different isotherms and isobars. A Lennard-Jones site-site interaction potential was used to model the molecular carbon dioxide interaction. The density and temperature dependence of the theoretical self-diffusion coefficients are shown to be in excellent agreement with experimental data when the minimum critical free volume is identified with the molecular volume. The self-diffusion coefficients thus computed are then used to compute the density and temperature dependence of the shear viscosity of liquid carbon dioxide by employing the density fluctuation theory formula for shear viscosity as reported in an earlier paper (J. Chem. Phys. 2000, 112, 7118). The theoretical shear viscosity is shown to be robust and yields excellent density and temperature dependence for carbon dioxide. The pair correlation function appearing in the theory has been computed by Monte Carlo simulations.

Generic van der Waals Equation of State, Modified Free Volume Theory of Diffusion, and Viscosity of Simple Liquids

The shear viscosity formula derived by the density fluctuation theory in previous papers is computed for argon, krypton, and methane by using the self-diffusion coefficients derived in the modified free volume theory with the help of the generic van der Waals equation of state. In the temperature regime near or above the critical temperature, the density dependence of the shear viscosity can be accounted for by ab initio calculations with the self-diffusion coefficients provided by the modified free volume theory if the minimum (critical) free volume is set equal to the molecular volume and the volume overlap parameter (alpha) is taken about unity in the expression for the self-diffusion coefficient. In the subcritical temperature regime, if the density fluctuation range parameter is chosen appropriately at a temperature, then the resulting expression for the shear viscosity can well account for its density and temperature dependence over the ranges of density and temperature experimentally studied. In the sense that once the density fluctuation range is fixed at a temperature, the theory can account for the experimental data at other subcritical temperatures on the basis of the intermolecular force only; the theory is predictive even in the subcritical regime of temperature. Theory is successfully tested in comparison with experimental data for self-diffusion coefficients and shear viscosity for argon, krypton, and methane.

Influence of pressure on ionic transport in amorphous electrolytes: Comparison between glasses and salt polymer complexes

Accurate conductivity measurements as a function of hydrostatic pressure (1 - 5000 bars) and temperature (20 - 150 ~ have been performed on a cationic inorganic glass and a cationic conducting polymer. In both cases, the conductivity decreases with increasing pressure and the variation of ln~ at constant temperature as a function of pressure gives straight lines with slopes which allow an "activation volume", AV*, to be obtained by the relationship (3lnt/bP)r = - (AV*/RT). In the case of silver metaphosphate glass, studied below its glass transition temperature, the activation volume (5 cm3.mo1-1) is temperature independent and equal to the molar volume of the silver cation. Since the transport mechanism implies a free energy barrier, this volume is a real activation volume, corresponding to the difference in volume between a mole of the moving species in its activated transition state and its volume at normal equilibrium. In the case of the sodium conductive polymer, studied above its glass transition temperature, the previous thermodynamic definition does not hold any more because the ionic transport follows a V.T.F. behaviour rather than an Arrhenius law. Consequently, AV* is an "apparent activation volume" without a simple physical meaning. Experimental values are higher (20 to 30 cma.mo1-1) and decrease with temperature. In this polymer, the mobility of the charge carriers is interpreted in terms of free volume mechanism. From the variations of the apparent activation volume with temperature, the critical free volume Vf* for an elementary displacement is estimated. For the Na + conductive ionomer Vf* is estimated to be equal to 13 cm3.mol 1. This large value would indicate the participation of macromolecular chain segments in the ionic transport.

Dilatometric measurements on metallic glass ribbons with a wide glass transition range

A special dilatometric device which avoids tensile stress to the specimen is used to examine structural relaxation, glass transition and crystallization of metallic glass ribbons of Al 7.5Cu 17.5Ni 10Zr 65 and Pd 40Ni 40P 20. The relaxation kinetics can be well described either in the free volume model or by the Kohlrausch-Williams-Watts formula or by an activation energy spectrum, all indicating co-operative atomic rearrangements. The first model yields for the product of the critical free volume and overlap factor, initiating a structural relaxation event, values of 0.17 (Al 7.5Cu 17.5Ni 10Zr 65) and 0.14 (Pd 40Ni 40P 20) of an atomic volume. The coefficient of thermal expansion (and its temperature dependence) is measured and found not to change with crystallization in the case of Al 7.5Cu 17.5Ni 10Zr 65, unlike that of Pd 40Ni 40P 20.