Isothermal Relaxation Process Research Articles

Research of the caged dynamics of clusters center atoms in the Pd82Si18 amorphous alloy

Abstract To date, there is still a lack of a comprehensive explanation for caged dynamics which is regarded as one of the intricate dynamic behaviors in amorphous alloys. This study focuses on Pd82Si18 as the research object to further elucidate the underlying mechanism of caged dynamics from multiple perspectives, including the cage’s lifetime, atomic local environment, and atomic potential energy. The results reveal that Si atoms exhibit a pronounced cage effect due to the hindrance of Pd atoms, resulting in an anomalous peak in the non-Gaussian parameters. An in-depth investigation was conducted on the caged dynamics differences between fast and slow Si atoms. In comparison to fast Si atoms, slow Si atoms were surrounded by more Pd atoms and occupied lower potential energy states, resulting in smaller diffusion displacements for the slow Si atoms. Concurrently, slow Si atoms tend to be in the centers of smaller clusters with coordination numbers of 9 and 10. During the isothermal relaxation process, clusters with coordination numbers 9 and 10 have longer lifetimes, suggesting that the escape of slow Si atoms from their cages is more challenging. The findings mentioned above hold significant implications for understanding the caged dynamics.

Mass Transfer through Vapor–Liquid Interfaces Studied by Non-Stationary Molecular Dynamics Simulations

Molecular dynamics (MD) simulations are highly attractive for studying the influence of interfacial effects, such as the enrichment of components, on the mass transfer through the interface. In a recent work, we have presented a steady-state MD simulation method for investigating this phenomenon and tested it using model mixtures with and without interfacial enrichment. The present study extends this work by introducing a non-stationary MD simulation method. A rectangular simulation box that contains a mixture of two components 1 + 2 with a vapor phase in the middle and two liquid phases on both sides is used. Starting from a vapor-liquid equilibrium state, a non-stationary molar flux of component 2 is induced by inserting particles of component 2 into the center of the vapor phase in a pulse-like manner. During the isothermal relaxation process, particles of component 2 pass through the vapor phase, cross the vapor-liquid interface, and enter the liquid phase. The system thereby relaxes into a new vapor-liquid equilibrium state. During the relaxation process, spatially resolved responses for the component densities, fluxes, and pressure are sampled. To reduce the noise and provide measures for the uncertainty of the observables, a set of replicas of simulations is carried out. The new simulation method was applied to study mass transfer in two binary Lennard-Jones mixtures: one that exhibits a strong enrichment of the low-boiling component 2 at the vapor-liquid interface and one that shows no enrichment. Even though both mixtures have similar transport coefficients in the bulk phases, the results for mass transfer differ significantly, indicating that the interfacial enrichment influences the mass transfer.

Observation of giant exchange bias effect in Ni–Mn–Ti all-d-metal Heusler alloy

We report a giant exchange bias (EB) field of about 3.68 kOe during field cooled process in all-d-metal Ni40(FeCo)4Mn36Ti20 Heusler alloy. The study of magnetic memory effect and isothermal magnetic relaxation processes suggest that the giant EB field arises due to the possible coexistence of antiferromagnetic (AFM) and ferromagnetic (FM) phase exchange interaction in the studied system at temperatures below 35 K. Furthermore, the temperature and cooling field dependence of EB effect are analyzed which are related to the change in unidirectional anisotropy at FM/AFM interface. The study of a well-established training effect confirms the intrinsic nature of the observed EB behavior. This result will open up a new way toward the development of EB materials considering all-d-metal Heusler alloy systems.

Atomic structure insight into crystallization of undercooled liquid metal Zr during isothermal relaxation processes

ABSTRACTThe crystallization of undercooled liquid zirconium (Zr) was investigated via molecular dynamics simulations. The atomic structures were characterised and analysed by means of pair distribution function, angular distribution function, and the largest standard cluster analysis. At low temperature (T = 1000 K), it is found that the crystallization begins at the initial stage of relaxation and takes the pathway of undercooled liquid (UCL)→BCC→HCP instead of UCL→HCP. The HCP-type medium-range orders (MROs) are formed from the inside of the precursors formed by the BCC-type MROs, and growing at the cost of the precursors, in agreement with the Ostwald’s step rule. The number of MROs is found to play a key role in forming the crystal phases in this process. However, at high temperature (T = 1200 K) the time-scale to reach crystallization is two orders of magnitude bigger than that of T = 1000 K. No intermediate stage of crystallization is observed. The undercooled Zr melts are directly transformed into BCC crystal phases. The max size of BCC-MROs is intimately correlated with the crystallization.

Relaxation of Ni-free Ti40Zr10Cu36Pd14 bulk metallic glass under mechanical stress

Dynamic mechanical behavior of Ti40Zr10Cu36Pd14 bulk metallic glass was investigated by mechanical spectroscopy. The mechanical spectra of Ti40Zr10Cu36Pd14 bulk metallic glass show the main α relaxation while the slow β relaxation is not evident. The isothermal relaxation process of the loss factor tanδ can be well described by the Kohlrausch-Williams-Watts (KWW) stretched exponential relaxation function. In the current study, the stretched exponential relaxation parameter βage remains constant below the glass transition temperature Tg, while the value increases when the temperature approaches Tg. In addition, atomic mobility of the Ti40Zr10Cu36Pd14 bulk metallic glass decreases during the physical aging.

Structural relaxation in AgPO3 glass followed by in situ ionic conductivity measurements

The structural relaxation kinetics of a silver meta-phosphate glass (AgPO3) is investigated using a method based on the isothermal variation of its ionic conductivity over time. Samples of AgPO3 glass from the same batch were pre-annealed at 433K or 418K and then relaxed at different temperatures within this temperature range, which is close to its glass transition temperature measured by differential scanning calorimetry, TgDSC=438K. Ionic conductivity data were continuously collected by impedance spectroscopy during the isothermal relaxation process. The variation of the electrical conductivity over time is well described by the Kohlrausch expression (Φ(t)=exp[−(t/τσK)β]), in which τσK is the characteristic relaxation time and β a stretch exponent. Different values of β were found when the glass structure expanded or contracted during relaxation. In addition, viscosity values calculated by the Maxwell relationship using <τ> from conductivity data and a shear modulus taken from the literature are in accordance with the experimental viscosity measured in the same temperature range, thus validating the use of ionic conductivity to unveil glass structural relaxation.

A note on overstress and over-thermodynamic forces derivation for elasto-viscoplastic media: Thermodynamic analysis of an isothermal relaxation process

In this work, we perform a thermodynamical analysis of an isothermal relaxation process inside the context of elasto-viscoplasticity under the assumption of small deformations. Departing from the one-dimensional Bingham rheological model and assuming that some key decompositions on stress, free energy, and dissipation are possible we demonstrate that, among all equilibrium states satisfying the yield criterion, the actual equilibrium state, given a prescribed total deformation, is the one which minimizes the viscous energy dissipated during the relaxation process. From the one-dimensional motivation we extend the formulation to the multidimensional hardening case. Therefore, based on concepts of thermodynamics with internal variables (TIV) and some results of convex analysis, we arrive at a constrained minimization problem whose solution are state equations for the “over quantities”, or for the equilibrium state, which are identical to those obtained from the minimum complementary free energy principle. This result brings some physical aspects which can aid the understanding of relaxation processes in elasto-viscoplastic media, providing physical foundations which can help the understanding of well established viscoplastic models, as well as the proposing of constitutive formulations and solution algorithms for this class of materials.

Simulation Study of Dynamic Features during the Isothermal Relaxation Processes in Supercooled Liquid and Glassy Pb

The molecular dynamics simulations on the isothermal relaxation properties of supercooled liquid and glassy Pb have been performed. The calculated diffusion constant of Pb is well agreed with the experimental result. Results indicate that the relaxations of supercooled and glassy Pb present more and more pronounced heterogeneity with decreasing temperature. The appearance of the second plateau of mean square displacement (MSD) and the non-zero plateau of Non-Gaussian parameter (NGP) is corresponding to the rest of structure rearrangement.

Hydrogen bonding effect on micellization and morphological transformations of the polystyrene-block-poly(ethylene oxide) micelles

Diblock copolymer polystyrene-block-poly(ethylene oxide) (PS-b-PEO) forms micelles in a mixed solvent of N,N-dimethylformamide (DMF)–water. Poly(acrylic acid) (PAA) and poly(methyl acrylic acid) (PMAA) were introduced to the solution in order to study the effect of hydrogen bonding (H-bonding) complexation on the micellization process. The H-bonding complexation changes the micellization free energy of PS-b-PEO, and more importantly affects the kinetics of the morphological transformation of the micelles with temperature, which provides helpful insights into the time-dependence of the isothermal relaxation process from non-equilibrium to equilibrium.

Kinetic details of crystallization in supercooled liquid Pb during the isothermal relaxation

The kinetic details of crystallization in supercooled liquid Pb during the isothermal relaxation process have been investigated by molecular dynamics simulations, and the microstructure evolution analyzed by the cluster-type index method (CTIM) and the tracing method. It has been found that, the dynamic features are consistently correlated with the microstructure evolution and the crystallization characteristics in the mean square displacement (MSD) and the non-Gaussian parameter (NGP): the β relaxation regime corresponds to the minor structural rearrangement because of the “cage effect”, and the atoms attempt to escape from the “cages”; the α relaxation regime is related to a more diffusive movement of atoms, and the appearance of the second plateau in MSD and the non-zero plateau in NGP corresponds to the completion of crystallization. In addition, three distinct stages of nucleation, growth of nuclei and coarsening of crystallites in the crystallization process have been clearly revealed.

Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics

Within the thermodynamic framework with internal variables, the classical Hamilton’s principle for elastic bodies is extended to inelastic bodies composed of materials whose free energy densities are point functions of internal variables, or the so‑termed Green-inelastic bodies, subject to finite deformation and non-conservative external forces. Yet this general result holds true even without the Green-inelasticity presumption under a more general interpretation of the infinitesimal internal rearrangement. Three special cases are discussed following the generalized form: (a) the Green-elastic bodies whose free energy can be identified with the strain energy; (b) the Green-inelastic bodies composed of materials compliant with the additive decomposition of strain; and (c) the Green-inelastic bodies undergoing isothermal relaxation processes where the thermodynamic forces conjugate to internal variables, or the so-termed internal forces prove to be potential forces. This paper can be viewed as an extension of Yang et al. [1].

Formation and evolution characteristics of bcc phase during isothermal relaxation processes of supercooled liquid and amorphous metal Pb

The formation and evolution characteristics of bcc phase during the isothermal relaxation processes for supercooled-liquid and amorphous Pb were investigated by molecular dynamics simulation and cluster-type index method (CTIM). It is found that during the relaxation process, the formation and evolution of bcc phase are closely dependent on the initial temperature and structure. During the simulation time scale, when the initial temperature is in the range of supercooled liquid region, the bcc phase can be formed and kept a long time; while it is in the range of glassy region, the bcc phase can be formed at first and then partially transformed into hcp phase; when it decreases to the lower one, the hcp and fcc phases can be directly transformed from the glassy structure without undergoing the metastable bcc phase. The Ostwald's “step rule” is impactful during the isothermal relaxation process of the supercooled and glassy Pb, and the metastable bcc phase plays an important role in the precursor of crystallization.

Kinetic details of nucleation in supercooled liquid Na: A simulation tracing study

The kinetic details of nucleation in supercooled liquid Na have been investigated by tracing the evolutions of dynamic and structural properties during the isothermal relaxation process. It is found that many different BCC clusters are formed with the disaggregations of icosahedron clusters during the α-relaxation regime. Those being smaller than the critical size are unstable due to their loose internal structures. The critical size of nucleus (about 100 atoms) obtained in present simulations does not deviate too much from that predicted by the classical nucleation theory. And the preferentially growing orientation of nucleus is close-packed (1 1 0) crystal face.

Effects of Monomer Functionality and Hydrogen Bonding on the Polymerization Kinetics and Properties of Thiol−Ene Networks

The effect of hydrogen bonding on both the kinetics and physical properties of photopolymerized thiol−ene systems has been determined by comparison of two thiol−ene systems, [butyl 3-mercaptopropionate/ pentaerythritol tetrakis(3-mercaptopropionate)]/triallyl-1,3,5-triazine-2,4,6(1H,3H,5H)-trione and [3-mercaptopropionic acid/pentaerythritol tetrakis(3-mercaptopropionate)]/triallyl-1,3,5-triazine-2,4,6(1H,3H,5H)-trione. Hydrogen bonding in the thiol−ene network incorporating 3-mercaptopropionic acid leads to enhanced glass transition temperatures, refractive index, Persoz hardness, elastic modulus values, isothermal enthalpic relaxation, and rubbery−glassy heat capacity differences compared to networks formed using butyl 3-mercaptopropionate. Sub-Tg aging analysis clearly shows that hydrogen bonding affects the isothermal enthalpic relaxation process.

Molecular dynamics simulations on crystallization of polyethylene/fullerene nanocomposites

Molecular dynamics simulations of polyethylene/fullerene (PE/C60) nanocomposites with different fullerene contents were performed. During the isothermal relaxation process of the PE/C60 nanocomposites, subglobules first appear around C60 molecules and the subglobules coalesce into single globule, then the globule evolves as an ordered structure with the C60 molecules being located at the free surface of the cluster. The simulation results show that the attractive van der Waals interactions control the relaxation process, and as the C60 content increases, the crystallinity of the ultimate structures of PE/C60 nanocomposites decreases.

Precise Measurement of Density in the Isothermal Relaxation Processes of Pd&lt;SUB&gt;42.5&lt;/SUB&gt;Cu&lt;SUB&gt;30&lt;/SUB&gt;Ni&lt;SUB&gt;7.5&lt;/SUB&gt;P&lt;SUB&gt;20&lt;/SUB&gt; and Zr&lt;SUB&gt;50&lt;/SUB&gt;Cu&lt;SUB&gt;40&lt;/SUB&gt;Al&lt;SUB&gt;10&lt;/SUB&gt; Glasses

The isothermal relaxation processes of bulk Zr 50 Cu 40 Al 10 and Pd 42.5 Cu 30 Ni 7.5 P 20 glasses were examined by density reduction associated with relaxation. Density experiments were carried out by buoyancy method at room temperature. The isothermal relaxation curves were best fitted by a stretched exponential function with a Kohlrausch exponent less than unity. Based on free volume model, the reduced free volume x as f = 0.0355 and flow defect concentration C as f = 5.80 x 10 -13 in as-quenched state was obtained for Pd 42.5 Cu 30 Ni 7.5 P 20 glass. However, the temperature at which the free volume started to deviate from equilibrium concentration on cooling of the melt was not in accordance with calorimetric glass transition temperature.

Roles of cyclic units in copolyethylene crystallization: a molecular dynamics simulation

Molecular dynamics (MD) simulations of several polyethylene copolymer chains containing 1,2-, 1,3- or 1,4-disubstituted cyclopentane or hexamethylene structures in the main chain (with 500 CH 2) are performed to investigate the influence of cyclic units on the crystallization properties of polyethylene (PE). From the isothermal relaxation process it is found that they generally collapse to a globule via a local collapse process. The copolymer chains containing 1,2-disubstituted cycloparaffin structures form more kinks and take shorter time to totally collapse into a single globule than the others. Moreover, from the morphology of the crystal structures after annealing it is found that the copolymer chains containing 1,2-disubstituted cycloparaffin structures can yield more ordered structures with cyclic units rejected to the fold surface. For the copolymer chains containing 1,3- or 1,4-disubstituted cycloparaffin, the lamellar structures are not perfect and some cyclic units are always incorporated in the crystalline phase.

Effect of initial strengthening on recovery stress generation and isothermal relaxation processes in TiNi alloys

Recovery stress (RS) generation and forced isothermal relaxation processes in Ti-50.5 at. % Ni and Ti-50.7 at. % Ni shape memory alloys were investigated using in situ X-ray structure analysis, X-ray texture analysis, transmission electron microscopy and mechanical tests. The alloys were subjected to thermomechanical treatments (TMT) including cold rolling followed by post-deformation heating in the range from 400 to 700°C for obtaining partially recovered, completely polygonized or recrystallized B2-austenite structures. Specimens containing partially recovered, polygonized or recrystallized structures obtained by thermomechanical treatment (TMT) were deformed in tension by 3 - 12 % strain inducing shape memory. When the austenite get low hardening by TMT or by deformation inducing SME, the RS generation is accompanied by elastic and plastic deformations. When the austenite get high hardening, the RS generation is accompanied by elastic deformation only. The isothermal RS relaxation is accompanied by elastic deformation of the austenite excluding the case of very high RS (> 1000 MPa) and recovery strain during relaxation (8 - 9%) when plastic deformation also takes place. During RS generation the reverse martensite transformation by the orientation variant « directly backwards» is restricted by external counteraction and other orientation variants can partially realize.

Kinetics of long-range order relaxation in Ni 3Al: The effect of stoichiometry

The isothermal relaxation of long-range order (LRO) after small temperature changes has been investigated in Ni 3Al intermetallic compounds (with 24.6, 25.0 and 26.5 at% Al) by measurements of the residual electrical resistivity. The equilibrium residual electrical resistivities were found to be consistent with theoretically calculated values of the LRO parameter. The approach to equilibrium could be satisfactorily represented by a sum of two exponentials; the relaxation rate is minimum at the stoichiometric composition. The activation enthalpies of the two processes are not significantly different (2.63 – 2.88 eV); they do not display an important composition dependence. A model is proposed for explaining the existence of the two isothermal relaxation processes.

Atomic Ordering and Martensitic Transformation in Cu-Zn-Al and Cu-Al-Ni Industrial Alloys

The isothermal relaxation process near room temperature in b Cu-Zn-Al and Cu-Zn-Al-Ni industrial alloys which follows a step quenching or an up quenching thermal treatment has been studied by isothermal calorimetric technique. The transition temperature Ms and its evolution have been obtained by differential scanning calorimetry and by detecting the acoustic emission. The dissipated energy of the sample measured during the relaxation process present a complex behaviour characterized by a continuous slowing down. On the other hand the evolution of Ms at the beginning of the phenomenon obeys a different law. We show that all measured evolutions are much more slow n the case of Cu-Zn-Al-Ni alloy, comparing to Cu-Zin-Al alloy. The presence of nickel, which slows diffusion processes can explain this behaviour influenced by quenching rate and annealing time. We interpret the relaxaton processes and the evolutions of Ms in term of atomic reordering (B2 and L21). These phenomena are so slow in Cu-Zn-Al-Ni alloys near room temperature that the equilibrium state of order cannot be reached