Undercooled Liquid Research Articles

Crystallization in three dimensions: Defect-driven topological ordering and the role of geometrical frustration

Herein, fundamentals of topology and symmetry breaking are used to understand crystallization and geometrical frustration in topologically close-packed structures. This frames solidification from a new perspective that is unique from thermodynamic discussions. Crystallization is considered as developing from undercooled liquids, in which orientational order is characterized by a surface of a sphere in four-dimensions (quaternion) with the binary polyhedral representation of the preferred orientational order of atomic clustering inscribed on its surface. As a consequence of the dimensionality of the quaternion orientational order parameter, crystallization is seen as occurring in "restricted dimensions." Homotopy theory is used to classify all topologically stable defects, and third homotopy group defect elements are considered to be generalized vortices that are available in superfluid ordered systems. This topological perspective approaches the liquid-to-crystalline solid transition in three-dimensions from fundamental concepts of: Bose-Einstein condensation, the Mermin-Wagner theorem and Berezinskii-Kosterlitz-Thouless (BKT) topological-ordering transitions. In doing so, in this article, concepts that apply to superfluidity in "restricted dimensions" are generalized in order to consider the solidification of crystalline solid states.

Unique interfacial reaction and so-induced change in mechanical performance of Sn–3.0Ag–0.5Cu/Cu solder joints formed during undercooled and eutectic liquid soldering processes

A novel technique is proposed to prepare Sn–3.0Ag–0.5Cu/Cu joints at three different processing temperatures, which are called undercooled liquid (UL, 213.0 °C), eutectic liquid (EL, 217.0 °C) and normal liquid (NL, 231.0 °C) soldering temperatures correspondingly, and each of them is lower than, equal to and higher than Sn–3.0Ag–0.5Cu solder’s melting point (217.0 °C), respectively. The interfacial reaction, intermetallic compound growth and mechanical performance of Sn–3.0Ag–0.5Cu/Cu joints formed during UL, EL and NL soldering processes were investigated systematically. Results show that for Sn–3.0Ag–0.5Cu solder as the undercooled liquid melt or eutectic liquid melt or normal liquid melt in the formation of joints, the thickness of interfacial intermetallic compound (IMC) layer in the joints increases with prolonging dwelling time. For three different liquid soldering processes, the change tendency of the interfacial IMC layer thickness is distinct. For joints formed at UL and EL temperatures, the excessive growth of primary Cu6Sn5 and interfacial IMC (mainly Cu6Sn5) can be suppressed during isothermally dwelling in the liquid state for more than 5 min. Ball shear test results show that solder joints formed at UL and EL temperatures have lower value of the maximum shear force (MSF) than those formed during the NL soldering process. For UL and EL types of joints, the fracture occurs either by shear slide fracture totally along the shear tool tip movement plane (i.e., in-plane shear slide fracture) or by shear slide fracture initially along the shear tool tip movement plane and afterwards shear deformation fracture in the solder matrix under the plane (i.e., out-of-plane shear slide and deformation mixed-mode fracture), while the fracture takes place in NL joints only by in-plane shear slide fracture mode.

Dynamic and structural heterogeneity in undercooled miscible and immiscible metallic liquid

Molecular dynamics computer simulations are performed to study the structure and dynamic relaxation of the metallic alloys Cu50Ag50 and Cu50Zr50 with and without miscibility gap, respectively. The interactions between the particles are modeled by an effective potential of the modified embedded atom method (MEAM). Cu50Zr50 undercooled liquid shows negative mixing enthalpy; the stronger interaction of heterogeneous atom pairs than that of homogeneous atom pairs, the longer the α-relaxation time and the lower the diffusion coefficient than that of the Cu50Ag50 liquid. Dynamic relaxation is related to the structural heterogeneity: the amount of five-fold symmetry (icosahedron-like) clusters is predominant in Cu50Zr50 melts, which hinders the movement of atoms and increases the dynamic relaxation time. The amount of non-five-fold symmetry (crystal-like) clusters is more pronounced in Cu50Ag50 melts, which leads to shorter dynamic relaxation time and enhanced crystallization of the Cu50Ag50 melt. The quantitative relationship between the five-fold symmetry parameter W and the diffusion coefficient D, as well as the α-relaxation time τα, is obtained in the two distinct undercooled liquids. The present work provides an understanding of the atomic-scale structure and the dynamic properties in the miscible and immiscible liquid mixtures.

Competitive Nucleation and Growth Between the Primary and Peritectic Phases of Rapidly Solidifying Ni–Zr Hypoperitectic Alloy

The Ni-16 at. pct Zr hypoperitectic alloy melt was substantially undercooled using an electromagnetic levitator and a drop tube. The undercooling-induced competitive growth between the primary Ni7Zr2 and peritectic Ni5Zr phases was revealed by observing of the recalescence process in situ and confirmed by analyzing the solidified microstructures, X-ray diffraction pattern as well as dendritic growth velocity. When the liquid undercooling is less than a critical value of 106 K, the primary Ni7Zr2 phase initially precipitates from the parent liquid, which is subsequently followed by the nucleation and growth of the peritectic Ni5Zr phase around it. The solidified microstructure consists of the Ni7Zr2 phase, the Ni5Zr phase, and inter-dendritic eutectics. The orientation relationship and interface characteristics of the Ni7Zr2 and Ni5Zr phases were investigated by electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). The EBSD results clearly demonstrate that the Ni7Zr2 and Ni5Zr phases have the parallel relationship of {111}Ni7Zr2 // {111}Ni5Zr. TEM analysis reveals that a large-scale flat interface exists between the Ni7Zr2 and Ni5Zr phases, indicating good lattice matching of the two phases along the phase boundary. Once the critical undercooling is exceeded, the peritectic Ni5Zr phase preferentially nucleates and grows from the undercooled melt by completely suppressing the formation of the primary Ni7Zr2 phase. The EBSD analysis shows that the peritectic Ni5Zr phase is highly orientated and its growth mode is almost parallel to the 〈110〉 directions. When containerlessly solidified during free fall, typical peritectic microstructures form in large droplets, while only peritectic phase appears in the small droplets. This result further confirms the strong competition between the primary and peritectic phases in the Ni–Zr hypoperitectic alloy induced by large undercoolings.

Melting of fluorphlogopite-plagioclase pairs at 1 atmosphere

Melting experiments on fluorphlogopite + plagioclase (An68) pairs have been performed at 1 atmosphere, as a function of temperature and run duration. Run products include, in addition to melt, spinel, forsterite and a newly formed calcic plagioclase. The solidus was located between 1100 and 1150°C and the amount of melt produced increases sharply at 1200°C. From this temperature, liquids are compositionally zoned between the two mineral interfaces, and the mica reacts out after sufficient time indicating the existence of a critical temperature of melting located between 1175 and 1200°C. These two temperature domains are also characterized by differences in plagioclase reaction textures, melt proportions and reaction rates. Textural and Sr isotopic studies of the plagioclases show that at all temperatures the first step of the melting reaction is characterized by congruent dissolution of the starting plagioclase followed by precipitation of the new plagioclase. At all temperatures the melt compositions are initially located on the intersection of the cotectic line and the starting plagioclase-fluorphlogopite tie-line. Below the critical temperature of melting these melts are metastable undercooled liquids. Above the critical temperature of melting there is an array of stable melt compositions located on the plagioclase- fluorphlogopite tie-line. In both cases the melt compositions evolve with time toward more albite-rich compositions in conjunction with the new plagioclase precipitation. The system fluorphlogopite-plagioclase thus provides an example where liquid compositions vary with time although plagioclase-melt interface equilibrium is satisfied. This is due to the involvement of a solid solution in the reaction. Above the critical temperature of melting, the rate-controlling process for melting is chemical diffusion in the melt. Below the critical temperature of melting the rate-limiting step is the formation of the metastable undercooled melt. The sluggishness of the melting reaction in this temperature regime is explained by the difficulty of forming such a melt.

Simulation of temperature, stress and microstructure fields during laser deposition of Ti–6Al–4V

We study the evolution of prior columnar β phase, interface L phase, and α phase during directional solidification of a Ti–6Al–4V melt pool. Finite element simulations estimate the solidification temperature and velocity fields in the melt pool and analyze the stress field and thermal distortions in the solidified part during the laser powder bed fusion process. A phase-field model uses the temperature and velocity fields to predict the formation of columnar prior-β(Ti) phase. During the solidification of the β phase from an undercooled liquid, the residual liquid below the solidus temperature within the β columns results in the α phase. The finite element simulated stress and strain fields are correlated with the length scales and volume fractions of the microstructure fields. Finally, the coalescence behavior of the β(Ti) cells during solidification is illustrated. The above analyses are important as they can be used for proactive control of the subsequent modeling of the heat treatment processes.

Liquid state property and intermetallic compound growth of Zr2Ni alloy investigated under electrostatic levitation condition

The liquid state property and intermetallic compound growth of Zr2Ni alloy were investigated by electrostatic levitation(ESL) technique. The relation between liquid undercooling and superheating followed a sigmoidal curve, which was probably attributed to the liquid structure transition. This assumption was supported by the density and viscosity measurement of liquid Zr2Ni alloy. Meanwhile, the diffusion-limited growth mechanism of Zr2Ni compound phase was demonstrated by the measured dendritic growth velocity. Within the undercooling range of 70–277 K(0.20 TL), the dendritic growth velocity displayed a parabolic relation versus undercooling, which achieved a maximum value of 27 mm s-1.

Atomic structure evolution of (CuZr)100-xAgx glass under compression deformation

Molecular dynamics simulations are performed to investigate the evolutions of strain localizations, short-range orders as well as the stability of the interpenetrating connection of icosahedra in (CuZr)100-xAgx (x = 0,10,20,33) glasses during compressive deformation based on the embedded atom method (EAM). Our finding indicates that (CuZr)100-xAgx (x≠0) undercooled liquid exhibits faster dynamics than Cu50Zr50, but stronger chemical heterogeneity. The addition of Ag atoms to the CuZr glass shows better plastic deformation, and the local shear strains distribute more homogeneously with increasing Ag content. Further research indicates that the Ag-centered full icosahedra (FI) are structurally less stable, although the total number of FI and connectivity of FI in multicomponent glasses become larger with increasing Ag content, the network formed by Ag-centered FI are also prone to be destroyed during deformation. These findings may suggest a link between the deformation and structural heterogeneity in ternary glasses.

Eshelby description of highly viscous flow-Half model, half theory.

A recent description of the highly viscous flow ascribes it to irreversible thermally activated Eshelby transitions, which transform a region of the undercooled liquid to a different structure with a different elastic misfit to the viscoelastic surroundings. The description is extended to include reversible Eshelby transitions, with the Kohlrausch exponent β as a free parameter. The model answers several open questions in the field.

Local atomic structure correlating to phase selection in undercooled liquid Ni-Zr peritectic alloy

The local atomic structure and its correlation with phase selection during rapid solidification of undercooled liquid Ni5Zr peritectic alloy has been investigated by combining the electrostatic levitation technique and first-principles molecular dynamics simulations. The calculated density agrees well with the present experimental measurements. The partial pair distribution functions indicate that liquid Ni5Zr alloy exhibits a remarkable chemical short range order, which leads to a preferred association of Ni and Zr atoms. Atomic three-dimensional structure analyses reveal that a high fraction of atom pairs locates in perfect or distorted icosahedral environments (>36.9%) although the number of the fully developed icosahedra or distorted icosahedra is rather rare (<2.5%), implying that this liquid contains a lot of fragmented clusters with perfect or distorted pentagonal faces. Moreover, we demonstrate that the short range orders of the undercooled liquid differ topologically from those in the ideal Ni5Zr crystal but are similar to those in the ideal Ni7Zr2 crystal in the temperature range from the liquidus temperature of 1612 K to 1400 K, which indicates that the nucleation of primary phase Ni7Zr2 from the undercooled liquid is structurally favored due to the low free energy barrier. However, the nucleation of primary Ni7Zr2 phase is presumed to be replaced by the direct formation of the peritectic Ni5Zr phase if a sufficient undercooling is achieved, which is ascertained by the solidified microstructures and X-ray diffraction patterns. These results shed light on the relationship between the local atomic structure and phase selection during the rapid solidification of the undercooled peritectic alloys.

Effect of samarium doping on the nucleation of fcc-aluminum in undercooled liquids

The effect of Sm doping on the fcc-Al nucleation was investigated in Al-Sm liquids with low Sm concentrations (xSm) with molecular dynamics simulations. The nucleation in the moderately undercooled liquid is achieved by the recently developed persistent-embryo method. Systematically computing the nucleation rate with different xSm (xSm = 0%, 1%, 2%, 3%, 5%) at 700 K, we found Sm dopant reduces the nucleation rate by up to 25 orders of magnitudes with only 5% doping concentration. This effect is mostly associated with the increase in the free energy barrier with minor contribution from suppression of the attachment to the nucleus caused by Sm doping.

Epoxy Resin Coatings Crystallization and Influence of Crystallinity on Shore Hardness and Tensile Properties

The epoxy resins are very popular and plentifully used synthetic resins. The bisphenol A-based (DGEBA) and bisphenol F-based epoxy resins (DGEBF) crystallization is phenomenon which is for that kind of resins natural. They are undercooled liquids and they tend to form the crystal structure at the ambient temperature. The subject of the research is to determine the effect of some crystallinity of DGEBF on chosen mechanical parameters. The degree of crystallinity was counted through the specific weights of crystallized bisphenol F-based epoxy resins. The prepared crystallized samples of DGEBA/DGEBF mixtures were mixed in appropriate weight ratio with isophorondiamine (IPD) based curing agent. Measured was hardness Shore D according to EN ISO 868 standard and tensile parameters according to EN ISO 527-1 standard. Furthermore, the effect of crystallinity on chosen mechanical parameters was observed. It was found out that with the higher crystallinity maximum tensile stress and hardness increased close to the standard parameters amorphous DGEBA and DGEBF.

Spatially-correlated site occupancy in the nonstoichiometric meta-stable [formula omitted]-Al60Sm11 phase during devitrification of Al-10.2 at.% Sm glasses

A metastable ε-Al60Sm11 phase appears during the initial devitrification of as-quenched Al-10.2 at.% Sm glasses. The ε phase is nonstoichiometric in nature since Al occupation is observed on the 16f Sm lattice sites. Scanning transmission electron microscopic images reveal profound spatial correlation of Sm content on these sites, which cannot be explained by the “average crystal” description from Rietveld analysis of diffraction data. Thermodynamically favorable configurations, established by Monte Carlo (MC) simulations based on a cluster-expansion model, also give qualitatively different correlation functions from experimental observations. On the other hand, molecular dynamics simulations of the growth of ε-Al60Sm11 in undercooled liquid show that when the diffusion range of Sm is limited to ∼4 Å, the correlation function of the as-grown crystal structure agrees well with that of the scanning transmission electronic microscopy (STEM) images. Our results show that kinetic effects, especially the limited diffusivity of Sm atoms plays the fundamental role in determining the nonstoichiometric site occupancies of the ε-Al60Sm11 phase during the crystallization process.

Structural origin of dynamical relaxation in undercooled Cu50Zr50 metallic liquid

Molecular dynamics (MD) simulation has been performed to explore the correlation between dynamic characteristics and structural heterogeneity in undercooled Cu50Zr50 melt based on the embedded atom method. It is found that atoms in the undercooled liquid can be classified into three groups in terms of the probability distribution of atoms' displacement, named ‘fast atoms’ (FAs), ‘intermediate atoms’ (IAs), ‘slow atoms’ (SAs). Meanwhile, the undercooled liquid can be divided into three temperature regime: as the temperature is higher than 1120 K, the distribution of FAs become network connectivity, in which the SAs region are surrounded; as the temperature is in the range from 1120 K to 900 K, the network of FAs region decompose into several isolated region gradually; after that the single relaxation separates into α- and β-relaxation at temperature lower than 900 K, the FAs region become isolated islands, while the SAs have connected into networks where the FAs regions are surrounded, which cause the significant decreasing of atomic mobility and sharp increasing of the relaxation time. The FAs, located in loose packaging and isolated region, which corresponds to β-relaxation reflected by the time-scale of intermediate plateau in mean-squared displacement (MSD) and intermediate scattering function (ISF). The SAs which develop into the backbone of the system and surround clusters formed by FAs, are responsible for the glass formation and have a connection with α-relaxation. The compressive deformation in the Cu50Zr50 metallic glass shows that the ‘fast atoms’, anticipating in β-relaxation of undercooled liquid, mostly are located in large shear strain zones and the structural heterogeneity of undercooled liquid inherits into the glass. Since metallic glass (MG) can be regarded as frozen undercooled liquid, our study is helpful for understanding the structural origins of dynamical relaxation in MGs.

Role of five-fold symmetry in undercooled Al-Cu binary alloys

We investigate the role of five-fold symmetry (FFS) in undercooled Al1-xCux liquids (x = 0.3 and 0.4) using ab initio molecular dynamics simulations. We show that the structure factors and pair-correlation functions display characteristic features which are compatible with the occurrence of FFS and the emergence of a medium range order (MRO) below a temperature TX located close to the liquidus temperature. Then, we demonstrate that the formation of MRO is associated with a strong increase in local FFS-motifs which become more and more connected with decreasing temperature. From the temperature dependence of dynamic properties, we find that TX corresponds also to the onset of dynamic phenomena, like the non-Arrhenius temperature dependence of transport properties and the emergence of dynamical heterogeneities (DHs). Finally, we clearly identify a relationship between the fivefold topology at the medium-range scale (IMRO) and the spatial distribution of DHs using isoconfigurational ensemble simulations. This questions the direct role of the connectivity of five-fold-based motifs found in IMRO in nucleation of the parent crystalline ground states, namely, Al2Cu and Al3Cu2, which also display local ordering with a significant degree of FFS.

Evolution of short range order in Ar: Liquid to glass and solid transitions–A computational study

The evolution of the short range order (SRO) as a function of temperature in a Lennard-Jones model liquid with Ar parameters was determined and juxtaposed with thermodynamic and kinetic properties obtained as the liquid was cooled (heated) and transformed between crystalline solid or glassy states and an undercooled liquid. The Lennard-Jones system was studied by non-equilibrium molecular dynamics simulations of large supercells (approximately 20000 atoms) rapidly cooled or heated at selected quenching rates and at constant pressure. The liquid to solid transition was identified by discontinuities in the atomic volume and molar enthalpy; the glass transition temperature range was identified from the temperature dependence of the self-diffusion. The SRO was studied within the quasi-crystalline model (QCM) framework and compared with the Steinhardt bond order parameters. Within the QCM it was found that the SRO evolves from a bcc-like order in the liquid through a bct-like short range order (c/a=1.2) in the supercooled liquid which persists into the glass and finally to a fcc-like ordering in the crystalline solid. The variation of the SRO that results from the QCM compares well with that obtained with Steinhardt’s bond order parameters. The hypothesis of icosahedral order in liquids and glasses is not supported by our results.

Phase field model of the nanoscale evolution during the explosive crystallization phenomenon

Explosive crystallization is a well known phenomenon occurring due to the thermodynamic instability of strongly under-cooled liquids, which is particularly relevant in pulsed laser annealing processes of amorphous semiconductor materials due to the globally exothermic amorphous-to-liquid-to-crystal transition pathway. In spite of the assessed understanding of this phenomenon, quantitative predictions of the material kinetics promoted by explosive crystallization are hardly achieved due to the lack of a consistent model able to simulate the concurrent kinetics of the amorphous-liquid and liquid-crystal interfaces. Here, we propose a multi-well phase-field model specifically suited for the simulation of explosive crystallization induced by pulsed laser irradiation in the nanosecond time scale. The numerical implementation of the model is robust despite the discontinuous jumps of the interface speed induced by the phenomenon. The predictive potential of the simulations is demonstrated by means of comparisons of the modelling predictions with experimental data in terms of in situ reflectivity measurements and ex-situ micro-structural and chemical characterization.

Investigation of Structure and Dynamics in Disordered Materials Using Containerless Techniques with In-Situ Quantum Beam and Thermophysical Property Measurements

The use of levitation (containerless) techniques can enable new scientific discoveries because deeply undercooled and metastable liquids can be achieved over a wide temperature range. This review article summarizes the state-of-art instrumentation for structure measurements at synchrotron radiation/neutron sources and for thermophysical property measurements not only on the ground but also in microgravity utilizing the International Space Station (ISS). Furthermore, we introduce recent scientific topics on high-temperature oxide liquids and oxide glasses synthesized from levitated undercooled liquids by the use of quantum beam measurements analyzed using advanced computation.

Effects of Undercooling and Cooling Rate on Peritectic Phase Crystallization Within Ni-Zr Alloy Melt

The liquid Ni-16.75 at. pct Zr peritectic alloy was substantially undercooled and containerlessly solidified by an electromagnetic levitator and a drop tube. The dependence of the peritectic solidification mode on undercooling was established based on the results of the solidified microstructures, crystal growth velocity, as well as X-ray diffraction patterns. Below a critical undercooling of 124 K, the primary Ni7Zr2 phase preferentially nucleates and grows from the undercooled liquid, which is followed by a peritectic reaction of Ni7Zr2+L → Ni5Zr. The corresponding microstructure is composed of the Ni7Zr2 dendrites, peritectic Ni5Zr phase, and inter-dendritic eutectic. Nevertheless, once the liquid undercooling exceeds the critical undercooling, the peritectic Ni5Zr phase directly precipitates from this undercooled liquid. However, a negligible amount of residual Ni7Zr2 phase still appears in the microstructure, indicating that nucleation and growth of the Ni7Zr2 phase are not completely suppressed. The micromechanical property of the peritectic Ni5Zr phase in terms of the Vickers microhardness is enhanced, which is ascribed to the transition of the peritectic solidification mode. To suppress the formation of the primary phase completely, this alloy was also containerlessly solidified in free fall experiments. Typical peritectic solidified microstructure forms in large droplets, while only the peritectic Ni5Zr phase appears in smaller droplets, which gives an indication that the peritectic Ni5Zr phase directly precipitates from the undercooled liquid by completely suppressing the growth of the primary Ni7Zr2 phase and the peritectic reaction due to the combined effects of the large undercooling and high cooling rate.

Structural relaxation and highly viscous flow.

The highly viscous flow is due to thermally activated Eshelby transitions which transform a region of the undercooled liquid to a different structure with a different elastic misfit to the viscoelastic surroundings. A self-consistent determination of the viscosity in this picture explains why the average structural relaxation time is a factor of eight longer than the Maxwell time. The physical reason for the short Maxwell time is the very large contribution of strongly strained inherent states to the fluidity (the inverse viscosity). At the Maxwell time, the viscous no-return processes coexist with the back-and-forth jumping retardation processes.