Quench Rate Research Articles

Defect production and quench dynamics in the three-dimensional Kitaev model

We study the quench dynamics of the three-dimensional Kitaev (spin) model under a linear drive using both exact numerical calculations and analytical "independent crossing approximation". Unlike the two-dimensional Kitaev model, the three-dimensional Kitaev model reduces to a multilevel Landau-Zener problem for each momentum. We show that for the slow quench, the defect density is proportional to the quench rate $1/\tau$. We find that the zeros of the relevant coupling between the levels determine the non-adiabatic condition for the production of defects. The contour on which the energy spectrum becomes gapless does not play an active role. The asymptotic behavior of the defect density crucially depends on the way the system reaches the non-adiabatic regime during the quenching process. We analytically show that defect correlation varies as $\tau^{-1} e^{-A/\tau}$, where $A$ is a constant independent of $\tau$. For the slow quench, the qualitative dependence of the entropy (produced during the quenching process) on the quench time is the same as that of the defect correlation, indicating a close connection between the defect correlation and the entropy content of the final state. Possible experimental realization of such quench dynamics is also described briefly.

Emergence of classical structures from the quantum vacuum

After a quantum phase transition the quantum vacuum can break up to form classical topological defects. We examine this process for scalar field models with $Z_2$ symmetry for different quench rates for the phase transition. We find that the number density of kinks at late times universally scales as $C m^{1/2} t^{-1/2}$ where $m$ is a mass scale in the model and $C\approx 0.22$; it does not depend on the quench timescale in contrast to the Kibble-Zurek scaling for thermal phase transitions. A subleading correction $\propto t^{-3/2}$ to the kink density depends on the details of the phase transition.

Quenched dynamics of artificial colloidal spin ice

Artificial spin ices are ideal frustrated model systems in which to explore or design emergent phenomena with unprecedented characterization of the constituent degrees of freedom. In square spin ice, violations of the ice rule are topological excitations essential to the kinetics of the system, providing an ideal testbed for studying the dynamics of such defects under varied quench rates. In this work we describe the first test of the Kibble-Zurek mechanism and critical coarsening in colloidal square and colloidal hexagonal ice under quenches from a weakly interacting liquid state into a strongly interacting regime. As expected, for infinitely slow quenches, the system is defect free, while for increasing quench rate, an increasing number of defects remain in the sample. For square ice, we find regimes in which the defect population decreases as a power law with decreasing quench rate. A detailed scaling analysis shows that for a wide range of parameters, including quench rates that are accessible by experiments, the behavior is described by critical coarsening rather than by the Kibble-Zurek mechanism, since the defect-defect interactions are long ranged. For quenches closer to the critical point, however, there can be a competition between the two mechanisms.

Perspectives on Quenching and Tempering 4340 Steel

Steels are ubiquitous due to their affordability and the landscape of useful properties that can be generated for engineering applications. But to further expand the performance envelope, one must be able to understand and control microstructure development by alloying and processing. Here we use multiscale, advanced characterization to better understand the structural and chemical evolution of AISI 4340 steel after quenching and tempering (Q&T), including the role of quench rate and short-time, isothermal tempering below 573 K (300 °C), with an emphasis on carbide formation. We compare the microstructure and/or property changes produced by conventional tempering to those produced by higher temperature, short-time “rapid” tempering. We underscore that no single characterization technique can fully capture the subtle microstructure changes like carbon redistribution, transition carbide and/or cementite formation, and retained austenite decomposition that occur during Q&T. Only the use of multiple techniques begins to unravel these complexities. After controlled fast or slow quenching, η transition carbides clearly exist in the microstructure, likely associated with autotempering of this high martensite start temperature (Ms) steel. Isothermal tempering below 598 K (325 °C) results in the relief of carbon supersaturation in the martensite, primarily by the formation of η transition carbides that exhibit a range of carbon levels, seemingly without substitutional element partitioning between the carbide and matrix phases. Hagg transition carbide is present between 300 °C and 325 °C. After conventional tempering at or above 598 K (325 °C) for 2 h, cementite is predominant, but small amounts of cementite are also present in other conditions, even after quenching. Previous work has indicated that silicon (Si) and substitutional elements partition between the cementite, which initially forms under paraequilibrium conditions, and the matrix. Phosphorous (P) may also be preferentially located at cementite/matrix interfaces after high temperature tempering. Slower quench rates result in greater amounts of retained austenite compared to those after fast quenching, which we attribute to increased austenite stability resulting from “autopartitioning”. Rapid, high temperature tempering is also found to diminish tempered martensite embrittlement (TME) believed to be associated with the extent of austenite decomposition, resulting in mechanical properties not attainable by conventional tempering, which may have important implications with respect to industrial heat treatment processes like induction tempering. Controlling the amount and stability of retained austenite is not only relevant to the properties of Q&T steels, but also next-generation advanced high strength steels (AHSS) with austenite/martensite mixtures.

Kibble-Zurek dynamics in a trapped ultracold Bose gas

The dynamical evolution of an inhomogeneous ultracold atomic gas quenched at different controllable rates through the Bose-Einstein condensation phase transition is studied numerically in the premise of a recent experiment in an anisotropic harmonic trap. Our findings based on the stochastic (projected) Gross-Pitaevskii equation are shown to be consistent at early times with the predictions of the homogeneous Kibble-Zurek mechanism. This is demonstrated by collapsing the early dynamical evolution of densities, spectral functions and correlation lengths for different quench rates, based on an appropriate characterization of the distance to criticality felt by the quenched system. The subsequent long-time evolution, beyond the identified dynamical critical region, is also investigated by looking at the behaviour of the density wavefront evolution and the corresponding phase ordering dynamics.

Machine-learned interatomic potentials by active learning: amorphous and liquid hafnium dioxide

We propose an active learning scheme for automatically sampling a minimum number of uncorrelated configurations for fitting the Gaussian Approximation Potential (GAP). Our active learning scheme consists of an unsupervised machine learning (ML) scheme coupled with a Bayesian optimization technique that evaluates the GAP model. We apply this scheme to a Hafnium dioxide (HfO2) dataset generated from a “melt-quench” ab initio molecular dynamics (AIMD) protocol. Our results show that the active learning scheme, with no prior knowledge of the dataset, is able to extract a configuration that reaches the required energy fit tolerance. Further, molecular dynamics (MD) simulations performed using this active learned GAP model on 6144 atom systems of amorphous and liquid state elucidate the structural properties of HfO2 with near ab initio precision and quench rates (i.e., 1.0 K/ps) not accessible via AIMD. The melt and amorphous X-ray structural factors generated from our simulation are in good agreement with experiment. In addition, the calculated diffusion constants are in good agreement with previous ab initio studies.

Quench Rate Study on AA7075 with Advanced Aging and T6

Quench Rate Study on AA7075 with Advanced Aging and T6

Revisiting water speciation in hydrous alumino-silicate glasses: A discrepancy between solid-state 1H NMR and NIR spectroscopy in the determination of X-OH and H2O

The speciation of water dissolved into and reacted with hydrous alumino-silicate glasses (of NaAlSi3O8 and “rhyolitic” compositions) quenched from high temperature is re-investigated where the predominant species are expected to be “X(Si and Al)-OH” and “H2O”. Only, two analytical methods are capable of assessing such speciation: Near InfraRed (NIR) spectroscopy and solid-state 1H Nuclear Magnetic Resonance (NMR) spectroscopy. It is observed that the apparent water speciation, as a function of total water content, as determined by NIR spectroscopy is nearly the opposite from what the 1H NMR data reveal. Deuterium (2H) NMR and silicon (29Si) NMR report consistent trends in apparent speciation (depolymerization) with those indicated by the 1H NMR data. Compared with four previous NMR studies of hydrous NaAlSi3O8 glasses it is shown that whereas NIR data always report the same apparent systematic variation in the intensity of the 4500 (“X-OH”) and 5200 (“H2O”) cm−1 bands with total water content, multiple 1H NMR studies of hydrous NaAlSi3O8 report a wide range in OH/H2O. The discrepancy between the various NMR studies likely reflects differences in how the various glasses were made. Specifically, quench rate (fast or slow) and synthesis pressure (higher or lower), might impose a strong effect on observed water speciation in glasses via 1H NMR. It is concluded that the application of NIR spectroscopy, specifically the use of the intensities of the 4500 (“X-OH”) and 5200 (“H2O”) cm−1 NIR bands, does not provide an accurate assessment of water speciation in hydrous alumino-silicate glasses. NIR spectroscopy does remain a very valuable analytical tool for determination of total water content.

Influence of particle size and manufacturing conditions on the recrystallization of amorphous Enzalutamide

Non-isothermal differential scanning calorimetry was used to study the influences of particle size and mechanically induced defects on the recrystallization kinetics of amorphous Enzalutamide. Enzalutamide prepared by hot melt extrusion and spray-drying was used as a model material. The recrystallization rate was primarily accelerated by the presence of the processing-damaged surface of the powder particles. The actual surface/volume ratio associated with decreasing particle size fulfilled only a secondary role. Interestingly, higher quench rate during the extrusion led to a formation of thermally less stable material (with the worse stability being manifested via lower activation energy of crystal growth in the amorphous matrix). This can be the consequence of the formation of looser structure more prone to rearrangements. The recrystallization kinetics of the prepared Enzalutamide amorphous materials was described by the two-parameter autocatalytic kinetic model. The modified single-curve multivariate kinetic analysis (optimized for the data obtained at heating rate 0.5 °C•min−1) was used to calculate the extrapolated kinetic predictions of long-term isothermal crystal growth. The predictions were made for the temperatures from the range of drug shelf-life and processing for each particle size fraction. By the combination of the mass-weighted predictions for the individual powder fractions it was possible to obtain a very reasonable (temperature-extrapolated) prediction of the crystallization rate for the as-prepared unsieved powdered amorphous Enzalutamide.

Quantum quench, large N, and symmetry restoration

We globally quench the theory of two dimensional massless fermions (many flavours) with quartic interactions by making the quartic coupling a smooth function of time. Working in a derivative expansion we show that the discrete ℤ2 symmetry in case of the Gross-Neveu model, and the U (1) symmetry in case of the Nambu-Jona-Lasinio2 model, are restored during the zero-temperature quench. For the Gross-Neveu model we show that this can be understood as an effective thermalization. The time of symmetry restoration shows scaling with the quench rate. We identify this with the Kibble-Zurek scaling in the problem. In a suitable double scaling limit, the symmetry restoration may be understood in terms of Liouville quantum mechanics.

Defect generation and dynamics during quenching in finite size homogeneous ion chains

An equally spaced linear chain of ions provides a test-bed for studying the defect formation during a topological phase transition from a linear to a zig-zag configuration. By using a particular axial potential leading to an homogeneous ion chain, the boundary conditions are not needed, allowing new rich defect dynamics to appear on an homogeneous system. A semi-empirical expression for the critical transition frequency provides an excellent agreement to the numerical results for low ion numbers. The non-adiabatic crossing of the phase transition shows different power-laws for the defect probability density for different quench rates regions. Information regarding defect dynamics is obtained through the measurement of the defect density at different times during the quench. By comparing the defect density and the correlation length dynamics among the different number of trapped ions, the role of the different defect loss mechanism can be deduced. An excellent agreement with the predictions given by the homogeneous Kibble–Zurek model is found on a finite size system of 30 ion system which can be tested in present ion trap experimental set-ups.

Landau-Zener transitions and adiabatic impulse approximation in an array of two Rydberg atoms with time-dependent detuning

We study the Landau-Zener (LZ) dynamics in a setup of two Rydberg atoms with time-dependent detuning, both linear and periodic, using both the exact numerical calculations as well as the method of adiabatic impulse approximation (AIA). By varying the Rydberg-Rydberg interaction strengths, the system can emulate different three-level LZ models, for instance, bow-tie and triangular LZ models. The LZ dynamics exhibits non-trivial dependence on the initial state, the quench rate, and the interaction strengths. For large interaction strengths, the dynamics is well captured by AIA. In the end, we analyze the periodically driven case, and AIA reveals a rich phase structure involved in the dynamics. The latter may find applications in quantum state preparation, quantum phase gates, and atom interferometry.

Vacancy and interstitial interactions with crystal/amorphous, metal/covalent interfaces

We use atomistic simulations to investigate the interaction of vacancies and interstitials with interfaces between a crystalline metal and an amorphous, covalently-bonded solid. We select the gold (Au)/silicon (Si) binary system as a model material and construct interface models along two different facets of crystalline Au and with amorphous Si (a-Si) created at three different quench rates. We compute formation energies of vacancies, self-interstitials, and interstitial impurities as a function of position relative to the interface and find that they have markedly lower values near the interface than in the interior of the adjoining phases. We conclude that crystal/amorphous, metal/covalent interfaces may be as effective at removing radiation-induced point defects as interfaces in polycrystalline metals composites. Moreover, irrespective of interface character, the average formation energies of all point defects at all the Au/a-Si interfaces we investigated are comparable. Thus, unlike in polycrystalline metals, where an interface’s crystallographic character has a marked effect on its interactions with point defects, all interface types in crystal/amorphous, metal/covalent composites may be equally effective at absorbing all radiation-induced defects.

Universal Anti-Kibble-Zurek Scaling in Fully Connected Systems.

We investigate the quench dynamics of an open quantum system involving a quantum phase transition. In the isolated case, the quench dynamics involving the phase transition exhibits a number of scaling relations with the quench rate as predicted by the celebrated Kibble-Zurek mechanism. In contact with an environment however, these scaling laws break down and one may observe an anti-Kibble-Zurek behavior: slower ramps lead to less adiabatic dynamics, increasing thus nonadiabatic effects with the quench time. In contrast to previous works, we show here that such anti-Kibble-Zurek scaling can acquire a universal form in the sense that it is determined by the equilibrium critical exponents of the phase transition, provided the excited states of the system exhibit singular behavior, as observed in fully connected models. This demonstrates novel universal scaling laws granted by a system-environment interaction in a critical system. We illustrate these findings in two fully connected models, namely, the quantum Rabi and the Lipkin-Meshkov-Glick models. In addition, we discuss the impact of nonlinear ramps and finite-size systems.

Investigation of the Quenching Rate Effect on the Ferromagnetic Properties of CuO Nanoparticles

We studied the effect of pressure in a plasma-chemical reactor on the magnetic properties of copper oxide nanoparticles. Plasma-chemical synthesis of copper oxide nanopowders was carried out using an oxygen plasma of an arc discharge at pressures of 40 Pa and 200 Pa. Transmission electron microscopy showed that the obtained samples were made up of highly agglomerated particles with average particle sizes of 31 nm and 27 nm, respectively. X-ray diffraction showed the presence of a single crystalline phase of CuO. Despite the insignificant difference in the average sizes, the nanoparticles exhibited radically different magnetic behavior. Using a vibrating superconducting quantum interference device magnetometer, it was shown that the magnetic properties of nanoparticles obtained at 40 Pa were close to the bulk material and exhibited weak ferromagnetism. The nanoparticles obtained at 200 Pa demonstrated a significant deviation from the properties of the bulk material, showed magnetic hardness, and shifts in the hysteresis loops.

Effect of Quench Rate on Mechanical Properties and Microstructure of 6082 Al-alloy

Effect of Quench Rate on Mechanical Properties and Microstructure of 6082 Al-alloy

Observation of generalized Kibble-Zurek mechanism across a first-order quantum phase transition in a spinor condensate.

The Kibble-Zurek mechanism provides a unified theory to describe the universal scaling laws in the dynamics when a system is driven through a second-order quantum phase transition. However, for first-order quantum phase transitions, the Kibble-Zurek mechanism is usually not applicable. Here, we experimentally demonstrate and theoretically analyze a power-law scaling in the dynamics of a spin-1 condensate across a first-order quantum phase transition when a system is slowly driven from a polar phase to an antiferromagnetic phase. We show that this power-law scaling can be described by a generalized Kibble-Zurek mechanism. Furthermore, by experimentally measuring the spin population, we show the power-law scaling of the temporal onset of spin excitations with respect to the quench rate, which agrees well with our numerical simulation results. Our results open the door for further exploring the generalized Kibble-Zurek mechanism to understand the dynamics across first-order quantum phase transitions.

Athermal ω phase transformation from β in Ti-28Ta driven by ultra-rapid quenching

The athermal ω phase has been reported to be preferably formed at the quench rate below 103 K/s in Ti-30 at.%Ta alloys. Contrary to this common viewpoint, this work presents a similar compositional alloy of Ti-28 at.%Ta with the existence of athermal ω fabricated by plasma rotating electrode process upon quenching at an ultra-high rate of 104–106 K/s. This study aims to probe the underlying mechanism for the athermal ω formation after ultra-rapid quenching of the Ti-28 at.%Ta. Microstructure and phase constituent of the ultra-rapid solidified (URS) Ti-28Ta were investigated. Results showed that the cellular-structured URS Ti-28Ta exhibited predominant β with martensitic α” and athermal ω. Elemental microsegregation is resulted in the URS Ti-28Ta with Ti atoms preferred to concentrate at the cellular walls while Ta accumulate in the matrix. Cellular walls are fully concentrated with martensitic α” and dislocations but free of ω, while the dislocation-free β matrix nearby the walls contains the athermal ω. The athermal ω is suppressed by the high-density dislocations at the grain boundaries, while compositional fluctuation due to the microsegregation in the metastable β matrix favor to form the athermal ω.

Quench-rate and size-dependent behaviour in glassy Ge2Sb2Te5 models simulated with a machine-learned Gaussian approximation potential

Phase-change memory materials are promising candidates for beyond-silicon, next-generation non-volatile-memory and neuromorphic-computing devices; the canonical such material is the chalcogenide semiconductor alloy Ge2Sb2Te5. Here, we describe the results of an analysis of glassy molecular-dynamics models of this material, as generated using a newly developed, linear-scaling (O(N)), machine-learned, Gaussian approximation potential. We investigate the behaviour of the glassy models as a function of different quench rates (varied by two orders of magnitude, down to 1 K ps−1) and model sizes (varied by two orders of magnitude, up to 24 300 atoms). It is found that the lowest quench rate studied (1 K ps−1) is comparable to the minimum cooling rate needed in order completely to vitrify the models on quenching from the melt.

Influence of wheel speed and ageing on nanostructure and magnetic properties of Cr-doped MnBi magnetic material

In the present work, Mn47Bi50Cr3 ribbons were synthesised employing melt spinning at different wheel speeds ranging from 16 to 28 m/s, to study the effect of quenching rate on the microstructure, morphology and magnetic properties of rapidly solidified alloy. X-ray diffraction studies indicate that the FWHM of diffraction peaks for MnBi increases with the increase in wheel speed, leading to a concurrent decrease in the mean grain size. This could be attributed to the high cooling rate causing homogeneous nucleation leading to refined grain size. The maximum value of coercivity of 11.9 kOe and saturation magnetisation of 54.2 emu/g was obtained for the alloy melt spun at 20 m/s, indicating dependence of coercivity on the grain size, and its orientation, which is largely controlled by the wheel speed. Also, XRD pattern confirms that the MnBi phase fraction is found to be maximum at this wheel speed. Therefore, high-performance nanocrystalline Mn47Bi50Cr3 magnetic material has been synthesised by adjusting the wheel speed and thereby tuning the quench rate. In addition, the phase transformation and variation with respect to temperature and time were studied using thermal analysis technique. Stability of magnetic properties of the alloy with respect to time was also studied after the ageing process.