Disorder Transition Temperature Research Articles

First-principles and cluster expansion study of the effect of magnetism on short-range order in Fe–Ni–Cr austenitic stainless steels

Short-range order (SRO), the regular and predictable arrangement of atoms over short distances, alters the mechanical properties of technologically relevant structural materials such as medium/high entropy alloys and austenitic stainless steels. In this study, we present a generalized spin cluster expansion (CE) model and show that magnetism is a primary factor influencing the level of SRO present in austenitic Fe–Ni–Cr alloys. The spin CE consists of a chemical cluster expansion combined with an Ising model for Fe–Ni–Cr austenitic alloys. It explicitly accounts for local magnetic exchange interactions, thereby capturing the effects of finite temperature magnetism on SRO. Model parameters are obtained by fitting to a first-principles data set comprising both chemically and magnetically diverse face-centered cubic configurations. The magnitude of the magnetic exchange interactions are found to be comparable to the chemical interactions. Compared to a conventional implicit magnetism CE built from only magnetic ground state configurations, the spin CE shows improved performance on several experimental benchmarks over a broad spectrum of compositions, particularly at higher temperatures due to the explicit treatment of magnetic disorder. We find that SRO is strongly influenced by alloy Cr content, since Cr atoms prefer to align antiferromagnetically with nearest neighbors but become magnetically frustrated with increasing Cr concentration. Using the spin CE, we predict that increasing the Cr concentration in typical austenitic stainless steels promotes the formation of SRO and increases order–disorder transition temperatures. This study underscores the significance of considering magnetic interactions explicitly when exploring the thermodynamic properties of complex transition metal alloys. It also highlights guidelines for customizing SRO through adjustments of alloy composition.

Configurational entropy of ice XIX and its isotope effect

Ice XIX is a partly hydrogen-ordered polymorph related to disordered ice VI, similar to ice XV. We here investigate the order–order–disorder sequence ice XIX→ice XV→ice VI based on calorimetry at ambient pressure both for D2O and H2O-ice XIX. From these data we extract configurational entropy differences between ice XIX, ice XV and ice VI. This task is complex because, unlike for all other ices, the order–disorder transition from ice XIX to ice VI takes place in two steps via ice XV. Even more challenging, these two steps take place in an overlapping manner, so that careful separation of slow kinetics is necessary. This is evidenced best by changing the heating rate in calorimetry experiments: For fast heating experiments the second step, disordering of ice XV, is suppressed because the first step, formation of ice XV from ice XIX, is too slow. The transient state ice VI‡ that is initially produced upon ice XIX decay then does not have enough time to convert to ice XV, but remains disordered all along. In order to tackle the challenge to determine the entropy difference between ice XIX and VI as well as the entropy difference between ice XV and VI we employ two different approaches that allow assessing the impact of kinetics on the entropy change. “Single peak integration” defines a kinetically limited result, but “combined peak integration” allows estimation of the true thermodynamic values. Our best estimate for the true value shows ice XIX to be much more ordered than ice XV (25 ± 3% vs 9 ± 4% of the Pauling entropy). For D2Oice XIX samples we obtain 28% of order, but only when a small number of fast H-isotope defects are used. In the second part we use these results to estimate the location of the ice XIX phase boundary both for protiated and deuterated ice XIX. The initial Clapeyron slope at ambient pressure is determined from the combination of neutron powder diffraction volume differences and calorimetry entropy differences data to be 21 K GPa−1 with an order–disorder transition temperature To-d(0.0 GPa) = 103 ± 1 K. An in situ bracketing experiment at 1.8 GPa yields To-d(1.8 GPa) = 116 ± 3 K, i.e., the phase boundary slope flattens at higher pressures. These data allow us to determine the region of thermodynamic stability of ice XIX in the phase diagram and to explain the surprising isotope shift reversal at 1.6 GPa compared to 0.0 GPa, i.e., why D2O-ice XIX disorders at lower temperatures than H2O-ice XIX at 1.6 GPa, but at higher temperatures at ambient pressures.

Chemical ordering induced elastic hardening and thermoelastic properties of β phase Mg1-xScx lightweight shape memory alloys

The effect of chemical ordering on the thermoelastic properties of Mg-Sc light weight shape memory alloys are studied by the exact muffin-tinorbital method. Chemical ordering has significant hardening effect on elastic properties of Mg-Sc alloys, the C' is increased by 21% for Mg76Sc24 alloy, and the elastic hardening due to ordering can properly explain the increase in Vickers hardness observed in experiment. The quasi-harmonic Debye-Grüneisen model simulated the order–disorder transition temperature reasonably. The vibrational entropy increase due to elastic softening induced by disordering contributes considerably in driving the order–disorder transition. Mg-Sc alloys in ordered phase shows better thermoelastic stability over well-known commercial Mg alloys, therefore, ordering treatment of Mg-Sc are beneficial for structural application of this family of alloys. The Sc atoms (Mg atoms either) in bcc nearest neighboring lattice repel each other to form a B2-type ordered phase, and resultantly, the s-d and p-d hybridization between nearest neighboring Mg and Sc atoms is the main electronic reason for elastic hardening. The findings in current article not only give insight into understanding the strengthening mechanism during the ordering process of Mg-Sc alloys, but also provides a useful reference for the future development and modification of their shape memory effects.

Microstructural Evolution and Mechanical Behaviour of Near-Eutectic High Entropy Alloy

In the current work, the thermal stability of the eutectic regions and precipitation and mechanical behaviour of near eutectic high-entropy alloy is studied. The alloy solidified as FCC and underwent sequential ordering to L12 with order–disorder transition temperature between 700°C and 1000°C. Cooling rate, variation in the concentration boundary layer, thermal gradient and interfacial energy were attributed to define the eutectic morphology (L12 and B2). Thermal exposure resulted in homogeneous precipitation of acicular Al-Ni-rich B2 phase within the proeutectic and irregular eutectic regions. The preferential B2 precipitation within the irregular eutectic regions was attributed to the lower stability and higher lattice strain associated with these regions. The FCC: B2 phase fraction after heat treatment was similar to that of the eutectic alloy. Furthermore, lamellar degradation, globularization and Ostwald ripening of the B2 phase were observed after heat treatment. Lamellar degradation occurred via mechanisms like cylinderization, edge spheroidization, termination migration and boundary splitting. The experimental observations on the phase evolution, stability and order–disorder transformation matched well with the CALPHAD predictions except for the σ phase formation. B2 precipitation during heat treatment enhanced the mechanical behaviour of the alloy. However, the work hardening rate was superior for as-cast alloy.

Nanotwin-assisted nitridation of quenched FeNi alloy nanopowders for rare-earth-free magnets

L10-ordered FeNi alloy with a high uniaxial magnetic anisotropy and large magnetic moment is a promising candidate for rare-earth-free permanent magnets applications. However, the synthesis of this chemically ordered phase remains a longstanding challenge because of its low chemical order–disorder transition temperature (200–320 °C). Although a non-equilibrium synthetic route based on a nitrogen topotactic reaction has been proposed as a valid approach, the volume fraction and degree of chemical ordering of the product phase are limited. Herein, we propose a promising approach that promotes the efficient formation of L10-ordered nitride phase in FeNi nanopowders by introducing a quenching treatment during a low-oxygen induction thermal plasma process. The quenched FeNi nanopowders possessed much smaller powder sizes (40.4 vs 74.0 nm), exhibited higher number densities of nanotwins (39.8% vs 24.1%) and formed much larger volume fraction (33.6 wt.% vs 0.6 wt.%) of ordered phase than the unquenched nanopowders. Notably, quenching-induced high-density nanotwins led to the dominant coverage of serrated {001} crystal facets over the surfaces of the FeNi nanopowders. Such unique features substantially accelerated the formation of the L10-ordered nitride phase in the FeNi nanopowders because the 〈001〉 crystallographic orientation had the highest nitrogen diffusivity. This work provides not only a valid synthetic approach for mass production of the L10-ordered nitride phase in FeNi nanopowders but also novel insights into the crystal-defect-assisted nitridation of nanomaterials.

Phase Control of Colloid-like Block Copolymer Micelles by Tuning Size Distribution via Thermal Processing

The formation of a Frank–Kasper (FK) phase in a one-component block copolymer (bcp) has been attributed to the sufficiently large conformational asymmetry parameter that leads to the deformation of the micellar core into the polyhedral shape templated by the Voronoi cells for relieving the packing frustration of the coronal blocks. Here we present the insight into the evolution of body-centered cubic (BCC) and Laves C14 phases from the corresponding metastable liquidlike packing (LLP) phases in a conformationally symmetric poly(2-vinylpyridine)-block-poly(dimethylsiloxane) (P2VP-b-PDMS) forming the colloid-like micelle with a hard P2VP core and a soft PDMS corona at the temperature of micelle ordering (Tgcorona < Ta < Tgcore). Different thermal processing conditions were applied to produce four distinct types LLP phase characterized by different average micelle size and size dispersity. The LLP phase was found to transform to BCC, C14 and a reorganized LLP phase with increasing polydispersity of particle size, showing the existence of a proper range of size dispersity for the formation of the Laves phase. The real-space analysis of the local environments of the particles revealed that the C14 phase can accommodate the particles with a broader range of interparticle distance and a less uniform local environment, such that the PDMS coronal blocks of the micelles with greater size dispersity suffered a lower degree of packing frustration when they organized into a C14 lattice. In view of the colloid-like nature of the micelle, a size fractionation process found in the crystallization of polydisperse colloidal particles was proposed as the mechanism for directing the effective development of C14 phase from the LLP phase. Due to the metastable nature of the ordered phases, their order–disorder transition temperatures were found to depend strongly on the structures of the LLP phases from which they developed and a strong memory effect underlying the phase transitions was identified.

Atomic Interactions and Order-Disorder Transition in FCC-Type FeCoNiAl1-xTix High-Entropy Alloys.

Single-phase high-entropy alloys with compositionally disordered elemental arrangements have excellent strength, but show a serious embrittlement effect with increasing strength. Precipitation-hardened high-entropy alloys, such as those strengthened by L12-type ordered intermetallics, possess a superior synergy of strength and ductility. In this work, we employ first-principles calculations and thermodynamic simulations to explore the atomic interactions and order–disorder transitions in FeCoNiAl1−xTix high-entropy alloys. Our calculated results indicate that the atomic interactions depend on the atomic size of the alloy components. The thermodynamic stability behaviors of L12 binary intermetallics are quite diverse, while their atomic arrangements are short-range in FeCoNiAl1−xTix high-entropy alloys. Moreover, the order–disorder transition temperatures decrease with increasing Ti content in FeCoNiAl1−xTix high-entropy alloys, the characteristics of order–disorder transition from first-principles calculations are in line with experimental observations and CALPHAD simulations. The results of this work provide a technique strategy for proper control of the order–disorder transitions that can be used for further optimizing the microstructure characteristics as well as the mechanical properties of FeCoNiAl1−xTixhigh-entropy alloys.

Block copolymer self-assembly: Melt and solution by molecular density functional theory.

The self-assembly of block copolymer melts and solutions with two-dimensional density inhomogeneity is studied using modified inhomogeneous statistical associating fluid theory (iSAFT). A real-space combinatorial screening method under density functional theory formalism is proposed and used to map out the phase diagram of block copolymer melts including order-disorder transitions and order-order transitions. The predicted phase diagram agrees well with molecular dynamics simulation and self-consistent field theory. The compressibility effect on order-disorder transition temperature for block copolymer melts is modeled using iSAFT. The pressure induced temperature change by theory has a similar trend to experimental studies. Then, the lyotropic and thermotropic self-assembly phase behavior of block copolymer solutions is investigated. Detailed density distributions by iSAFT provide insight into the lyotropic properties of the block copolymer solutions at the molecular level. The effect of the block copolymer molecular architecture is studied by comparing block copolymers with different molecular packing parameters. Block copolymer solutions in the inverted hexagonal phase are predicted by theory for the block copolymer having a large molecular packing parameter. Finally, solvent selectivity is studied by modeling the block copolymers in a neutral good solvent. The enhanced local solvent concentration predicted by theory explains the reason for fewer ordered phases found in experiments.

Stability and ordering of bcc and hcp TiAl+Mo phases: An ab initio study

Atomic ordering in bcc and hcp TiAl+Mo alloys near equiatomic TiAl composition is investigated by different ab initio tools. We show that small addition of Mo, about 5 at. %, is enough to make bcc alloys with more than 50 at. % of Ti stable with respect to the hcp alloys. Moreover, such alloying also leads to stabilizing the B2 ordered structure with respect to its B22 modification, which is the bcc-based ground state structure of binary TiAl. The site preference of Mo in the B2 and B19 ordered alloys is investigated by different methods: in the dilute limit, using the transfer energy formalism; in concentrated alloys, from the total energies of disordered and partially ordered alloys in the mean-field coherent potential approximation; and from Monte Carlo simulations. These methods produce consistent results for the B2 phase predicting a strong preference of Mo to Al sublattice. The site preference of Mo in the B19 phases varies from a weak preference for Al sites in the single impurity calculations to a quite strong preference for Ti sites in the mean-field approximation and finally to a strong Al preference in Monte Carlo simulations. Mo alloying dramatically increases the order–disorder transition temperatures in bcc and hcp Al-deficient Ti0.5Al0.5−xMox alloys.

Role of Heat Treatment on Atomic Order and Ordering Domains in Ni45Co5Mn36.6In13.4 Ribbons

The effects of cooling rate and annealed temperature on the state of atomic order and microstructure of L21 domains of Ni45Co5Mn36.6In13.4 ribbons are investigated comprehensively. The state of atomic order is quantitatively studied by in situ X-ray diffraction (XRD), and the microstructure of ordered domains is revealed by transmission electron microscopy (TEM). As-spun ribbons show B2 structure of low atomic order, exhibiting the dispersive L21 domains’ morphology. By applying heat treatment around the order–disorder transition temperature followed by furnace cooling or quenching into water, respectively, we found the strong dependence of ordered domains on cooling rates. Furnace cooling samples show L21 domains with small sized antiphase boundary, revealing a high degree of atomic order, while quenching hinders the formation of ordered domains. Annealing above the order–disorder transition temperature followed by quenching preserves the disordered atomic state with the mixture of L21 structure in B2 matrix.

Identifying a critical micelle temperature in simulations of disordered asymmetric diblock copolymer melts

In melts of highly asymmetric diblock copolymers, copolymers self-assemble into spherical micelles. Indirect evidence has long suggested the existence of two distinct characteristic temperatures in such materials: A critical micelle temperature (CMT) at which a dense fluid of micelles appears over a narrow range of temperatures and an order disorder transition (ODT) temperature at which micelles crystallize. In this article, molecular dynamics simulations are used to definitively confirm the correctness of this picture in melts of high molecular weight polymers, and to show that the CMT occurs very near where self-consistent field theory predicts the ODT to occur.

Controlling phase and rheological behaviours of hexagonal lyotropic liquid crystalline templates for nanostructural administration and retention

Introducing polymerizable monomers into a binary hexagonal lyotropic liquid crystalline (LLC) template is a straightforward way for retaining the nanostructure but will decrease attractive intra- and inter- aggregate interactions. It is therefore crucial to understand the interfacial interactions at nanoscale after introducing the monomers but prior to polymerization. Herein, active species, poly (ethylene glycol) diacrylate (PEGDA) and 2-hydroxyethyl methacrylate (HEMA), were introduced into hexagonal LLC of dodecyl trimethylammonium bromide and water to explore the structural variables, dimensional stability, and dynamic property. At a proper volume ratio of PEGDA/HEMA (1/4), the system presents excellent homogeneity with a higher dimensional stability and lower dynamic property from rheological assessments, thereby achieving robust, free-standing, and transparent membranes after photo-polymerization. The unique property of the system also lies in the much lower order–disorder transition temperature (45 °C) that facilitates the reorientation of mesochannels. They are in contrast inaccessible for the ternary system only with PEGDA, though the nanostructure for both systems could be retained. An insight into subtle variations in these parameters allows us to prepare a polymerizable template possessing higher dimensional stability and suitable flexibility via molecular design, thereby enabling simultaneous structural alignment and retention for the development of functional nanomaterials.

Composition Stability and Cr-Rich Phase Formation in W-Cr-Y and W-Cr-Ti Smart Alloys

W-Cr-Y smart alloys are potential material candidates for plasma facing components due to their protective behaviour during the loss-of-coolant accident (LOCA), while maintaining beneficial properties of W during the normal operation of the fusion power plant. During plasma exposure, the lighter alloying elements are preferentially sputtered at the surface, but in case of a LOCA, the plasma quenches and sputtering stops and diffusion of the alloying elements to the surface becomes intensive. The diffusion of Cr to the surface due to alloying elements (Y, Ti) yields a protective oxide layer stopping the sublimation of WO3. The phase stability and short-range ordering of ternary alloys in W-Cr-Y(Ti) systems has been investigated, using combination of Density Functional Theory (DFT) and Cluster Expansion (CE) methods with Monte-Carlo (MC) simulations. It has been found out from the DFT calculations, that all pairs in the W-Cr-Y system have positive values of the enthalpy of mixing, while most of the Cr-Ti and Ti-W binary structures have negative enthalpies of mixing. The shift in the short-range order as a function of temperature between Cr and W has been predicted as a result of Y addition in W-Cr-Y alloys compared to W70Cr30, by around 400 K towards lower temperatures. A strong tendency towards clustering of Y has been observed even at elevated temperatures (1800 K). The decrease of the order–disorder transition temperature (ODTT) as a result of the Y addition has been observed, while the addition of Ti has not shown any significant changes in the ordering of W-Cr-Ti alloys compared to W-Cr alloy. Our MC simulations showed that for the W70Cr29Y1 alloy the enthalpy of mixing (Hmix) value is positive in the whole analysed temperature range. Free energy of mixing above 1000 K has been calculated from the first nearest neighbours approximation for W70Cr29Y1 and W70Cr29Ti1 alloys. The results of the present investigations provide an insight enabling for optimizing chemical composition of materials for future plasma facing components.

Nanostructural Rearrangement of Lamellar Block Polymers Cured in the Vicinity of the Order–Disorder Transition

The application of large amplitude oscillatory shear (LAOS) to block polymers near their order–disorder transition temperature (TODT) has previously been shown to induce morphological transitions a...

Effective interaction model for coupled magnetism and phase stability in bcc Fe-Co systems

We present an ab-initio-based effective interaction model (EIM) for the study of magnetism, thermodynamics, and their interplay in body-centered cubic Fe-Co alloys, with Co content from 0 to 70%. The model includes explicitly both spin and chemical variables. For the former, a Heisenberg formalism is adopted. But, the spin magnitude of each Fe atom varies according to its local chemical environment, following a simple rule determined by density functional theory (DFT) calculations. The proposed model is able to describe precisely the ground-state magneto-energetic landscape of both chemically ordered and disordered Fe-Co systems, as given by DFT and experiments. In combination with on-lattice Monte Carlo simulations, it enables an accurate prediction at finite temperatures. In particular, the Curie point and the chemical order–disorder (B2-A2) transition temperature are accurately predicted, for all the concentrations considered. A strong dependency of the chemical transition temperature on the magnetic configuration is evidenced and analyzed. We also suggest a more important effect of magnetic rather than vibrational entropy on the chemical transition. However, this transition is not affected by a commonly accessible external magnetic field.

Molecular Simulations of Laser Spike Annealing of Block Copolymer Lamellar Thin-Films.

We use molecular dynamics simulations to study the phase behavior of a coarse-grained lamella-forming A-b-B diblock copolymer under thin-film soft confinement for different heating cycle lengths, film thicknesses, and substrate-polymer affinities. This model describes the effect on thin-film morphology with a free surface (air-polymer interface) and a solid substrate. Our simulation results were first validated by showing that they capture changes for the order-disorder transition temperature with annealing conditions consistent with those found in laser spike annealing experiments, when the vertical lamella phase formed on neutral substrates. In addition, simulations with a substrate selective for a particular block revealed the formation of other phases, including a mixed vertical-horizontal lamella and a metastable island phase having horizontal but incomplete lamella layers. The nanoscale roughness features of this island phase, and hence its surface wettability, can be tuned with suitable choices of chemistry and annealing conditions.

Bicontinuous Porous Nanomaterials from Block Polymers Radically Cured in the Disordered State for Size-Selective Membrane Applications

Solution-cast blends of lamellar-forming poly(styrene-stat-butadiene)-block-poly(lactide), P(S-s-B)-b-PLA, and peroxide were heated above their effective order–disorder transition temperature, TODT...

Sequence Effects on Block Copolymer Self-Assembly through Tuning Chain Conformation and Segregation Strength Utilizing Sequence-Defined Polypeptoids

Polymers with sequence control offer the possibility of tuning segregation strength with comonomer sequence instead of chemical identity. Here, we have synthesized polystyrene-b-polypeptoid diblock copolymers that differ only in the sequence of comonomers in the polypeptoid block, where nonpolar phenyl side chains are incorporated to tune compatibility with polystyrene. Using small-angle X-ray scattering, we see that these materials readily self-assemble into lamellae, with domain spacings and order–disorder transition temperatures varying with sequence, despite identical composition. The ordered state is likely governed by chain conformational effects that localize compatibilizing comonomers at the block–block interface. These altered chain conformations are supported by simulations with self-consistent field theory (SCFT) and lead to the observed changes in domain spacing. However, the trends seen in the order–disorder transition are not captured by SCFT simulations or effective χ parameters, measured i...

Ordering of carbon in highly supersaturated α-Fe

Metropolis Monte Carlo is used to investigate the Zener ordering as the carbon content of body centered cubic iron is increased. Thanks to a fast simulation algorithm, the equilibrium state for a wide range of temperature and carbon content are investigated. These results are compared to a thermodynamical mean-field model that accounts for long range elastic interaction and configurational entropy. At carbon levels of above 2 at.%, it is found that the mean-field model overestimates the order–disorder transition temperature. This is due to local repulsive C–C interactions not accounted for in the mean-field model. Forbidding some strongly repulsive configurations leads to a better agreement between the mean-field model and Metropolis Monte Carlo simulations. At high concentration carbon atoms in solid solution exhibits local configurations typical of the Fe16C2 carbide.

Unusual irradiation-induced disordering in Cu3Au near the critical temperature: An in situ study using electron diffraction

Abstract