Stacking fault energy (SFE) plays an important role in deformation mechanisms and mechanical properties of face-centered cubic (fcc) metals and alloys. In metastable fcc alloys, the SFEs determined from density functional theory (DFT) calculations and experimental methods often have opposite signs. Here, we show that the negative SFE by DFT reflects the thermodynamic instability of the fcc phase relative to the hexagonal close-packed one; while the experimentally determined SFEs are restricted to be positive by the models behind the indirect measurements. We argue that the common models underlying the experimental measurements of SFE fail in metastable alloys. In various concentrated solid solutions, we demonstrate that the SFEs obtained by DFT calculations correlate well with the primary deformation mechanisms observed experimentally, showing a better resolution than the experimentally measured SFEs. Furthermore, we believe that the negative SFE is important for understanding the abnormal behaviors of partial dislocations in metastable alloys under deformation. The present work advances the fundamental understanding of SFE and its relation to plastic deformations, and sheds light on future alloy design by physical metallurgy.
Metastable alloys with transformation/twinning-induced plasticity (TRIP/TWIP) can overcome the strength-ductility trade-off in structural materials. Originated from the development of traditional alloys, the intrinsic stacking fault energy (ISFE) has been relied to tailor TRIP/TWIP in high-entropy alloys (HEA), but with limited quantitative success. Herein, we demonstrate a new strategy for designing metastable HEAs and validate its effectiveness by discovering seven new alloys with experimentally observed metastability for TRIP/TWIP. We propose unstable fault energies as the more effective de…
A series of structural polytypes formed in an Mg-1at.%Zn-2at.%Y alloy has been identified, which are reasonably viewed as long-period stacking derivatives of the hcp Mg structure with alternate AB stacking of the close-packed atomic layers. Atomic-resolution Z-contrast imaging clearly revealed that the structures are long-period chemical-ordered as well as stacking-ordered; unique chemical order along the stacking direction occurs as being synchronized with a local faulted stacking of AB'C'A, where B' and C' layers are commonly enriched by Zn/Y atoms.
The generalized stacking fault energy is a key ingredient to mesoscale models of dislocations. Here we develop an approach to quantify the dependence of generalized stacking fault energies on the degree of chemical disorder in multicomponent alloys. We introduce the notion of a "configurationally-resolved planar fault" (CRPF) energy and extend the cluster expansion method from alloy theory to express the CRPF as a function of chemical occupation variables of sites surrounding the fault. We apply the approach to explore the composition and temperature dependence of the unstable stacking fault e…
The generalized stacking fault (SFE) energy curves of pure gold (Au) and its binary alloys with transition metals are determined from density functional theory (DFT). Alloy elements Ag, Al, Cu, Ni, Ti, Zr, Zn, In, Ga, Sn, Mn, Cd, Sn, Ta and Cr are substituted into Au at concentrations up to 4%. A comparison of various proposed methodologies to calculate SFEs is given. The intrinsic SFE decreases for all alloying elements from its value for pure Au, but SFE energies (both stable and unstable) vary strongly with the distance of the alloying element from the stacking fault region, and with alloy …
In a recent paper, Zhang et al. [Acta Materialia 152 (2018) 96] studied the in-plane ordering of the long-period stacking ordered (LPSO) structure in Mg-Al-Y alloys. In addition to the well-known L12 type building cluster, they proposed three new types of metastable building clusters. However, we will show that these new types of building clusters are caused by the superimposition of L12 type clusters located in different domains. In addition, the experimental evidence for domain structures in a similar alloy system Mg-Al-Gd is provided.
In order to clarify thermodynamic stability of Mg-based long-period stacking ordered (LPSO) structure, we systematically study energetic preference for alloys on multiple stacking with different composition for random mixing of constituent elements, Mg, Y, and Zn based on special quasirandom structure (SQS). Through calculation of formation free energy of SQS, Mg-Y-Zn alloy exhibits phase separation into Mg- and Y-Zn rich phase, which is consistent with previous theoretical studies. Bulk modulus of SQSs for multiple compositions, stacking sequences, and atomic configuratons ranges around 35 GP…
Point defect species and concentrations in metastable Fe-C alloys are determined using density functional theory and a constrained free-energy functional. Carbon interstitials dominate unless iron vacancies are in significant excess, whereas excess carbon causes greatly enhances vacancy concentration. Our predictions are amenable to experimental verification; they provide a baseline for rationalizing complex microstructures known in hardened and tempered steels, and by extension other technological materials created by or subjected to extreme environments.
The transitional state of ordering in the long-period stacking ordered (LPSO) structure in Mg-Al-Gd alloy has been investigated by scanning transmission electron microscopy. It is found that the domains are the origin of observed transitional state. Three new patterns of clusters at this state can be fully explained by the superimposition of L12 type clusters located in different domains. The domains are further verified by different tilted views. Growth of preferred domains during ageing process will result in final ordered LPSO structure. Based on the idea of domains, less ordered LPSO struc…
Stacking fault energy (SFE) is an essential parameter for characterizing mechanical properties. However, in high entropy alloys (HEAs), the local chemical environment varies significantly across different stacking fault planes, resulting in a substantial fluctuation of SFE values rather than a unique value, which prohibits the prediction of the local SFE. Herein, we proposed an effective descriptor based on the local concentration ratio near stacking fault to quantitatively predict the local SFE of refractory HEAs. We find that the role of a given element in determining SFE strongly depends on…
Based on state-of-the-art density-functional-theory methods we calculate the stacking-fault energy of the paramagnetic random Fe-22.5at.%Mn alloy between 300-800 K. We estimate magnetic thermal excitations by considering longitudinal spin-fluctuations. Our results demonstrate that the interplay between the magnetic excitations and the thermal lattice expansion is the main factor determining the anti-Invar effect, the hcp-fcc transformation temperature, and the stacking-fault energy, which is in excellent agreement with measurements.
Stacking Fault Energy (SFE) is an intrinsic alloy property that governs much of the plastic deformation mechanisms observed in fcc alloys. While SFE has been recognized for many years as a key intrinsic mechanical property, its inference via experimental observations or prediction using, for example, computationally intensive first-principles methods is challenging. This difficulty precludes the explicit use of SFE as an alloy design parameter. In this work, we combine DFT calculations (with necessary configurational averaging), machine-learning (ML) and physics-based models to predict the SFE…
The CoCrFeNi alloy is widely accepted as an exemplary stable base for high entropy alloys (HEAs). Although various investigations prove it to be stable solid solution, its phase stability is still suspicious. Here, we identified that the CoCrFeNi HEA was thermally metastable at intermediate temperatures, and composition decomposition occurred after annealed at 750oC for 800 hrs. The increased lattice distortion induced by minor addition of Al into the CoCrFeNi base accelerated the composition decomposition and a second fcc phase with a different lattice constant occurred in the long time annea…
Nanostructured Fe40Ni40P14B6 alloys ingots of diameter 3~5 mm could be synthesised by a metastable liquid state spinodal decomposition method. The molten Fe40Ni40P14B6 alloy was purified by means of the fluxing technique and thus a large undercooling could be achieved. For undercooling Delta T > 260 K, the microstructure of the undercooled specimen had exhibited liquid state spinodal decomposition in the undercooled liquid state. The microstructure could be described as two intertwining networks with small grains dispersed in them. For undercooling Delta T > 290 K, the overall microstructure o…
We study the effect of Stacking Fault Energy (SFE) on the deformation behaviour of copper and copper-aluminium alloys using Molecular Dynamics (MD) simulation. We find that both yield stress and the magnitude of stress drop at yield decrease with increasing Al content. This "anomalous" softening behaviour is explained on the basis of nucleation controlled yielding behaviour. Further, the decrease in stress drop is rationalised in terms of the stored energy available at yielding - we show that this decreases with increasing Al. As a result, the maximum dislocation density is found to decrease w…
First-principles alloy theory is used to establish the $γ$-surface of Fe-Cr-Ni alloys as function of chemical composition and temperature. The theoretical stacking fault energy (SFE) versus chemistry and temperature trends agree well with experiments. Combining our results with the recent plasticity theory based on the $γ$-surface, the stacking fault formation is predicted to be the leading deformation mechanism for alloys with effective stacking fault energy below about 18 mJ m$^{-2}$. Alloys with SFE above this critical value show both twinning and full slip at room temperature and twinning …
The origin of the phase stability of 18$R$ Mg-Zn-Y alloys with a long-period stacking order (LPSO) is studied using first-principles calculations. We calculate the heat of formation as a function of the number of Zn vacancies to discuss the role of Zn atoms. The calculated convex hull indicates that the Zn atoms in the LPSO alloys are stable even if they number about half of the Y atoms. The bonding state with Zn $p$ orbitals leads to the stability of the LPSO structure because the partial density of states of Mg nearest to the solute cluster forms a valley structure.
Cooperative growth of the structure units (SUs) in a 14H type long-period stacking ordered (LPSO) structure has been observed, and there is no obvious accumulation of transformation strain at the growth fronts. The atomic structures at this front are further characterized by Cs-corrected scanning transmission electron microscopy, and the partial dislocations associated SUs are uniquely defined based on the observations at different zone axes. It is found that the Burgers vectors of neighbouring partials are alternatively opposed so that the transformation strain is self-accommodated. Furthermo…
We investigate the formation of long-period stacking ordered (LPSO) structure for Mg-Y-Zn ternary alloys based on the short-range order (SRO) tendency of energetically competitive disordered phases. We find that unisotropic SRO tendencies for structures with stacking faults cannot be simply interpreted by arithmetic average of SRO for constituent fcc and hcp stackings, indicating that the SRO should be significantly affected by periodically-introduced stacking faults. We also find that SRO for neighboring Y-Zn pair, which should have positive sign to form specific L12 type cluster found in LPS…
Body-centered cubic (bcc) refractory multicomponent alloys are of great interest due to their remarkable strength at high temperatures. Meanwhile, further optimizing the chemical compositions of these alloys to achieve a combination of high strength and room-temperature ductility remains challenging, which would require systematic predictions of the correlated alloy properties across a vast compositional space. In the present work, we performed first-principles calculations with the special quasi-random structure (SQS) method to predict the unstable stacking fault energy ($γ_{usf}$) of the $(1…
Technological applications of novel metastable materials are frequently inhibited by abundant defects residing in these materials. Using first-principles methods we investigate the point defect thermodynamics and phase segregation in the technologically-important metastable alloy GaAsBi. Our calculations predict defect energy levels in good agreement with abundant previous experiments and clarify the defect structures giving rise to these levels. We find that vacancies in some charge states become metastable or unstable with respect to antisite formation, and this instability is a general char…
A new \textit{D0$_{23}$} metastable phase of Cu$_3$Au is found to grow at the interfaces of Au/Cu multilayers deposited by magnetron sputtering. The extent of formation of this novel alloy phase depends upon an optimal range of interfacial width primarily governed by the deposition wattage of the dc-magnetron used. Such interfacially confined growth is utilized to grow a $\sim$ 300 nm thick Au/Cu multilayer with thickness of each layer nearly equal to the optimal interfacial width which was obtained from secondary ion mass spectrometry (SIMS) data. This growth technique is observed to enhance …
High-entropy alloys (HEAs) are an intriguing new class of metallic materials due to their unique mechanical behavior. Achieving a detailed understanding of structure-property relationships in these materials has been challenged by the compositional disorder that underlies their unique mechanical behavior. Accordingly, in this work, we employ first-principles calculations to investigate the nature of local chemical order and establish its relationship to the intrinsic and extrinsic stacking fault energy (SFE) in CrCoNi medium-entropy solid-solution alloys, whose combination of strength, ductili…
We investigate thermodynamic behaviors of dilute Mg-Zn-Y ternary alloys to form a unique solute-enriched stacking-fault (SESF), which is an intrinsic-II type stacking-fault (I2-SF) enriched by the Zn and Y atoms and represents the structural-unit of the long-period stacking/order (LPSO) phase. SESF in the hexagonal-close-packed (hcp) Mg matrix forms a local face-centered-cubic (fcc) environment, and hence our thermodynamic analysis is based on the Gibbs energy comparison between hcp and fcc phases over the Mg-Zn-Y ternary composition ranges, using the calculation of phase diagrams (CALPHAD) me…
Interstitials (carbon and nitrogen) are crucial alloying elements for optimizing the mechanical performance of the twinning-induced plasticity (TWIP) steels in terms of the stacking fault energy (SFE). First-principles calculations have been performed to study the effect of interstitial-induced lattice expansion on the SFE. Comparing the predictions with the SFEs measured for alloys containing C and N, our results suggest that the dominant effect of these interstitials on the SFE is due to the lattice expansion effect.
Predicting the mechanical failure of parts in service requires understanding their deformation behavior, and associated dynamic microstructural evolution up to the near-atomic scale. Solutes are known to interact with defects generated by plastic deformation, thereby affecting their displacement throughout the microstructure and hence the material mechanical response to solicitation. This effect is studied here in a polycrystalline Ni-based superalloy with two different Nb contents that lead to a significant change in their creep lifetime. Creep testing at 750C and 600 MPa shows that the high-…
The cubic $Ia\bar{3}$ (BC8) and tetragonal $P4_32_12$ (ST12) high pressure modifications of Si and Ge are attractive candidates for applications in optoelectronic, thermoelectric or plasmonic devices. Si$_x$Ge$_{1-x}$ alloys in BC8/ST12 modifications could help overcome the indirect and narrow band gaps of the pure phases and enable tailoring for specific use-cases. Such alloys have experimentally been found to be stable at ambient conditions after release from high pressure synthesis, however their fundamental properties are not known. In this work, we employ {\it ab initio} calculations base…
In general, with the addition of solutes, the yield strength of alloys is expected to increase and this phenomenon is known as solid solution strengthening. However, reports on the ``anomalous'' softening with alloying additions are not uncommon; for example, it is known that the heterogeneous nucleation of dislocations at the sites of solute atoms can lead to softening. In this study, using Molecular Dynamics (MD) simulations, we show anomalous softening in Cu-Al alloys deformed at 300 K; specifically, not only the yield stress but also the magnitude of stress drop at yield decrease with incr…
Hydrogen embrittlement in Zr alloy fuel cladding is a primary safety concern for water based nuclear reactors. Here we investigated the stabilisation of planar defects within the forming hydrides by Sn, the primary alloying element of Zircaloy-4 used in the cladding. In order to explain formation of hydrides and planar defects observed in our experiments, we performed atomic-scale ab initio calculations focusing on the solute interactions with generalized stacking faults in hcp $α$-Zr and fcc zirconium hydrides. Our calculations showed that an increase in Sn concentration leads to a stabilisat…
Thermodynamic bulk phase diagrams have become the roadmap used by researchers to identify alloy compositions and process conditions that result in novel materials with tailored microstructures. Recent experimental studies show that changes in the alloy composition can drive not only transitions in the bulk phases present in a material, but also in the concentration and type of defects they contain. Defect phase diagrams in combination with density functional theory provide a natural route to study these chemically driven defects. Our results show, however, that direct application of thermodyna…
We calculate the cohesive energies of Fe-based glass-forming alloys in the B-Fe-Y-Zr quaternary system. Our {\it ab-initio} calculations fully relax atomic positions and lattice parameters yielding enthalpies of mixing at T=0K. We examine both the known equilibrium and metastable phases as well as a selection of plausible structures drawn from related alloy systems. This method, generally reproduces experimentally determined phase diagrams while providing additional information about energetics of metastable and unstable structures. In particular we can identify crystalline structures whose fo…
High-Ti induced planar-fault transformation toward superlattice extrinsic stacking faults and microtwins in crept CoNi-based superalloys
Helmholtz-Zentrum Hereon（赫尔姆霍茨-海雷恩中心）；Tsinghua University（清华大学）；University of Stuttgart（斯图加特大学）；University of Twente（特文特大学）；Southeast University（东南大学）；Central South university（中南大学）
Compositionally complex materials (CCMs) present a potential paradigm shift in the design of magnetic materials. These alloys exhibit long-range structural order coupled with limited or no chemical order. As a result, extreme local environments exist with a large opposing magnetic energy term, which can manifest large changes in the magnetic behavior. In the current work, the magnetic properties of (Cr, Mn, Fe, Ni) alloys are presented. These materials were prepared by room-temperature combinatorial sputtering, resulting in a range of compositions with a single BCC structural phase and no chem…
Stacking fault energy (SFE) is of the most critical microstructure attribute for controlling the deformation mechanism and optimizing mechanical properties of austenitic steels, while there are no accurate and straightforward computational tools for modeling it. In this work, we applied both thermodynamic modeling and machine learning to predict the stacking fault energy (SFE) for more than 300 austenitic steels. The comparison indicates a high need of improving low-temperature CALPHAD (CALculation of PHAse Diagrams) databases and interfacial energy prediction to enhance thermodynamic model re…
Research over the years has shown that the formation of the Fe$_3$Si phase in FINEMET (Fe-Si-Nb-B-Cu) alloys leads to superior soft magnetic properties. In this work, we use a CALPHAD approach to derive Fe-Si phase diagrams to identify the composition-temperature domain where the Fe$_3$Si phase can be stabilized. Thereafter, we have developed a precipitation model capable of simulating the nucleation and growth of Fe$_3$Si nanocrystals via Langer-Schwartz theory. For optimum magnetic properties, prior work suggests that it is desirable to precipitate Fe$_3$Si nanocrystals with 10-15 nm diamete…
We propose a new microscopic model for the $\{001\}$ planar defects in diamond commonly called platelets. This model is based on the formation of a metastable stacking fault, which can occur because of the ability of carbon to stabilize in different bonding configurations. In our model the core of the planar defect is basically a double layer of three-fold coordinated $sp^2$ carbon atoms embedded in the common $sp^3$ diamond structure. The properties of the model were determined using {\it ab initio} total energy calculations. All significant experimental signatures attributed to the platelets…
The formation energy of the interface between face-centered cubic (fcc) and hexagonal close packed (hcp) structures is a key parameter in determining the stacking fault energy (SFE) of fcc metals and alloys using thermodynamic calculations. Often the contribution of the planar fault energy to the SFE has the same order of magnitude as the bulk part, and thus the lack of a precise information about it can become the limiting factor in thermodynamic predictions. Here, we differentiate between the actual interfacial energy for the coherent fcc(111)/hcp(0001) interface and the "pseudo-interfacial …
Using an effective genetic algorithm, we uncover the structure of a metastable Al41Sm5 phase that supplements its family sharing similar short-range orders. The phase evolves upon heating an amorphous Al-9.7at.%Sm ribbon, produced by melt-spinning. The dynamical phase selection is discussed with respect to the structural connections between the short-range packing motifs in the amorphous precursor and those observed in the selected phases. The phase elucidated here is one of several newly discovered large-unit-cell phases found to form during devitrification from the glass in this binary syste…
Chemical short-range order controls deformation pathways in a complex concentrated alloy
Federal University of São Carlos（圣卡洛斯联邦大学）；Uppsala University（乌普萨拉大学）；Wallenberg Initiative Materials Science for Sustainability, Uppsala University（乌普萨拉大学瓦伦堡可持续发展材料科学倡议）；Massachusetts Institute of Technology（麻省理工学院）；The University of Manchester（曼彻斯特大学）；Baylor University（贝勒大学）；AF Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson AFB（赖特-帕特森空军基地材料与制造局空军研究实验室）
Phase change alloys are used for non-volatile random access memories exploiting the conductivity contrast between amorphous and metastable, crystalline phase. However, this contrast has never been directly related to the electronic band structure. Here, we employ photoelectron spectroscopy to map the relevant bands for metastable, epitaxial GeSbTe films. The constant energy surfaces of the valence band close to the Fermi level are hexagonal tubes with little dispersion perpendicular to the (111) surface. The electron density responsible for transport belongs to the tails of this bulk valence b…
The hexagonal-2H crystal phase of Ge recently emerged as a promising direct bandgap semiconductor in the mid-infrared range providing new prospects of additional optoelectronic functionalities of group-IV semiconductors (Ge and SiGe). The controlled synthesis of such hexagonal (2H) Ge phase is a challenge that can be overcome by using wurtzite GaAs nanowires as a template. However, depending on growth conditions, unusual basal stacking faults (BSFs) of I$_3$-type are formed in the metastable 2H structure. The growth of such core/shell heterostructures is observed in situ and in real-time by me…
