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10 pages, 1981 KiB

Open AccessArticle

Effects of Zn and Mg Segregations on the Grain Boundary Sliding and Cohesion in Al: Ab Initio Modeling

by Andrey Kuznetsov, Lidia Karkina, Yuri Gornostyrev and Pavel Korzhavyi

Metals 2021, 11(4), 631; https://doi.org/10.3390/met11040631 - 13 Apr 2021

Cited by 8 | Viewed by 1728

Abstract

The formation of Zn and Mg segregations at a tilt Σ5{013} <100> grain boundary (GB) in Al and the effects of these solutes on deformation behavior of polycrystalline Al were investigated using ab initio total energy calculations. Using a step-by-step modeling of the [...] Read more.

The formation of Zn and Mg segregations at a tilt Σ5{013} <100> grain boundary (GB) in Al and the effects of these solutes on deformation behavior of polycrystalline Al were investigated using ab initio total energy calculations. Using a step-by-step modeling of the segregation process, we found that the formation of a thick segregation layer of Zn at the GB is energetically preferable, while the formation of an atomically thin segregation layer is expected in the case of Mg. To reveal the effect of segregation on the cohesive properties of Al GBs, we calculated the energy of cleavage decohesion and the shear resistance for GB sliding. We show that the segregation of Zn results in a substantial decrease in barriers for GB sliding, while the segregation of Mg increases the barriers. The results obtained allow us to explain experimental findings and demonstrate a strong relationship between chemical bonding of solute atoms, their segregation ability, and GB strength. Full article

(This article belongs to the Special Issue Atomistic Modelling and Simulation of Structural and Phase Stability in Metals and Alloys)

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16 pages, 4284 KiB

Open AccessFeature PaperArticle

Free Energy of Metals from Quasi-Harmonic Models of Thermal Disorder

by Pavel A. Korzhavyi and Jing Zhang

Metals 2021, 11(2), 195; https://doi.org/10.3390/met11020195 - 21 Jan 2021

Cited by 1 | Viewed by 2506

Abstract

A simple modeling method to extend first-principles electronic structure calculations to finite temperatures is presented. The method is applicable to crystalline solids exhibiting complex thermal disorder and employs quasi-harmonic models to represent the vibrational and magnetic free energy contributions. The main outcome is [...] Read more.

A simple modeling method to extend first-principles electronic structure calculations to finite temperatures is presented. The method is applicable to crystalline solids exhibiting complex thermal disorder and employs quasi-harmonic models to represent the vibrational and magnetic free energy contributions. The main outcome is the Helmholtz free energy, calculated as a function of volume and temperature, from which the other related thermophysical properties (such as temperature-dependent lattice and elastic constants) can be derived. Our test calculations for Fe, Ni, Ti, and W metals in the paramagnetic state at temperatures of up to 1600 K show that the predictive capability of the quasi-harmonic modeling approach is mainly limited by the electron density functional approximation used and, in the second place, by the neglect of higher-order anharmonic effects. The developed methodology is equally applicable to disordered alloys and ordered compounds and can therefore be useful in modeling realistically complex materials. Full article

(This article belongs to the Special Issue Atomistic Modelling and Simulation of Structural and Phase Stability in Metals and Alloys)

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8 pages, 2045 KiB

Open AccessArticle

Segregation of P and S Impurities to A Σ9 Grain Boundary in Cu

by Cláudio M. Lousada and Pavel A. Korzhavyi

Metals 2020, 10(10), 1362; https://doi.org/10.3390/met10101362 - 13 Oct 2020

Cited by 7 | Viewed by 1947

Abstract

The segregation of P and S to grain boundaries (GBs) in fcc Cu has implications in diverse physical-chemical properties of the material and this can be of particular high relevance when the material is employed in high performance applications. Here, we studied the [...] Read more.

The segregation of P and S to grain boundaries (GBs) in fcc Cu has implications in diverse physical-chemical properties of the material and this can be of particular high relevance when the material is employed in high performance applications. Here, we studied the segregation of P and S to the symmetric tilt Σ9 (

2 \bar{2} \bar{1}

) [110], 38.9° GB of fcc Cu. This GB is characterized by a variety of segregation sites within and near the GB plane, with considerable differences in both atomic site volume and coordination number and geometry. We found that the segregation energies of P and S vary considerably both with distance from the GB plane and sites within the GB plane. The segregation energy is significantly large at the GB plane but drops to almost zero at a distance of only ≈3.5 Å from this. Additionally, for each impurity there are considerable variations in energy (up to 0.6 eV) between segregation sites in the GB plane. These variations have origins both in differences in coordination number and atomic site volume with the effect of coordination number dominating. For sites with the same coordination number, up to a certain atomic site volume, a larger atomic site volume leads to a stronger segregation. After that limit in volume has been reached, a larger volume leads to weaker segregation. The fact that the segregation energy varies with such magnitude within the Σ9 GB plane may have implications in the accumulation of these impurities at these GBs in the material. Because of this, atomic-scale variations of concentration of P and S are expected to occur at the Σ9 GB center and in other GBs with similar features. Full article

(This article belongs to the Special Issue Atomistic Modelling and Simulation of Structural and Phase Stability in Metals and Alloys)

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16 pages, 3379 KiB

Open AccessArticle

Lattice Stability and Elastic Properties of Zr-Ti-X Alloys (X = Al, V) by the First Principles Study

by Wenxiong Duan, Xiaoping Liang, Xiangguan Yang, Yu Wang and Baifeng Luan

Metals 2020, 10(10), 1317; https://doi.org/10.3390/met10101317 - 01 Oct 2020

Cited by 3 | Viewed by 2441

Abstract

Based on a certain ratio of Zr and Ti atomic fractions according to Zr₄₇Ti₄₅Al₅V₃ (wt.%), the lattice constants, lattice stability, and elastic properties of Zr-Ti-X alloys (X = Al, V) in body-centered cubic (BCC) (β phase) [...] Read more.

Based on a certain ratio of Zr and Ti atomic fractions according to Zr₄₇Ti₄₅Al₅V₃ (wt.%), the lattice constants, lattice stability, and elastic properties of Zr-Ti-X alloys (X = Al, V) in body-centered cubic (BCC) (β phase) and hexagonal close-packed (HCP) (α phase) crystal structures were studied using first-principles calculations. It is shown that Al acts as an α stabilizer for Zr-Ti-Al alloys and V can stabilize the β phase for Zr-Ti-V alloys. As the mass fraction of Al increases from 4 wt.% (Zr₅₅Ti₄₁Al₄) to 6.8 wt.% (Zr_53.2Ti₄₀Al_6.8), these alloys all have relatively good strength, hardness, and rigidity, however, their ductility deteriorated with the increasing of Al mass fraction. When the mass fraction of V in Zr-Ti-V alloys is 2.4 wt.%, Zr_55.6Ti₄₂V_2.4 (wt.%) achieved the best strength, hardness, and rigidity, when the mass fraction of V increases from 0 (Zr₅₇Ti₄₃) to 12 wt.% (Zr_50.2Ti_37.8V₁₂), their ductility improved. The changes of phase compositions and structure with Al content or V content distinctly affect mechanical properties of ternary Zr-Ti-X alloys (X = Al, V), the amount of Zr and Ti could be factors that impact the mechanical properties of the multiphase Zr₄₇Ti₄₅Al₅V₃ from the point of view of ternary Zr-Ti-Al and Zr-Ti-V compositions. Full article

(This article belongs to the Special Issue Atomistic Modelling and Simulation of Structural and Phase Stability in Metals and Alloys)

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19 pages, 7809 KiB

Open AccessArticle

DFT-CEF Approach for the Thermodynamic Properties and Volume of Stable and Metastable Al–Ni Compounds

by Silvana Tumminello, Mauro Palumbo, Jörg Koßmann, Thomas Hammerschmidt, Paula R. Alonso, Silvana Sommadossi and Suzana G. Fries

Metals 2020, 10(9), 1142; https://doi.org/10.3390/met10091142 - 24 Aug 2020

Cited by 4 | Viewed by 3872

Abstract

The Al–Ni system has been intensively studied both experimentally and theoretically. Previous first-principles calculations based on density-functional theory (DFT) typically investigate the stable phases of this system in their experimental stoichiometry. In this work, we present DFT calculations for the Al–Ni system that [...] Read more.

The Al–Ni system has been intensively studied both experimentally and theoretically. Previous first-principles calculations based on density-functional theory (DFT) typically investigate the stable phases of this system in their experimental stoichiometry. In this work, we present DFT calculations for the Al–Ni system that cover stable and metastable phases across the whole composition range for each phase. The considered metastable phases are relevant for applications as they are observed in engineering alloys based on Al–Ni. To model the Gibbs energies of solid phases of the Al–Ni system, we combine our DFT calculations with the compound energy formalism (CEF) that takes the Bragg–Williams–Gorsky approximation for the configurational entropy. Our results indicate that the majority of the investigated configurations have negative energy of formation with respect to Al fcc and Ni fcc. The calculated molar volumes for all investigated phases show negative deviations from Zen’s law. The thermodynamic properties at finite temperatures of individual phases allow one to predict the configurational contributions to the Gibbs energy. By applying a fully predictive approach without excess parameters, an acceptable topology of the DFT-based equilibrium phase diagram is obtained at low and intermediate temperatures. Further contributions can be added to improve the predictability of the method, such as phonons or going beyond the Bragg–Williams–Gorsky approximation that overestimates the stability range of the ordered phases. This is clearly demonstrated in the fcc order/disorder predicted metastable phase diagram. Full article

(This article belongs to the Special Issue Atomistic Modelling and Simulation of Structural and Phase Stability in Metals and Alloys)

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19 pages, 8182 KiB

Open AccessArticle

Atomistic Simulation of the Strain Driven Phase Transition in Pure Iron Thin Films Containing Twin Boundaries

by Yunqiang Jiang, Binjun Wang, Chun Xu and Jianguo Zhang

Metals 2020, 10(7), 953; https://doi.org/10.3390/met10070953 - 15 Jul 2020

Cited by 1 | Viewed by 2554

Abstract

Using molecular dynamics (MD) simulation, the strain-induced phase transitions in pure body-centered-cubic (bcc) iron (Fe) thin films containing twin boundaries (TBs) with different TB fractions and orientations are studied. Two groups of bcc thin films with different TB-surface orientation relationships are designed. In [...] Read more.

Using molecular dynamics (MD) simulation, the strain-induced phase transitions in pure body-centered-cubic (bcc) iron (Fe) thin films containing twin boundaries (TBs) with different TB fractions and orientations are studied. Two groups of bcc thin films with different TB-surface orientation relationships are designed. In film group 1, the (112) [

11 \bar{1}

] TBs are perpendicular to the (

11 \bar{1}

) free surfaces, while the (112) [

11 \bar{1}

] TBs are parallel to the free surfaces in film group 2. We vary the TB numbers inserted into the films to study the effect of TB fraction on the phase transition. Biaxial strains are applied to the films to induce the bcc to close packed (cp) phase transition. The critical strain, at which the first phase transition takes place, decreases with the TB fraction increase in film group 1 with a perpendicular TB-surface orientation, while such a relationship is not observed in film group 2 with parallel TB-surface orientation. We focus on the free surface and TB as the nucleation positions of the new phase and the afterward growth. In addition, the dynamics of the phase transition is discussed. This work may help to understand the mechanism of phase transition in nanoscale or surface-dominant systems with pre-existing defects. Full article

(This article belongs to the Special Issue Atomistic Modelling and Simulation of Structural and Phase Stability in Metals and Alloys)

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18 pages, 5651 KiB

Open AccessArticle

First Principles Investigation on Thermodynamic Properties and Stacking Fault Energy of Paramagnetic Nickel at High Temperatures

by Jing Zhang and Pavel A. Korzhavyi

Metals 2020, 10(3), 319; https://doi.org/10.3390/met10030319 - 28 Feb 2020

Cited by 7 | Viewed by 3473

Abstract

Reliable data on the temperature dependence of thermodynamic properties of alloy phases are very useful for modeling the behavior of high-temperature materials such as nickel-based superalloys. Moreover, for predicting the mechanical properties of such alloys, additional information on the energy of lattice defects [...] Read more.

Reliable data on the temperature dependence of thermodynamic properties of alloy phases are very useful for modeling the behavior of high-temperature materials such as nickel-based superalloys. Moreover, for predicting the mechanical properties of such alloys, additional information on the energy of lattice defects (e.g., stacking faults) at high temperatures is highly desirable, but difficult to obtain experimentally. In this study, we use first-principles calculations, in conjunction with a quasi-harmonic Debye model, to evaluate the Helmholtz free energy of paramagnetic nickel as a function of temperature and volume, taking into account the electronic, magnetic, and vibrational contributions. The thermodynamic properties of Ni, such as the equilibrium lattice parameter and elastic moduli, are derived from the free energy in the temperature range from 800 to 1600 K and compared with available experimental data. The derived temperature dependence of the lattice parameter is then used for calculating the energies of intrinsic and extrinsic stacking faults in paramagnetic Ni. The stacking fault energies have been evaluated according to three different methodologies, the axial-next-nearest-neighbor Ising (ANNNI) model, the tilted supercell approach, and the slab supercell approach. The results show that the elastic moduli and stacking fault energies of Ni decrease with increasing temperature. This “softening” effect of temperature on the mechanical properties of nickel is mainly due to thermal expansion, and partly due to magnetic free energy contribution. Full article

(This article belongs to the Special Issue Atomistic Modelling and Simulation of Structural and Phase Stability in Metals and Alloys)

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12 pages, 30157 KiB

Open AccessFeature PaperArticle

Alloying Element Segregation and Grain Boundary Reconstruction, Atomistic Modeling

by Lidia Karkina, Iliya Karkin, Andrey Kuznetsov and Yuri Gornostyrev

Metals 2019, 9(12), 1319; https://doi.org/10.3390/met9121319 - 06 Dec 2019

Cited by 8 | Viewed by 3833

Abstract

Grain boundary (GB) segregation is an important phenomenon that affects many physical properties, as well as microstructure of polycrystals. The segregation of solute atoms on GBs and its effect on GB structure in Al were investigated using two approaches: First principles total energy [...] Read more.

Grain boundary (GB) segregation is an important phenomenon that affects many physical properties, as well as microstructure of polycrystals. The segregation of solute atoms on GBs and its effect on GB structure in Al were investigated using two approaches: First principles total energy calculations and the finite temperature large-scale atomistic modeling within hybrid MD/MC approach comprising molecular dynamics and Monte Carlo simulations. We show that the character of chemical bonding is essential in the solute–GB interaction, and that formation of directed quasi-covalent bonds between Si and Zn solutes and neighboring Al atoms causes a significant reconstruction of the GB structure involving a GB shear-migration coupling. For the solutes that are acceptors of electrons in the Al matrix and have a bigger atomic size (such as Mg), the preferred position is determined by the presence of extra volume at the GB and/or reduced number of the nearest neighbors; in this case, the symmetric GB keeps its structure. By using MD/MC approach, we found that GBs undergo significant structural reconstruction during segregation, which can involve the formation of single- or double-layer segregations, GB splitting, and coupled shear-migration, depending on the details of interatomic interactions. Full article

(This article belongs to the Special Issue Atomistic Modelling and Simulation of Structural and Phase Stability in Metals and Alloys)

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17 pages, 5637 KiB

Open AccessArticle

Large-Scale Molecular Dynamics Simulations of Homogeneous Nucleation of Pure Aluminium

by Michail Papanikolaou, Konstantinos Salonitis, Mark Jolly and Michael Frank

Metals 2019, 9(11), 1217; https://doi.org/10.3390/met9111217 - 12 Nov 2019

Cited by 21 | Viewed by 5456

Abstract

Despite the continuous and remarkable development of experimental techniques for the investigation of microstructures and the growth of nuclei during the solidification of metals, there are still unknown territories around this topic. The solidification in nanoscale can be effectively investigated by means of [...] Read more.

Despite the continuous and remarkable development of experimental techniques for the investigation of microstructures and the growth of nuclei during the solidification of metals, there are still unknown territories around this topic. The solidification in nanoscale can be effectively investigated by means of molecular dynamics (MD) simulations which can provide a deep insight into the mechanisms of the formation of nuclei and the induced crystal structures. In this study, MD simulations were performed to investigate the solidification of pure Aluminium and the effects of the cooling rate on the final properties of the solidified material. A large number of Aluminium atoms were used in order to investigate the grain growth over time and the formation of stacking faults during solidification. The number of face-centred cubic (FCC), hexagonal close-packed (HCP) and body-centred cubic (BCC) was recorded during the evolution of the process to illustrate the nanoscale mechanisms initiating solidification. The current investigation also focuses on the exothermic nature of the solidification process which has been effectively captured by means of MD simulations using 3 dimensional representations of the kinetic energy across the simulation domain. Full article

(This article belongs to the Special Issue Atomistic Modelling and Simulation of Structural and Phase Stability in Metals and Alloys)

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12 pages, 2615 KiB

Open AccessArticle

The Nucleation and the Intrinsic Microstructure Evolution of Martensite from 332 〈 113 〉 β Twin Boundary in β Titanium: First-Principles Calculations

by Qiu-Jie Chen, Shang-Yi Ma and Shao-Qing Wang

Metals 2019, 9(11), 1202; https://doi.org/10.3390/met9111202 - 07 Nov 2019

Cited by 5 | Viewed by 2586

Abstract

A clear understanding on the inter-evolution behaviors between

\{332\} {⟨ 113 ⟩}_{β}

twinning and stress-induced martensite (SIM) α″ in β-Ti alloys is vital for improving its strength and ductility concurrently. As the preliminary step to better understand these complex behaviors, the nucleation [...] Read more.

A clear understanding on the inter-evolution behaviors between

\{332\} {⟨ 113 ⟩}_{β}

twinning and stress-induced martensite (SIM) α″ in β-Ti alloys is vital for improving its strength and ductility concurrently. As the preliminary step to better understand these complex behaviors, the nucleation and the intrinsic microstructure evolution of martensite α″ from

\{332\} {⟨ 113 ⟩}_{β}

twin boundary (TB) were investigated in pure β-Ti at atomic scale using first-principles calculations in this work. We found the α″ precipitation prefers to nucleate and grow at

\{332\} {⟨ 113 ⟩}_{β}

TB, with the transformation of

\{332\} {⟨ 113 ⟩}_{β}

TB→

\{130\} ⟨ \bar{3} {10 ⟩}_{α ″}

TB. During this process, α″ precipitation firstly nucleates at

\{332\} {⟨ 113 ⟩}_{β}

TB and, subsequently, it grows inwards toward the grain interiors. This easy transition may stem from the strong crystallographic correspondence between

\{332\} {⟨ 113 ⟩}_{β}

and

\{130\} ⟨ \bar{3} {10 ⟩}_{α ″}

TBs, and the region close to the

\{332\} {⟨ 113 ⟩}_{β}

TB presents the characteristics of intermediate structure between β and α″ phases. Kinetics calculations indicate the α″ phase barrierlessly nucleates at

\{332\} {⟨ 113 ⟩}_{β}

TB rather than in grain interior, where there is higher critical driving energy. Our calculations provide a unique perspective on the “intrinsic” microstructure evolution of martensite α″ from

\{332\} {⟨ 113 ⟩}_{β}

TB, which may deepen our understanding on the precipitation of martensite α″ and the inter-evolution behaviors between

\{332\} {⟨ 113 ⟩}_{β}

twinning and martensite α″ in β-Ti alloys at atomic scale. Full article

(This article belongs to the Special Issue Atomistic Modelling and Simulation of Structural and Phase Stability in Metals and Alloys)

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Review

Jump to: Research

32 pages, 1960 KiB

Open AccessReview

Calphad Modeling of LRO and SRO Using ab initio Data

by Masanori Enoki, Bo Sundman, Marcel H. F. Sluiter, Malin Selleby and Hiroshi Ohtani

Metals 2020, 10(8), 998; https://doi.org/10.3390/met10080998 - 24 Jul 2020

Cited by 2 | Viewed by 3139

Abstract

Results from DFT calculations are in many cases equivalent to experimental data. They describe a set of properties of a phase at a well-defined composition and temperature, T, most often at 0 K. In order to be practically useful in materials design, [...] Read more.

Results from DFT calculations are in many cases equivalent to experimental data. They describe a set of properties of a phase at a well-defined composition and temperature, T, most often at 0 K. In order to be practically useful in materials design, such data must be fitted to a thermodynamic model for the phase to allow interpolations and extrapolations. The intention of this paper is to give a summary of the state of the art by using the Calphad technique to model thermodynamic properties and calculate phase diagrams, including some models that should be avoided. Calphad models can decribe long range ordering (LRO) using sublattices and there are model parameters that can approximate short range ordering (SRO) within the experimental uncertainty. In addition to the DFT data, there is a need for experimental data, in particular, for the phase diagram, to determine the model parameters. Very small differences in Gibbs energy of the phases, far smaller than the uncertainties in the DFT calculations, determine the set of stable phases at varying composition and T. Thus, adjustment of the DFT results is often needed in order to obtain the correct set of stable phases. Full article

(This article belongs to the Special Issue Atomistic Modelling and Simulation of Structural and Phase Stability in Metals and Alloys)

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