Ising-like models for stacking faults in a free electron metal

We propose an extension of the axial next nearest neighbour Ising (ANNNI) model to a general number of interactions between spins. We apply this to the calculation of stacking fault energies in magnesium—particularly challenging due to the long-ranged screening of the pseudopotential by the free electron gas. We employ both density functional theory (DFT) using highest possible precision, and generalized pseudopotential theory (GPT) in the form of an analytic, long ranged, oscillating pair potential. At the level of first neighbours, the Ising model is reasonably accurate, but higher order terms are required. In fact, our ‘ AN N NI model’ is slow to converge—an inevitable feature of the free electron-like electronic structure. In consequence, the convergence and internal consistency of the AN N NI model is problematic within the most precise implementation of DFT. The GPT shows the convergence and internal consistency of the DFT bandstructure approach with electron temperature, but does not lead to loss of precision. The GPT is as accurate as a full implementation of DFT but carries the additional benefit that damping of the oscillations in the AN N NI model parameters are achieved without entailing error in stacking fault energies. We trace this to the logarithmic singularity of the Lindhard function.

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Failure of pseudopotential theory in stacking-fault energies of copper alloys1)

phys stat sol (a) ◽

10.1002/pssa.2210310147 ◽

1975 ◽

Vol 31 (1) ◽

pp. K27-K30 ◽

Cited By ~ 5

Author(s):

H. R. Leribaux

Keyword(s):

Stacking Fault ◽

Pseudopotential Theory ◽

Stacking Fault Energies

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Generalised stacking fault energies of copper alloys - density functional theory calculations

Journal of Mining and Metallurgy Section B Metallurgy ◽

10.2298/jmmb181128020m ◽

2019 ◽

Vol 55 (2) ◽

pp. 271-282

Author(s):

M. Muzyk ◽

K.J. Kurzydłowski

Keyword(s):

Density Functional Theory ◽

Transition Metal ◽

Density Functional ◽

Copper Alloys ◽

Density Functional Theory Calculations ◽

Stacking Fault ◽

Alloying Element ◽

Functional Theory ◽

Work Hardening Rate ◽

Stacking Fault Energies

Generalised stacking fault energies of copper alloys have been calculated using density functional theory. Stacking fault energy of copper alloys is correlated with the d?electrons number of transition metal alloying element. The tendency to twiningis also modified by the presence of alloying element in the deformation plane. The results suggest that Cu ?transition metal alloys with such elements as Cr, Mo, W, Mn, Re are expected to exhibit great work hardening rate due to the tendency to emission of the partial dislocations.

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Ab Initio Study of Elastic and Mechanical Properties in FeCrMn Alloys

Materials ◽

10.3390/ma12071129 ◽

2019 ◽

Vol 12 (7) ◽

pp. 1129 ◽

Cited By ~ 3

Author(s):

Vsevolod Razumovskiy ◽

Carola Hahn ◽

Marina Lukas ◽

Lorenz Romaner

Keyword(s):

Mechanical Properties ◽

Density Functional ◽

Magnetic State ◽

Stacking Fault ◽

Functional Theory ◽

Temperature Changes ◽

Practical Applications ◽

Solid Solution Strengthening ◽

Solution Strengthening ◽

Stacking Fault Energies

Mechanical properties of FeCrMn-based steels are of major importance for practical applications. In this work, we investigate mechanical properties of disordered paramagnetic fcc FeCr 10 – 16 Mn 12 – 32 alloys using density functional theory. The effects of composition and temperature changes on the magnetic state, elastic properties and stacking fault energies of the alloys are studied. Calculated dependencies of the lattice and elastic constants are used to evaluate the effect of the solid solution strengthening by Mn and Cr using a modified Labusch-Nabarro model and a model for concentrated alloys. The effect of Cr and Mn alloying on the stacking fault energies is calculated and discussed in connection to possible deformation mechanisms.

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Stacking-Fault Energies in Silicon, Diamond, and Silicon Carbide

MRS Proceedings ◽

10.1557/proc-141-343 ◽

1988 ◽

Vol 141 ◽

Cited By ~ 3

Author(s):

P. J. H. Denteneer

Keyword(s):

Silicon Carbide ◽

Density Functional ◽

Density Functional Method ◽

Stacking Faults ◽

Functional Method ◽

Negative Energy ◽

Perfect Crystal ◽

Stacking Fault ◽

Theoretical Approaches ◽

Stacking Fault Energies

AbstractStacking faults in a perfect crystal can be seen as limiting structures of certain series of polytypes of that crystal. A parametrization of the energy of polytypes in terms of interaction constants between layers therefore allows for the calculation of stacking-fault energies. The first-principles pseudopotential-density-functional method is used to calculate total energies of a few simple polytypes of silicon and carbon. The energies of intrinsic and extrinsic stacking faults (γISF and γESF , respectively) in silicon and diamond that follow from these calculations are in much better agreement with available experimental numbers than in previous theoretical approaches. I find: γISF = 47 mJm-2 and γESF = 36 mJm-2 for Si, γISF = 300 mJm-2 and γESF = 253 mJm-2 for diamond. From recently published similar calculations for polytypes of silicon carbide one obtains a negative energy for the extrinsic stacking fault, if zincblende silicon carbide is taken as the unfaulted structure, suggesting the observed occurrence in nature of polytypism in silicon carbide.

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Generalized Stacking Fault Energies of Aluminum Alloys–Density Functional Theory Calculations

Metals ◽

10.3390/met8100823 ◽

2018 ◽

Vol 8 (10) ◽

pp. 823 ◽

Cited By ~ 11

Author(s):

Marek Muzyk ◽

Zbigniew Pakieła ◽

Krzysztof J. Kurzydłowski

Keyword(s):

Density Functional Theory ◽

Aluminum Alloys ◽

Density Functional ◽

Density Functional Theory Calculations ◽

Stacking Fault ◽

Functional Theory ◽

Partial Dislocations ◽

Work Hardening Rate ◽

Generalized Stacking Fault ◽

Stacking Fault Energies

Generalized stacking fault energies of aluminum alloys were calculated using density functional theory. Stacking fault energy of aluminum alloys was correlated with the d-electrons number of transition metal alloying elements. The tendency to twinning is also modified by the presence of the alloying element in the deformation plane. Our results suggest that Al alloys, with such elements as Zr, Nb, Y, Mo, Ta, and Hf, are expected to exhibit a strong work hardening rate due to emission of the partial dislocations.

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Interionic Pair Potential, hard sphere diameter and entropy of mixing of NaCd compound forming binary molten alloys under the framework of Pseudopotential theory

JOURNAL OF ADVANCES IN CHEMISTRY ◽

10.24297/jac.v10i6.5513 ◽

2014 ◽

Vol 10 (6) ◽

pp. 2843-2852

Author(s):

Sujeet Kumar Chatterjee ◽

Lokesh Chandra Prasad ◽

Ajaya Bhattarai

Keyword(s):

Nearest Neighbor ◽

Effective Interaction ◽

Pair Potential ◽

Sphere Diameter ◽

Compound Formation ◽

Pseudopotential Theory ◽

Energy Of Mixing ◽

Asymmetric Behaviour ◽

Statistical Mechanical ◽

Free Energy Of Mixing

The observed asymmetric behaviour of mixing of NaCd liquid alloys around equiatomic composition with smaller negative values for free energy of mixing at compound forming concentration, i.e. GMXS = -4.9KJ at Ccd =0.66 has aroused our interest to undertake a theoretical investigation of this system.A simple statistical mechanical theory based on compound formation model has been used to investigate the energetics of formation of intermetallic compound Cd2Na in the melt through the study of entropy of mixing.Besides, the interionic interactions between component atoms Na and Cd of the alloys have been understood through the study of interionic pair potential фij(r), calculated from pseudopotential theory in the light of CF model.Our study of фij(r) suggest that the effective interaction between Na-Na atoms decreases on alloying with Cd atom, being minimum for compound forming alloy( Cd 0.66 Na 0.34 ).The nearest neighbor distance between Na-Na atoms does not alter on alloying. Like wise Na-Na, effective interaction between Cd-Cd atom decreases from pure state to NaCd alloys, being smaller at compound forming concentration Cd 0.66 Na 0.34.The computed values of SM from pseudopotential theory are positive at all concentrations, but the agreement between theory and experimental is not satisfactory. This might be happening due to parameterisation of σ3 and Ψcompound.

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Ab Initio Calculation of Mechanical Properties of Stacking Fault in 3C-SiC: Effect of Stress and Doping

Materials Science Forum ◽

10.4028/www.scientific.net/msf.717-720.415 ◽

2012 ◽

Vol 717-720 ◽

pp. 415-418

Author(s):

Yoshitaka Umeno ◽

Kuniaki Yagi ◽

Hiroyuki Nagasawa

Keyword(s):

Mechanical Properties ◽

Ab Initio ◽

Density Functional ◽

Stacking Faults ◽

Single Layer ◽

Local Strain ◽

Density Functional Theory Calculations ◽

Stacking Fault ◽

Functional Theory ◽

N Doping

We carry out ab initio density functional theory calculations to investigate the fundamental mechanical properties of stacking faults in 3C-SiC, including the effect of stress and doping atoms (substitution of C by N or Si). Stress induced by stacking fault (SF) formation is quantitatively evaluated. Extrinsic SFs containing double and triple SiC layers are found to be slightly more stable than the single-layer extrinsic SF, supporting experimental observation. Effect of tensile or compressive stress on SF energies is found to be marginal. Neglecting the effect of local strain induced by doping, N doping around an SF obviously increase the SF formation energy, while SFs seem to be easily formed in Si-rich SiC.

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