![Atomistic aspects of materials properties | Structure and energy of stacking faults8
§ A growth fault is formed by removing an A plane above a B
plane, and then shearing the remaining planes above the B
plane by
𝟏
𝟑
[𝟏"𝟏𝟎𝟎], resulting in . . .ABAB ̇ACBCB. . .
Growth Fault
TYPES OF STACKING FAULTS
Effects of Alloying Elements on Stacking Fault Energies and Electronic Structures of Binary Mg Alloys: A First-Principles Study , William Yi Wang et al, Materials Research Letters
Schematic structure of the Mg–X alloys with different stacking faults (shown as (0001)
miller plane), a growth fault
©SchematicstructureoftheMg–Xalloyswithdifferentstackingfaults(shownas(0001)millerplane),agrowthfaultislicensedunderCCBY3.0byTaylor&Francis](https://image.slidesharecdn.com/structureandenergyofstackingfaultsnithinthomas-200716150433/85/Structure-and-Energy-of-Stacking-Faults-Nithin-Thomas-8-320.jpg)
![Atomistic aspects of materials properties | Structure and energy of stacking faults9
Deformation Fault
§ A deformation fault is formed by a shearing of
𝟏
𝟑
[𝟏"𝟏𝟎𝟎],
resulting in . . .ABA ̇𝐁 ̇𝐂ACA. . .
TYPES OF STACKING FAULTS
Effects of Alloying Elements on Stacking Fault Energies and Electronic Structures of Binary Mg Alloys: A First-Principles Study , William Yi Wang et al, Materials Research Letters
Schematic structure of the Mg–X alloys with different stacking faults (shown as (0001)
miller plane), a deformation fault
©SchematicstructureoftheMg–Xalloyswithdifferentstackingfaults(shownas(0001)millerplane),adeformationfaultislicensedunderCCBY3.0byTaylor&Francis](https://image.slidesharecdn.com/structureandenergyofstackingfaultsnithinthomas-200716150433/85/Structure-and-Energy-of-Stacking-Faults-Nithin-Thomas-9-320.jpg)
![Atomistic aspects of materials properties | Structure and energy of stacking faults12
STACKING FAULT ENERGY
§ The stacking-fault energy is a materials property on a very
small scale.
§ It is noted as γSFE in units of energy per area.
§ A stacking fault is an interruption of the normal stacking
sequence of atomic planes in a close-packed crystal
structure. These interruptions carry a certain energy defined
as the stacking-fault energy.
Successive steps for gamma-line calculation. A rigid body shear
is applied (at 30 GPa here) on Mg-Pv along [010] and in (100).
http://umet.univ-lille1.fr/Projets/RheoMan/en/to-learn-more-about/generalized-stacking-faults.php
©Imagereproducedwithspecialpermissionfornon-commercialusebyProf.PatrickCordierFMSAFAGU,InstitutUniversitairedeFrance,France](https://image.slidesharecdn.com/structureandenergyofstackingfaultsnithinthomas-200716150433/85/Structure-and-Energy-of-Stacking-Faults-Nithin-Thomas-12-320.jpg)
![Atomistic aspects of materials properties | Structure and energy of stacking faults25
ATOMISITIC METHODS FOR DETERMINATION OF SFE
§ In the supercell approach, an SQS consisting of 9 [B1B10] planes
containing 108 atoms was constructed by considering three-
dimensional periodic boundary conditions.
§ A vacuum region of more than 10 Å was added and a stacking fault
was inserted by rigidly shifting the upper four [B1B10] layers in the [112]
or [B110] directions.
§ This process was repeated for every possible position of the stacking
fault and the stacking sequence was manually changed in order to
ensure that the stacking fault was always located in the middle of the
supercell.
EISF and E0 are the energies of configurations
with and without the ISF respectively and A is the
ISF area.](https://image.slidesharecdn.com/structureandenergyofstackingfaultsnithinthomas-200716150433/85/Structure-and-Energy-of-Stacking-Faults-Nithin-Thomas-25-320.jpg)
Structure and Energy of Stacking Faults - Nithin Thomas
- 1. STRUCTURE AND ENERGY OF STACKING FAULTS Nithin Thomas, Dr. habil. Thomas Hammerschmidt nithin.thomas@rub.de 14/07/2020 Bochum ©Imagereproducedwithspecialpermissionfornon-commercialusebyProf.PatrickCordierFMSAFAGU,InstitutUniversitairedeFrance,France
- 2. § Stacking faults § Types of Stacking Faults § Stacking fault energy (SFE) § Importance of SFE § Structure of Stacking faults § Atomistic methods for determination of SFE § Summary 2 Atomistic aspects of materials properties | Structure and energy of stacking faults CONTENTS https://www.materialsdesign.com/datasheet/SQS ©ImagereproducedwithspecialpermissionfromMaterialsDesignEurope
- 3. STACKING FAULTS Definition and illustration.
- 4. Atomistic aspects of materials properties | Structure and energy of stacking faults4 STACKING FAULTS : C B A C B A C : § Real materials deviate from ideality. § Real materials, unlike ideal crystals possess defects or crystal imperfections controls the physical and mechanical properties of the material. § Stacking Fault is a two-dimensional surface defect which is the fault in the periodic stacking sequence of a crystal.
- 5. Atomistic aspects of materials properties | Structure and energy of stacking faults5 STACKING FAULTS : C B A C B A C : : A C B A B A C B : + Fault HCP CCPCCP Fault Plane Schematic representation of stacking in F.C.C crystals A B C
- 6. Atomistic aspects of materials properties | Structure and energy of stacking faults6 STACKING FAULTS A C B A C B A C B : C B A C B A C : B A C B A B A C B § There is no change in orientation of the crystal across the stacking fault. § Crystal on one side of SF is shifted by a non-lattice translation with respect to the crystal on the other side.
- 7. TYPES OF STACKING FAULTS Growth Fault, Deformation Fault and Extrinsic Fault
- 8. Atomistic aspects of materials properties | Structure and energy of stacking faults8 § A growth fault is formed by removing an A plane above a B plane, and then shearing the remaining planes above the B plane by 𝟏 𝟑 [𝟏"𝟏𝟎𝟎], resulting in . . .ABAB ̇ACBCB. . . Growth Fault TYPES OF STACKING FAULTS Effects of Alloying Elements on Stacking Fault Energies and Electronic Structures of Binary Mg Alloys: A First-Principles Study , William Yi Wang et al, Materials Research Letters Schematic structure of the Mg–X alloys with different stacking faults (shown as (0001) miller plane), a growth fault ©SchematicstructureoftheMg–Xalloyswithdifferentstackingfaults(shownas(0001)millerplane),agrowthfaultislicensedunderCCBY3.0byTaylor&Francis
- 9. Atomistic aspects of materials properties | Structure and energy of stacking faults9 Deformation Fault § A deformation fault is formed by a shearing of 𝟏 𝟑 [𝟏"𝟏𝟎𝟎], resulting in . . .ABA ̇𝐁 ̇𝐂ACA. . . TYPES OF STACKING FAULTS Effects of Alloying Elements on Stacking Fault Energies and Electronic Structures of Binary Mg Alloys: A First-Principles Study , William Yi Wang et al, Materials Research Letters Schematic structure of the Mg–X alloys with different stacking faults (shown as (0001) miller plane), a deformation fault ©SchematicstructureoftheMg–Xalloyswithdifferentstackingfaults(shownas(0001)millerplane),adeformationfaultislicensedunderCCBY3.0byTaylor&Francis
- 10. Atomistic aspects of materials properties | Structure and energy of stacking faults10 Extrinsic Fault § An Extrinsic Fault is generated by inserting an extra C plane into the ideal HCP structure, resulting in . . .ABA ̈B ̈C ̈ABAB. . . TYPES OF STACKING FAULTS Effects of Alloying Elements on Stacking Fault Energies and Electronic Structures of Binary Mg Alloys: A First-Principles Study , William Yi Wang et al, Materials Research Letters Schematic structure of the Mg–X alloys with different stacking faults (shown as (0001) miller plane), a Extrinsic fault ©SchematicstructureoftheMg–Xalloyswithdifferentstackingfaults(shownas(0001)millerplane),aextrinsicfaultislicensedunderCCBY3.0byTaylor&Francis
- 11. STACKING FAULT ENERGY Definition and examples.
- 12. Atomistic aspects of materials properties | Structure and energy of stacking faults12 STACKING FAULT ENERGY § The stacking-fault energy is a materials property on a very small scale. § It is noted as γSFE in units of energy per area. § A stacking fault is an interruption of the normal stacking sequence of atomic planes in a close-packed crystal structure. These interruptions carry a certain energy defined as the stacking-fault energy. Successive steps for gamma-line calculation. A rigid body shear is applied (at 30 GPa here) on Mg-Pv along [010] and in (100). http://umet.univ-lille1.fr/Projets/RheoMan/en/to-learn-more-about/generalized-stacking-faults.php ©Imagereproducedwithspecialpermissionfornon-commercialusebyProf.PatrickCordierFMSAFAGU,InstitutUniversitairedeFrance,France
- 13. 13 Material SFE (mJm-2) Brass <10 Stainless Steel <10 Silver (Ag) 25 Gold (Au) 75 Silicon (Si) >42 Nickel (Ni) 90 Copper (Cu) 70 - 78 Magnesium (Mg) 125 Aluminium (Al) 160 - 250 Stacking Fault Energies of some common metals and alloys Atomistic aspects of materials properties | Structure and energy of stacking faults Deformation and Fracture Mechanics of Engineering Materials. John Wiley & Sons, Inc. p. 80. Hertzberg, Richard W.; Vinci, Richard P.; Hertzberg, Jason L. (2013).
- 14. IMPORTANCE OF STACKING FAULT ENERGY Relevance of SFE in deformation of crystals
- 15. Atomistic aspects of materials properties | Structure and energy of stacking faults15 IMPORTANCE OF STACKING FAULT ENERGY § Stacking Fault Width can be geometrically defined as the distance between two dislocation partials. § SF Width determines the mode of deformation. § Cross-slip is the movement of a screw dislocation from one allowable slip plane to another. § SF Width is inversely proportional to SFE. § When SF Width is low, SFE is high as Cross-slip forms easily and results in easy deformation. § A reduction in SFE enhances twinnability and ductility of the material and dislocation slip dominates in high SFE materials. SFE ∝ 1 SFE Width ∝ Cross-slip ∝ 1 Creep Resistance
- 16. STRUCTURE OF STACKING FAULTS Structure of dislocation cores
- 17. Atomistic aspects of materials properties | Structure and energy of stacking faults17 STRUCTURE OF STACKING FAULTS § Dislocation core is a region of crystal lattice around the dislocation line in which the relative displacements of the neighbouring atoms exceed the elastic limit (say 2% in terms of the local shear strain). § Peierls stress is an idealized concept, defined as the minimal stress to move a dislocation at zero temperature. § Peierls barrier is defined as the energy barrier that a straight dislocation must surmount in order to move to a neighbouring lattice position - Peierls valley.
- 18. Atomistic aspects of materials properties | Structure and energy of stacking faults18 STRUCTURE OF STACKING FAULTS § Much of the dislocation behaviour observed in FCC metals and alloys results from the Shockley dissociation, by which perfect 1 2 ⟨110⟩ dislocations split into two partial dislocations, bounding an area of stacking fault. § In FCC materials stable stacking faults are found only in the {111} planes. § The three layers are shifted by 1 3 ⟨111⟩ along the plane normal, forming a repeat pattern with periodicity ⟨111⟩. A B C
- 19. Atomistic aspects of materials properties | Structure and energy of stacking faults19 STRUCTURE OF STACKING FAULTS § A partial dislocation loop can be viewed as the boundary separating an area of I.S.F from the rest of the plane. § This partial shift can occur in any of the three equivalent directions 𝑏#$, 𝑏#%, 𝑏#& § To make a complete (perfect) dislocation, two atomic layers bounding the ISF inside the first partial loop is to be shifted again along another partial shift direction. § However, to avoid the atoms moving on top of each other, the second shift should be chosen from a different set of three partial shift directions. § Clearly, for every perfect dislocation with Burgers vector 𝑏, only one combination of partial shifts 𝑏#$ and 𝑏#% exists that avoids atomic run-ons and then only if introduced in a certain order. 𝑝 𝑏!" 𝑏!# 𝑏!$ 𝑏! 𝑏" 𝑏# Schematic representation of the burgers vectors 𝑏!,#,$ and partial Burgers vectors 𝑏%!,%#,%$ on the {111} plane.
- 20. ATOMISITIC METHODS FOR DETERMINATION OF SFE First principle calculations of SFE.
- 21. Atomistic aspects of materials properties | Structure and energy of stacking faults21 ATOMISITIC METHODS FOR DETERMINATION OF SFE § Ab-initio total-energy calculations were based on density-functional theory as implemented in the Vienna ab initio simulation package (VASP). § Exchange and correlation interactions are described using a gradient corrected functional in the Perdew-Burke-Ernzerhof (PBE) form. § Electron-ion interactions were treated within the Projector Augmented Wave (PAW) method (From VASP). § The energy cutoff for the plane-wave basis set was set to be 270 eV unless indicated. § The energy convergence was set to be 10−6 eV. § All calculations were performed with spin-polarization to account for the magnetic properties of considered alloys.
- 22. Atomistic aspects of materials properties | Structure and energy of stacking faults22 ATOMISITIC METHODS FOR DETERMINATION OF SFE § The chemical disorder was modelled using Special Quasirandom Structures (SQS) developed to predict self-averaging quantities of alloys using finite size supercells. § SQS structure was constructed by optimization of the Warren- Cowley Short Range Order (SRO) parameters α𝒊𝒋 𝒎 . § The optimization of SRO was achieved by swapping elemental species with a Monte Carlo algorithm. § The decision whether to accept or to reject the exchange is made according to the standard Metropolis scheme. § In this way, the closest random structure at a given supercell size was generated.
- 23. Atomistic aspects of materials properties | Structure and energy of stacking faults23 ATOMISITIC METHODS FOR DETERMINATION OF SFE Crystal structure of CuAu metal alloy and InGaAs2 semiconductor alloy as generated by MedeA Special Quasirandom Structures https://www.materialsdesign.com/datasheet/SQS ©ImagereproducedwithspecialpermissionfromMaterialsDesignEurope ©ImagereproducedwithspecialpermissionfromMaterialsDesignEurope ©ImagereproducedwithspecialpermissionfromMaterialsDesignEurope
- 24. Atomistic aspects of materials properties | Structure and energy of stacking faults24 ATOMISITIC METHODS FOR DETERMINATION OF SFE § Two methods are used for calculation of SFE. § In the first approach, a parameterized model is obtained by mapping the stacking sequence onto a one-dimensional Axial Next Nearest Neighbour Ising (ANNNI) model. § In this model, the ab initio total energy is expressed as a sum of coupling energies between individual planes that is then truncated to a finite number of neighbouring layers, under the assumption that the fault interactions are short ranged. § The SFE can then be deduced from the calculated coupling constants. § This approach can be generalized to the AIM model by including higher order terms in the expansions. Edhcp, Ehcp and Efcc are the total energy per atom of the dhcp, hcp and fcc phase, respectively
- 25. Atomistic aspects of materials properties | Structure and energy of stacking faults25 ATOMISITIC METHODS FOR DETERMINATION OF SFE § In the supercell approach, an SQS consisting of 9 [B1B10] planes containing 108 atoms was constructed by considering three- dimensional periodic boundary conditions. § A vacuum region of more than 10 Å was added and a stacking fault was inserted by rigidly shifting the upper four [B1B10] layers in the [112] or [B110] directions. § This process was repeated for every possible position of the stacking fault and the stacking sequence was manually changed in order to ensure that the stacking fault was always located in the middle of the supercell. EISF and E0 are the energies of configurations with and without the ISF respectively and A is the ISF area.
- 26. Atomistic aspects of materials properties | Structure and energy of stacking faults26 SUMMARY § Stacking Fault is a two-dimensional surface which is the fault in the periodic stacking sequence of a crystal. § There are different types of Stacking Faults depending on the relative position of the fault plane. § SFE ∝ 1 SFE Width ∝ Cross-slip ∝ 1 Creep Resistance § In FCC materials stable stacking faults are found only in the {111} planes. § We study the SFEs and γ surfaces for a series of Ni-based CSAs based on first- principles calculations using both supercell methods and the axial interaction model (AIM) § In the supercell method, the whole γ surface is obtained by sliding the upper half of the cell with respect to the lower half by mapping the stacking sequence into a 1D Ising model.
- 27. Atomistic aspects of materials properties | Structure and energy of stacking faults27 SUMMARY § We show that some CSAs exhibit low, even negative SFE at low temperature that suggests HCP is more stable than FCC. § However, calculation of the temperature dependence of SFE for some CSAs reveals an HCP to FCC transition that is driven by the vibrational entropy. § These results may help to understand the lattice stability and dislocation behaviours in CSAs.
- 28. 28 Atomistic aspects of materials properties | Structure and energy of stacking faults FURTHER READING § Demonstration for SFE calculation using DFT Click here § First-principles calculations of generalized-stacking-fault-energy of Co-based alloys Click here § Generalized stacking fault energy in magnesium alloys: Density functional theory calculations Click here § Stacking fault energies of face-centered cubic concentrated solid solution alloys Click here § Dislocation Core Effects on Mobility Click here