Materials with high melting temperatures (over 2000°C) tend to be brittle at ambient and even relatively high temperatures. High melting temperatures originate in strong interatomic bonding arising from formation of dd or dp bonds that also affect and/or control crystal structures and properties of extended defects, such as dislocations, grain boundaries. These, in turn, govern plastic deformation and fracture. General goal: Establish relationship between electronic structure and mechanical behavio

Cawkwell, Marc J

Gröger, Roman

Vitek, Vaclav

English

ScholarlyCommons@Penn

University of PennsylvaniaScholarlyCommonsEnergy Research Group Posters Energy Research GroupMarch 2007Atomistic Studies of Deformation and Fracture inMaterials with Mixed Metallic and CovalentBondingVaclav VitekUniversity of Pennsylvania, vitek@seas.upenn.eduMarc J. CawkwellUniversity of PennsylvaniaRoman GrögerUniversity of PennsylvaniaFollow this and additional works at: http://repository.upenn.edu/pennergy_postersPoster presented at The Search for a Sustainable Energy Future: Challenges for Basic Research, A Mini-Symposium sponsored by the Energy WorkingGroup at Penn, March 9, 2007.This paper is posted at ScholarlyCommons. http://repository.upenn.edu/pennergy_posters/1For more information, please contact libraryrepository@pobox.upenn.edu.Vitek, Vaclav; Cawkwell, Marc J.; and Gröger, Roman, "Atomistic Studies of Deformation and Fracture in Materials with MixedMetallic and Covalent Bonding" (2007). Energy Research Group Posters. 1.http://repository.upenn.edu/pennergy_posters/1Atomistic Studies of Deformation and Fracture in Materials with MixedMetallic and Covalent BondingAbstractMaterials with high melting temperatures (over 2000°C) tend to be brittle at ambient and even relatively hightemperatures. High melting temperatures originate in strong interatomic bonding arising from formation ofdd or dp bonds that also affect and/or control crystal structures and properties of extended defects, such asdislocations, grain boundaries. These, in turn, govern plastic deformation and fracture.General goal: Establish relationship between electronic structure and mechanical behaviorCommentsPoster presented at The Search for a Sustainable Energy Future: Challenges for Basic Research, A Mini-Symposium sponsored by the Energy Working Group at Penn, March 9, 2007.This other is available at ScholarlyCommons: http://repository.upenn.edu/pennergy_posters/1Atomistic Studies of Deformation and Fracture in Materials with Mixed Metallic and Covalent BondingV. Vitek, M. Cawkwell and R. GrögerDepartment of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104MOTIVATION OF RESEARCHMaterials with high melting temperatures (over 2000°C) tend to be brittle at ambient and even relatively high temperatures.High melting temperatures originate in strong interatomic bonding arising from formation of dd or dp bonds that also affect and/or control crystal structures and properties of extended defects, such as dislocations, grain boundaries.  These, in turn, govern plastic deformation and fracture.General goal: Establish relationship between electronic structure and mechanical behaviorMaterials studiedBCC transition metals: Mo, W, Nb, Ta, VFCC transition metal: IridiumIntermetallic compounds: MoSi2, Mo5Si3, Ir3Nb, Ir3Zr Ecoh = Epair + Ebond + EenvElectrostatic and overlap ion core repulsion represented by pair potentialFitting: Lattice constants, elastic moduli, relative stabilityBond energy arising from formation of the valence band by d and p electronsContains dependence on bond anglesFitting: Radial dependence of bond integrals and band filling to ab initio DFT based calculationsEnvironmentally dependent repulsive term arising from repulsion experienced by the sp-electrons squeezed into the interstitial volumes by the strong cohesion provided by the d-electronsFitting: Cauchy pressuresBOND-ORDER POTENTIALSSemi-empirical tight-binding based scheme that describes physically correctly angular dependencies of covalent bondsUnlike commonly used tight-binding, bond-order potentials are a real-space method that includes both covalent d-d and d-p bonds and nearly free s and p electronsbond , ,, ,j i i ji j iE HBOND ORDER is evaluated for a given Hamiltonian in real space using Lanczosrecursion method and the many-body expansion for the bond-order,j iBOND INTEGRALS :  Two-center approximation with usual Slater-Koster angular dependence.Fitted to reproduce results of ab initio calculations,Hi jBond integrals for Mo d-orbitalss-orbitald-bond is screened by the valence s-orbitals of a neighboring atom.This bond can be either weakened or strengthened.Environmental screeningis an essential ingredientDISLOCATION CORE STRUCTURE AND DISLOCATION GLIDE IN MOLYBDENUM AND TUNGSTENCORE STRUCTURE OF THE 1/2[111] SCREW DISLOCATION IN MOLYBDENUM Bond-order potential and ab-initio DFT-based calculations of Woodward and RaoMOLYBDENUMTension and compression compared with corresponding pure shear in the direction of the Burgers vectorIf only the shear stress parallel to the Burgers vector controled glide the CRSS would be the same for pure shear, tension and compressionEFFECT OF SHEAR STRESSES PERPENDICULAR TO THE BURGERS VECTORTENSIONCOMPRESSIONC > T C < T>0Tension-compression asymmetry based on the theoryFULL AGREEMENT WITH EXPERIMENTSHollang, Hommel and Seeger, Phys. Stat. Sol. 160, 329, 1997Hollang and Seeger, Materials Transactions, JIM 40, 141, 20008.6x10 4s- 15.9x10 7s- 1Temperature (degrees K)Thermal pa rt of the yield str ess (MP a)Temperature dependence introduced 0= exp(- H/kT)Temperature (degrees K)Thermal pa rt of the yield str ess (MP a)8.6x10 4 s- 1CompressionTensionFracture surface of Ir single crystalTransgranularcleavage up to 500°CCleavage is preceded by extensive neck-free plastic deformationTwo core configurations of the screw 1/2<110> dislocationScrewcomponentEdgecomponentSpreading intoTwo {111} planesMetastable structure unstable in other fcc metalsATHERMAL CROSS-SLIP IN FCC IRIDIUMNon-planar core serves as an intermediary for athermal cross slip along long segments of screw dislocationsUnusually high density of Frank-Read sources generated by double cross-slip.  These sources are distributed homogeneously throughout the sample.Rapid increase of dislocation density with strain but no strain localization and no necking occurs.Unusually rapid work-hardening limiting relaxation of stress concentrations. Fracture results as a consequence of hardening.IRIDIUM FUTURE RESEARCHSHORT TERMProperties of special and general grain boundaries in iridium and comparison with other fcc metals to clarify the propensity for intergranular brittleness in polycrystalline iridium.Studies of stacking faults and dislocations in molybdenum silicides: MoSi2 (tetragonal C11b, hexagonal C40, orthorhombic C54) and Mo5Si3 (D8m).LONG TERMTransition bcc metals (Mo, W, Ta, Nb, V)Establish general rules of the dependence of their plastic behavior on electronic structure, in particular filling of the d-band.  Investigate effects of point defects, in particular interstitials produced by irradiation, impurities and alloying elements on dislocation glide and thus deformation and fracture of these materials.Ferromagnetic ironDevelopment and testing of BOP that includes ferromagnetism.  Using this BOP to investigate  dislocations, interstitials, grain boundaries, alloying elements and their interactions in bcc iron with emphasis on effects of ferromagnetism and comparison with non-magnetic bcc metals.Core displacements0 00 00 0 0

Atomistic Studies of Deformation and Fracture in Materials with Mixed Metallic and Covalent Bonding

Kosmopolis

University of Pennsylvania
ScholarlyCommons
Energy Research Group Posters Energy Research Group
March 2007
Atomistic Studies of Deformation and Fracture in
Materials with Mixed Metallic and Covalent
Bonding
Vaclav Vitek
University of Pennsylvania, vitek@seas.upenn.edu
Marc J. Cawkwell
University of Pennsylvania
Roman Gröger
University of Pennsylvania
Follow this and additional works at: http://repository.upenn.edu/pennergy_posters
Poster presented at The Search for a Sustainable Energy Future: Challenges for Basic Research, A Mini-Symposium sponsored by the Energy Working
Group at Penn, March 9, 2007.
This paper is posted at ScholarlyCommons. http://repository.upenn.edu/pennergy_posters/1
For more information, please contact libraryrepository@pobox.upenn.edu.
Vitek, Vaclav; Cawkwell, Marc J.; and Gröger, Roman, "Atomistic Studies of Deformation and Fracture in Materials with Mixed
Metallic and Covalent Bonding" (2007). Energy Research Group Posters. 1.
http://repository.upenn.edu/pennergy_posters/1
Atomistic Studies of Deformation and Fracture in Materials with Mixed
Metallic and Covalent Bonding
Abstract
Materials with high melting temperatures (over 2000°C) tend to be brittle at ambient and even relatively high
temperatures. High melting temperatures originate in strong interatomic bonding arising from formation of
dd or dp bonds that also affect and/or control crystal structures and properties of extended defects, such as
dislocations, grain boundaries. These, in turn, govern plastic deformation and fracture.
General goal: Establish relationship between electronic structure and mechanical behavior
Comments
Poster presented at The Search for a Sustainable Energy Future: Challenges for Basic Research, A Mini-
Symposium sponsored by the Energy Working Group at Penn, March 9, 2007.
This other is available at ScholarlyCommons: http://repository.upenn.edu/pennergy_posters/1
Atomistic Studies of Deformation and Fracture in Materials with Mixed 
Metallic and Covalent Bonding
V. Vitek, M. Cawkwell and R. Gröger
Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104
MOTIVATION OF RESEARCH
Materials with high melting temperatures (over 2000°C) tend to be 
brittle at ambient and even relatively high temperatures.
High melting temperatures originate in strong interatomic bonding 
arising from formation of dd or dp bonds that also affect and/or 
control crystal structures and properties of extended defects, such 
as dislocations, grain boundaries.  These, in turn, govern plastic 
deformation and fracture.
General goal: Establish relationship between electronic structure 
and mechanical behavior
Materials studied
BCC transition metals: Mo, W, Nb, Ta, V
FCC transition metal: Iridium
Intermetallic compounds: MoSi2, Mo5Si3, Ir3Nb, Ir3Zr
 
Ecoh = Epair + Ebond + Eenv
Electrostatic and overlap ion core 
repulsion represented by pair potential
Fitting: Lattice constants, elastic 
moduli, relative stability
Bond energy arising from formation of the 
valence band by d and p electrons
Contains dependence on bond angles
Fitting: Radial dependence of bond integrals 
and band filling to ab initio DFT based 
calculations
Environmentally dependent 
repulsive term arising from 
repulsion experienced by 
the sp-electrons squeezed 
into the interstitial volumes 
by the strong cohesion 
provided by the d-electrons
Fitting: Cauchy pressures
BOND-ORDER POTENTIALS
Semi-empirical tight-binding based scheme that describes 
physically correctly angular dependencies of covalent bonds
Unlike commonly used tight-binding, bond-order potentials 
are a real-space method that includes both covalent d-d and 
d-p bonds and nearly free s and p electrons
bond , ,
, ,
j i i j
i j i
E H
BOND ORDER is evaluated for a given 
Hamiltonian in real space using Lanczos
recursion method and the many-body 
expansion for the bond-order
,j i
BOND INTEGRALS :  Two-center approximation 
with usual Slater-Koster angular dependence.
Fitted to reproduce results of ab initio calculations
,Hi j
Bond integrals for Mo 
d-orbitals
s-orbital
d-bond is screened by the 
valence s-orbitals of a 
neighboring atom.
This bond can be either 
weakened or strengthened.
Environmental screening
is an essential ingredient
DISLOCATION CORE STRUCTURE AND DISLOCATION GLIDE IN MOLYBDENUM AND TUNGSTEN
CORE STRUCTURE OF THE 1/2[111] 
SCREW DISLOCATION IN MOLYBDENUM 
Bond-order potential and ab-initio DFT-
based calculations of Woodward and Rao
MOLYBDENUM
Tension and compression compared with corresponding 
pure shear in the direction of the Burgers vector
If only the shear stress parallel to the Burgers vector controled glide 
the CRSS would be the same for pure shear, tension and compression
EFFECT OF SHEAR STRESSES 
PERPENDICULAR TO THE BURGERS VECTOR
TENSIONCOMPRESSION
C > T C < T
>0
Tension-compression asymmetry based on the theory
FULL AGREEMENT WITH 
EXPERIMENTS
Hollang, Hommel and Seeger, Phys. Stat. 
Sol. 160, 329, 1997
Hollang and Seeger, Materials 
Transactions, JIM 40, 141, 2000
8.6x10 4s- 1
5.9x10 7s- 1
Temperature (degrees K)
T
he
rm
al
 p
a r
t o
f t
he
 y
ie
ld
 s
tr
es
s 
(M
P
a)
Temperature dependence introduced 0= exp(- H/kT)
Temperature (degrees K)
T
he
rm
al
 p
a r
t o
f t
he
 y
ie
ld
 s
tr
es
s 
(M
P
a)
8.6x10 4 s- 1
Compression
Tension
Fracture surface of Ir single crystal
Transgranular
cleavage up to 500°C
Cleavage is preceded 
by extensive neck-free 
plastic deformation
Two core configurations of the screw 1/2<110> dislocation
Screw
component
Edge
component
Spreading into
Two {111} planes
Metastable 
structure unstable 
in other fcc metals
ATHERMAL CROSS-
SLIP IN FCC IRIDIUM
Non-planar core serves 
as an intermediary for 
athermal cross slip 
along long segments of 
screw dislocations
Unusually high density of Frank-Read sources 
generated by double cross-slip.  These sources 
are distributed homogeneously throughout the 
sample.
Rapid increase of dislocation density with strain 
but no strain localization and no necking occurs.
Unusually rapid work-hardening limiting 
relaxation of stress concentrations. 
Fracture results as a consequence of hardening.
IRIDIUM FUTURE RESEARCH
SHORT TERM
Properties of special and general grain boundaries in 
iridium and comparison with other fcc metals to clarify 
the propensity for intergranular brittleness in 
polycrystalline iridium.
Studies of stacking faults and dislocations in 
molybdenum silicides: MoSi2 (tetragonal C11b, 
hexagonal C40, orthorhombic C54) and Mo5Si3 (D8m).
LONG TERM
Transition bcc metals (Mo, W, Ta, Nb, V)
Establish general rules of the dependence of their 
plastic behavior on electronic structure, in particular 
filling of the d-band.  Investigate effects of point 
defects, in particular interstitials produced by 
irradiation, impurities and alloying elements on 
dislocation glide and thus deformation and fracture of 
these materials.
Ferromagnetic iron
Development and testing of BOP that includes 
ferromagnetism.  Using this BOP to investigate  
dislocations, interstitials, grain boundaries, alloying 
elements and their interactions in bcc iron with 
emphasis on effects of ferromagnetism and 
comparison with non-magnetic bcc metals.
Core 
displacements
0 0
0 0
0 0 0


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Atomistic Studies of Deformation and Fracture in Materials with Mixed Metallic and Covalent Bonding

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