First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline:...
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Transcript of First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline:...
First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass
Outline:Introduction to metallic glass
Computational thermodynamics
“Stabilization” of glassy stateDestabilization of competing phasesIron-based bulk metallic glass
Current ResearchFirst principles molecular dynamicsChemical bondingElastic moduli → ductility
Co-workers:
Joe Poon (University of Virginia) (DARPA-PI)Gary Shiflet (University of Virginia) Michael Gao (Virginia/CMU)
Don Nicholson (Oak Ridge National Lab)Miguel Fuentes (Oak Ridge/CMU)Marek Mihalkovic (Slovakia/CMU)Yang Wang (Pittsburgh Supercomputer Center)
Ganesh Panchapakesan (CMU)Siddartha Naidu (CMU)Libo Xie (CMU)
Funding: DARPA, Office of Naval Research
Amorphous metal (metallic glass):
A solid metal with the structure of a liquid
How Why
Then Rapidly quench (106K/s) a thin ribbonor sputter a thin filmPure element or binary alloy
Fe-B (Honeywell/Allied Signal)
Fundamental science
Low-loss transformer cores
Now Slowly cool (1K/s) a bulk sample
Many-component alloy
Zr-Ti-Cu-Ni-Be (Cal-Tech)
Fe-B-C-Cr-Mo-Y (U. Va.)
Structural materials
Net-shape casting
Near-perfect elasticity
Golf club heads + ….
Fundamental science
Amorphous metal (metallic glass):
Bouncing Ball Demo (Liquid Metal Tech.)
Enthalpy of formationFirst-principles calculations
Known LT stable
Known HT stable
Known metastable
Unknown/hypothetical
First-Principles Thermodynamics
Use program VASP with PAW potentials, GGAFully relax all structures to optimal configurationsSubtract from tie-line to obtain enthalpy of formation (T=0K)Apply statistical mechanics to incorporate temperature
Strategies for reaching finite temperature:Alloy Theoretic Automated Toolkit (Axel van de Walle, CalTech)
fitfc determines vibrational free energy in quasiharmonic approximationmaps/emc2 determines free energy of chemical substitution
CALculation of PHAse Diagrams (e.g. ThermoCalc®)Develop database of thermodynamic dataImprove and constrain database using first-principles data
Cohesive energy database (http://alloy.phys.cmu.edu)Enthalpies of ~ 2500 structures in 200 binary and 100 ternary+ systems
Enthalpy of formationFirst-principles calculations
Known LT stable
Known HT stable
Known metastable
Unknown/hypothetical
B6Fe23 in C6Cr23 prototype, Pearson notation cF116
Fe
B
Y
C
Er
Cr
Mo
C6Fe21Y2 in C6Cr23 prototype cF116Wyckoff class 8c, Voronoi type (0,0,12,4)
Ternary Enthalpy diagram
Some DARVA-Glass101DARVA-Glass101 can form 9 mm Fe-SAM
Joe Poon (experimentalist, University of Virginia)
Fe48B6C15Y2Mo14Cr15
Other predictions:
•Previously unknown compounds and their structurese.g. predict occurrence of C2Fe2Y in tI10 structure
•Previously unknown structures of known compoundse.g. identify structure of B4FeY as oP24
•Resolved correlations among mixed/partially occupied sitese.g. Fe17Zr2.hR19 replaces Fe2 pair with Zr; structure of elemental -Boron
•Revised assessments of composition, thermal stabilitye.g. reported high temperature phase BZr.cF8 is only metastable
•Investigated previously unstudied phase diagramse.g. B-Y-Zr and Fe-Y-Zr
•Proposed new quasicrystal-forming compounde.g. B-Mg-Ru
Current Research: Design for greater ductility
Strategy:Presumed dependence of ductility on B/G ratioB=Bulk modulusG=Shear modulusNote B/G Poisson Ratio Prefer high B/G ratio, > 0.32
How to predict and control elastic moduli?Need to understand structure and bonding (?)
Fe48B6C15Er2Mo14Cr15
First Principles Molecular Dynamics
Iron
Boron
Carbon
Chromium
Molybdenum
Erbium
Tempering Molecular Dynamics
Swap temperatures of runs with probabilityP~exp(-E*(1/kBT))
Tl=1423, Tx=819, Tg=777 (K)
Iron Pair Correlation FunctionsLiquid Fe48B6C15Er2Mo14Cr15 T=1000K (VASP-TMD)
Boron Pair Correlation FunctionsLiquid Fe48B6C15Er2Mo14Cr15 T=1000K (VASP-TMD)
Carbon Pair Correlation FunctionsLiquid Fe48B6C15Er2Mo14Cr15 T=1000K (VASP-TMD)
Erbium Pair Correlation FunctionsLiquid Fe48B6C15Er2Mo14Cr15 T=1000K (VASP-TMD)
Molybdenum Pair Correlation FunctionsLiquid Fe48B6C15Er2Mo14Cr15 T=1000K (VASP-TMD)
Chromium Pair Correlation FunctionsLiquid Fe48B6C15Er2Mo14Cr15 T=1000K (VASP-TMD)
{Compound}.{Pearson}
(electronegativity)
QC
(2.55)
QFe
(1.83)
QMo/QCr
(1.75*/1.66)
QEr/ QY
(1.24/1.22)
CFe3.hP8
C@octahedron
− 0.50 +0.17
CFe3.oP16
C@trigonal prism
− 0.43 +0.14
CFe10Mo2Y.tI28
C@octahedron
− 0.52 − 0.03 ± .04 +0.16 +0.45
CEr2Fe14.tP68
C@trigonal prism
− 0.43 − 0.00 ± .06 +0.22
CCr2Fe14.cF64
C@octahedron
− 0.51 +0.05 ± .02 +0.14
CEr2Fe17.hR22
C@octahedron
− 0.44 +0.04 ± .02 +0.32
C6Fe21Mo2.cF116
C@distorted TP
− 0.41 +0.09 ± .05 +0.27
Charge Transfer
(* Interpolated value for Mo, standard = 2.16)
C (s) +Fe (spd)
Fe (spd)+ Mo (d)
C (p)
Electronic Density of States
COOP: Crystal Orbital OverlapPopulation (Hoffmann ~1983)
orbitaliatom
ii Rrcr
jijij
i RrRrccr
ijj
jii
ii OcccQ
,
2COOP
COHP: Crystal Orbital HamiltonPopulation (Dronskowski & Blöchl ~ 1993)
orbitaliatom
ii Rrcr
drHE
ijj
jii
ii HccEE
,
COHP
Total (integrated) [email protected] (TB-LMTO)
i-COHP values (eV/bond)in BC7Cr2Fe18Mo4.oP16 (TB-LMTO)
BCr
2.1
BFe
1.7
BMo
1.5
CCr
3.1
CFe
2.8
CMo
2.3
CrFe
0.7
CrMo
1.2
FeFe
0.5
FeMo
1.1
Conclusions
Computational Thermodynamics:First-principles calculations valuable source of T=0K enthalpiesResearch needed on finite temperature methods
Stat. Mech. (ATAT)/Thermodynamics (CALPHAD)Applicable to many problems in materials designPredicted role of large atoms in metallic glass stabilization
Amorphous metal structure and bonding:MD can achieve liquid and supercooled liquid structureCan classify bonding according to ionicity and covalencyHow to use this information to improve ductility?
Strain Accommodation in Fe65B6C15Mo14
Table of strain ratios
CMo 0.55CFe 0.83BMo 0.89BFe 0.91FeFe 1.02FeMo 1.04FeEr 1.15