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)

Self-Consistent Charge DensityMo2@CFe3.oP16

CFe

Mo

CMo

Fe

{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

Energy-projected (differential) COHPMo2@CFe3.oP16 (TB-LMTO)

Bonding

Antibonding

Total (integrated) COHPMo2@CFe3.oP16 (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