First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline:...

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First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics “Stabilization” of glassy state Destabilization of competing phases Iron-based bulk metallic glass Current Research First principles molecular dynamics Chemical bonding Elastic moduli → ductility

Transcript of First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline:...

Page 1: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

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

Page 2: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

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

Page 3: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

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

Page 4: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

Amorphous metal (metallic glass):

Bouncing Ball Demo (Liquid Metal Tech.)

Page 5: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.
Page 6: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

Enthalpy of formationFirst-principles calculations

Known LT stable

Known HT stable

Known metastable

Unknown/hypothetical

Page 7: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

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

Page 8: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

Enthalpy of formationFirst-principles calculations

Known LT stable

Known HT stable

Known metastable

Unknown/hypothetical

Page 9: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

B6Fe23 in C6Cr23 prototype, Pearson notation cF116

Page 10: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.
Page 11: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

Fe

B

Y

C

Er

Cr

Mo

Page 12: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

C6Fe21Y2 in C6Cr23 prototype cF116Wyckoff class 8c, Voronoi type (0,0,12,4)

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Ternary Enthalpy diagram

Page 14: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

Some DARVA-Glass101DARVA-Glass101 can form 9 mm Fe-SAM

Joe Poon (experimentalist, University of Virginia)

Fe48B6C15Y2Mo14Cr15

Page 15: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

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

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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 (?)

Page 17: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

Fe48B6C15Er2Mo14Cr15

First Principles Molecular Dynamics

Iron

Boron

Carbon

Chromium

Molybdenum

Erbium

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Tempering Molecular Dynamics

Swap temperatures of runs with probabilityP~exp(-E*(1/kBT))

Tl=1423, Tx=819, Tg=777 (K)

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Iron Pair Correlation FunctionsLiquid Fe48B6C15Er2Mo14Cr15 T=1000K (VASP-TMD)

Page 20: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

Boron Pair Correlation FunctionsLiquid Fe48B6C15Er2Mo14Cr15 T=1000K (VASP-TMD)

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Carbon Pair Correlation FunctionsLiquid Fe48B6C15Er2Mo14Cr15 T=1000K (VASP-TMD)

Page 22: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

Erbium Pair Correlation FunctionsLiquid Fe48B6C15Er2Mo14Cr15 T=1000K (VASP-TMD)

Page 23: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

Molybdenum Pair Correlation FunctionsLiquid Fe48B6C15Er2Mo14Cr15 T=1000K (VASP-TMD)

Page 24: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

Chromium Pair Correlation FunctionsLiquid Fe48B6C15Er2Mo14Cr15 T=1000K (VASP-TMD)

Page 25: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

Self-Consistent Charge [email protected]

CFe

Mo

CMo

Fe

Page 26: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

{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)

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C (s) +Fe (spd)

Fe (spd)+ Mo (d)

C (p)

Electronic Density of States

Page 28: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

COOP: Crystal Orbital OverlapPopulation (Hoffmann ~1983)

orbitaliatom

ii Rrcr

jijij

i RrRrccr

ijj

jii

ii OcccQ

,

2COOP

Page 29: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

COHP: Crystal Orbital HamiltonPopulation (Dronskowski & Blöchl ~ 1993)

orbitaliatom

ii Rrcr

drHE

ijj

jii

ii HccEE

,

COHP

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Energy-projected (differential) [email protected] (TB-LMTO)

Bonding

Antibonding

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Total (integrated) [email protected] (TB-LMTO)

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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

Page 33: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

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?

Page 34: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

Strain Accommodation in Fe65B6C15Mo14

Page 35: First Principles Total Energy Calcuations Applied to the Design of a Bulk Metallic Glass Outline: Introduction to metallic glass Computational thermodynamics.

Table of strain ratios

CMo 0.55CFe 0.83BMo 0.89BFe 0.91FeFe 1.02FeMo 1.04FeEr 1.15