role of atomic-scale modeling in materials design discovery

Role of Atomic-Scale Modeling in

Materials Design Discovery

Susan B. Sinnott

Department of Materials Science and Engineering

Penn State University

University Park, PA

XV Brazil MRS Meeting

September 27, 2016

Materials State Awareness with Atomic and

Nanometer Scale Computational Methods• Electronic-structure level

• High fidelity methods available:

• Quantum chemical approaches

• Density functional theory (DFT)

• Off-the-shelf codes widely available

• Wide-spread understanding of strengths and limitations

Atomic-scale level

Many-body, realistic potentials have been available for over 30 years

Ideal for examining systems under extreme environments

Necessary to investigate chemistry + microstructure + mechanics +

mechanisms + …..

Physics-based model development

Inform microscale and mesoscale models

Explain experimental observations (strong “suggestion about

what the atoms are doing”)

MAX Phases

10/4/2016

9 M elements

× 12 A elements

× 2 X elements

× 3 values of n

648 MAX phases

50/50 solid solutions also

possible for M, A, and X

31,590 MAX phases

(10,530 M2AX phases)

Example 1: Material by Design

Thermodynamic stability of existing M2AX phases

10/4/2016 4

Stability trends among M2AX phases

5

Valence mismatch

Radius mismatch

Electronegativity mismatch

Total ionicity

Total # of valence electrons

% of M2AX phases that are stable vs…

Magnetic M2AX Phases

Cr2InN & Cr4(CdIn)N2 show ferromagnetic ordering at 0K

10/4/2016 6

Cr2InN Cr4(CdIn)N

Formation

energy

(meV/atom)

7 21

Magnetization

energy (meV/Cr

atom)

68 70

Final magnetic

moment

(μB/Cr atom)1.08 1.18

MXene Synthesis

10/4/2016 7

Immersion in H2O/HF

(0.5M)

2D Material Formation Energies

10/4/2016 8

Ex.) Ef(Ti2CO2) = E(Ti2CO2) - E(TiC) – E(TiO2)

2D materials will never be “stable” compared to 3D

competing phases, but with a low enough

metastability they can be stabilized kinetically.

Comparing O, F, & OH Binding Energies

9

Eb = E Mn+1XnTm – E Mn+1Xn –m

2E T2 – mμT

Coated MXene

Bare MXene

Surface species reference

Surface species chemical potential

μO = ΔGf

H2O − 2μH

μOH = ΔGf

H2O −μH

μF = ΔGfHF

− μH

All depend on μH

Ashton, et al. Journal of Physical Chemistry C (2016)

Comparing O, F, & OH Binding Energies

10

Ti2C Sc2C

For all transition metals other than Sc, O binding is

preferred for all 𝜇𝐻.

Ashton, et al. Journal of Physical Chemistry C (2016)

MXene Formation Energies

10/4/2016 11

V2CO2 has the highest

formation energy of all

MXenes that have been

synthesized to date.

All MXenes below

V2CO2 (within the

yellow threshold) should

be creatable from a

thermodynamic

perspective.

Li-Ion Battery Anode Candidate Criteria

• Stable

• Lightweight

• Inexpensive

• High capacity

• Low diffusion barrier

• Minimal swelling during charge/discharge

10/4/2016 12

Tin+1CnO2 & Vn+1CnO2

Diffusion Pathways in Multilayer MXenes

10/4/2016 13

O (over)O (under) Li

(a) (b)

[0100]

[1000]

a

b

[1200]

[1100]

Monolayer Multilayer

ΔE (eV)

1.0

2.0

3.0

4.0

Voltage Profiles

10/4/2016 14

V = −E Mn+1XnO2Lix1

− E Mn+1XnO2Lix0− (x1 − x0)E(Li)

x1−x0

Ashton, et al. Applied Physics Letters (2016)

Comparison of Anode-Related Properties

10/4/2016 15

MXene

Gravimetric

Capacity

(mAh/g)

Volumetric

Capacity

(Ah/L)

Volume

Expansion

(%)

Diffusion

Barrier

(eV)

Ti2CO2 192 346 0.32 0.63

Ti3C2O2 134 240 -0.1 0.60

Ti4C3O2 103 187 0.34 0.73

V2CO2 276 379 2.82 0.82

V3CO2 192 263 1.93 0.52

V4C3O2 148 205 1.64 0.42

Ashton, et al. Applied Physics Letters (2016)

Example 2: Nickel-Based Superalloy Design

BRI: Searching for RE Alternative

through Crystal Engineering

• Used in high temperature-applications such as gas-turbines1

• Two phases present:γ- Ni matrix

γ’- Ni3Al (~ 70% volume)

Microstructure of γ-γ’ phases of Ni

single crystal superalloys2

L12 – Al at

corners, Ni at

face-centers

1. R Schafrik and R Sprague; Adv. Mat. and Proc. 162 (2004)

2. P Caron and O Lavigne; J. Aerospace Lab. 3 (2011)

Objective: Identify alternative, earth-

abundant alternatives to rare earth

metals in Ni-based superalloys



Defect Formation Energy

Defect formation energy of incorporating dopant X is defined as:

Etot[Xq] = total energy of the system with the defect

Etot[bulk] = total energy of the system without the defectn = number of atoms added (n > 0) or removed (n < 0)μi = chemical potential of species i

X Ef (XAl) (eV) Ef (XNi) (eV)

B 2.60 0.87

Cr 1.40 (1.351) 0.93 (0.921)

Ce 0.81 1.81

Zr 0.10 (0.041) 0.31 (0.201)

1. D E Kim, S L Shang, Z K Liu; Intermetallics 18 (2010)



DFT-Materials Informatics-Experiment

• Defect formation energy

CrAl > CrNi

• From the principle component analysis (PCA) plot, materials informatics (by Krishna Rajan) concludes that Cr prefers Al site without DFT calculation results.

Experimental validation

from Jim LeBeau:

Cr EDS map corresponds

with the Al EDS map

Chemical design vector: mapping a ‘periodic table’ for alloys

Grant # FA9550-12-1-0456

Reporting period: Jan.2013-May 2014

Sims, Stoloff and

Hagel (1986) /

Pollak and Tin

(2006)

• New guide for seeking

similarity of elements

with respect to

influence of alloy

properties

• Captures information

not possible from

periodic table

mapping of elements

Informatics work

of Krishna Rajan

Materials State Awareness with Atomic and

Nanometer Scale Computational Methods• Electronic-structure level

• High fidelity methods available:

• Quantum chemical approaches

• Density functional theory (DFT)

• Off-the-shelf codes widely available

• Wide-spread understanding of strengths and limitations

• Atomic-scale level

• Many-body, realistic potentials have been available for over 30 years

• Ideal for examining systems under extreme environments

• Necessary to investigate chemistry + microstructure + mechanics +

mechanisms + …..

• Physics-based model development

• Inform microscale and mesoscale models

• Explain experimental observations (strong “suggestion about

what the atoms are doing”)

30 Years of Many-Body Atomic-Scale

Potentials (Reactive Force Fields)

May 2012 issue

Historically developed for materials

with specific types of chemical bonds

Tersoff potentials for Si

Brenner or REBO potential for C,H

+ O,F,S,….

AIREBO

EAM potentials for metals

MEAM for metals and oxides

EAM+ES for metals and oxides

Rigid ion (Buckingham) potentials for

ionically bound materials

Used to examine phenomena at the

atomic and nanometer scale and

develop a qualitative, mechanistic

understanding

Metallic

IonicCovalent Bone/biocomposites

Aqueous biological systems

Interconnects

Corrosion/Oxidation

Thermal barrier coatingsCatalysts

Multicomponent Systems

• Inherent to many

applications

• Challenging for:

• First-principles electronic

structure methods (large

systems, lacking usual

symmetry)

• Atomic-scale methods

because of their

heterogeneous nature

• This need spurred the

development of next

generation potentials

(COMB, ReaxFF, and

others)

S.R. Phillpot and

S.B. Sinnott,

Science (2009)

Example 3: Cu (001)/a-SiO2 Interfaces

Structural properties of the interface

Oxidation of Cu is limited to the first two Cu layers; formation of Cu2O

Type of interfaceW (J/m2) Cu-O

(%)Exp COMB

Cu/a-SiO2 + 0 VO 0.5 - 1.2 a

0.6 - 1.4 b

1.810 22

Cu/a-SiO2 + 10 VO 0.629 13

Cu/a-SiO2 + 20 VO 0.289 11

a Oh, et al., J. Am. Ceram. Soc. (1987)b Pang and Baker, J. Mater. Res. (2005)

• Cu-O bonds play crucial roles in adhesion

of the interface

• Adhesion of Cu/dielectric layer decreases

with O defects

Introduced O vacancies at the interface

0, 10 and 20 VO

Charge Transfer Across the Interface

DFT: Nagao et al., COMB: Shan et al.

-10 0 10-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

<n(

D)>

(A-3)

Distance (angstrom)

COMB



Example 4: Deformation of metals - Ni

dislocations within grains are generated and

evolve over time

grain are in the BCC arrangement

Common

neighbor analysis

Polycrystalline Ni after being

subjected to tensile test with

constant strain rate (=4x10-9 s-1)

1. A. Kumar, T. Liang, A. Chernatynskiy, Z. Lu, M. Noordhoek, K. Choudhary, S.R. Phillpot, S.B. Sinnott; J. Phys.:

Condensed Matter (in preparation)

2. Y. Mishin, D. Farkas, M.J. Mehl, D.A. Papaconstantopoulos; Phys. Rev. B 59 (1999)

Stacking fault energies:

<112> and <101>

COMB Ni potential1 EAM Ni potential2

Stacking fault energy of Ni1

compared with EAM2 potential

Centro-symmetry analysis



Al deformation predicted by different potentials

COMB Al potential1 EAM Al potential2 Stacking fault energies:

<112> and <101>

Stacking fault energy of Al1

compared with EAM2 potential

1. A. Kumar, T. Liang, A. Chernatynskiy, Z. Lu, M. Noordhoek, K. Choudhary, S.R. Phillpot, S.B. Sinnott; J. Phys.:

Condensed Matter (in preparation)

2. Y. Mishin, D. Farkas, M.J. Mehl, D.A. Papaconstantopoulos; Phys. Rev. B 59 (1999)

Potential energy surface

illustrating the <112> barrier

to be less than the <101>

barrier1



Mechanical deformation of Ni3Al at the g/g’ interface

1. A. Kumar, T. Liang, A. Chernatynskiy, Z. Lu, M. Noordhoek, K. Choudhary, S. R. Phillpot, S.B. Sinnott (in

preparation)

2. M.H. Yoo, M.S. Daw, M.I. Baskes, V. Vitek, D.J. Srolovitz, Eds.; New York: Plenum Press; 1989. p. 401.

Thermostat

Active

Rigid moving

Rigid moving

Thermostat

Active

Ni3Al

Ni

τzx

Z

[010]

X

[101]

Y

[10 -1]τzx

• Edge dislocations at the Ni-Ni3Al interface

• Predict mechanisms associated with

applied shear stress and dislocation

motion

Ni3Al Ec

(eV/atom)B

(GPa)G

(GPa)

COMB1 -4.61 198 93

exp.2 -4.62 195 96

Simulation box size:

16.67x16.67x9.21 nm3

Total number of

atoms: 179,600

Dislocation

Technical Fundamental Barriers• Parameterization of transferrable, next-generation potentials is non-

trivial. For some historical potentials, numerous parameterizations exist.

The general equation for COMB is:

.

• Validation of predicted trends and quantification of error bars.

• Comfort within the broader community of how and when potentials work

well and when the transferability of parameterized properties breaks

down. The materials community is familiar with strengths and limitations

of electronic structure calculations and continuum level (e.g., finite-

element level modeling). Non-experts are less comfortable with atomic-

scale methods.

• Dissemination is straightforward, maintenance is challenging!

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Databases and cyberinfrastructure

• Enable the rapid design of materials

• Materials Project (MIT)

• AFLOWLIB (Duke)

• CAVS CyberDesign (Mississippi State)

• Readily access computational tools and data

• nanoHUB (Purdue)

• CAMS (Florida)

• Improve atomic-scale methods

• NIST Interatomic Potentials Repository Project

• OpenKIM (Minnesota)

• Navigating materials cyberinfrastructures

• TMS

Challenges and needs that will shape future directions

• Big-picture challenges:

• What is the role of theory/computational modeling in the design, processing, and application of materials?

• How do we integrate the latest computational approaches with experimental data to improve predictability?

• To what extent are computational methodologies available that are applicable to the physics of interest in actual systems (materials, length and time scales)?

• How do we ensure the next generation of scientists and engineers can work in this new paradigm?

• What is needed:

• Natural workflow from discovery codes to predictive software• Tight integration between processing, characterization, and computational

approaches• Accurate error bars for the results of theoretical/computational method

results• Widespread dissemination of software with robust documentation