SustainableCentre for

Chemical Technologies

Prof. Aron Walsh

Department of Chemistry University of Bath

a.walsh@bath.ac.uk

From theory to solar cells

Lecturers

Dr Keith Butler Degree in Medicinal Chemistry (Dublin)

Postdoctoral Fellow (Hybrid Perovskites)

Dr Jarvist Frost Degree in Physics (Imperial College London)

Postdoctoral Fellow (Energy Materials)

Prof. Aron Walsh Degree in Computational Chemistry (Dublin)

Professor of Materials Theory

Overview

Background: Materials Modelling is widely used as a tool for characterisation and prediction in materials science. There is an expanding literature on solar energy (e.g. active layers, interfaces, transparent conducting oxides). Aim: To have a basic understanding of the terms and concepts, with the ability to critically assess research papers in your field.

Mini-Module Outline

Class philosophy Theory à Practice à Applications

Course structure Three lectures with class literature review

1.  Modelling (AW) Electrons in a periodic potential

2. Interfaces (KTB) Workfunctions, band bending and contacts

3. Multi-scale (JMF) Bridging from atoms to solar cells

Literature Review

Small Group Activity Task 1 (this afternoon): Find a relevant research paper that uses materials modelling in the context of photovoltaics. Task 2 (tomorrow morning): 15 minute presentation & discussion of the paper (including possible limitations of the approach).

Recommended General Textbooks Bonding in Solids •  Electronic Structure and Chemistry of Solids,

P. A. Cox, Oxford Publishing (1987) •  Principles of the Theory of Solids, J. M. Ziman,

Cambridge Press (1979) Computational Chemistry •  Molecular Modelling, A. Leach, Prentice Hall (2001) •  Introduction to Computational Chemistry,

F. Jensen, Wiley (2006) Density Functional Theory for Solids •  Electronic Structure, R. M. Martin, Cambridge (2008) •  Planewaves, Pseudopotentials and the LAPW Method,

D.J. Singh, Kluwer (1994)

Materials Modelling

1.  Theory: What Equations to Solve

2.  Practice: Codes & Supercomputers

3.  Applications: From Kesterites to Hybrid Halide Perovskites

The Scientific Method

*Robert Boyle (left); William Hamilton (right)

Theory “Laws”

Experiment “Evidence”

Models “Chemical Intuition”

Computation “in silico”

A Multi-Scale Simulation Toolbox

Quantum Mechanics

HΨ = EΨKinetic and Potential Energy Operators

H = T + VNon-relativistic Relativistic

Schrödinger (1887, Vienna)

Dirac (1902, Bristol)

Electronic Structure Techniques

E[Ψ] → E[ρ]

Density based quantum

mechanics

Wavefunction based quantum

mechanics

Methods Hatree-Fock

Møller–Plesset Coupled Cluster

Configuration Interaction

Methods Thomas–Fermi

Density Functional Dynamical Mean Field

Optimised Effective Potential

Density Functional Theory (DFT) Kohn-Sham DFT (Physical Review 1965)

Use one-electron Ψ that reproduce true interacting ρ

Core Electrons all-electron

pseudopotential frozen-core

Hamiltonian non-relativistic

scalar-relativistic spin-orbit coupling

Periodicity 0D (molecules)

1D (wires) 2D (surfaces) 3D (crystals)

Electron Spin restricted unrestricted non-collinear

Basis Set plane waves numerical orbitals analytical functions

Functional beyond…….. hybrid-GGA meta-GGA GGA LDA

QMC GW RPA TD-DFT

Materials Modelling with DFT Input

Chemical Structure or Composition

Output

Total Energy + Electronic Structure

Structure atomic forces

equilibrium coordinates atomic vibrations

phonons elastic constants

Thermodynamics internal energy (U)

enthalpy (H) free energy (G)

activation energies (ΔE)

Electron Energies density of states band structure effective mass tensors electron distribution magnetism

Excitations transition intensities absorption spectra dielectric functions spectroscopy

Range of Applications

Materials Characterisation

Bulk physical and chemical properties.

Chemical Reactions

Catalysis; lattice defects; redox chemistry.

Materials Engineering

Beneficial dopants, alloys or morphology.

Substrate & Device Effects Interfacial & strain phenomena.

Amorphisation Conduction states in

InGaZnO4

Hybrid Network Photochromic MIL-125

Understanding known compounds and designing new materials

Exact Solution: Hydrogen

Building blocks for chemical bonding in all matter

From Atoms to Molecules (σ bonds)

Linear Combination of Atomic Orbitals

Ψ(r) = ciϕi (r)i∑

ϕ(r) = 1Nre−αr

2

ϕ(r) = 1Nre−αr

ϕ(r) = 1Neikr

Gaussian functions (e.g. GAUSSIAN) Slater functions (e.g. ADF) Plane waves (e.g. VASP) Numeric atom-centred functions (e.g. FHI-AIMS, SIESTA)

From simultaneous differential equations to linear algebra:

Basis Set Convergence

Source: Volker Blum – FHI-AIMS Summer School (2013)

From Molecules to Crystals Lattice: an infinite array of points generated by translation operations: R = n1a1+n2a2+n3a3 ñInteger Lattice vectorñ

Ψ(r) = u(r)eikrBloch Wave

Felix Bloch (1928)

Wavefunction of a particle in a periodic potential (λ=2π/k)

1D Bonding

Anti-Bonding

2D

k-point Sampling All unique values of wave vector k are within the First Brillouin Zone (primitive unit cell of the reciprocal lattice). We just need to sample appropriately. Dense k-point grids are used for converged total energy & property calculations, but ‘band structures’ are conventionally plotted along high symmetry lines.

Monkhorst & Pack, Physical Review B 13, 5188 (1976)

Lattice Settings: Diamond

1 0 00 1 00 0 1

!

!

0 0.5 0.50.5 0 0.50.5 0.5 0

!

!

Conventional cubic cell 8 atoms

Primitive fcc cell 2 atoms

Iterative Solutions: Electrons & Ions

Input (ρtrial)

Electronic Minimisation

•  Start from atomic or random density

•  Apply variational principle

•  Unique solution for closed-shell systems

Output (ρ)

Input (xyztrial)

Ionic Minimisation

•  Start from X-ray or guess structures

•  Calculate forces (-dE/dr)

•  Usually exploring local structure

Output (xyz)

(choice: diagonalisation method and mixing between steps)

(choice: algorithm, e.g. conjugate gradient, quasi-Newton, molecular dynamics)

Self-Consistent Cycle

(choice: algorithm, e.g. conjugate gradient, quasi-Newton, molecular dynamics)

Source: Martijn Marsman – FHI-AIMS Summer School (2011)

Materials Modelling

1.  Theory: What Equations to Solve

2.  Practice: Codes & Supercomputers

3.  Applications: From Kesterites to Hybrid Halide Perovskites

Supercomputers (Top500.org – 11.14)

Next Step: Exascale Computing

1,000,000,000,000,000,000 floating point operations per second

1000 times faster calculations than current supercomputers

100 Megawatt power consumption (1 million 100W lightbulbs)

5 years before we have access

Tiered Computing Resources

Local: Desktops

(4 – 8 cores)

Departmental: Servers

(10s cores)

University: Clusters

(1000s cores)

National: Supercomputers (100,000s cores)

BALENA Modest production runs and project students.

ARCHER Large-scale production runs (limited by wall-time).

NEON Interactive jobs; testing; non-standard implementations.

Popular DFT Packages •  CASTEP (Plane wave – pseudopotential)

•  CP2K (Mixed Gaussian/plane wave)

•  FHI-AIMS (Numeric orbitals – all electron)

•  GPAW (Numeric orbitals – pseudopotential)

•  QUANTUM-ESPRESSO (Plane wave – pseudopotential)

•  SIESTA (Numeric orbitals - pseudopotential)

•  VASP (Plane wave – pseudopotential)

•  WIEN2K (Augmented plane wave – all electron)

With the same exchange-correlation functional, all codes

should produce the same equilibrium properties.

Vienna Ab Initio Simulation Package A widely used code from Austria (Prof. Georg Kresse):

•  License fee ~€5000 (small academic group) •  Site: http://www.vasp.at •  Forum: http://cms.mpi.univie.ac.at/vasp-forum •  Wiki: http://cms.mpi.univie.ac.at/wiki •  Many pre- and post-processing tools. •  Visualisation: http://jp-minerals.org/vesta

A popular package because of reliable pseudopotentials for periodic table (benchmarked against all-electron methods).

Compiling VASP (and other codes) General Requirements: Program source code (e.g. x.f, x.f90, x.c); Makefile or configure script; Math libraries; Fortran or C compiler Common Compilers: Intel Fortran (ifort); Portland Group (pgf90); Gnu-Fortran (gfort); Pathscale (pathf90); Generic links (f77 or f90) Common Libraries: LAPACK (Linear algebra - diagonalisation) - ScaLAPACK (Distributed memory version) BLAS (Linear algebra – vector / matrix multiplication) BLACS (Linear algebra communication subprograms) Examples: MKL (Intel); ACML (AMD); GotoBLAS

Example Makefile (customised section only) FC = ifort FFLAGS = -O3 LAPACKBLAS = -L/$(MKL) -lmkl_intel_lp64 \

-lmkl_intel_thread -lmkl_core -lmkl_lapack USE_MPI = yes MPIFC = mpif90

…type “make”, the code will compile and a binary file is created. Test and benchmark!

[Tip: intel-mkl-link-line-advisor for optimal MKL flags]

VASP Input Files

•  POSCAR (“Position Card”)

•  POTCAR (“Potential Card”)

•  INCAR (“Input Card”)

•  KPOINTS (k-point Sampling)

All four files should be in the same directory for VASP to run successfully. Caution: The order of the elements in POTCAR must be

the same as POSCAR.

VASP Output Files

•  OUTCAR (“Output Card”)

•  CONTCAR (“Continue [Positions] Card”)

•  DOSCAR (“Density of States Card”)

•  CHGCAR (“Charge Density Card”)

•  vasprun.xml (Auxiliary output as xml)

A number of additional files that are generated depending on flags set in INCAR.

Caution: If NSW > 0, a number of the properties are

averaged over past structures (rerun with NSW=0 at end).

Step 1: Structure Generate crystal structure by hand, from supplementary

information, or from a database (e.g. ICSD).

Step 1: Structure Check POSCAR

Step 2: Create other Input Files

cat ./C/POTCAR ./N/POTCAR ./H/POTCAR ./Pb_d/POTCAR ./I/POTCAR > POTCAR

INCAR (Partial)

KPOINTS

Step 3: Run VASP

Let’s see…

Step 4: Investigate Output Files

•  OUTCAR – all basic output (including energy and forces)

•  CONTCAR – the final structure

•  DOSCAR – the electronic density of states

•  PROCAR – the detailed band structure

•  CHGCAR – the total electron density

See group guide for more details: http://people.bath.ac.uk/aw558/presentations/

Many scripts and tools available online!

Dependence on Exc

Journal of Chemical Physics 123, 174101 (2005) Recommend: PBEsol (GGA for solids) & HSE06 (Screened hybrid GGA)

Electronic Spectroscopy

Source: Patrick Rinks (FHI-AIMS Workshop 2011)

Approximate: Kohn-Sham eigenvalues Accurate: Quasi-particle energies (GW) TD-DFT/BSE

Photoemission (DFT vs XPS): HgO

Chemical Physics Letters 399, 98 (2004) [1st Publication!]

XPS (weighted DOS)

O K XES (O 2p DOS)

The DFT Band Gap There is much debate (and literature) on whether the electronic band gap is a ground state property and whether the exact exchange-correlation functional would reproduce it, e.g.

Sham and Schluter, PRL 51, 1888 (1983)

Eg = IP – EA For finite systems: the ionisation potentials can be far from the Kohn-Sham eigenvalues. For solids: Eg = IP – EA = -εKS

VB + εKSCB

[Dilute limit: a one-electron change in an extended system]

DFT Caution! While crystal structures, band widths and density of states can be well described, many (LDA and GGA) functionals predict band gaps too small. This results in an exaggerated dielectric response (too polarisable) and an incorrect onset of optical absorption. Common solutions: •  Scissors operator (shift conduction band

eigenvalues to match experimental gap). •  Use a hybrid exchange-correlation functional,

which reproduces the band gap. •  Go beyond DFT….

Beyond DFT Many-body GW theory

L. Hedin, Phys. Rev. 139, A796 (1965) From Kohn-Sham eigenvalues to quasi-particle electron addition (N+1) and removal (N-1) energies. Limitations: •  Self-consistency •  No total energy •  Excitons à GW+BSE Source: Patrick Rinke

Time-dependent DFT E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984) Inclusion of time-dependent potentials (electric, etc). Limitations: •  Unknown functional (kernel) / different approximations •  Few full implementations for extended solids

Materials Modelling

1.  Theory: What Equations to Solve

2.  Practice: Codes & Supercomputers

3.  Applications: From Kesterites to Hybrid Halide Perovskites

Multi-component Semiconductors

Multernary Materials Screening •  Build database of plausible (stoichiometric) materials. •  Assess structural, electronic and thermodynamic properties. •  Screen & tailor for specific applications.

2

4 2

Quaternary Semiconductors Predicted (and Confirmed) Photovoltaic Absorbers

Cu2ZnSnS4, Cu2ZnSnSe4 and Cu2ZnGeS4 Applied Physics Letters 94 041903 (2009) [> 340 citations]

Predicted Spin-transport Materials ZnSiAl2As4, CdGeAl2As4 and CuAlCd2Se4 Applied Physics Letters 95 052102 (2010)

Predicted Topological Insulators Cu2HgPbSe4, Cu2CdPbSe4 and Ag2HgPbSe4

Physical Review B 83 245202 (2011)

Cu2ZnSnS4 (13% Record Efficiency)

Advanced Energy Materials 2, 400 (2012)

•  Crystal structure (kesterite vs stannite vs disordered) •  Band gaps (as a function of composition) •  Phase stability (disproportionation into secondary phases) •  Lattice defects (origin of electrons and holes)

Beyond Periodic Solids: Point Defects

Defects: Theory & Experiment

Calculable Observable

Total Energy Differences

•  Heats of formation and reaction: relative stabilities

and concentrations. •  Diffusion barriers.

Defect Ionisation Energy (Vertical)

Optical absorption; photoluminscence; photoconductivity.

Defect Ionisation Energy (Adiabatic)

Deep-level transient spectroscopy; thermally stimulated conductivity.

Defect Vibrational Modes •  IR / Raman spectra. •  Diffusion rates; free energy.

Defect Concentrations in Cu2ZnSnS4

Advanced Materials 25, 1522 (2013)

22

0.5

1

1.5

2

2.5E

lem

ent

Rat

io

1e+14

1e+16

1e+18

1e+20

Def

ect

Den

sity

0.1

0.2

0.3

Fer

mi

En

erg

y

-0.5 -0.4 -0.3 -0.2 -0.1 0

Cu (eV)

1e+14

1e+16

1e+18

Hole

Den

sity

VCu

+ZnCu

CuZn

CuZn

-

VCu

-

Cu

Zn

Sn

ZnSn

+2ZnCu

2CuZn

+SnZn

0.5

1

1.5

2

2.5

Ele

men

t R

atio

1e+14

1e+16

1e+18

1e+20

1e+22

Def

ect

Den

sity

0.1

0.2

0.3

Fer

mi

En

erg

y

-1.4 -1.3 -1.2 -1.1 -1

Zn (eV)

1e+14

1e+16

1e+18

Hole

Den

sity

ZnSn

+2ZnCu

CuZn

CuZn

-

Cu

Zn

Sn

VCu

+ZnCu

2CuZn

+SnZn

0.5

1

1.5

2

2.5

Ele

men

t R

atio

1e+14

1e+16

1e+18

1e+20

1e+22

Def

ect

Den

sity

0

0.05

0.1

0.15

Fer

mi

En

ergy

-0.4 -0.3 -0.2 -0.1 0

Cu (eV)

1e+16

1e+17

1e+18

Ho

le D

ensi

ty

VCu

+ZnCu

CuZn

CuZn

-V

Cu-

Cu

Zn

Sn

ZnSn

+2ZnCu

VCu

2CuZn

+SnZn

0.5

1

1.5

2

2.5

Ele

men

t R

atio

1e+14

1e+16

1e+18

1e+20

Def

ect

Den

sity

0

0.1

0.2

Fer

mi

En

erg

y

-1.3 -1.25 -1.2 -1.15 -1.1 -1.05 -1

Zn (eV)

1e+15

1e+16

1e+17

1e+18

Hole

Den

sity

ZnSn

+2ZnCu

CuZn

CuZn

-

Cu

Zn

Sn

VCu

+ZnCu

VCu

-

2CuZn

+SnZn

0.5

1

1.5

2

2.5

Ele

men

t R

atio

1e+14

1e+16

1e+18

1e+20

Def

ect

Den

sity

0.05

0.1

0.15

0.2

Fer

mi

Ener

gy

-1 -0.8 -0.6 -0.4

Sn (eV)

1e+16

1e+17

Ho

le D

ensi

ty

ZnSn

+2ZnCu

CuZn

CuZn

-

Cu

Zn

Sn

VCu

+ZnCu

2CuZn

+SnZn

(c) Cu2ZnSnS4

(b) Cu2ZnSnS4

(a) Cu2ZnSnS4 (d) Cu2ZnSnSe4

(e) Cu2ZnSnSe4

(f) Cu2ZnSnSe4

0.5

1

1.5

2

2.5

Ele

me

nt

Rat

io

1e+14

1e+16

1e+18

1e+20

1e+22

De

fect

De

nsi

ty

0.1

0.15

0.2

Ferm

i En

erg

y

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0

Sn (eV )

1e+14

1e+16

Ho

le D

en

sity

ZnSn

+2ZnCu

CuZn

CuZn

-

Cu

Zn

Sn

2CuZn

+SnZn

FIG. 13: The calculated change of the element ratio, defect density (cm°3), Fermi energy (in eV relative to VBM) and holedensity (cm°3) of Cu2ZnSnS4 (left column): (a) µ

Cu

changes from -0.52 to 0 eV, with µZn

=-1.23 eV and µSn

=-0.50 eV; (b) µZn

changes from -1.53 to -0.93 eV, with µCu

=-0.20 eV and µSn

=-0.50 eV; (c) µSn

changes from -1.35 to 0 eV, with µCu

=-0.20 eVand µ

Zn

=-1.23 eV; and of Cu2ZnSnSe4 (right column): (d) µCu

changes from -0.4 to 0 eV, with µZn

=-1.17 eV and µSn

=-0.62eV; (e) µ

Zn

changes from -1.3 to -1.0 eV, with µCu

=-0.20 eV and µSn

=-0.62 eV; (f) µSn

changes from -1.2 to -0.25 eV, withµ

Cu

=-0.20 eV and µZn

=-1.17 eV. The vertical lines in the figure show the chemical potential corresponding to the point P inFig. 4.

“Cu-rich” “Cu-poor”

Cu:Zn:Sn

Defects

Carriers

μelectron

Hybrid Halide Perovskites

Snaith (Oxford)

Grätzel (EPFL)

Park (SKKU)

Il Seok (KRICT)

APL Mater. 1, 042111 (2013); Nano Letters 14, 2484 (2014)

A B X3 a (Å) Eg (eV)

NH4+ Pb I 6.21 1.38

CH3NH3+ Pb I 6.29 1.67

CH(NH2)2+ Pb I 6.34 1.55

(1991) Dye cell à (2015) Perovskite cell [20.1% efficiency] See Mendeley Group “Hybrid Perovskite Solar Cells”

CH3NH3PbI3 (or MAPI for short) Configuration: PbII [5d106s26p0]; I-I [5p6]

F. Brivio et al, Physical Review B 89, 155204 (2014) Relativistic QSGW theory with Mark van Schilfgaarde (KCL)

Conduction Band

Valence Band

Dresselhaus Splitting (SOC) [Molecule breaks

centrosymmetry]

First-principles Dynamics (300 K) “MAPI is as soft as jelly”

25 fs per frame

J. M. Frost et al, APL Materials 2, 081506 (2014)

Jarvist

http://dx.doi.org/10.6084/m9.figshare.1061490

ß Focus on one CH3NH3 ion

3D periodic boundary

(80 - 640 atoms)

Domains of Molecular Dipoles

Ferroelectric Hamiltonian (Monte Carlo solver)

Regions of high (red) and low (blue) electrostatic potential

J. M. Frost et al, APL Materials 2, 081506 (2014)

Mixed Ionic-Electronic Conductors

Angewandte Chemie 54, 1791 (2015); Under Review (2015)

Lecture 1 Conclusions

For reliable materials modelling, follow : :

•  Basis sets & k-points •  Forces & cell pressure

: •  Exchange-correlation functional

: •  Measured values and properties •  Previous calculations

NATURE CHEMISTRY | VOL 7 | APRIL 2015 | www.nature.com/naturechemistry 1

news & views

Materials chemists are spoiled for choice. The 98 naturally occurring elements of the periodic table give

rise to 4,753 potential binary compounds (that is, C2

98), 152,096 ternary compounds and 3,612,280 quaternary compounds, assuming equal amounts of each element in a single phase. The combinations exceed 65 million for a five-component system. This is an underestimate of the number of accessible materials owing to variations in stoichiometry (for example Pb and O can form Pb2O, PbO, PbO2 and Pb3O4) and atomic arrangement (for example TiO2 is naturally found in the anatase, rutile and brookite polymorphs, with several other phases accessible synthetically). More realistic estimates place the total number of possible materials as a googol (10100), which is more than the number of atoms in the known universe (see discussions at http://hackingmaterials.com).

The search for new materials thus requires navigating a multidimensional landscape of bewildering complexity. The motivation, however, is strong. Every advance in technology, including those for energy generation, storage and conversion, requires or would benefit from new components. The objective is to reduce cost, increase performance or replace rare elements with more sustainable earth-abundant alternatives. Given the vast quantity of potential materials, even the most extensive high-throughput experimental or computational set-up will not succeed in screening all possibilities given realistic time and funding constraints. A key question is how to identify the specific arrangement of elements that produce the properties of interest as efficiently as possible? Writing in Nature Chemistry, Kenneth Poeppelmeier, Alex Zunger and co-workers have now tackled this issue using first-principles thermodynamics, and followed up their predictions with experimental validation1.

The rapid increase in computer processing power and the availability of large-scale supercomputers has placed

simulation at the forefront of the search for new materials2. Using quantum mechanical techniques, quantitative information on the structure and properties of a material can be provided at relatively modest computational and economic cost. Efforts such as the Materials Project have succeeded in tabulating the properties of many known inorganic systems, with more than 33,000 compounds in their current database3. For materials discovery, the most pragmatic approach is to introduce simulation constraints. By fixing the chemical composition, novel polytypes can be explored through crystal structure prediction, with many successes for microporous materials4. Alternatively, by fixing the crystal structure, the screening of different combinations of elements can be used to identify previously overlooked stable compositions5,6. As search algorithms are improving, such constraints are gradually being overcome7,8.

In the work of Poeppelmeier, Zunger and co-workers1, a valiant route was taken. They chose to fix the valence state of their target compounds to satisfy the 18-electron rule, and screen both the chemical composition and crystal structure. From 483 chemically plausible ternary compounds with 18 valence electrons, 83 have been previously reported, leaving 400 ‘missing’ compounds. A rigorous multi-step selection process was implemented (Fig. 1

shows one such process), and validated by ‘searching’ known compounds — the method did correctly predict their stability and structures. A crystal structure search was carried out to ensure a global minimum configuration was identified, and the vibrational spectrum of each candidate material was investigated to confirm its dynamic stability. Finally thermodynamic calculations were performed to ensure stability with respect to each competing phase. This screening procedure ensures that fanciful predictions of hypothetical compounds with exotic properties are avoided. In the end only 54 candidates survived — that is, were predicted to be stable — and of these, 15 new materials were successfully synthesized.

One of the roles of materials prediction in this study is to reduce the possible phase space and direct synthetic efforts to the most realistic and important targets. The simulations also provide valuable information to expedite the characterization of the novel compounds, ranging from predicted crystal structure parameters to vibrational and electronic spectral signatures. For all 15 materials predicted then synthesized in the study, the simulated and measured X-ray and electron diffraction patterns are in very good agreement. Although in the past materials modelling has been largely responsive to experiment, the predictive power of

INORGANIC MATERIALS

The quest for new functionalityBuilding on our understanding of the chemical bond, advances in synthetic chemistry, and large-scale computation, materials design has now become a reality. From a pool of 400 unknown compositions, 15 new compounds have been realized that adopt the expected structures and properties.

Aron Walsh

Structuralprediction

Propertysimulation

Targetedsynthesis

Chemicalinput

Figure 1 | A modular materials design procedure, where an initial selection of chemical elements is subject to a series of optimization and screening steps. Each step may involve prediction of the crystal structure, assessment of the chemical stability or properties of the candidate materials, before being followed by experimental synthesis and characterization. A material may be targeted based on any combination of properties, for example, a large Seebeck coefficient and low lattice thermal conductivity for application to heat-to-electricity conversion in a thermoelectric device.