Ab Initio Electronic Structure Calculations for Nuclear Materials

J.-P. Crocombette and F. Willaime

Commissariat a I’Energie Atomique, DEN, Service de Recherches de Metallurgie Physique, Gif-sur-Yvette, France © 2012 Elsevier Ltd. All rights reserved.

1.08.1

Introduction

224

1.08.2

Methodologies and Tools

224

1.08.2.1

Theoretical Background

224

1.08.2.2

Codes

225

1.08.2.2.1

Basis sets

225

1.08.2.2.2

Pseudoization schemes

226

1.08.2.3

Ab Initio Calculations in Practice

227

1.08.2.3.1

Output

227

1.08.2.3.2

Cell sizes and corresponding CPU times

227

1.08.2.3.3

Choices to make

228

1.08.3

Fields of Application

228

1.08.3.1

Perfect Crystal

229

1.08.3.1.1

Bulk properties

229

1.08.3.1.2

Input for thermodynamic models

229

1.08.3.2

Defects

229

1.08.3.2.1

Self-defects

229

1.08.3.2.2

Hetero-defects

230

1.08.3.2.3

Point defect assemblies

230

1.08.3.2.4

Kinetic models

230

1.08.3.2.5

Extended defects

230

1.08.3.3

Ab Initio for Irradiation

230

1.08.3.3.1

Threshold displacement energies

230

1.08.3.3.2

Electronic stopping power

230

1.08.3.4

Ab Initio and Empirical Potentials

231

1.08.4

Metals and Alloys

231

1.08.4.1

Pure Iron and Other bcc Metals

232

1.08.4.1.1

Self-interstitials and self-interstitial clusters in Fe and other bcc metals

232

1.08.4.1.2

Vacancy and vacancy clusters in Fe and other bcc metals

234

1.08.4.1.3

Finite temperature effects on defect energetics

235

1.08.4.2

Beyond Pure Iron

236

1.08.4.2.1

helium-vacancy clusters in iron and other bcc metals

236

1.08.4.2.2

From pure iron to steels: the role of carbon

236

1.08.4.2.3

Interaction of point defects with alloying elements or impurities in iron

237

1.08.4.2.4

From dilute to concentrated alloys: the case of Fe-Cr

237

1.08.4.2.5

Point defects in hcp-Zr

238

1.08.4.3

Dislocations

238

1.08.5

Insulators

240

1.08.5.1

Silicon Carbide

240

1.08.5.1.1

Point defects

240

1.08.5.1.2

Defect kinetics

241

1.08.5.1.3

Defect complexes

242

1.08.5.1.4

Impurities

242

1.08.5.1.5

Extended defects

243

1.08.5.2

Uranium Oxide

243

1.08.5.2.1

Bulk electronic structure

243

1.08.5.2.2

Point defects

244

1.08.5.2.3

Oxygen clusters

244

1.08.5.2.4

Impurities

245

1.08.6

Conclusion

245

References

246

Abbreviations

bcc

Body-centered cubic

CTL

Charge transition levels

DFT

Density functional theory

DLTS

Deep level transient spectroscopy

EPR

Electron paramagnetic resonance

fcc

Face-centered cubic

FLAPW

Full potential linearized augmented plane waves

FP

Fission products

GGA

Generalized gradient approximation

LDA

Local density approximation

LSD

Local spin density approximation

LVM

Local vibrational modes

PAW

Projector augmented waves

PL

Photo-luminescence

RPV

Reactor pressure vessel

SIA

Self-interstitial atom

SQS

Special quasi-random structures

TD-DFT

Time dependent density functional theory

1.08.1 Introduction

Electronic structure calculations did not start with the so-called ab initio calculations or in recent years. The underlying basics date back to the 1930s with an understanding of the quantum nature of bonding in solids, the Hartree and Fock approximations, and the Bloch theorem. A lot was understood of the elec­tronic structure and bonding in nuclear materials using semiempirical electronic structure calculations, for example, tight binding calculations.1 The impor­tance ofthese somewhat historical calculations should not be overlooked. However, in the following sections, we focus on ‘ab initio’ calculations, that is, density functional theory (DFT) calculations. One must acknowledge that ‘ab initio calculations’ is a rather vague expression that may have different meanings depending on the community. In the present chapter we use it, as most people in the materials science community do, as a synonym for DFT calculations.

The popularity of these methods stems from the fact that, as we shall see, they provide quantitative results on many properties of solids without any adjustable parameters, though conceptual and technical difficul­ties subsist that should be kept in mind. The presen­tation is divided as follows. Methodologies and tools are briefly presented in the first section. The next two sections focus on some examples of ab initio results on metals and alloys on one hand and insulating materials on the other.