Density functional calculations for small iron clusters
with substitutional phosphorus
T. Nakazawa, T. Igarashi,T.Tsuru,
Y. Kaji and S. Jitsukawa
Japan Atomic Energy Agency
nakazawa.tetsuya@jaea.go.jp

14th International Conference on Fusion Reactor Materials (ICFRM-14)
September 6-11, 2009
Sapporo, JapanAbstract
The embrittlement is known to be caused by phosphorus (P)segregation at grain boundaries (BGs) in iron (Fe) alloy. Effects of P
substitutions on binding energies and electronic structures ofoctahedral Fe cluster are investigated using density functionalcalculations in order to understand nature of bonding between Pand Fe atoms at GBs. The binding energies increase in Fe3P3 andFe-rich clusters while they decrease in P-rich clusters. The changesof binding energies are closely connected to the charge transferfrom Fe to P atoms. The charge transfer leads to both stronger andweaker bonds in mixed Fe-P clusters. The weaker bonds due toless charge occur embrittlement. The calculations indicate that thebinding energies and chemical bondings are affected by atomic
configurations of P atoms in Fe-P clusters.

Background and Objective
BackgroundThe embrittlement in Fe alloy under thermal or irradiation environmentis the serious issue for structural materials in fusion and fission reactors.
The embrittlement is closely connected to the segregation of impurities
at GB.
The impurity segregation at the GBs is promoted by irradiation.
P atom is one of the impurities in Fe alloy, and is considered to be one of
the embrittling elements.
The P segregation is believed to weaken cohesion at Fe GBs.

Objective
Understanding on effects of P atoms segregated at Fe GBs.
We perform ab initio calculations on the changes of binding
energies and structural and electronic properties of Fe6 cluster
induced by P substitutions.

Summary
Our DFT calculations predict effects of P substitutions for equilibrium geometry,binding energy and electron properties of Fe6 clusters. Based on the calculations
the effects of chemical bonding on GB embrittlement is considered. The changes ofbinding energies in Fe-P clusters are found to be closely connected to the chargetransfer from Fe to P atoms. As shown by calculations of Fe3P3 and Fe-rich clusters,a small number of P atoms stabilize the Fe GBs as well as lead to the strengtheningof Fe-P bonds and the weakening of Fe-Fe bonds. The weaker bondings due to lesscharge occur embrittlement while the stronger bondings due to more charge
stabilize GBs. In contrast to this, a large number of P atoms, which is adjacent toeach other, induce unstable GBs due to weaker Fe-P and P-P bondings, and theweaker bondings occur embrittlement.

Atomic configurations of GBs with P-enrichment induced by irradiation are complex.
As shown by our calculations, the cause of P embrittlement is affected by the atomic
configurations of P atoms in GB. Thus, the effects of more than one P segregation
should not be neglected.

Computational details
Theory: DFT-(U)B3LYP/LanL2DZ
Code: Gaussian03
Clusters: Fe6-xPx (0≤x≤6)
Binding energies (Eb): The binding energies per atom ofclusters are calculated with respect to the Fe atom with
M = 5 and P atom with M = 4. M means spin multiplicities.
Natural population analysis: electron configuration, natural
population and natural atomic orbital (NAO) bond order
are calculated.

Optimized Fe-P clusters
523146(a) Fe6 (D4h)(b) Fe5P (C4v)(c) Fe4P2 (D4h) (d) Fe4P2 (C2v)(f) Fe3P3 (C2v)(g) Fe2P4 (D4h) (h) Fe2P4 (C2v)(e) Fe3P3 (C3v)(i) FeP5 (C4v):Fe atom,(j) P6 (D4h):P atomBinding energies, bond lengths, and NAO
bond orders of Fe-P clusters
Re

NAO bond order

SystemSymm.

M

EbFe-Fe

Fe6

D4h

21

1.85

2.43, 2.45

Fe5PC4v

162.002.42, 2.53

2.49

0.28, 0.34,
0.38

0.39, 0.40

Fe4P2D4h13

2.11

2.42

2.50

0.22

0.37, 0.40

C2v

13

2.19

2.56, 2.74

2.38, 2.40

3.72

0.23, 0.28

0.49, 0.44

0.07

C3v

12

1.97

2.46

2.60

2.50

0.41

0.29

0.54

C2v

10

2.06

2.46, 2.67

2.34, 2.36,
2.42

3.47

0.14, 0.12

0.46, 0.48,
0.42

0.10

D4h

7

1.83

2.37

2.82

0.37, 0.38

0.37

C2v

7

1.86

2.37, 2.48

2.23, 3.07

0.48, 0.34

0.89, 0.21

FeP5

C4v

4

1.58

2.48

2.57, 2.76

0.33, 0.35

0.49, 0.35

P6

D4h

31.09Fe3P3

Fe2P4

2.37

Fe-P

P-P

Fe-Fe

Fe-P

P-P

0.36

2.61, 2.82

0.25

0.45, 0.26

Eb: eV/atom, Re: ÅNatural electron configurations and naturalpopulations of Fe-P clusters (1)SystemSymm.

Atom

Natural electron configuration

Natural population

Fe6

D4h

Fe(1-4)[core]4s1.093d6.814p0.085s0.014d0.02

0.00

Fe(5, 6)

[core]4s1.093d6.804p0.085s0.014d0.02

0.01

Fe(1, 3)

[core]4s0.863d6.824p0.064d0.015s0.014d0.01

0.24

Fe(2, 4)

[core]4s0.743d6.934p0.064d0.010.25

P(5)[core]3s1.903p4.01

-0.91

Fe(6)

[core]4s1.183d6.764p0.105s0.024d0.01-0.06

Fe(1, 3)

[core]4s0.583d6.844p0.044d0.01

0.53

Fe(2, 4)

[core]4s0.623d6.924p0.034d0.015p0.01

0.41

P(5, 6)[core]3s1.913p4.02-0.94

Fe(1,2)[core]4s0.853d6.824p0.074d0.01

0.24

P(3,4)[core]3s1.913p3.88-0.80

Fe(5,6)[core]4s0.603d6.784p0.054d0.02

0.55

Fe(1, 2, 5)[core]4s0.813d6.644p0.084d0.01

0.44

P(3, 4, 6)[core]3s1.903p3.54

-0.44

Fe5P

Fe4P2C4v

D4hC2v

Fe3P3C3v

Natural electron configurations and naturalpopulations of Fe-P clusters (2)SystemSymm.

Atom

Natural electron configuration

Natural population

Fe3P3

C2v

Fe(1)

[core]4s0.543d6.854p0.054d0.01

0.55

P(2, 4)[core]3s1.913p3.80

-0.72

P(3)

[core]3s1.933p3.48-0.42

Fe(5, 6)

[core]4s0.523d6.764p0.054d0.025p0.01

0.65

P(1-4)[core]3s1.913p3.36-0.27

Fe(5, 6)

[core]4s0.383d7.014p0.044d0.02

0.54

Fe(1, 2)

[core]4s0.553d6.774p0.064d0.025p0.01

0.61

P(3, 4)[core]3s1.873p3.264p0.01-0.14

P(5,6)[core]3s1.933p3.53-0.47

P(1, 3)[core]3s1.913p3.29-0.21

P(2, 4)[core]3s1.913p3.22

-0.14

Fe(5)

[core]4s0.413d6.884p0.054d0.01

0.64

P(6)

[core]3s1.873p3.074p0.01

0.05

P(1-4)[core]3s1.933p3.09

-0.02

Fe2P4

D4h

C2v

FeP5P6C4v

D4h

Calculations on Fe6 cluster
Our calculated bond lengths are consistent with the previousresults (2.29 - 2.53 Å) and are very close to nearest
neighbour distance of bulk iron (2.48 Å), while calculated
binding energy is smaller than the previous results (3.77 eV/atom).
The electron configuration calculated for Fe atom is
4s1.093d6.80 which is very close to that of the metal or large
clusters (4s13d7).

Calculations on P6 cluster
For P6 (D4h) cluster, our calculations find the M=3 ground state withbond length of 2.61 - 2.82 Å and binding energy of 1.09 eV/atom.
The previous LSDA calculations based on the Car-Parrinello method
on various structure of P6 have predicted that bond length range from2.01 to 2.40 Å. The binding energies of P6 (C2v and D3h) clusters
calculated using the generalized gradient approximations havepredicted to be 3.06 and 3.02 eV/atom, respectively.
The above differences between our calculations and previous
calculations result from different treatment of electron in clusters
rather than differences in structure and exchange-correlation energy.
The spin-restricted calculations generally lead to shorter bond lengths
and larger binding energies because of neglecting the spin dependenceof exchange and correlation.

Effects of P substitutions (1)Effects on binding energy:
Fe3P3 and Fe-rich clusters have larger binding energies.
P-rich clusters have smaller binding energies.
Effects on bonding strength:
In the Fe3P3 (C2v) and Fe-rich clusters, the stronger Fe-P and weaker
Fe-Fe bondings caused by the charge transfer due to the P
substitutions.
In Fe3P3 (C3v) cluster, stabilization of Fe3 and P3 units lead to theweaker Fe-P bonding.
In P-rich clusters, decrease in binding energies corresponds to theweaker Fe-P and P-P bondings.

Effects of P substitutions (2)Effects on electronic structure:
The P substitution causes the charge transfer from Fe to P atoms.
The charge transfer leads to the stronger and weaker bondings inFe-P clusters.

The P embrittlement of Fe GB is closely connected with thechange of electronic structure due to atomic configurations of P
atoms in GBs.

Thank you for your stop.
If you have a interest in this work,
please contact me.
Email: nakazawa.tetsuya@jaea.go.jp