Xuebang Wu and C.S. Liu

Influence of alloying additions on grain boundary cohesion in tungsten: First-principles predictions

Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, PR China

2016 Joint ICTP/CAS/IAEA School and Workshop on PMI in Fusion Device

Background and objective

GB models and Methodology

Main results

Summary

Outline

Background

W is considered as the leading candidate for the PFM because of its excellent physical properties.

W exhibits serious embrittlement, such as low-T brittleness, irradiation brittleness and recrystallization brittleness.

Hurishita et al, Phys. Scr. T 159 (2014) 014032

Impurities, such as O and N, which segregate in the grain boundary (GB) are thought to be one of the main causes of intergranular fracture .

Background

Some effective ways to improve the properties:

Microalloying: solid solution with Ta, V, Re, Ti, Zr

Nanostructured alloys: ODS, TaC, TiC, ZrC GB engineering: optimize GB structure, grain size and texture

Tan et al., JNM 441, 661–666 (2013)

In all of these areas, understanding and controlling the properties of W at intergranular regions is highly valued, especially for the effect of impurities on the GB strength.

Background

• Since it is difficult to obtain effective information on the effects of impurity atoms on GB strength experimentally, theory study via FP calculations provides useful insight into the mechanism controlling the strength, toughness, and resistance to impurity embrittlement.

• Simulation studies have successfully used to study effects of solutes on GB strength in many metals, Fe, Al, Ni, Cu, Mg, and Zr.

Fe Geng, Olson, Freeman, Gao Science PRBAl Lu, Yamamoto, Olson PRB, Acta 2005-2012 Cu Finnis, Duscher, Kang Nature, NM, PRLNi Sob, Yamaguchi Science, Prog. Mater. Sci.Mg Nie Science 2013Zr Christensen JNM 2010

Two methods were adopted:

Background

1. Enegetics based on Rice-Wang model:(Embrittling impurities have stronger binding to surface than to GB)

Xseg GB BulkE E E

( ) ( )X XSE GB FS GB GB FS FSE E E E E E E

“+”“-”

Yamaguchi, Metall Mater Trans A 42A, 319 (2011)

“+”“-”

Background2. FP computational tensile test:(a uniaxial tensile strain is applied in the direction normal to GB plane )

0frac

E EES

max ( ) fracEf

e

W

W

W

W

PRB 82, 224107 (2010);Acta Mater. 59, 6155 (2011);Metall Mater Trans A 42A, 330 (2011)

Objective

To reveal the dependence of the GB strengthening on the GB structures and the solute itself To provide a reference in designing W-based materials with

improved cohesion by solutes

We focus on the segregation and strengthening behaviors of transition metal elements (3d, 4d and 5d) in a series of low-Σ symmetric tilt W GBs with [001], [110] and [111] tilt axes.

Solutes

Background and objective

GB models and Methodology

Main results

Summary

Outline

X

Y

Z

Grain Boundary

Free Surface

Free Surface

Grain 2

Grain 1

Vacuum

8 low-Σ symmetric tilt W GBs with [001], [110] and [111] tilt axes

6 substitutional sites along the GB/FS (1-6)

GB structures

Exper. Images Vs Models

Σ5(310) GB(Novoselov et al, Physics of the Solid State, 2014, 56, 1401-1407)

Σ3(112) GB(Lejcek P, Grain boundary segregation in metals: Springer Science & Business Media; 2010, Page 12)

• A first-principles method, DFT

• VASP code

• PAW-GGA

• Ecut: 500 eV

• Force on each atom : less than 10-3eV/Å

Methodology

GB structures

GB sliding and migration

Σ5(210)

Background and objective

GB models and Methodology

Main results

Summary

Outline

Segregation energy and strengthening energy

• Eseg is negative for undersized solutes, indicating that these atoms are stable in GBs. And they leads to a GB cohesion enhancement .

• For oversized solutes, the situation is complex. Eseg and ΔESE shows a positive or negative value at different positions.

Σ3(111)[110]

Common solutes Ti, V, Ta, Re, Hf and Ru

• γ , both Eseg and ΔESE .

• For Σ3(112), strengthening is weakest

• Ti, V and Ta do not show a strong segregation to GBs and their strengthening are less pronounced

• Hf and Ru remain in the GBs and increases the strength at Σ11(323) significantly

Dense segregation of atomsFor the segregation of dopant dimers at the same layer into the GB

Eseg are almost twice the values of single atoms. This indicates that the impurity atoms will occupy the most stable positions until all available positions are exhausted

Strengthening of dimers is roughly proportional to the planar concentration of the solute.

For dense segregation of atoms to different layers of the GB Segregation sequence of multiple atoms

and their effects on the GB strength were also studied, the results show that the GB strength does not vary significantly.Σ3(111)[110]

γ

• ΔESE increases with the increasing radius of solute. Size effect plays a major role in the solute effect on GB strength.

• For a certain metallic radius, ΔESE decreases with increasing γ. The solutes tends to increase the strength for GBs with larger γ values

Dependence of ΔESE on the metallic radii of solutes

General trend of ΔESE of solutes in different metals

• A similar trend is observed for the change of ΔESE of solutesacross the TM series.

• Variation trend of ΔESE may rely mainly on the properties ofsolutes but the magnitude depends on the solvent and the GBstructures.

FP tensile tests

0.0 0.1 0.2 0.3 0.4 0.5 0.60

2

4

6

8

Stage IIIStage II

Sep

arat

ion

ener

gy (J

/m2 )

Separation / nm

W bulk W GB W GB+Ru(2) W GB+Ru(1)

(a)

Stage I

0.0 0.1 0.2 0.30

10

20

30

Tens

ile st

ress

(GPa

)

Separation / nm

W bulk W GB W GB+Ru(2) W GB+Ru(1)

(b)

0.23 0.24 0.252526272829

Tens

ile st

ress

• Three distinctive stages exits during tensile test (Elastic, plastic,and broken).

• σmax is largest for bulk W (29.48 GPa), smaller for clean GB(26.52), and Ru segregation at site 1 causes a small reduction(26.38) and a slight increase (26.65) at site 2.

Σ3(111)[110]

saturation

I W(1)-W(4)<I W(1)-W(-4)<I W(1)-W(-2)<I W(1)-W(-2)<I Ru(2)-W(4)

Elastic Plastic Broken

Charge density during straining

The GB strengthening depends strongly on the GB structures.

For all GBs the strengthening energies of elements correlate positively with their metallic radii, implying that the size effect plays a major role in the GB strengthening in W.

The oversized solutes (Zr, Nb, Hf, Ta) act as cohesion enhancers when segregated in the GB plane, while the undersized elements (Ru, Rh, Re, Os, Ir) strengthen the GBs at the nearest neighbor positions.

The presence of Zr/Ta/Re impurity leads to an increase of the theoretical tensile strength and the GB cohesion, suggesting that the improved fracture resistance by Re, Ta and Zr originates mainly from the GB strengthening.

Summary

Thanks for your attention！Welcome to Hefei！

Test of GB structures

GBs Σ3(111) Σ5(310) Σ5(210)

No. of atoms

124 124 62 62 124 39 39 78

dvacuum (Å) 10 15 10 15 10 10 15 10

γ (J/m2) 2.29 2.29 2.23 2.18 2.19 3.12 3.11 3.14

Grain boundary energies (γ) of typical Σ3(111), Σ5(310) and Σ5(210) GBs with different numbers of atoms and vacuum thickness.

GB models

Schematic representation of the unit cells. (a) GB s. (b) bulk and (c) free surface

Case Positions ofTa atoms

Total segregation energy (eV)

Case Positions ofRe atoms

Total segregation energy (eV)

Ta -6 − Re -6 −1 -0.24 1 -0.212 0.45 2 -0.583 -0.13 3 -0.15

-0.01 4 -0.072Ta -6+1 − 2Re -6+1 −

1+2 0.46 1+2 -0.551+3 -0.15 1+3 -0.141+4 0.004 1+4 -0.0462+3 0.60 2+3 -0.45

3Ta -6+1+2 − 3Re -6+1+2 −1+3+(-2) 0.45 1+2+(-2) -0.381+3+(-3) -0.10 1+2+3 -0.06

1+3+2 0.51 1+2+(-3) -0.13

Segregation energies of multiple Ta or Re atoms at the different positions in the Σ3(111) GB.

Possible fracture paths for (a) W GB with an impurity atom in site 1, (b) site 2, (c) two impurity atoms in sites 1 and 3, (d) sites 1 and 2. The red and gray spheres represent the impurity atom and W atoms. Fracture surfaces are marked with dashed lines.

Case Positions of atoms Fracture path Fracture energy (J/m2)

Clean GB 1-1 4.66Ta 1 1-1 4.67Re 2 2-1 4.70

2-2 4.712-3 6.55

2Ta 1+3 3-1 4.673-2 4.783-3 5.633-4 4.78

2Re 1+2 4-1 4.704-2 4.684-3 6.57

TaRe 1+2 4-1 4.684-2 4.734-3 5.70

TaRu 1+2 4-1 4.744-2 4.664-3 5.68

Calculated fracture energies of pairs of 2Ta, 2Re, Ta/Re, and Ta/Ru atoms at the different positions in the Σ3(111) GB. The fracture energies for the preferred fracture paths are marked in bold.