quantifying irradiation defects in zr alloys: a comparison ... · springer berlin heidelberg new...

Nuclear Materials Research GroupDepartment of Mechanical and Materials Engineering

Levente Balogh1, Fei Long1, Zhongwen Yao1, Michael Preuss2, Hamidreza Abdolvand3, Mark Daymond1

1Department of Mechanical and Materials Engineering, Queen’s University, Kingston, ON, Canada

2The University of Manchester, Manchester Materials Science Centre, Grosvenor Street, Manchester, United Kingdom

3Department of Materials, University of Oxford, UK

Quantifying irradiation defects in Zr alloys: a comparison between transmission electron

microscopy and diffraction line profile analysis

Nuclear Materials Research Group • Department of Mechanical and Materials Engineering • Queen’s University, Kingston, Canada

2

Gary S. Was, “Fundamentals of Radiation Materials Science”,Springer Berlin Heidelberg New York, 2007.

Materials properties and microstructure are strongly related

GrowthIrradiation creep

M Griffiths, M.H. Loretto, R.E. SmallmanJ. Nucl. Materials, v115, p313, 1983


Comparing results by TEM & X-ray in Zr For cold-work dislocations, TEM & X-ray

populations seem to agree well (at low dislocation densities)

For irradiation dislocations, do not agree well, even at low densities.

(qualitatively yes, but not quantitatively) Want to have accurate density numbers for Plasticity models Irradiation creep & growth predictions

relaxation at stress concentration


Seeing dislocations by TEM & X-rayTEM X-rayDirect view & count Indirect via modelIndividual dislocations PopulationsLaborious / slow to get statistics

Quick & easy to get statistics

Can determine b Need to know possible b: estimateamounts of different b present

Can determine l, with work Can not determine lFCC get screw vs edge ratioHCP <a>:<a+c>:<c> ratio

Good at low to medium densities

Good at all densities (dependent on resolution of instrument)

Thin film effects Bulk average


5

nano-SiC-D sintered at 1820 oC at 8 GPa

nano-SiC-D sinteredat 2320 oC at 8 GPa

L. Balogh, S. Nauyoks, T. W. Zerda, C. Pantea, S. Stelmakh, B. Palosz, T. Ungár,Mater. Sci. Eng. A, 487, (2008) 180‐188.

Diffraction peak widths and shapes are correlated with the microstructure


6

2 2 2 2,exp 2size L gA L A L g L

Fundamental equation of diffraction line broadeningWarren & Averbach:

Fourier transformof a

broadened diffraction peakshape

Contribution ofcrystallite size

distributionContribution of the

microstrain distribution found in the specimen

Warren, B. E. and Averbach, B. L. (1950) J. Appl. Phys. 21, 595.Warren, B. E. (1959) Progr. Metal Phys. 8, 147-202.


7

for dislocation structures : 2,gL

2

2, 4g L

Cb f

0.5

LM

Wilkens, M. (1970b). Phys. Status Solidi A, 2, 359-370.Wilkens, M. (1987). Phys. Status Solidi A, 104, K1.Krivoglaz, M. A. (1969). Theory of X-ray and Thermal Neutron Scattering byReal Crystals. New York: Plenum PressUngár T., Borbély A. Appl. Phys. Lett. 69 (1996) 3173-3175.Ungár T., Tichy G. Phys. Status Solidi A 171 (1999) 425-434.

- Dislocation densityM - Dislocation arrangementC - Dislocation contrast factor => Burgers vector types

0.52

0

lndensME Gb

r

Nuclear Materials Research GroupDepartment of Mechanical and Materials Engineering

TT

M – the dislocation arrangement parameter

random correlated, high dipole character

E. Schafler, et al. Acta Mat. 53 (2005) 315-322.

Mrand Mcorr>>


9

T

gb

T g

b

gb 0dislocation is visible dislocation is invisible

strong contrast weak contrast

gb = 0

strong line broadening weak line broadening

C: the dislocation contrast factor carries information about the Burgers vector types present in the crystal


10

Jostsons, A., Kelly, P. M. and Blake, R. G., Journal of Nuclear Materials, 66 (1977) 236-256

gb 0 gb = 0

The effect of the dislocation contrast factors in TEM


1111

Physically modeled Experimentally determined

Measured pattern

Ungár T., Borbély A. Appl. Phys. Lett. 69 (1996) 3173-3175.

Ungár T., Tichy G. Phys. Status Solidi A 171 (1999) 425-434.

Ungár T., Gubicza J., Ribárik G., Borbély A. Journal of Applied Crystallography 34 (2001) 298.

Ribárik G., Gubicza J., Ungár T., Mat. Sci. Eng. A 387-389 (2004) 343-347.

IMeas < = > IStrain * ISize * IPlanarFault * IInstr + BG

The quantitative microstructure evaluation is performed using:

eCMWP (extended Convolutional Multiple Whole Profile) method


12The simultaneous modeling of multiple reflections, measured with high resolution and good counting statistics makes it possible to evaluate

quantitatively the microstructural parameters

G. Ribárik, N. Audebrand, H. Palancher, T. Ungár and D. Louër, J. Appl. Cryst. (2005). 38, 912–926


13

‐ The dislocation loops are approximated with polygons, N=274‐ The contrast factors of the individual edges are calculated using

ANIZC (A. Borbély, J. Dragomir‐Cernatescu, G. Ribárik, T. Ungár, J. Appl. Cryst. 36 (2003) 160‐162. )

Let us account for what we know about radiation defects - specific geometry model


Contrast factors in hexagonal polycrystalsfor any dislocation type have an hk.l dependence:

where x = (2/3)(l/ga)2 , g = 1/dhk.l

In a hcp polycrystal the dislocation contrast factors can be describedfor any hkl reflection by two parameters: q1 and q2

I. C. Dragomir & T. Ungár, J. Appl Cryst (2002) 35, 556.

Chk.l = Chk.0 [ 1 + q1x + q2x2]


15

The effect of ellipticity on the average contrast factors: <a> type dislocation loop in Zr.

0

0.1

0.2

0.3

0 0.4 0.8 1.2 1.6

1/3<1 1 -2 0>, [1 1 -2 0] a/b = 1/6a/b = 1/2a/b = 1a/b = 2a/b = 6

Aver

age

cont

rast

fact

or

x = (2/3)*(L/ga)^2

Chk.l

10.0 41.1 20.3 31.6 10.3 10.4 00.2

Chk.l = Chk.0 [ 1 + q1x + q2x2]


16

0

0.1

0.2

0.3

0 0.4 0.8 1.2 1.6

dislocations from plasticity<a>-loops, ellipticity of 1.5

Ave

rage

con

trast

fact

or

x = (2/3)*(L/ga)^2

Chk.l

10.0 41.1 20.3 31.6 10.3 10.4 00.2

Contrast for ‘typical’ population of cold‐work dislocations compared to a‐loops


17

<a>, n=[11‐20]g=1‐100

<a>, n=[11‐20]g=01‐10

<a>, n=[11‐20]g=10‐10

Contrast of the <a> loop, b=<11‐20> & n=[11‐20] type when viewed using a 10.0 type reflection

[0001]

Average 10‐10 Average 1‐100Average 01‐10


18Dislocation loop density from TEM measurements

Jostsons, A., Kelly, P. M. and Blake, R. G., Journal of Nuclear Materials, 66 (1977) 236-256.

Dislocation density:

Δ ∆ ∆ ∆ ∆

Uncertainty of the density:


19Neutron irradiated Zr-2.5Nb alloy

• Removed from pressure tubes in a CANDU reactor.• Cold worked prior to service.• 7 years of service.• 250C, close to the cooling water inlet.• Neutron fluence 1.6x1024/m2.

Samples provided by:Bruce Power and Chalk River Laboratories, CNL, Canada

Zr‐2.5Nb


20High resolution time‐of‐flight neutron diffraction measurements performed at theNeutron Powder Diffractometer (NPDF), Lujan Neutron Scattering Center, LANL

• NPDF can be used to collect goodquality data for Line Profile Analysis

d/d 0.15%

• World leader in pair distribution function (pdf) studies


21

9 9.6 10.2 10.8 11.4

Irradiated Zr-2.5NbUnirradiated Zr-2.5Nb

K (1/nm)

20.3 21.0 21.1 11.4 21.2 10.5 21.3

Inte

nsity

(a.u

.)

Significant line profile broadening is observed, which is strongly hk.l dependent


22

0

0.02

0.04

0.06

0.08

4 6 8 10 12

Unirradiated Zr-2.5NbIrradiated Zr-2.5Nb

FWHM

(1/nm

)

K (1/nm)

00.2

21.3

10.5

11.421.110.4

00.4

11.2

10.311.010.2

10.1

21.2

Full‐width at half maximum; Coarse representation of dislocation density / size


Effect of internal stress distributions not due to dislocations?

Estimate with CPFE calculation


24

0

0.02

0.04

0.06

0.08

4 6 8 10 12

Unirradiated Zr-2.5NbNeutron irradiated Zr-2.5Nb

Simulated residual thermal strains

Simulated residual strains after 4% tensile def (RD)

FWHM

(1/nm

)

K (1/nm)

Possible residual intergranular strains influence the accuracy of LPA measurements less than ~ 10%-15%


25

0

0.02

0.04

0.06

0.08

0 1 2 3 4 5 6

Unirradiated Zr-2.5NbIrradiated Zr-2.5Nb

KC1/2 (1/nm)

FWHM

(1/nm

)

≅0.9

2

Traditional expression1; just using FWHM, not doing full peak-fit

1. Ungár, T. (2008). Powder Diffr. 23, 125–132


26

0

0.04

0.08

0.12

9.5 10 10.5 11

Unirradiated Zr-2.5Nb

Measured pattern (every 2nd point shown)Theoretical patternDifference

Inten

sity (

a. u.)

K (1/nm) 0

0.04

0.08

0.12

9.5 10 10.5 11

Irradiated Zr-2.5Nb

Measured pattern (every 2nd point shown)Theoretical patternDifference

Inten

sity (

a. u.

)K (1/nm)Experimental

dataNon‐

irradiatedIrradiated

q1 0.51 ± 0.05 ‐0.42 ± 0.05

q2 ‐0.43 ± 0.05 ‐0.03 ± 0.05

Full pattern fit - neutron irradiated Zr-2.5Nb alloy


27

Sample Total dislocation density(1014 m‐2)

Dislocations created by plasticity (1014 m‐2)

Density of <a>‐type dislocation

loops(1014 m‐2)

Total ratio of<a> type

ratio of<c+a> type

Non‐irradiated Zr‐2.5Nb

5.8 ± 0.2 5.8 ±0.2

70% ±3%

30% ±3%

N/A

Irradiated Zr‐2.5Nb

20.4 ± 1.1 5.1 ±1.3

15.3 ± 2a/b = 1.5 ± 0.5

Dislocation densities obtained by using theoretical contrast factors specific to irradiation defects

Using cold-work populations to describe radiation: 24 ± 1Using just FWHM: 11 ± 1


28

Foil thickness, h 54 nmAverage loop size, <D> 4.35 nmDensity, 1.0E+15 nm-2

Bright field (BF) and weak‐beam dark field (WBDF) images of the same areaImage pair #5


29

0

20

40

60

80

0 2 4 6 8 10

Numb

er of

loop

s

Dislocation Loop Diameter (nm)

Histogram of the loop diameters measured in image pair #5

<D> = 4.35 nm


30Image pair # Dislocation

loop density

(1014 m-2)

Mean loop diameter <D>

(nm)

TEM foil thickness

(nm)

1 10.6 3.23 562 11.4 3.69 763 10.3 3.74 564 8.75 3.56 565 10.0 4.35 546 9.29 4.11 557 9.17 4.69 538 9.56 4.15 579 9.28 4.01 7810 8.24 3.72 7811 6.84 4.46 78

Average 9.4Standard deviation

1.17

Eleven BF‐WBDF image pairs were used to calculate the average dislocation density


31Source of uncertainty

Value Resulting uncertainty of

the dislocation loop density

(1014 m-2)Uncertainty of

<D> (nm)± 0.5 ± 1.18

Uncertainty of h (nm)

± 3 ± 0.45

Relative uncertainty of N

± 0.05 ± 0.47

Relative uncertainty of A

± 0.01 ± 0.09

Total uncertainty of the dislocation loop density

(1014 m-2)

± 2.2

Dislocation loop density from TEM:(9.4 ± 2.2)*1014 m-2

Estimated uncertainty of the dislocation loop density based on error propagation


32

Radiation defect densities obtained by:Transmission Electron

Microscopy (TEM)Diffraction line profile analysis

(DLPA)

(9.4 ± 2.2)x1014 m-2 (15.3 ± 2)x1014 m-2


33The simulated contrast of a loop:only 2/3 of the loops are visible in a TEM image created with {10.1}

0.6

0.1


34

Radiation defect densities obtained by:TEM TEM, corrected for

the loop contrast effect

Diffraction line profile analysis

(DLPA)

(9.4 ± 2.2)x1014 m-2 (14.1 ± 3.3)x1014 m-2 (15.3 ± 2)x1014 m-2


35Conclusions & summary

• Diffraction Line Profile Analysis (DLPA) is a powerful tool for the quantitative characterization of the microstructure, including irradiation damage.

• DLPA and microscopy methods (TEM, SEM, …) are complementary characterization techniques.

• Introducing specific microstructure models for irradiation defects can help with the interpretation of the diffraction data

• In this case it was possible to get agreement between the X-ray and TEM. Comparison between more samples irradiated under different conditions is required.


36

Acknowledgements

Thank you for your attention!

Kate Page, LANL, USA

Joan Siewenie, LANL, USA

Malcolm Griffiths, CNL, Canada

Colin Judge, CNL, Canada

Wenjing Li, CNL, Canada

quantifying irradiation defects in zr alloys: a comparison ... · springer berlin heidelberg new...

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