The Precipitation of Hydrides in Zirconium Alloys

253 Pages·2015·11.19 MB·English

by  Matthew S. Blackmur

T P H
HE RECIPITATION OF YDRIDES IN
Z A
IRCONIUM LLOYS
A thesis submitted to The University of Manchester for the degree of Doctor of
Philosophy, in the Faculty of Engineering and Physical Sciences

MATTHEW SEBASTIAN BLACKMUR

2015 ◦ MMXV
MATERIALS PERFORMANCE CENTRE
SCHOOL OF MATERIALS
The Precipitation of Hydrides in Zirconium Alloys

Contents
Table of Figures .............................................................................................................................. 4
Table of Tables ............................................................................................................................... 7
Table of Equations ......................................................................................................................... 8
Abstract .......................................................................................................................................... 9
Declaration ................................................................................................................................... 10
Copyright Statement .................................................................................................................... 10
Acknowledgements ...................................................................................................................... 12
1. Introduction ......................................................................................................................... 13
1.1. The Nuclear Reactor ........................................................................................ 13
1.2. The Reactor Core ............................................................................................. 17
1.3. Nuclear Fuel Cladding ...................................................................................... 18
1.4. Structure, Justification and Aims of Thesis ....................................................... 20
2. Literature Review ................................................................................................................. 23
2.1. Zirconium Fundamentals ................................................................................. 23
2.1.1. Origins ........................................................................................................ 23
2.1.2. Non-Nuclear Uses ...................................................................................... 24
2.1.3. Common Alloys .......................................................................................... 24
2.1.4. Microstructure and Properties .................................................................. 26
2.2. In-Reactor Degradation of Zirconium ............................................................... 33
2.2.1. Aqueous Corrosion .................................................................................... 33
2.2.2. Hydriding of Zirconium .............................................................................. 36
2.2.3. The Impact of Hydrides .............................................................................. 48
2.3. X-Ray Diffraction .............................................................................................. 56
2.3.1. Fundamentals ............................................................................................ 56
2.3.2. The Synchrotron Accelerator and X-Ray Diffraction .................................. 59
2.3.3. Synchrotron Studies of the Zirconium-Hydrogen System .......................... 62
3. Methodology........................................................................................................................ 67
3.1. Sample Specifications ...................................................................................... 67
1 | Contents
The Precipitation of Hydrides in Zirconium Alloys

3.1.1. Base Material ............................................................................................ 67
3.1.2. Hydrogen Charging .................................................................................... 70
3.2. Synchrotron X-Ray Diffraction ......................................................................... 70
3.3. In-Situ Environment ......................................................................................... 72
3.4. Thermal Operations ......................................................................................... 74
3.4.1. Non-Hydrogen-Charged Sample (S1)......................................................... 74
3.4.2. Hydrogen-Charged Sample (S2) ................................................................ 76
3.5. Data Reduction and Pre-Analysis ..................................................................... 78
3.5.1. Deconvolution of Material Reflection Profiles ........................................... 78
3.5.2. Debye-Scherrer Ring Integration ............................................................... 83
3.6. Quantitative Analysis of Diffraction Patterns .................................................. 85
3.6.1. Single Reflection Analysis .......................................................................... 86
3.6.2. The Rietveld Method for Structural Model Refinement ............................ 87
3.6.3. Preparation for Rietveld Refinement of Structural Models ....................... 92
3.6.4. Application of the Rietveld Method for Refinement ................................. 93
3.6.5. The Le Bail Method for Structural Model Refinement .............................. 97
3.6.6. Application of the Le Bail Method for Refinement .................................... 98
3.7. Data Analysis ................................................................................................... 99
3.7.1. Phase Weight Percentages ...................................................................... 100
3.7.2. Strain Evolution ....................................................................................... 101
3.8. Experimental Discrepancies .......................................................................... 102
3.8.1. Temperature Measurement .................................................................... 102
3.8.2. Non-Systematic Noise ............................................................................. 105
3.8.3. Hydrogen Concentration ......................................................................... 107
4. First Proposed Manuscript – Diffusion ............................................................................... 113
4.1. Foreword ....................................................................................................... 113
4.2. Manuscript .................................................................................................... 114
4.3. Annex – Phase Field Modelling ...................................................................... 146
4.3.1. Background ............................................................................................. 146
Contents | 2
The Precipitation of Hydrides in Zirconium Alloys

4.3.2. Results ...................................................................................................... 149
5. Second Proposed Manuscript – Kinetics ............................................................................ 156
5.1. Foreword........................................................................................................ 156
5.2. Manuscript ..................................................................................................... 157
5.3. Annex – Transmission Electron Microscopy ................................................... 185
6. Third Proposed Manuscript – Strain Evolution .................................................................. 189
6.1. Foreword........................................................................................................ 189
6.2. Manuscript ..................................................................................................... 190
7. Additional Manuscripts ...................................................................................................... 224
8. Final Conclusions ................................................................................................................ 225
9. Further Work ..................................................................................................................... 229
9.1. Non-Hydrogen-Charged Sample (S3) ............................................................. 230
9.2. Hydrogen Charged Sample (S4) ..................................................................... 231
10. Appendices .................................................................................................................... 233
10.1. Appendix I – Rietveld Refined Structural Model (TOPAS INP Format)........ 233
10.2. Appendix II – Le Bail Refined Structural Models (TOPAS INP Format) ........ 235
11. Bibliography ................................................................................................................... 237

A thesis composed of 83043 words.
3 | Contents
The Precipitation of Hydrides in Zirconium Alloys

Table of Figures
Figure 1. Schematic of a Boiling Water Reactor (BWR) [9]. ......................................................... 15
Figure 2. Schematic of a Pressurised Water Reactor (PWR) [9]. ................................................. 16
Figure 3. Schematic diagram of fuel rod, coolant and control rod interaction [7]. ..................... 18
Figure 4. Scale schematics of (a) α-zirconium hexagonal close packed (b) β-zirconium body
centered cubic and (c) δ-hydride face centered cubic crystal structures. ................................... 28
Figure 5. Pure zirconium pressure-temperature phase diagram (reproduced from [40]). .......... 29
Figure 6. Weight gain as a function of oxidation time up to 100 days at 400 °C (reproduced from
[52]). ............................................................................................................................................ 32
Figure 7. Hydrogen pickup performance of zircaloy-4 with average burnup [70]. ...................... 35
Figure 8. Zirconium-hydrogen binary phase diagrams illustrating two alternative possibilities for
the stability of the δ- and γ-phases (reproduced from [80]). ...................................................... 37
Figure 9. Hydrogen evolution with temperature in Zircaloy-4 sheet (reproduced from [90]). .... 39
Figure 10. TEM observation of γ-phase micro-hydride stacking in Zircaloy-2, with a schematic
diagram of the impact of stacking geometry on apparent macro-hydride trace (reproduced from
[99]). ............................................................................................................................................ 42
Figure 11. Three inter-granular hydride forms, (a) along both boundary sides, (b) cross boundary,
(c) along boundary one side (reproduced from [82]). ................................................................. 43
Figure 12. Matrix-hydride crystallographic orientation relationship. .......................................... 43
Figure 13. TEM and SAD images of Zircaloy-2 showing both α and δ phases (reproduced
from [103]). ................................................................................................................................. 44
Figure 14. Effect of applied tensile stress on hydride orientation, (a) unstressed orientation,
(b) stress induced reorientation perpendicular to applied load (reproduced from [108]). ......... 46
Figure 15. The mechanical effect of hydriding [15] (reproduced from (a) [123] and (b) [122]). . 50
Figure 16. Micrograph of hydride reorientation and failure through DHC produced by notching a
specimen (reproduced from [131]). ............................................................................................ 53
Figure 17. DHC rate as a function of thermal history (reproduced from [140]). ......................... 55
Figure 18. Schematic of the crack velocity to stress intensity factor relationship for DHC,
(reproduced from [140]). ............................................................................................................ 56
Figure 19. The interaction between scattered waves, showcasing (a) destructive and
(b) constructive interference [142]. ............................................................................................ 57
Figure 20. Schematic representations of (a) Debye-Scherrer diffraction cones,
(b) a Debye-Scherrer ring pattern and (c) a diffractogram. ......................................................... 58
Figure 21. (a) Bragg-Brentano (reflection) and (b) Debye-Scherrer (transmission), and
(c) image plate diffraction geometries. ....................................................................................... 59
Table of Figures | 4
The Precipitation of Hydrides in Zirconium Alloys

Figure 22. The European Synchrotron Radiation Facility, photograph reproduced from [151]. .. 62
Figure 23. Sample physical geometry. ......................................................................................... 67
Figure 24. Representative (a) high magnification grain map and (b) low magnification texture and
orientation map, with associated pole figure. ............................................................................. 69
Figure 25. (a) Diffraction geometry, (b) sample-detector distance variation and (c) geometry for
calculating sample-detector distance. ......................................................................................... 71
Figure 26. ElectroThermal Mechanical Tester (ETMT) sample mounting schematic. .................. 74
Figure 27. Thermal profile and gauge volume displacement relative to material axial centre as a
function of time for the non-charged sample (S1). ...................................................................... 75
Figure 28. Thermal profile and gauge volume displacement relative to material axial centre as a
function of time for the hydrogen-charged sample (S2). ............................................................. 77
Figure 29. Diffraction patterns from (a) cerium dioxide (a standard reference material), and
(b) hydrogen charged Zircaloy-4 (S2). .......................................................................................... 78
Figure 30. Lanthanum hexaboride (a) Debye-Scherrer rings, and (b) diffractogram. .................. 80
Figure 31. The experimental profile compared with the CuK emission profile........................... 82
α
Figure 32. Partial integration positions and ranges...................................................................... 84
Figure 33. A schematic of a single reflection (points) modelled with a profile function (solid line),
with residuals plotted (undulating line at zero axis), Full Width Half Maximum (FWHM) and
centroid marker (vertical line) added. ......................................................................................... 87
Figure 34. Unit cell schematic showing length and angle parameters [197]................................ 90
Figure 35. Schematic showing multiple solutions to reflection overlap during analysis of a single
Bragg reflection. ........................................................................................................................... 91
Figure 36. Increasing the number of Bragg reflections considered in conjunction with performing
full pattern simulation potentially provides a single solution. ..................................................... 91
Figure 37. Observed diffraction pattern from sample S2 at 40 °C using (a) linear and (b) logarithmic
scales, and (c) spatial positions of Bragg reflections. ................................................................... 93
Figure 38. Excessive reflection drift from a lack of limits, after reflection extinction. ................. 96
Figure 39. Pyrometer temperature as a function of thermocouple temperature. .................... 103
Figure 40. Lattice parameter evolution during C1, comparing the thermocouple and pyrometer
as measures of temperature. ..................................................................................................... 104
Figure 41. Non-systematic noise in phase profile intensity, with comparatively noise free weight
fraction data............................................................................................................................... 106
Figure 42. Phase profile intensity noise (a) as a function of current, and (b) represented as a
histogram of intensity values. .................................................................................................... 107
Figure 43. Terminal solid solubility determination using the offset method. ............................ 108
Figure 44. Modelled matrix lattice distortion from dissolved hydrogen. ................................... 110
5 | Table of Figures
The Precipitation of Hydrides in Zirconium Alloys

Figure 45. Chemically induced lattice dilatation in the ‘a’ lattice parameter. ........................... 111
Figure 46. Single hydride phase field model simulation showing (a) XX planar stress, (b) YY planar
stress, (c) XY shear stress, and (d) the Von Mises stress, for a single hydride measuring 190 nm
after 0.01 seconds of precipitation. .......................................................................................... 149
Figure 47. Hydrogen concentration relative to the initial uniform hydrogen content. ............. 151
Figure 48. Calculated hydrostatic stress map. ........................................................................... 152
Figure 49. (a) Experimentally observed hydride strings/stacks in Zircaloy-4 [218], and (b) hydride
precipitation simulations after 0.01 seconds, demonstrating the result of potential sympathetic
nucleation. ................................................................................................................................. 154
Figure 50. Zircaloy-4 TEM micrograph at 17,000x magnification, observed in the 0002𝛼 direction.
.................................................................................................................................................. 185
Figure 51. (a) Geometry boxes drawn on large hydrides, (b) nearest neighbour
centroid-to-centroid distances, (c) projections of hydride major axes for relative angle
measurements, and (d) identification of small hydrides from ‘coffee-bean’ contrast strain lobes,
and potential SPPs. .................................................................................................................... 186
Figure 52. ‘Coffee-bean’ strain contrast features, thought to be hydrides, at (a) 350,000x,
(b) 125,000x, (c) 125,000x, and (d) 26,000x magnification. ...................................................... 188
Figure 53. Other potential hydride-like features at 86,000x magnification............................... 188
Figure 54. (a) Sample S3 and S4 geometry (b) finite element simulation of the stress fields
established under a 250 N applied load. ................................................................................... 229
Figure 55. Non-charged sample tri-axial strain field mapping of sample S2. ............................. 231
Figure 56. Charged sample notch tip hydride mapping of sample S3 under applied load. ....... 232
Table of Figures | 6
The Precipitation of Hydrides in Zirconium Alloys

Table of Tables
Table 1. Neutron capture cross sections for elements with relatively high melting
temperatures [13]. ....................................................................................................................... 20
Table 2. Standard compositions for zirconium alloys in weight percentages [27,29,32–34]. ...... 26
Table 3. Zirconium lattice parameters, crystal structure and stable temperatures [35]. ............. 28
Table 4. Zirconium hydride compositions & crystallographic structures [61,81]. ........................ 37
Table 5. Matrix-hydride interfacial strains (Barrow et al.)/stress free transformation strains
(Carpenter) [85,86]. ..................................................................................................................... 38
Table 6. Zircaloy-4 chemical composition. ................................................................................... 67
Table 7. Sample descriptions and as-charged hydrogen concentrations. .................................... 70
Table 8. Thermocouple and pyrometer linear model parameters. ............................................ 103
Table 9. Solubility temperatures and hydrogen concentration calculated from the offset method.
................................................................................................................................................... 109
Table 10. Sample descriptions and calculated hydrogen content. ............................................. 112
Table 11. Phase field modelling parameters. ............................................................................. 148
Table 12. Maximum compressive and tensile stresses in the matrix. ........................................ 150
Table 13. Sample specifications revisited................................................................................... 230
7 | Table of Tables
The Precipitation of Hydrides in Zirconium Alloys

Table of Equations
Equation 1 ................................................................................................................................... 33
Equation 2 ................................................................................................................................... 58
Equation 3 ................................................................................................................................... 72
Equation 4 ................................................................................................................................... 85
Equation 5 ................................................................................................................................... 88
Equation 6 ................................................................................................................................... 88
Equation 7 ................................................................................................................................... 97
Equation 8 ................................................................................................................................. 100
Equation 9 ................................................................................................................................. 101
Equation 10 ............................................................................................................................... 101
Equation 11 ............................................................................................................................... 102
Equation 12 ............................................................................................................................... 105
Equation 13 ............................................................................................................................... 109
Equation 14 ............................................................................................................................... 109
Equation 15 ............................................................................................................................... 109
Equation 16 ............................................................................................................................... 152
Table of Equations | 8
The Precipitation of Hydrides in Zirconium Alloys

Abstract
This alternative format thesis is submitted by Matthew Sebastian Blackmur to The
University of Manchester for the degree of Doctor of Philosophy in the year of 2015,
entitled “The Precipitation of Hydrides in Zirconium Alloys”. The thesis first introduces
the topic of nuclear energy and provides a brief section on plant familiarisation, after
which zirconium nuclear fuel cladding is explained, and an in-depth literature review is
presented on the in-service degradation of this component from hydriding. The concept
of synchrotron X-ray diffraction is elucidated, and examples of its use are given, relevant
to the topic of this work.
The experimental section discusses an initial quantification of the Zircaloy-4
material used throughout the present work, and documents in minutia the process of
collecting and analysing in-situ synchrotron X-ray diffraction data. The experimental
campaign discussed within involved a series of consecutive thermal cycles designed to
investigate the redistribution of hydrogen as a function of thermal and concentration
gradients; the kinetics of precipitation during isothermal dwells at reactor relevant
temperatures; and the evolution of strain in the matrix and hydride during these dwells.
As an alternative style thesis, these three topics are separated into three independent
proposed manuscripts, produced in a format ready for publication.
The diffusion and redistribution paper observes localised enrichment and
depletion that occurs as a function of time and temperature, investigating the flux of
hydrogen that results from concentration and thermal gradients, and introduces the
concept of hydrogen trapping. The second manuscript documents evidence of the rate
limiting kinetics for hydride precipitation seen at elevated temperatures, and describes a
model for nucleation, developed to support the experimentally produced results. The
final manuscript investigates the nature of the strains that evolve in the matrix and
hydride phases during precipitation and growth, highlighting slow-strain rate relaxation
in both phases and examining the constraining effect that the matrix has on the hydride
precipitates.
Lastly, the themes from each of the three manuscripts are drawn together in a
final conclusion, after which further experimental analysis that is to be performed as part
of this experimental campaign is outlined.
9 | Abstract