Abstract
Precise control and characterization of coating thickness are critical for ensuring the reliability and safety integrity of zirconium alloy claddings used in nuclear reactors.However conventional thickness measurement techniques are often limited by destructive testing requirements, low efficiency, or restricted applicability to complex geometries. In this study, the Energy-Dispersive X-ray Fluorescence (EDXRF) technique combined with the fundamental parameter (FP) method is proposed as a rapid, accurate, and non-destructive approach for determining the thickness of zirconium alloy coatings. The theoretical basis of EDXRF and the implementation of the FP algorithm are described, followed by a systematic evaluation of their applicability to zirconium-based coatings with varying thicknesses. Experimental validation demonstrates that the relative error of the measured thickness can be maintained within ±5%, confirming the robustness and reliability of this method. The proposed FP-EDXRF approach provides a promising tool for quality assurance and process optimization of zirconium alloy coatings in the nuclear power industry.
Full Text
Preamble
Thickness Determination
Method
Based Energy-Dispersive X-Ray
Fluorescence and Application in Zirconium Alloy Coatings
Yongli Zhang Cheng Hailiang First Research Institute, Nuclear Power Institute China, Chengdu 610005, China; College Nuclear Technology Automation Engineering, Chengdu University Technology, Chengdu 610000, China; Nuclear Physics Department, China Institute Atomic Energy, Beijing 102413, China E-mail:
Abstract
Precise control characterization coating thickness critical ensuring reliability safety integrity zirconium alloy claddings nuclear reactors.
However conventional thickness measurement techniques often limited destructive testing requirements, efficiency, restricted applicability complex geometries. study, Energy-Dispersive X-ray Fluorescence (EDXRF) technique combined fundamental parameter
method
proposed rapid, accurate, non-destructive approach determining thickness zirconium alloy coatings. theoretical basis EDXRF implementation algorithm described, followed systematic evaluation their applicability zirconium-based coatings varying thicknesses.
Experimental validation demonstrates relative error measured thickness maintained within confirming robustness reliability method. proposed EDXRF approach provides promising quality assurance process optimization zirconium alloy coatings nuclear power industry. words:
Energy-dispersive X-ray fluorescence; fundamental parameter method;
zirconium alloy; coating thickness; non-destructive testing
1. Introduction
Zirconium alloys, widely nuclear claddings their neutron absorption, mechanical properties, corrosion resista enhance accident tolerance, coatings applied, offering excellent corrosion resistance irradiation stability high-temperature steam oxidation resistance high-temperature diffusivity However, loss-of-coolant accidents (LOCAs), zirconium alloy cladding tubes maintain their structural integrity.
Specifically, zirconium reacts (during service high-temperature, high-pressure water superheated steam) zirconium dioxide hydrogen reaction releases substantial amounts hydrogen. these cases, coatings degrade through oxidation, blistering, spallation, ultimately exposing substrate promoting hydrogen uptake Accurate measurement coating thickness therefore crucial evaluating their protective performance service reliability.
Currently, several
methods
exist measuring thickness zirconium alloy coatings, including ultrasonic pulse reflection ultrasonic scanning microscopy current testing cross-sectional metallographic techniques.
Among them, ultrasonic pulse reflection
method
realizes measurement coating thickness virtue reflection characteristics ultrasonic waves interfaces different media conventional non-destructive testing method.
However, limited sensitivity resolution device,
method
struggles detect thickness micron-scale coatings. basic principle ultrasonic scanning microscopy
method
calculate thickness obtain internal information material measuring round-trip propagation ultrasonic pulses material. obtain interface echoes utilizing acoustic impedance differences between materials acquire reflected signals relying uniformly distributed particles interface.
Moreover, adjustable detection frequency range advantageous dealing
complex interfaces microstructures.
method
strong dependence probe frequency, coupling filtering links strictly controlled during operation current testing technique based principle electromagnetic induction, enabling current tested workpiece mutually coupled system. thickness workpiece changes, impedance system changes accordingly. difficult
method
accurately detect thickness micron-scale coatings. cross-sectional
method
metallographic thickness measurement
method
require cutting, mounting, grinding, polishing samples.
After that, cross-sections samples observed using scanning electron microscope metallographic microscope respectively, measure thickness substrate coating contour.
These
methods
belong destructive testing drawback complex sample preparation procedures.
Therefore, rapid, non-destructive, equipment-independent
method
capable accurately measuring multi-layer micron-scale coatings highly desirable quality control process optimization.
Energy-dispersive X-ray fluorescence (EDXRF) technology
method
elemental composition
analysis
based fluorescent X-rays generated excited substances. widely applied composition content
analysis
multiple fields, materials science, archaeology, metal smelting, detection electronic electrical products. technology offers precision, efficiency, non-destructiveness, application nuclear material coatings remains limited. this, paper takes applying EDXRF technology thickness measurement zirconium alloy coatings, providing
method
detecting stability failure surface coating thickness metal alloy materials future. study, fundamental parameter
method
EDXRF applied first measure coating thickness zirconium alloys.
method
validated multiple zirconium alloy samples different thicknesses, demonstrating
precision, non-destructiveness, potential real-time assessment coating stability failure nuclear applications.
2. Materials
principles
2.1 Reference
samples study, alloy selected substrate material, chemical composition presented Table components alloy include Impurity components strictly controlled: fraction individual impurity exceed wt.%, total impurities depend production testing. substrate samples square specimens dimensions Subsequently, sides samples mechanically polished using 400#, 600#, 800#, 1000# sandpapers. ultrasonically cleaned ethanol minutes dried compressed Balance impurity (e.g., etc.) Notes*:
Impurities alloy typically include trace elements impurity content usually wt.%, total impurities depending production testing.
Afterwards, coatings different thicknesses deposited alloy substrate samples plating (AIP) technology. study, experiments, providing basic establishing accurate quantitative relationship between coating thickness characteristic X-ray intensity.
2.2 Energy
dispersive X-ray fluorescence measurement monolayer thickness, schematic diagram process exciting primary fluorescence target element parallel X-rays wavelength incident sample shown
Schematic diagram parallel X-rays wavelength incident monolayer sample, exciting primary fluorescence target element. intensity incident X-rays wavelength respectively.
X-rays through homogeneous material thickness density target element concentration interact atoms material photoelectric effect, Compton scattering, Rayleigh scattering, leading attenuation their intensity.
X-rays reach depth photoelectrically absorbed elements target material within infinitesimal volume exciting primary fluorescent photons elements. process closely related absorption factor absorption edge, fluorescence yield transition probability These fluorescent photons ultimately attenuated, emitted within certain spatial solid angle recorded detector intrinsic detection efficiency Thus, total primary fluorescent intensity recorded detector detailed derivation process referred previous previous expressions given below.
� 1 =
� � = � � � � � � (3)
where, absorption coefficient sample X-rays wavelength absorption coefficient sample characteristic wavelength target element; photoelectric absorption coefficient target element X-rays wavelength angle between incident sample surface; angle between emergent sample normal; minimum wavelength primary spectrum; maximum wavelength primary spectrum excite target element produce photoelectric effect. thickness monolayer approaches infinity, primary fluorescence intensity target element detected detector given below.
� � →∞ =
Since total incident photon intensity equals photon intensities energy wavelength), shown continuous integral converted summation operation resulting simplified formulas given below.
� 1 =
incident X-rays interact multi-element sample, addition directly exciting target element generate primary fluorescence, generates secondary, tertiary, other higher-order fluorescence, caused absorption enhancement effect (i.e., primary fluorescence energy other elements higher absorption energy target element) Typically, tertiary fluorescence excited accounts total fluorescence intensity, tertiary higher orders fluorescence neglected. primary secondary fluorescence target element considered study shown assumed original X-rays through homogeneous material thickness density interacts atoms element (concentration material, resulting attenuation excitation characteristic X-rays element energy these characteristic higher photoelectric absorption target element (element further excite target element generate secondary fluorescence.
Through spherical coordinate integration, expressions total secondary fluorescent photon intensity target element excited element derived below.
Schematic diagram parallel X-rays wavelength incident monolayer sample, exciting secondary fluorescent target element.
� � → � =
� =0 � = �
������
, � max =
� , � ' =
� � , � = [ � 0 ( �
characteristic X-ray intensity generated element material after absorbing original X-rays wavelength photoelectric absorption coefficient element material original X-rays wavelength absorption factor, fluorescence yield, transition probability element respectively; absorption coefficient material characteristic element photoelectric
absorption coefficient element material characteristic element absorption coefficient material secondary fluorescence element angle between secondary fluorescence sample normal; Width denotes width sample. sample contains multiple elements (e.g., excite target element physical mechanism, secondary fluorescence intensities element should summed.
Thus, total secondary fluorescence intensity detected expressed below.
� 2 = � = � � = � � � → � �
Schematic diagram parallel X-rays wavelength incident bilayer sample, exciting secondary fluorescent target element. following, formulae determining thickness coating substrate derived. sample, first layer coating element), thickness denoted second layer substrate, which regarded infinitely thick film. original X-rays wavelength incident sample, secondary fluorescence target element coating excited zirconium impurity elements substrate captured detector. formulas total secondary fluorescence intensity detected detector shown (13):
� 2 =
� = � � = � ( � min
� , � ' =
� � , � = [ � 0 ( �
absorption coefficients coating substrate layer X-rays wavelength respectively; absorption coefficient coating X-rays wavelength generated element study, total intensity fluorescence detected detector photon intensities primary fluorescence secondary fluorescence, shown (14). absence standard samples, fluorescence counts measured detector cannot directly absolute intensity.
Thus, relative intensity employed, which defined ratio fluorescence count target element sample certain coating thickness element thickness layer containing target element infinitely large. instance, mentioned earlier, target element calculation formula shown (15).
Since zirconium alloy substrate itself contains interfere finally detected signal coating.
Therefore, following discussion, element unique substrate
selected target element, calculation formula relative fluorescence intensity shown (16).
� = � 1 + � 2
� _ � � � � =
� _ � � � � =
2.3 Correlation
between characteristic intensity coating thickness work, fundamental parameter
method
commonly approach XREDF coating
analysis
employed calculate surface coating thickness zirconium alloy samples.
Based series basic physical parameters rigorous theoretical formulas fluorescence intensity,
method
first computes theoretical intensity. Subsequently, theoretical intensity compared actual measured intensity, thickness value continuously corrected using iterative formula until preset accuracy requirement combining fluorescence theoretical formula spectral (17)) First Value Theorem Integrals, simplified formula relative intensity spectral (20)) derived.
� _ � � � � =
� _ � � � � = � − � 1 ∗ � �
coating thickness, coating density, absorption coefficient coating primary incident radiation, absorption coefficient coating characteristic X-rays target element weighted function value.
Since calculation coating thickness involves nonlinear relationships (e.g., aforementioned exponential attenuation term) direct analytical solution exists, coupled errors actual measurements models potential parameter coupling effects, iterative
method
adopted gradually correct thickness value. Specifically, current calculation
result
compared measured value, repeated iterative adjustments performed approach value. iterative correction formula coating thickness given (21).
� = � �
where measured value calculated value during iteration. ython programming. thickness coating zirconium alloy sample calculated iteratively fundamental parameter method, simplified flowchart algorithm shown Figure
Begin Input initial values Using calculate thickness Calculate theoretical fluorescence intensity through Eg Calculate theoretical coating thickness d´ through Eg with R Output d
method
EDXRF. convergence limit, thickness zirconium alloy substrate coating thickness measured fluorescence intensity coated side, zirconium alloy. theoretical intensity
of the zirconium alloy with a thickness of 2mm (d → 0 ) in this work.
3.1 Measurement
device Energy-dispersive X-ray fluorescence (EDXRF) measur homemade system, which consists silver (Ag)-anode X-ray voltage Si-PIN semiconductor detector resolution detector collimator, X-ray collimator, sample stage, electronic components acquisition processing, shown
Infinitesimal volume Coating
Substrate Sample stage Schematic EDXRF measurement system structure Electrons X-ray accelerated bombard silver target, generating primary X-rays continuous spectral distribution including bremsstrahlung characteristic X-rays. simulating process using Monte Carlo method, original X-ray spectral distribution obtained, shown Notably, distinct characteristic peaks observed spectrum, including (~22.1 keV), (~24.9 keV), (~2.9 keV), (~3.1 keV). general, lower absorption energy, easier excite characteristic X-rays series. sample, measurement minutes, coated (substrate) sample measured three times, average value calculated.
X-ray spectral distribution silver target obtained Monte Carlo
3.2 Experiment
process
original spectra coated sample shown Figs. Within energy range distinct characteristic (~5.4 (~5.9 peaks observed.
Meanwhile, range obvious characteristic (~15.7 (~17.6 peaks present. original spectra sample displayed Figs. characteristic peaks found, photon count originating primary secondary fluorescence element inherently present zirconium alloy. range distinct characteristic peaks observed well, photon count increases significantly, maximum value reaching approximately 10,000.
Sample 1# (Coating) Sample 1# (Coating) Counts Counts Energy (keV) Energy (keV) Figure (Color online) energy spectra sample (coated side) three measurements.
Ordinate presented (natural logarithm) scale; Ordinate presented linear scale Sample 1# (Substrate) Sample 1# (Substrate) Counts Counts Energy (keV) Energy (keV) Figure (Color online) energy spectra sample (back side) three
measurements. Ordinate presented (natural logarithm) scale; Ordinate presented linear scale energy-dispersive X-ray fluorescence (EDXRF) analysis, baseline correction first spectral
analysis
crucial ensures accuracy subsequent procedures, including multi-peak
analysis
content quantification. appropriately selecting baseline points spectral fitting, baseline accurately estimated Figs. spectra coated sample after baseline subtraction baseline correction, respectively.
Baseline-corrected spectrum Raw spectrum Baseline Sample 1# (Coating) Counts Energy (keV) Raw spectrum Baseline Baseline-corrected spectrum Sample 1# (Substrate) Counts Energy (keV) Baseline-corrected spectrum Sample 1# (Coating) Counts Energy (keV) Baseline-corrected spectrum Sample 1# (Substrate) Counts Energy (keV) Figure (Color online) procession sample (coated side). (a)Baseline; Baseline corrected spectrum Figure (Color online) procession sample (back side). (a)Baseline; Baseline corrected spectrum. significant difference components between substrate coating coating contains Crand lacks which unique
substrate distinction between achieved comparing fluorescence intensity After obtaining baseline-corrected energy spectrum, necessary first determine position characteristic peak, identify boundaries (defined positions where intensity fluctuates within baseline range), subsequently calculate characteristic peak. serves basis subsequent analysis.
Table presents relative intensities samples, average counts characteristic coating where denotes coating thickness), relative deviation. standard deviation average counts calculated using error propagation formula where represents number measurements fluorescence intensity measurement. zirconium coating sample (where denotes coating thickness sample) Samples Average count coated Average count Relative intensities study, X-rays incident sample coating, counts detected originate primary fluorescence substrate, secondary fluorescence substrate excited fluorescence other elements. defined ratio total counts (back sample). samples measured
follows: 40.76, 51.07, 67.95, 33.93, 52.87, 36.10, 32.01, 25.41, Subsequently, using fundamental parameter
method
Figure multiple iterations, calculated values coating thickness samples finally obtained.
discussion
Scanning Electron Microscopy (SEM) characterize coating thickness different alloy samples,
results
presented Figure shown figure, coating thickness samples ranges approximately coating sample, different positions selected
� � =1 � � � � ) and
thickness measurement, average value
� − 1 � =1 � ( � � − � ) 2 � ) of the actual
standard deviation ( � � =
thickness calculated. specific listed Table these reference thickness study.
Figure (Color online) characterization
results
(Reference thickness) coating Samples
calculated thicknesses required
method
proposed study obtained using
method
EDXRF Table presents calculated thicknesses, reference thicknesses, relative errors coatings amples calculation standard deviation calculated thickness value relatively
complex. The parameter � =
follows standard normal distribution Then, multiple random samplings performed fluorescence relative intensity shown (23).
formulas, � 푅� =
regarded conventional value
the measured relative intensity. � 푅� =
deviation relative intensity. random number sampled range Finally, sampled substituted fundamental parameter
method
iterated multiple times obtain coating thickness sampling result.
Combined standard deviation calculation formula, deviation calculated thickness value sample's coating obtained.
2 dt ∈ 0,1 （ 22 ）
� = � � = −∞
푅� = � 푅� + � 푅� � �
comparison groups reveals Samples exhibit relatively large relative errors, maximum value reaching 7.33%. phenomenon attributed inhomogeneity coating structure these samples. contrast, Samples small deviations between calculated thicknesses reference thicknesses, relative errors controlled within which fully demonstrates systematic stability feasibility proposed method. further
analysis
error sources indicates
calculated thickness greater reference thickness, indicates overestimation thickness, which mainly caused local thickening coating (even coating uniformly structured overall, horizontal deviation between bottom surface sample contact surface sample stage indirectly phenomenon). calculated thickness reference thickness, reflects underestimation thickness, which
result
measurement errors introduced during coating thickness characterization using Sample Calculated thickness Relative error Reference thickness Calculated thickness Reference thickness
20 Relative error
Coating thickness (μm) Relative error (%) Sample Column charts showing reference thickness calculated thickness coatings samples relative error (blue line).
zirconium alloy sample thickness under different coating thicknesses obtained theoretical fluorescence formula, shown Figure observed initial close decreases gradually increase coating thickness, thickness reaches approximately approaches tends stabilize. contrast, initial close increases rapidly coating thickness rises, thickness around approaches reaches saturation. this, target element, maximum measurable coating thickness reach serves target element, maximum measurable coating thickness limited attributed exhibits larger absorption coefficient compared coating thickness exceeds becomes nearly constant, making impossible characterize samples thicker coatings using rays.
Cr_Ka Zr_Ka Relative intensity function coating thickness (nm). abscissa presented scale.
5. Conclusion
work, fundamental parameter
method
based Energy-Dispersive X-ray Fluorescence (EDXRF) successfully applied thickness measurement zirconium alloy cladding coatings.
Compared conventional techniques cross-sectional metallographic
measurements,
method
offers significant advantages terms non-destructiveness, rapid detection, elimination complex sample preparation.
Validation experiments performed zirconium alloy samples different coating thicknesses demonstrated maximum relative error 7.33%, primarily attributed coating microstructural inhomogeneity, while deviations samples within These
results
confirm reliability, stability, accuracy EDXRF approach zirconium alloy coating thickness evaluation.
Furthermore,
method
shows great potential real-time monitoring characterization coating degradation behaviors (e.g., swelling, spalling) zirconium alloy claddings under service conditions, providing valuable quality assurance safety management nuclear power plants.
CRediT authorship contribution statement Yongli: Conceptualization,
method
design, formal analysis, investigation,
initial draft writing, data collation, and validation.
Zhang Jian:
Method
design, software development/maintenance, formal analysis, investigation, validation, review, editing.
Cheng: Sample preparation curation. Hailiang: Supervision guidance, review, editing.
Acknowledgments
research financially supported National Natural Science Foundation China [grant numbers 12305336] Scientific Research Program Young Talent China National Nuclear Corporations [JTYC-QMX-2024-0102] Continuous Basic Scientific Research Project under Contract BJ020261224905.
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