Electromagnetic evaluation of hydrogen content in Zr 2.5%Nb alloy

R.Grimberg 1, M.L.Craus 1,2 , A.Savin 1, R.Steigmann 2, M.Ruch 3 1 National Institute of Research and Development for Technical Physics, Iasi, Romania 2 Joint Institute for Nuclear Research, Dubna, Russia 3 CNEA, Buenos Aires, Argentina Abstract Zr 2.5%Nb alloys have wide utilization in nuclear energy engineering, being used at the fabrication of pressure tubes from Pressurized Heavy Water Reactors (PHWR). This paper proposes to present an electromagnetic method for determination of diffused hydrogen/deuterium content based on the measurement of conductivity, correlating the theoretical results with those experimental obtained on samples cropped from non-irradiated pressure tubes. The methods can be used directly, the results being obtained by data inversion.

Keywords: PHWR, hydrogen content, electromagnetic nondestructive evaluation method, conductivity

1. Introduction Zirconium alloys represents the majority of structural materials from nuclear reactors, Light Water Reactors types (LWR) and Pressurized Heavy Water reactor” (PHWR). Zirconium alloys are exclusively used at the manufacturing of nuclear fuel cladding, nuclear fuel bundle subassemblies and fuel channels. During the reactor functioning, the zirconium alloy absorbs hydrogen or deuterium that can appear due to the radiolysis of water used as coolant agent or due to heavy water according to the reactions

→ + HO2 H 2 O (a) → + D2 O D 2 O (b) Also, hydrogen and deuterium can appear due to oxidation of zirconium alloys + → + Zr 2H2 O ZrO 2 2H 2 (c) + → + Zr 2D2 O ZrO 2 2D 2 (d) Hydrogen in solid solution diffuses due to the existence of concentration, temperature and stress gradients. Hydrogen has low solubility in zirconium alloys, fact that leads to formation of zirconium hydride. These hydrides are brittle, worsening the mechanical properties of zirconium alloys [1]. The embrittlement of zirconium alloys in the presence of hydrogen includes hydrogen diffusion, energy transfer and forming of brittle hydride. All these phenomena are connected. Special efforts are made for understanding, modeling and detecting by nondestructive procedures of cracks that appears due to the coupling of the three mechanisms presented above. Theoretical and experimental investigations were made on unirradiated zirconium alloy samples as well as on samples irradiated with 10 19 neutrons/s flux. Probable, the most exhaustive experimental studies are those made by Electric Power Research Institute, department of nuclear fuel – USA [2]. Few conclusions of this study show that - Small hydrides with lenticular shapes of those transverse section is smaller than 3mm 2 have minor influence over the bulk properties of zirconium alloys irradiated with internal neutron fluxes. The apparition of hydrides with larger area of transverse section leads to breaks in materials, even at relative small pressure. - Hydrides with large transversal section lead to the reduction of elastic deformation after a linear relation with report between the area of these hydrides and the area of affected region on the zirconium alloy. - Cracks are initiated in the region where are lenticular shape hydride with large area and that propagate from outside to inside. The opening of the cracks appears above the hydride or immediately below the hydride and usually they have 45 0 tilting. During the period 2000-2006, the International Atomic Energy Agency, Vienna has initiated a research program with the aim of finding the best methods for detection and evaluation of discontinuities, blisters and hydrogen content on pressure tubes [3], [4]. For determination of hydrogen content from Zr 2.5%Nb alloys, two methods have been proposed: - ultrasound method [5] - electromagnetic methods [3] that determine the conductivity of Zr alloys with different quantities of absorbed hydrogen, the correlation between the electrical conductivity and hydrogen concentration being experimentally established. In this paper we present an electromagnetic method for determination of the Zr 2.5%Nb alloy conductivity, presenting the way of solving the forward problem, the linearization and inversion procedures, and the experimental data.

2. Determination of conductibility for Zr-2.5%Nb alloys that contain hydrogen in different proportions

For a circular eddy current coil with rectangular cross-section, closed-form solutions for impedance are given in [6], [7], [8]. The active resistance of the coil will be neglected, the apparition of a real term in the expression of the impedance being due to the presence of a conductive material. The impedance of the coil, in air, Z air is given by [6] ∞ − 2πj ωµ µ n 2 I2 ( kr, kr ) e kl −1  Z =0 0 i 1 +  dk (1) air 2 − 2∫ 5 k  l() r0 r i 0 k  

-7 where µ0=4 πx10 H/m – the permeability of vacuum, n – the number of coil turns, r 0 – outer b radius, r i – inner radius, l- the length of the coil, I(,) a b= xJ () x dx , J 1(x) is the Bessel function ∫ 1 a of the first kind. It can be calculated using Struve functions [9].

In a point of coordinate (x 0, y 0), at height h over an amagnetic conductive plate ( µr=1) with H thickness and having local electrical conductivity σ(x 0, y 0), the impedance of the same coil will be ∞ 2πj ωµ n 2 I2 ( kr, kr ) Z() x, y =0 0 i ⋅ 0 0 2 − 2∫ 5 l() r0 r i 0 k

 1 −−+()() − −+ 222le+ kl −+() e2klh +− ee2 kh 2 klh 2 ⋅  k  (2)

−2γ ()x , y H    ()γ 2()xy,− k 2 1 − e 0 0   0 0 ()    ⋅ dk  − γ () γ ()    γ 2+− 2 2,xyH0 0 −γ + 2, xyH0 0 ()()xyk0, 0 ( 1 e) 2,1 kxy()0 0 ( e )       γ2( ) = 2 − ωµσ ( ) where xy00, k j 000 xy , . The last factor from (2) is the one that contains the information about the electrical conductivity of the material under testing. We will develop a linearized relation between the observed impedance modification and the conductivity modification. We note − γ () γ 2() − 2 − 2x0 , y 0 H ( xy0, 0 k)( 1 e ) θ () = (3) x0, y 0 , k − γ () γ () γ2+− 2 2,xyH0 0 − γ + 2, xyH0 0 ()()xyk0, 0 () 1 e 2,1 kxy()0 0 () e The eq.(3) can be developed into a Taylor series around the value σ0 that represents the value of electrical conductivity of the considered Zr alloy and which do not contain diffused hydrogen. ∂θ (x, y , k ) θ()()xyk,,= θ0 xyk ,, +−() σσ 0 0 + ... (4) 00 00 0 ∂σ σ= σ 0 Introducing (4) in (2) we can write formally ∞ ∂θ (x, y , k ) 2 ZxyZxy()()(),=+−0 ,()σσ xy , Ak () 0 0 dkO +−() σσ (5) 00 00 00 0 ∫ ∂σ 0 σ= σ 0 0 where the kernel A represents the factors from eq. (2) that contains the conductivity. Due to the convolution nature of the problem ∂θ (x, y , k ) δ
Z( k ) =() σ − σ 0 0 (6) 0 ∂σ σ= σ 0 with δ
Z( k ) the Fourier transform of the variation of the impedance. Using the relations presented in [10] is obtained δZ= U δσ (7) where U is the matrix of the model with NxN dimensions having as unknown the modification of conductivity δσ. For inversion, different procedures can be used [11], [12]. Despite the model matrix U is sufficient smooth, the existence of the noise making that the matrix shall be enough ill- conditioned. This fact has imposed a previous regularization using Levenberg-Marquardt procedure, the value of regularization parameter being 10 -12 . The proper inversion was effectuated using generalized inversion in Moore-Penrose sense.

3. Studied samples

The hydrogen diffusion into the walls of pressure tubes from CANDU nuclear reactors depends by thermal gradient. The diffusion become accelerated if in the cold points are cracks and other mechanical stress concentrators. During the Coordinates Research Project on Intercomparison of Techniques for Pressure Tubes Inspection and Diagnostics, CRP:13.30.10 – IAEA Vienna [13], samples that contains different concentration of diffused hydrogen were prepared from Zr-2.5%Nb alloy pressure tubes. The analysis of AFM images shows that thickness of zirconium oxides appeared on the sample’s surface is smaller than 0.7 µm (Figure 1). Samples from pressure tubes with 28x28x4.18mm 3 have been taken into study (Figure 2). Because the zirconium burns in air and the temperature of ignition is relatively small, the samples have been cropped using an electro discharge machine. The initial hydrogen content was lower than 2ppm (this is the limit of detection).

Figure 1. AFM image of sample#05 Figure 2. Sample used for noninvasive determination of hydrogen and hydride content;

The hydrogen absorption has been made into a Sieverts device that consists from a quartz tube connected to a high vacuum system and to a hydrogen injection system (99.999% purity). The heat treatments were performed by moving the tube into an instrumented furnace. The temperature was measured with a thermocouple installed inside the hydrogenation chamber, placed few millimeters above the sample. The hydrogen estimated concentrations were calculated from the difference between the initial and final pressures measured at room temperature, assuming ideal gas behavior. The real concentration of hydrogen was determined using the differential scanning calorimeter (DSC) method. The features of the samples are presented in Table 1. The samples were examined by metallographic method, using a classical chemical attack for Zr alloys, to determine the hydrogen concentration from which zirconium hydrides are formed as well as the threshold from which hydrides disposed after radial direction appear. Using a LakeShare VSM 7410 Vibrating Sample Magnetometer, the relative magnetic permeability has been determined for the samples taken in study as being 1.01 ±0.005.

Table 1. The features of the studied samples No Sample Geometrical Hydr ogen [ppm ] Observation dimension determined by [mm 3] DSC 1 01 28x28x4.18 ≤ 2 Serves as etalon -does not exist ZrH 2 2 05 28x28x4.18 ≤ 2 Serves as etalon -does not exist ZrH 2 3 13 28x28x4.18 3 Serves to determine the detection lim it 4 06 28x28x4.18 18 ZrH 2 has not been detected 5 07 28x28x4.18 34 ZrH 2 has not been detected 6 18 34 ZrH has not been detected - Serves to determine the 28x28x4.18 2 measurement errors 7 08 60 It appears ZrH in low concentration di sposed after 28x28x4.18 2 circumferential direction 8 35 87 It appears ZrH 2 in high concentration disposed after 28x28x4.18 circumferential direction, it also appears ZrH 2 disposed after radial direction 9 25 87 It appears ZrH 2 in high concentration disposed aft er 28x28x4.18 circumferential direction, it also appears ZrH 2 disposed after radial direction 10 36 89 It appears ZrH 2 in high concentration disposed after 28x28x4.18 circumferential direction, it also appears ZrH 2 disposed after radial direction

4. Experimental set-up

The eddy current transducer, one coil type has been connected to a Network/Spectrum/Impedance Analyzer – Agilent 4395A, programmed to effectuate a frequency swap in the range 10kHz -100kHz, corresponding to a standard skin depth between 3.7mm and 1.2mm for a material with 1.89x10 6S/m (the conductivity of Zr-2.5%Nb alloy having 3ppm H 2). The image of the transducer is presented in Figure 3a and the dimensions are given in Figure 3b. During the measurements, the correction for 1m coaxial cable for connection has been made.

a b Figure 3. The transducer and experimental layout: a) one coil transducer; b) geometrical dimensions: r i=4.5mm; r 0=6.5mm; l=2mm, number of turns=100.

In figure 4 is presented the equipment for experimental measurement.

Figure 4. Experimental set-up

For every frequency used, the memorized results represent the mean of 100 measurements. The self-inductance of the measure coil was 892.17 µH, the resistance in continuum current was 30.3216 Ω. Both measurements have been made with Agilent 4395A at 10kHz frequency, the coil being placed at large distance from any metallic part.

5. Experimental Results

The eddy current transducer was placed on the concave side, as well as on the convex side of the examined samples, thus the axis of the transducer coincides with the radial direction of the samples. The following results represent the mean of the resistance and inductive reactance of the transducer for the two positions mentioned above. In each of the positions, 100 measurements have been made. The principally perturbing factor is the measurement noise. Working at 10kHz and performing 100 measurements, the obtained mean value is the best estimation of the real value. It is evidently that the temperature influences both the electric conductivity of analyzed zirconium alloy and the electrical resistance of the eddy current transducer. From this reason, the temperature in the room where the measurements have been performed was maintained relatively constant at (22 ± 2) 0C. In Figure 5 is presented the dependency of eddy current transducer resistance by frequency when were placed on free space and over the samples with different concentration of diffused hydrogen. It can be observed that the real component of the transducer impedance in free space presents a small increasing with frequency. For the transducer over the studied samples, the real component of the impedance increase almost linear with frequency. It is hard to establish the way in which the hydrogen content diffused in zirconium, alloy influence the dependence of transducer impedance by frequency. In Figure 6 is presented the dependence by the frequency of the eddy current transducer inductive reactance.

Figure 5. Dependence of eddy current Figure 6. Dependence of eddy current transducer impedance vs. frequency transducer inductive reactance vs. frequency

It can be observed that the dependence by frequency of inductive reactance is practically linear. In the same time, the inductive reactance of the transducer in free space is much bigger than the one of the transducer placed over the studied samples with high content of diffused hydrogen. In Figure 7, we present the dependency normalized inductive reactance ( Lω/ L ω ) by the 0 normalized resistance of the transducer for all examined samples, in case in which the frequency of the alternative current which circulate through the transducer varies between 10kHz – 100kHz. Examining the data in the Figure 7, it can be seen that the samples having equal concentrations of hydrogen have perfectly similar behavior, the values of the normalized inductive reactance, as well as of the normalized resistance varying with less than 2%. The extremely detailed analysis of the measurements errors presented in [14] indicates similar values in the case of plane samples. These measurements have been considered data for the inversion, with a view to determine the electrical conductivity of the Zirconium alloys with different quantities of hydrogen. The inversion has been made for 91 equidistant frequencies within the range 10 kHz – 100 kHz. In order to obtain the fitting of experimental results with the model, given by the equation (1), the procedure indicated in [6]. Due to the fact that in the equation (1) does not exist the possibility of evaluating the DC resistance of the transducer, from the experimental results has been subtracted the value of the DC resistance, also determined experimentally. The results of the inversion are presented in Table 2. The dependency of electrical conductivity of Zr-2.5%Nb alloys, obtained by inversion, function of the hydrogen content is presented in Figure 8. The analysis of Zr hydrides was made by metallographic examination. In this purpose, the Zr- 2.5%Nb samples with different hydrogen concentration were special prepared. After polishing, the samples have suffered a chemically pickling with solution made from 50% distilled water, 45% nitric acid and 5% HF. The attack was made at room temperature during 3 minutes. The metallographic examination was made in transversal radial plane with metallographic microscope type BX51 – Olympus, USA, using a digital camera DP72- Olympus USA.

Figure 7. Normalized inductive reactance Figure 8. The electrical conductivity v.s. vs. normalized resistance for examined hydrogen concentration samples

Table 2. Experimental results No Sample Hidrogen content Electr ical Obs. [ppm] conductivity [MS/m] 1 01 ≤ 2 1.89 Value indicated by pr oducer 2 05 ≤ 2 1.89 Value due by producer 3 13 3 1.83 ± 0.05 Standard deviation (class ical calculated) 4 06 18 1.79 ± 0.05 Standard deviation (class ical calcul ated) 5 07 34 1.73 ± 0.05 Standard deviation (class ical calculated) 6 18 34 1.74 ± 0.05 Practically the same value of the sample no. 07 7 08 60 1.68 ± 0.05 - 8 35 87 1.61 ± 0.05 - 9 25 87 1.61 ± 0.05 Rigorous value of the co nductivity like in the case of the sample no. 35 10 36 89 1.59 ± 0.05 -

Conclusions

Measuring the modification of the impedance of an eddy current transducer with unique coil , and utilizing a simple inversion procedure starting from a linearized model, it is possible to determine the conductivity of the Zr2.5% alloys used in the fabrication of the pressure tubes from the nuclear PHWR power plants, with different hydrogen contents. When the electrical conductivity of the alloys exceeds a threshold value of .1.68MS/m, the development of the Zr hydrides oriented after a circumferential direction pressure tubes walls is possible. If the electrical conductivity exceeds 1.61MS/m, the Zr hydrides start to change orientation after radial direction. In this situation, blisters and hydrogen delayed cracking is possible to appear.

Acknowledgments This paper is partially supported by Romanian Ministry of Education, Research, Youth and Sports under Nucleus Program, Contract No. PN 09 43-01-04 and Project Bilateral Cooperation JINR Dubna - 3900-4-09/11 -04-4-1069-2009/2011..

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