Hydrogen Solubility in Zirconium Alloys

Abstract

Analysis of the published to date results for hydrogen solubility in zirconium alloys—core structural materials of water-cooled nuclear reactors is presented. Data for hydrogen solubility in Russian domestic and foreign zirconium alloys are summarized.

APPENDIX

Let us list the main methods that are used to measure hydrogen solubilities in zirconium alloys.

—The dilatometric method (see, for example, [22, 23]) is based on the measurement of dilatation, i.e., an increase in one of the sample dimensions (most often, the length) when hydrides appear at the material in macroscopic amounts. The increase in the sample volume under the precipitation of hydrides is caused by the fact that the specific volume of δ-hydride is significantly (by 17%) higher than those of the matrix. The method is rather crude, since it does not take into account the structure of the hydride phase, relaxation of the lattice around hydrides, or the possibility of the fact that the volume of the sample can be affected by the hydrogen in the solid solution. In addition, to observe dilatation level sufficient for measurements, the hydrogen concentration in the material should be higher than a certain threshold. This could be the reason for the underestimated values of the solubilities obtained by this method [23].

—The pressure–concentration–temperature (Р–С–Т) method. The specific features of the method are described, for example, in [14]. The method is based on the application of Sievert’s law, which relates hydrogen concentration ${{c}_{H}}$ in a dilute solid solution and partial pressure p for gaseous molecular hydrogen above the sample surface in equilibrium: ${{c}_{H}}\sim \sqrt p$. The proportionality coefficient in Sievert’s law for low hydrogen concentrations and pressures depends only on temperature. The determination of hydrogen solubility with the use of this method consists of the following procedures. A sample is placed in a closed evacuated volume, and the container is filled with molecular hydrogen. The experimental facility allows to measure pressure and temperature. The hydrogen concentration in the sample, when equilibrium has been achieved, is determined by the difference in the partial pressures of molecular hydrogen in the gas phase at the initial moment and after the equilibration. While hydrogen is in a solid solution, the dependence of c on $\sqrt p$ is linear. As soon as hydrogen begins to precipitate in the form of hydrides, Sievert’s law is violated, and a kink appears on the corresponding curve. The position of this kink is used to determine hydrogen solubility. The measurements using the Р–С–Т method [14] and the analysis of the published data presented in [12] have shown that the proportionality coefficient in Sievert’s law substantially depends on the alloying level of the material. Therefore, to compare the results obtained using P–C–T with the results of other methods, it is necessary to use samples with the same composition. This could explain the overestimated results for hydrogen solubility [14] in comparison with the values determined by other methods for other samples. Another possibility is that, in accordance with the processes occurring in a closed volume during hydrogen absorbtion, the solubility recorded by the P–C–T method represents TSSP, whereas the comparison has been made with the TSSD results. In any case, this method is no longer being developed, since owing to the complicated interpretation of the results, it was practically abandoned in the 1970s.

—In [12], the diffusion pair method is used to determine hydrogen solubility: two parts of the sample are welded, the first of which is hydrogenated to a known concentration, and the second one is in the as-received material without hydrogen. Next, the resulting sample—a diffusion pair—is heated and annealed at a temperature in the range from 250 to 550°C until the thermodynamic equilibrium is reached. The sample is then cooled down slowly to avoid supersaturation. The parameters of the samples are chosen so that the second part of the sample, initially free of hydrogen, contained after annealing the entire hydrogen in the form of a solid solution. In this experiment scenario at the beginning of heating the hydrogen dissolves into the first part of the sample to attain the TSSD, whereas during further annealing at a fixed temperature, this dissolved hydrogen is getting uniformly distributed throughout both parts of the sample. By measuring the hydrogen concentration in the second part of the sample via vacuum extraction method and knowing the initial hydrogen concentration in the first part, the TSSD at the annealing temperature can be calculated. The diffusion pair method can also be extended to determine: the TSSP value, the diffusion coefficient of hydrogen in the material, and a number of other characteristics [19].

—Among the direct methods for measuring the hydrogen solubilities in zirconium alloys, first of all, differential scanning DSC calorimetry should be noted (see, for example, [9, 18, 23, 24]). The DSC method uses a calorimeter with two chambers combined into one system so that the thermodynamic conditions during the heating and cooling are identical. The sample is placed into the first chamber, and the standard reference sample without a phase transition at the temperature range of interest is placed into the other one. This is followed by the slow heating and then by the slow cooling of the entire system at a constant rate. During this heat treatment, the temperature of the standard sample changes monotonically, whereas the change of the second sample temperature decelerates in the vicinity of the transition point (owing to the latent heat of the first-order phase transitions). The use of the differential technique is forced by the too little value of the effect. During heat treatment, the temperatures of both samples are measured and a graph is plotted for the dependence of the rate of the temperature difference on the current temperature. Further, according to the graph, the transition temperature is determined. Most publications of DSC results indicate that the transition temperature corresponds to the minimum point of this graph. This may be why the author of the review [7] gave a value for the error of the DSC method greater than 20–30°С, although according to the data reported, for example, in [23], where the DSC method had been directly used, we could conclude that the error value is no less than 10°C. In addition, a specially performed analysis [25] has shown that the closest value to the transition temperature corresponds to the minimum point on the curve of the temperature difference depending on time.

—In the last decade some powerful synchrotron X-ray sources were put into operation around the world. So, another method for direct observation of the phase transition in the zirconium alloy–hydrogen system has appeared [1]. The synchrotron XRD technique is traditionally used in X-ray structural analysis and crystallography; however, the power of laboratory sources is sufficient only to obtain a diffraction pattern in reflection or in transmission, but only for very thin samples. The powerful X-ray sources have made it possible to obtain real-time diffraction patterns with the use of thick samples subjected to loading and heat treatment. The following experimental scheme is used: a sample, fixed in the grips of a test-machine in a thermal chamber, is placed between the source and the receiver of synchrotron X-ray radiation. The receiver records a diffraction pattern from the sample. Although initially the sample is at a room temperature and contains hydrogen in the form of hydrides and a solid solution, the diffraction pattern shows the maxima not only originated from the zirconium lattice but also those from the hydrides. As heating progresses, the hydrides dissolve, whereas the intensity of the peaks from zirconium hydrides in the diffraction pattern decreases. When there is no macroscopic amount of hydrides left in the sample, the intensity is equal to the background. The temperature at which this occurs corresponds to the TSSD temperature. In a similar manner, when the sample is cooled, the TSSP temperature can be obtained. Based on the results of measurements using one sample with a fixed hydrogen concentration c₁, the method makes it possible to obtain the entire part of the phase diagram for concentrations c < c₁. To do this, it is necessary to plot a curve for the hydrogen concentration in a solid solution depending on the temperature.

Currently, this method is used not only for the solubility measurements. For example, the authors of [4] obtained a left-hand side of the zirconium–hydrogen phase diagram for a hydrogen concentrations from 0 to 450 ppm by the synchrotron XRD technique using Zircaloy-4 samples. The authors of [26] studied the precipitation of zirconium δ-hydride plates in Zircaloy-4 for normal operation temperature modes and for modes with a rapid temperature change. In [27] the synchrotron XRD method was used to study the kinetics of hydride precipitation in Zircaloy-4, whereas in [28] even the phenomenon of the hydrides reorientation during heat treatment in  the presence of tensile mechanical stresses was studied.

—Another method for the hydrogen solubility measurements in zirconium alloys (internal friction method (IF)) is based on the fact that the dynamic elasticity modulus of the material changes when inclusions (hydrides) appear; i.e., a change in the propagation velocity of longitudinal waves and in the corresponding damping factor is observed. Most often, the measurements are performed at a resonant frequency; then the attenuation can be directly determined from the width of the obtained resonance curve. In the IF experiments, as a rule, elastic waves in an ultrasonic range are used (see, for example, [8, 29, 30]). These waves are emitted and recorded by a piezoelectric element. If a sample containing a sufficient concentration of hydrogen is heated and simultaneously the IF and the dynamic elasticity modulus are measured, then a singularity appears on the curves for these values depending on temperature when passing through the solubility point. In the case of the dynamic elasticity modulus, the slope of the graph changes, whereas in the case of a logarithmic damping decrement, a kink is observed. As indicated in [30], when applying the methods of IF and the dynamic elasticity modulus, a problem arises to prove the selection of the point that corresponds to the phase transition. In addition, (for example, in [8]), a number of curves for the damping decrement and the dynamic elasticity modulus depending on temperature are presented, according to which the phase transition point can be determined. However, on some curves presented in this publication, the singularity is not distinguishable, and since the method for extracting the result is not presented, some doubts arise about the result and the accuracy of the method.

Thus, at the moment, the DSC method and synchrotron XRD should be considered to be among the most promising methods for measuring hydrogen solubilities in zirconium alloys. The rest of the listed methods are either less accurate or require additional work in order to construct a suitable procedure for the extraction of results from the experimental data and to minimize errors.