The δ′/δ phase transition in hafnium hydride and deuteride

Abstract

Bulk samples of hafnium (Hf) hydride and deuteride were prepared and the thermal properties, heat capacity (C_P) and thermal conductivity (κ) were measured. In the C_P–temperature curves for both samples, typical lambda-type peaks were observed at around 350 K, which was due to the second-order phase transition from the δ′-phase to the δ-phase. In Hf hydride, it is considered that the δ′-phase and the δ-phase consist of regularly arranged and randomly arranged hydrogen atoms, respectively. Therefore, it can be said that the δ′/δ phase transition observed in both Hf hydride and deuteride is an order–disorder phase transition. The values of κ as well as C_P changed significantly at around the phase transition temperature.

Keywords:

• hafnium hydride
• hafnium deuteride
• neutron control material
• fast reactor
• phase transition
• heat capacity
• thermal conductivity

1. Introduction

Boron carbide (B₄C) is currently used as a neutron control material in fast reactors. However, the lifetime of the B₄C control rod is restricted mainly by pellet-cladding mechanical interaction failure due to helium gas swelling, which is caused by the nuclear reaction of ¹⁰B(n,α)⁷Li. Recently, hafnium (Hf) hydride has been a focus of attention as an advanced neutron control material [1,2]. Since hydrogen can moderate fast neutrons and Hf has a large capture cross section for thermal neutrons, Hf hydride would be an effective neutron control material in fast reactors. In addition, no helium gas is produced during neutron absorption in Hf because the nuclear reaction is expressed as ¹⁷⁷Hf(n,γ)¹⁷⁸Hf(n,γ)¹⁷⁹Hf(n,γ)¹⁸⁰Hf. Furthermore, since the daughter nuclides ¹⁷⁸Hf and ¹⁷⁹Hf also have large cross sections for thermal neutron capture as well as the parent nuclide ¹⁷⁷Hf, long lifetime of the control rod of more than 40 years can be expected [1,2].

When utilizing Hf hydride as a neutron control material, the thermal properties such as the heat capacity (C_P) and thermal conductivity (κ) need to be understood. A few data on the thermal and thermomechanical properties of Hf hydride have been reported [3,4]. On the other hand, a phase transition between the δ′-phase and the δ-phase has been observed at around 350 K for Hf hydride (HfH_x, x = ∼1.6) [5], and thus the behavior of C_P and κ would change significantly below and above the phase transition temperature. Here, the purpose of the present study is to understand the phase transition in detail and to reveal its effect on C_P and κ of Hf hydride and deuteride. The reason why we covered not only Hf hydride but also deuteride is that the thermal properties and phase state of Hf deuteride have been scarcely studied. Note that the prime objective of the present study is to investigate and collect the fundamental physical properties of Hf hydride and deuteride, in order to contribute to practical application of Hf hydride neutron control rod in fast reactors. Bulk samples of Hf hydride and deuteride were fabricated and their temperature dependences of C_P and molar volume were measured to understand the phase transition mechanism. As for Hf deuteride, κ was also evaluated at around the phase transition temperature.

2. Experimental

Bulk samples of Hf hydride and deuteride were directly prepared from Hf metal with 99.9% purity in a Sieverts’ apparatus. The sample sizes were generally 10 mm×10 mm×1 mm for thermal diffusivity (α) measurement and 2 mm×2 mm×0.5 mm for C_P measurement. First, the samples were introduced into the Sieverts’ apparatus. After evacuating in the apparatus below the pressure of 8×10⁻⁶ Pa, the samples in the reaction chamber were heated up to 1173 K with a rate of temperature increase of approximately 200 K/h and kept at that temperature for 24 hours for degassing. Then, appropriate amount of pure hydrogen (7N) or deuterium (5N) gas was passed through a liquefied nitrogen tarp and held in the reserve tank, followed by slowly introduced over several days to the reaction chamber which was kept at 1073 K. After introducing the appropriate amount of the hydrogen or deuterium gas in the reserve tank, the temperature of the reaction chamber fell to room temperature very slowly with a rate of temperature decrease of approximately 20 K/h in order to prevent the sample's pulverization.

The phase structure of the samples was investigated using powder X-ray diffraction (XRD) with Cu-Kα radiation at room temperature. Crystallographic orientation measurement was performed using a field emission type scanning electron microscope equipped with an electron backscatter diffraction system. The sample density (d) was calculated from the weight and dimensions. Values of the hydrogen isotope content in Hf hydride and deuteride, i.e., x in HfH_x and HfD_x, were determined from the weight change before and after hydrogenation.

C_P was measured up to 673 K using two apparatuses. From approximately 1.9 K to room temperature, C_P was measured based on a relaxation calorimetry technique by using Physical Properties Measurement System (Quantum Design, Inc.), while above room temperature a differential scanning calorimeter (DSC) was used. In the DSC measurement, sapphire was used as the standard material. In order to evaluate the temperature dependence of molar volume, high-temperature XRD analysis was carried out in a helium gas flow atmosphere. The measurements were performed at 5 K steps from room temperature to 380 K. As for Hf deuteride, α was measured from room temperature to 420 K under vacuum using the laser flash method. The value of κ was then calculated based on the relationship κ = α×C_P×d.

3. Results and discussion

From the weight change before and after hydrogenation, the sample compositions were determined to be HfH_1.63, HfD_1.53, and HfD_1.60. The hydrogen isotope content was also evaluated from the measured pressure change during hydrogenation, and it was confirmed that the values determined using both methods were in good agreement with each other.

Figure 1 shows the XRD patterns of the samples of HfH_1.63 and HfD_1.60, in which the peak positions corresponding to the δ′-phase HfH_1.53 [6] and the δ-phase HfD_1.628 [6] are shown for comparison. According to the Hf–H binary phase diagram [7], in the hydrogen content range around 1.6, there exist two phases, viz., the δ′-phase and the δ-phase. The δ′-phase is stable at around room temperature, while the δ-phase is stable at higher temperatures. When the hydrogen content H/Hf is around 1.6, the δ-phase is stable above approximately 373 K [7]. It is well known that both the δ′-phase and the δ-phase of Hf hydride have a defect anti-fluorite structure. However, the crystal system is different, i.e., tetragonal with c/a < 1 for the δ′-phase [8] and cubic for the δ-phase. In the XRD patterns of the samples, no peaks other than the peaks associated with Hf hydride and deuteride were observed.

Figure 1. XRD patterns of the samples of HfH_1.63 and HfD_1.60, together with the peak positions corresponding to the δ′-phase HfH_1.53 and the δ-phase HfD_1.628.

Figure 2 shows a typical example of the crystal orientation map obtained for the HfD_1.53 sample. It was confirmed that (1) there were no apparent crystalline orientations; (2) the sample contained no remarkable microcracks or voids; and (3) the grain sizes were around 30 μm. Similar results were obtained for other samples with different compositions. Thus it can be said that the samples prepared in the present study were isotropic polycrystalline high-quality materials.

Figure 2. Crystal orientation map obtained for the HfD_1.53 sample.

Figure 3 shows the XRD pattern of the HfD_1.60 sample in the 2θ range from 60° to 80°. At around 2θ = 67°, the (211) and (103) peaks were clearly observed. As can be seen in the peak positions of the δ′-phase HfH_1.53 (Figure 1), there exist two adjacent peaks at around 2θ = 38° and 67°. It is considered that this peak separation is caused by the shrinking of the crystal lattice along the c axial direction, and thus this would be a typical evidence of formation of the δ′-phase. It was confirmed from the XRD measurement that the HfD_1.60 sample was the δ′-phase. On the other hand, in the XRD pattern of the HfH_1.63 sample, such clear peak separation was not confirmed.

Figure 3. XRD pattern of the HfD_1.60 sample in the 2θ range from 60° to 80°.

Figure 4 shows the temperature dependence of C_P of the samples of HfH_1.63 and HfD_1.60. In the C_P–temperature curves for both samples, typical lambda-type peaks were observed at around 350 K, which was due to the second-order phase transition from the δ′-phase to the δ-phase. Although it was not confirmed from the XRD analysis that the HfH_1.63 sample was the δ′-phase, the C_P result supported that the HfH_1.63 sample was the δ′-phase at room temperature and with increasing temperature it underwent the phase change to the δ-phase. The peak positions for HfH_1.63 and HfD_1.60 were 320 and 360 K, respectively. Based on the Hf–H phase diagram [7], the higher hydrogen content leads to a lower phase transition temperature. In the present case, however, it is not clear whether the difference in the phase transition temperature observed in HfH_1.63 and HfD_1.60 is caused by the difference in the hydrogen isotope content or the isotope effect. It is thought that the larger C_P of HfD_1.60 than that of HfH_1.63 is caused by the difference in the frequencies of hydrogen and deuterium in the vibration term for the optical mode [9]. At 600 K, the C_P value of the δ-phase HfH_1.63 was 53 J mol⁻¹ K⁻¹, which was slightly larger than the theoretically calculated value (48 J mol⁻¹ K⁻¹) of the δ-phase HfH_1.73 [10]. One of the reasons for this difference is an electronic contribution to C_P, which has not been taken into consideration in the theoretical calculation. On the other hand, Arita et al. [5] reported a C_P value of approximately 40 J mol⁻¹ K⁻¹ at 600 K for the ϵ-phase HfH_1.83, which was significantly lower than the C_P value of the δ-phase HfH_1.63 obtained in the present study. Further investigation is needed to clarify the reason for this difference.

Figure 4. Temperature dependence of heat capacity (C_P) of the samples of HfH_1.63 and HfD_1.60.

Figure 5 shows the temperature dependence of the molar volume of HfH_1.63 and HfD_1.60, obtained from high-temperature XRD measurements. It can be seen that the molar volume of both HfH_1.63 and HfD_1.60 changed continuously during the phase transition. This is a typical evidence of the second-order phase transition. Since no significant volume change occurs, the cladding tubes of the Hf hydride neutron control rod are hardly subjected to stress from the Hf hydride pellets during the phase transition.

Figure 5. Temperature dependence of the molar volume of HfH_1.63 and HfD_1.60.

There exist various examples of the second-order phase transition, including conducting–superconducting transition in metals at low temperatures, order–disorder transitions in alloys, the onset of ferromagnetism, and the fluid–superfluid transition of liquid helium. In the hydrides of group IV elements, ZrH_x and TiH_x, an order–disorder phase transition has been observed, in which a phase containing regularly arranged hydrogen atoms transforms to a phase containing randomly arranged hydrogen atoms with increasing temperature [11]. It is well known that the δ-phase Hf hydride has a defect anti-fluorite crystal structure with randomly arranged hydrogen atoms. On the other hand, the distribution state of hydrogen atoms in the δ′-phase Hf hydride has yet to be completely revealed. Nonetheless, it is considered that the δ′/δ phase transition in Hf hydride and deuteride observed in the present study is an order–disorder transition similar to those observed in ZrH_x and TiH_x.

Finally, the effect of the phase transition on κ of Hf deuteride is discussed. As for Hf hydride, the samples for C_P and α measurements with almost the same hydrogen content could not be obtained. Thus, the α measurement was performed only for Hf deuteride. Figure 6 shows the temperature dependences of α, C_P, d, and κ of the HfD_1.60 sample. The temperature dependence of d was evaluated from the temperature dependence of molar volume. Here, the temperature range was set to be from room temperature to 420 K, because the phase transition temperature determined from the C_P measurement was 360 K. In calculating κ using the equation κ = α×C_P×d, the numerical data obtained by fitting the experimental results for α, C_P, and d were used. As can be seen in Figure 6, α and d changed continuously during the phase transition. Thus, a lambda-type peak observed in the κ–temperature curve was caused by the temperature dependence of C_P. Although a smooth curve is drawn in the temperature dependence of α, there is a possibility that a part of heat given by laser shot may be consumed by the phase transition. Actually, a small peak can be seen in the α vs. T curve around the phase transition temperature. The δ-phase showed lower κ values than those of the δ′-phase. One possible reason for this is the random arrangement of hydrogen atoms in the δ-phase. To clarify the magnitude relationship in κ between the δ′-phase and the δ-phase, the electrical conductivity should be measured because not only phonons but also electrons carry heat. In addition, to understand the mechanism of the phase transition, further investigations about reversibility and kinetics are needed.

Figure 6. Temperature dependences of thermal diffusivity (α), heat capacity (C_P), density (d), and thermal conductivity (κ) of the HfD_1.60 sample.

4. Summary

In this study, bulk samples of Hf hydride and deuteride, HfH_x and HfD_x, x = ∼1.6, were prepared and their thermal properties were investigated. From the temperature dependences of C_P and the molar volume, it was found that the second-order phase transition existed in both Hf hydride and deuteride at around 350 K. It is considered that this transition is one of the order–disorder phase transition of hydrogen isotope atoms in the crystal lattices of Hf hydride and deuteride. Not only C_P but also κ showed a lambda-type peak in its temperature dependence. The δ-phase with randomly arranged hydrogen isotope atoms showed lower κ values than those of the δ′-phase with regularly arranged ones. The results obtained in this study will provide essential basic information when Hf hydride is used as control rods in future fast reactors.

Acknowledgements

The present study includes results from “Development Study of Fast Reactor Core with Hydride Neutron Absorber” entrusted to Tohoku University by the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT).