- Email: [email protected]
Experimental study and thermodynamic description of the erbium–hydrogen–zirconium ternary system
Journal of Nuclear Materials 456 (2015) 7–16
Contents lists available at ScienceDirect
Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat
Experimental study and thermodynamic description of the erbium–hydrogen–zirconium ternary system Aurore Mascaro a,b, Caroline Toffolon-Masclet a, Caroline Raepsaet c, Jean-Claude Crivello b, Jean-Marc Joubert b,⇑ a b c
CEA-Saclay, Nuclear Energy Division, Nuclear Materials Department, SRMA, LA2M, 91191 Gif-Sur-Yvette, France Chimie Métallurgique des Terres Rares, Institut de Chimie et des Matériaux Paris-Est, CNRS, Université Paris-Est Créteil, 2-8 rue H. Dunant, 94320 Thiais, France CEA-Saclay, DSM/IRAMIS/NIMBE/LEEL, 91191 Gif-Sur-Yvette, France
a r t i c l e
i n f o
Article history: Received 26 February 2014 Accepted 6 September 2014 Available online 16 September 2014
a b s t r a c t The erbium–hydrogen–zirconium (Er–H–Zr) ternary system has been investigated experimentally at 350 °C using high purity materials. The extent of the ternary homogeneity domains have been measured using two combined experimental techniques: X-ray diffraction and ion beam analysis. An isothermal section is proposed according to these measurements. The three binary systems Er–H, Er–Zr and H–Zr were already assessed using the Calphad method. After making them compatible with each other and assigning the enthalpy of formation of the new generated end-members (including in H–Zr system) to the results of DFT calculations, the ternary system has been calculated without using any ternary parameter. The calculated isothermal section at 350 °C shows a fair agreement with the experimental data and the behavior at higher temperature is predicted. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction In order to increase the cycle length and the fuel burn up of light water reactors such as PWR (Pressurized Water Reactors), new cladding concepts are being developed. A solution currently studied at CEA consists of inserting solid burnable poisons, such as gadolinium or erbium, inside the cladding [1,2]. This new cladding tube is constituted by an internal layer made of zirconium alloy enriched in erbium, which is inserted between two regular zirconium base alloy layers. In PWRs, the cladding is surrounded by pressurized water (350 °C, 155 bars). Under these conditions, the water molecules dissociate at the surface and a part of the hydrogen released diffuses inside the cladding. Thus, it is interesting to have a precise knowledge of the interactions between hydrogen and the Zr(Er) inner layer. In the present study, the ternary system Er–H–Zr has been studied experimentally at the service temperature and described thermodynamically from the three associated binaries after making them compatible with each other. A literature survey on the present system is given in Section 2. In Section 3, the experimental work is described. DFT investigation is detailed ⇑ Corresponding author. Tel.: +33 1 49 78 13 44; fax: +33 1 49 78 12 03. E-mail address: [email protected] (J.-M. Joubert). http://dx.doi.org/10.1016/j.jnucmat.2014.09.015 0022-3115/Ó 2014 Elsevier B.V. All rights reserved.
in Section 4, followed by the thermodynamic calculations presented in Section 5. 2. Literature survey 2.1. The H–Zr binary system This system has been studied experimentally several times. It has also been thermodynamically assessed by four different authors [3–6]. The reported phases are the two allotropic forms of zirconium aZr and bZr, three different hydrides, c-ZrH, d-ZrH2 and e-ZrH2, and the H2 gas phase. The crystal structures of the solid phases are detailed in Table 1. Four invariant reactions can be observed in this system: a peritectoid reaction around 277 °C, a eutectoid reaction at 549 °C and two gas-peritectoid reactions at 797 °C and 867 °C. 2.2. The Er–H binary system The Er–H binary system has been re-evaluated recently and optimized thermodynamically [7]. This system is constituted by an aEr solid solution, two hydrides: b-ErH2 and c-ErH3 obtained by hydrogen occupancy of the interstitial sites of fcc and hcp
8
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
structures, respectively, and the H2 gas phase. The crystal structures of the solid phases can be found in Table 2. This system also shows two gas-peritectoid reactions at 433 °C and 1161 °C. 2.3. The Er–Zr binary system The Er–Zr binary system has been recently re-determined and optimized thermodynamically [8]. This system is constituted by two terminal hcp solid solutions aEr and aZr, separated by a miscibility gap, the bcc solution based on Zr at higher temperature and the liquid phase. The crystal structures of all the phases of this system can be found in Tables 1 and 2. Two invariant reactions can be observed in this system: a eutectoid reaction at 1045 °C and a eutectic reaction at 1380 °C. 3. Experimental work 3.1. Synthesis of the samples For the synthesis of the samples, distilled erbium (purity of 99.95%, China Rare Metals) and distilled zirconium (Van Arkel, purity of 99.98%) have been used as starting metals. Pure hydrogen (99.9999%) has been used for the hydrogenation. The raw metals were conserved in a glove box under argon atmosphere, to avoid oxidation in air. Just before synthesis, the zirconium was filed to remove the surface layer which could have been contaminated. Due to irregular shapes, the erbium could not be filed. Er–Zr samples of 2–3 g have been synthesized by arc melting under argon atmosphere (U grade, 800 mbar) purified by melting a zirconium getter. The samples have always been melted three times without important weight losses and turned upside down to homogenize them. Then, the samples were annealed over 6 weeks (1000 h) at 800 °C in order to reach thermodynamic equilibrium at this temperature. At this step, the samples were checked by X-ray diffraction (XRD) and Electron Probe Micro Analysis (EPMA). Then, they were cut into small pieces and introduced into stainless steel sample holders which were placed in a resistance furnace at 350 °C for the hydrogenation. The container was connected to a Sieverts’ apparatus working in a hydrogen atmosphere. The hydrogen pressure in the different volumes allows for monitoring of the chemical composition of the samples. To reach thermodynamic equilibrium, the ternary samples were kept inside the furnace at 350 °C during at least 3 days (72 h). Samples with higher hydrogen content (more than approximately 30 at.%) did not show any change after 3 days. The samples with lower hydrogen content were kept seven days. Note that equilibrium between hydrogen and alloys is reached much faster than between the metallic elements themselves. This behavior has already been observed in the case of the hydrogenation of Pd–Rh alloys [9]. These later alloys decompose according to the low temperature Pd–Rh miscibility gap in the presence of hydrogen at a temperature at which they would never reach equilibrium without the presence of hydrogen. However, it is possible that, very close to the Er–Zr binary border, the equilibrium can never be reached at 350 °C. Finally, the samples were air quenched. After the synthesis, the stainless steel sample holder can be opened
Table 2 Crystal structure of the phases of the Er–H binary system. Data
aEr
b-ErH2
c-ErH3
Space group
P63/mmc
Phase prototype Lattice parameters
Mg a = 3.559 Å c = 5.587 Å [37]
Fm3m CaF2 a = 5.123 Å
P3c1 HoH3 a = 6.272 Å c = 6.526 Å [38,41,42]
References
[38–41]
under ambient atmosphere due to the high stability of the hydride phases in air. 3.2. Phase structure characterization and chemical composition investigation In order to determine the phases involved in the different equilibria, each sample has been characterized by XRD at room temperature on a Bruker D8 Advance diffractometer (copper radiation, 40 kV, 40 mA, Bragg–Brentano geometry, h–h mode, step-by-step scan). The samples with high hydrogen content are powders and can be measured without any preparation. The samples with low hydrogen content that cannot be reduced into powder have been measured in the massive form. The XRD patterns have been processed by Rietveld refinement [10] using the Fullprof program [11], to refine the cell parameters and obtain the mass fraction of each phase. Hydrogen composition in the different phases cannot be determined by usual means. To determine the chemical composition of each phase, ion beam analysis has been used at the nuclear microprobe of DSM/IRAMIS/SIS2M/LEEL [12], CEA Saclay, France. For these measurements, combined RBS (Rutherford Back-Scattering) and ERDA (Elastic Recoil Detection Analysis) has been used [13]. RBS is sensitive to the heavy elements, such as Er, Zr or Au coating and allows the quantification of Er and Zr, while ERDA quantifies exclusively the H content. Before the analysis, the samples have been prepared in small brass tubes filled with resin, polished, joined together and then metalized with a gold coating of roughly 10 nm. For the analysis, a 3 lm 3 lm alpha beam of 3 MeV has been used. Due to the grazing angle incidence of the ERDA experimental configuration, it corresponds to a 12 lm 3 lm beam at the surface of the sample which may limit the analysis of small precipitates. Counting time was between half an hour for the samples with higher hydrogen content and few hours for those with low hydrogen content. After the analysis, the raw data were sorted with the RISMIN software [14] in order to obtain the different cartographies and spectra. Then, the SIMNRA software [15] was used to determine the elemental composition from the ERDA and RBS spectra. 3.3. Results 20 ternary samples were synthesized in the whole composition range at 350 °C and analyzed by XRD at room temperature. The results of the characterization of these samples is presented in Table 3. An example of a diffraction pattern analyzed with the Riet-
Table 1 Crystal structure of the phases of the H–Zr binary system. Data
aZr
bZr
c-ZrH
d-ZrH2
e-ZrH2
Space group
P63/mmc
Fm3m CaF2 a = 4.777 Å
I4/mmm
Mg a = 3.233 Å c = 5.148 Å [32]
Im3m W a = 3.610 Å
P42/n
Phase prototype Lattice parameters References
[33]
ZrH a = 4.586 Å c = 4.948 Å [34]
[35]
ThH2 a = 3.495 Å c = 4.463 Å [36]
Table 3 Lattice parameters of the different samples determined by XRD and their chemical composition measured by ERDA + RBS. Sample composition
Phases
at.%
H/M
Er1Zr27H72
Er0.05Zr0.95H2.57
e-ZrH2
Er1Zr95H4
Er0.01Zr0.99H0.04
d-ZrH2
Er2Zr29H69
Er0.05Zr0.95H2.23
Er2Zr94H4
Er0.025Zr0.975H0.04
Er2.3Zr38.7H59
Er0.05Zr0.95H1.43
Mass fraction (%)
4.507
Er2.2Zr43.5H63.3
Er0.05Zr0.95H1.38
aZr
4.783 3.247
5.190
/ Er1.0Zr98.2H0.8
/ Er0.01Zr0.99H0.01
e-ZrH2
99
3.513
4.512
Er1.9Zr35.2H62.9
Er0.05Zr0.95H1.70
d-ZrH2
1 99
4.785 3.239
5.163
/ Er2.5Zr96.8H0.7
/ Er0.025Zr0.975H0.01
93 7
4.787 3.248
5.212
Er2.1Zr35.9H62.0 /
Er0.06Zr0.94H1.63 /
27 12 61
4.786 5.157 3.242
5.159
/ / Er4.2Zr89.7H6.1
/ / Er0.04Zr0.96H0.06
1 99
4.781 3.242
5.164
/ Er6.5Zr92.9H0.6
/ Er0.07Zr0.93H0.01
1 98 1
4.782 3.243 5.140
5.160
/ Er6.5Zr92.9H0.6 /
/ Er0.07Zr0.93H0.01 /
39 57 4
4.803 3.257 5.172
5.181
/ Er14.6Zr82.9H2.5 /
/ Er0.15Zr0.85H0.03 /
b-ErH2
1 98 1 1 98 1
4.789 3.250 5.140 4.802 3.260 5.163
/ Er7.9Zr90.9H1.2 / / Er9.6Zr89.1H1.3 /
/ Er0.08Zr0.92H0.01 / / Er0.10Zr0.90H0.01 /
/ / Er22.1Zr7.3H70.6
/ / Er0.75Zr0.25H2.40
Er13.2Zr27.5H59.3 Er19.65Zr19.65H60.7
Er0.32Zr0.68H1.46 Er0.50Zr0.50H1.54
Er16.8Zr20.6H62.6 Er22.6Zr15.1H62.3
Er0.45Zr0.55H1.63 Er0.60Zr0.40H1.65
d-ZrH2 d-ZrH2 b-ErH2
Er0.05Zr0.95H0.11
d-ZrH2
aZr Er5Zr91H4
Er0.05Zr0.95H0.04
d-ZrH2
aZr b-ErH2 Er5.5Zr67H27.5
Er0.075Zr0.925H0.38
d-ZrH2
aZr b-ErH2 Er7Zr89H4
Er0.075Zr0.925H0.04
d-ZrH2
aZr Er9.5Zr85H5.5
Er0.1Zr0.9H0.06
b-ErH2 d-ZrH2
aZr
5.164
5.168
Er16.5Zr13.5H70
Er0.55Zr0.45H2.33
e-ZrH2 b-ErH2 c-ErH3
27 1 72
3.500 5.092 6.244
Er18.3Zr20.6H61.1
Er0.47Zr0.53H1.57
d-ZrH2 b-ErH2
28 72
4.822 5.091
Er19Zr15H66
Er0.55Zr0.45H1.94
e-ZrH2 b-ErH2
39 61
3.497 5.096
b-ErH2 c-ErH3
1 99
5.111 6.255
6.497
/ Er25.4Zr1.2H73.4
/ Er0.95Zr0.05H2.76
b-ErH2 c-ErH3
96 4
5.105 6.252
6.493
Er32.0Zr1.8H66.2 Er30.5Zr1.8H67.7
Er0.95Zr0.05H1.96 Er0.93Zr0.07H2.06
Er25Zr1.5H73.5 Er29Zr2H69
Er0.95Zr0.05H2.80 Er0.95Zr0.05H2.23
4.630 6.469
4.631
Er31Zr8.5H60.5
Er0.78Zr0.22H1.53
b-ErH2
100
5.050
Not analyzed
Not analyzed
Er45Zr12.5H42.5
Er0.78Zr0.22H0.74
aZr aEr
/ / /
3.257 3.567 5.051
5.127 5.579
/ Er59.0Zr16.6H24.4 Er27.3Zr7.7H65.0
/ Er0.78Zr0.22H0.32 Er0.78Zr0.22H1.86
Er47Zr2H51
Er0.95Zr0.05H1.04
2 98
3.548 5.107
5.562
Er76.3Zr3.2H20.5 Er35.8Zr1.5H62.7
Er0.96Zr0.04H0.26 Er0.96Zr0.04H1.68
1 49 50
3.196 3.536 5.096
5.294 5.546
/ Er82.8Zr10.2H7.0 Er33.6Zr4.1H62.3
/ Er0.89Zr0.11H0.08 Er0.89Zr0.11H1.65
b-ErH2
aEr b-ErH2
Er51Zr6H43
Er0.9Zr0.1H0.75
aZr aEr b-ErH2
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
3.506
3 97
aZr Er4.5Zr85.5H10
Composition measured by ERDA H/M
100
aZr Er0.05Zr0.95H0.16
Composition measured by ERDA at.%
c (Å)
aZr
Er4Zr82H14
Lattice parameters a (Å)
9
10
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
Intensity (counts)
20000
10000
0
δ-ZrH 2 β-ErH 2
Fig. 4. This isothermal section presents two solid solutions (aEr and aZr) and four hydrides (b-ErH2, c-ErH3, d-ZrH2 and e-ZrH2). aEr, contrary to aZr, has a large ternary extension. c-ErH3 and eZrH2 have small ternary extensions while d-ZrH2 and b-ErH2 have important extensions into the phase diagram. Nevertheless, a miscibility gap has been evidenced between these two hydrides with the same CaF2 structure type. Finally, the isothermal section is characterized by the presence of a large field of three-phase equilibrium between aEr, aZr and b-ErH2 that has been evidenced in several samples. 3.4. Discussion
30
40
50
60
70
80
90
100
110
120
2 (°) Fig. 1. X-ray diffraction pattern of sample Er18.3Zr20.6H61.1 with the calculated pattern involving the two phases d-ZrH2 and b-ErH2. The difference is shown below. This sample is characteristic of the presence of a miscibility gap in the phase with CaF2 structure.
Fig. 2. ERDA H mapping showing hydrides (in blue and red) in Er9.5Zr85H5.5 sample.
veld method for the phase characterization is presented in Fig. 1. With ion beam analysis, we obtain element mapping as shown in Fig. 2. RBS and ERDA spectra are extracted with the SIMNRA software for H-rich (blue1 and red in Fig. 2) and H-poor (white and light blue in Fig. 2) regions (Fig. 3). The RBS spectrum gives the Er and Zr contribution. The Au coating can be seen as a thin peak at high energies. In the ERDA spectrum an important difference can be observed between the hydride region and the solid solution. Indeed, hydrides give rise to a much larger signal than solid solutions. Thanks to the analysis of each sample with XRD and combined RBS-ERDA, a 350 °C isothermal section of the ternary phase diagram may be plotted (Fig. 4). Note that, due to slight composition deviations, the point representative of the composition of several samples may not exactly fall in the corresponding equilibrium evidenced in Table 3. Also, in some cases, the ERDA hydrogen concentration measurement in precipitates of a minor phase may be biased by the presence of the surrounding matrix. For this reason, the same equilibrium (e.g. aEr–aZr–b-ErH2) may be measured differently in different samples. We chose to leave all the different measurements in Table 3 to show the scatter and the drawing may result from the analysis of different samples showing the same equilibrium but with different phase amounts. From this analysis, we drew the isothermal section as the most probable in
1 For interpretation of color in Fig. 2, the reader is referred to the web version of this article.
All the crystal structures and the lattice parameters found in this study using XRD measurements followed by Rietveld refinement are consistent with the literature. The spatial resolution of ERDA combined with RBS analysis (12 lm 3 lm) is not sufficient to resolve small precipitates or fine microstructure of solid solutions. No valid chemical composition can be obtained for these individual small areas. This explains the unmeasured phases in Table 3. The 350 °C experimental isothermal section only contains already known phases and is consistent with the reported binary borders. No ternary compound has been evidenced. Yet, a very large extension of both CaF2-type hydrides is observed leaving a tiny miscibility gap between them. No data is available in the literature on the Er–H–Zr ternary system. However, two other rare earth–H–Zr ternary systems have been investigated so far. The Y–H–Zr has been studied by Shcherbak et al. [16] and Fadeyev et al. [17] and presents a miscibility gap between the CaF2 hydrides (d-ZrH2 and YH2) from 25 °C to 900 °C with no reported mutual solubilities. In contrast, the Sc–H–Zr ternary system studied by Semenenko et al. [18] shows a complete homogeneity domain between the two CaF2 structures. The Er–H–Zr system stands between these two opposite behaviors with a CaF2 phase presenting both a miscibility gap at 350 °C and extended solubility ranges on its two sides. 350 °C corresponds to the service temperature in a PWR. The present results show that, for the amount of erbium foreseen in our application that is 3–6 wt% Er (1.5–3 at.% Er), hcp phase is in equilibrium with d-ZrH2, which is the usual hydride formed in PWR reactors. 4. DFT investigation The heats of formation of hydrides and enthalpies of mixing of several solutions were calculated in the frame of the Density Functional theory (DFT) [19]. For the solutions (Er, Zr) and (Er, Zr)H2, we used the Special Quasi-Random Structures (SQS) [20] technique. 4.1. Methodology The DFT calculations were carried out using the Vienna ab initio simulation package (VASP) [21,22]. The generalized gradient approximation was used for the exchange and correlation energy included in the PBE functional [23]. An energy cutoff of 400 and 800 eV was used for the plane-wave basis set for calculations using SQS procedure and determination of heat of formation, respectively. Both the internal cell parameters and atomic coordinates were relaxed, carefully preserving the original crystal symmetries for the SQS structures. For the heat of formation of the ordered hydrides, the contributions from zero-point energies (ZPE) of the H atoms were estimated within the Einstein model. The SQS structures at 3 compositions (0.25, 0.5, 0.75) of binary (Er, Zr) solutions have been taken from the literature in fcc [24], bcc [25] and hcp [26] structures within the 16-atom description. In addition, infinite
11
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
Δ
Fig. 3. RBS (a) and ERDA (b) spectra of the Er47Zr2H51 sample.
ε
Fig. 4. Er–H–Zr experimental isothermal section at 350 °C.
dilution is modelled by the calculation at 1/16 and 15/16 compositions for all solid solutions using a supercell. For the SQS of (Er, Zr)H2, we have used a fcc based SQS cell with additional hydrogen atoms in the tetragonal interstitial sites in order to reproduce the CaF2 structure type. 4.2. Heat of formation of hydrides As described in the following section (5. Thermodynamic modelling), the model used for both hcp and fcc phases in the Er–H system generates new end-members in the Zr–H system with hydrogen in octahedral or triangular and/or tetrahedral sites. The heat of formation of these metastable compounds in the Zr–H system has been calculated with a procedure similar to that used for the Er–H system [27]. The tetragonal e-ZrH2 phase has also been calculated for both ZrH2 and ErH2 compositions. Fig. 5 presents the results obtained for the different configurations in Zr–H system. The ground state represented as a solid line is in agreement with the experimental observation. Table 4 presents the numerical results of all the calculations. The enthalpies of formation of both d and e phases compare very well with recent DFT calculations [6]. The small difference observed (3–6 kJ mol1 f.u.) may be explained by a different choice of pseudo-potentials. 4.3. Enthalpies of mixing of (Er, Zr) solutions Fig. 6 shows the enthalpies of mixing in fcc, bcc and hcp phases of the Er–Zr system. Whatever the structure, these energies are positive, including in hcp, the stable structure of both elements at 0 K. As observed in other systems, the magnitude of the enthalpy
Fig. 5. DFT calculated enthalpies of formation per mole of compound of the ZrHx compounds.
of mixing is similar for fcc and hcp. The repulsive character is more pronounced in the bcc phase. The SQS structure relaxation has been done in 2 steps. First, only the cell volume is allowed to relax, then, the internal parameters are optimized keeping the obtained volume fixed. The results at both steps are presented in Fig. 6. Those obtained at the second step are in better agreement with the enthalpies deduced from the thermodynamic assessment of the system [8]. In spite of this result, it is still not clear which kind of relaxation best describes the actual thermodynamic properties. This kind of comparison needs to be extended to a larger number of systems before hasty use of SQS results in thermodynamic assessments.
4.4. Enthalpies of mixing of (Er, Zr)H2 hydride As described in Section 3, a miscibility gap has been evidenced between the two CaF2 hydrides (d-ZrH2 and b-ErH2), and was the motivation to estimate the enthalpies of mixing in (Er, Zr)H2. The calculated results with the two relaxation schemes are illustrated in Fig. 7. Both result sets present positive and symmetric mixing energies which gives rise to a symmetric miscibility gap at low temperature as evidenced experimentally. The critical temperature TC could be roughly estimated considering that at TC, the excess mixing energy compensates the configurational energy in the middle of the miscibility gap, i.e. TC = DHmix/(R ln ½) = 474 or 954 K with the first or second relaxation scheme, respectively.
12
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
Table 4 DFT calculation results on the binary systems, ZPE contribution included. Composition Zr ZrH ZrH2 ZrH3 ErH2 a
HCP-trian DHfor (J mol1) a
0 25,857 132,895 168,834 See [27]
HCP-octa DHfor (J mol1) a
0 53,498 132,895 97,500
FCC DHfor (J mol1)
Tetragonal DHfor (J mol1)
3902 57,566 158,335 119,159
None None 164,529 None 205,126
a
a
Stable phase.
Fig. 6. SQS calculated enthalpies of mixing of (Er, Zr) binary system in (a) fcc, (b) bcc and (c) hcp with 2-step structure relaxation scheme: volume () and internal parameters (N). Solid line corresponds to the energy assessed in [8] (the fcc value has been taken equal to hcp).
Fig. 7. SQS calculated enthalpies of mixing of (Er, Zr)H2 hydrides in CaF2 structure within the 2-step structure relaxation scheme: volume () and internal parameters (N).
5. Thermodynamic modelling The Er–H–Zr phase diagram has been obtained by the projection of the three associated binaries using Thermo-Calc software [28]. The two binary systems Er–H and Er–Zr have been thermodynamically described only once in the literature [7,8] and both descriptions have been accepted. The choice made for the H–Zr system is justified hereunder. Finally, the models have been made compatible between the three binaries in order to perform the calculation of the ternary system.
5.1. Different H–Zr optimizations The H–Zr binary system has been assessed by Dupin et al. [3], Königsberger et al. [4] and Ukita et al. [5]. In none of the assessments has the liquid phase been considered. Differences are noted concerning the number of solid phases considered and the choice
of the model for interstitial solutions. Königsberger et al. considered only one of the three hydrides (d-ZrH2), Dupin et al. only two (d-ZrH2 and e-ZrH2) while Ukita et al. considered all of them (d-ZrH2, e-ZrH2 and c-ZrH). As shown in Table 5, all the phases are described using the sublattice model [29]. From this Table, one may also observe the differences concerning the choice of the multiplicity of the interstitial sites. Königsberger et al. and Dupin et al. use the same multiplicity for HCP_A3 (aZr) solid solution though they do not consider the same sites (octahedral in one case, half of the tetrahedral sites in the other case). Ukita et al. on the contrary, considered a multiplicity of 2 corresponding to the tetrahedral sites. In the BCC_A2 phase (bZr), the multiplicities are also different: 1.5, 3 and 6 for the different authors. For a deeper discussion about these different assumptions, see Ref. [30]. For our calculation, the description of Dupin et al. was preferred because it used much less optimized parameters than Ukita et al. and because it described the e-ZrH2 phase contrary to Königsberger et al. The absence of the c-ZrH phase is not an issue since it is a low temperature phase, stable far below the investigated temperatures. It may be easily added to the description of Dupin et al. as shown recently by Zhong and Macdonald [6]. 5.2. Comparison of the models used in the three binaries In order to combine the three binaries, each similar phase has to be described by the same model. The models used for each phase of the Er–H, Er–Zr and H–Zr binary systems are compared in Table 6. 5.2.1. Gas and liquid phases The only species considered in the gas phase is the di-hydrogen H2 in the Er–H binary system. In the H–Zr binary system, the considered gaseous species are H, H2, Zr and Zr2. The gas phase is described as an ideal gas with ideal mixing of the different species. The liquid phase has not been described in either of the two binary metal-hydrogen systems and is only described in the Er–Zr binary system. A substitutional solution model has been used and no hydrogen solubility was considered [8]. It is, regardless, extremely low at the temperatures at which the liquid appears.
13
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16 Table 5 Comparison of the models used for the H–Zr assessments (h stands for vacancy). Phase
Phase name
Dupin et al. [3] octa
aZr
HCP_A3 BCC_A2 FCC_C1 ZRH2_EPSILON ZRH_GAMMA
Königsberger et al. [4] tetra
(Zr)(h) (H, h) (Zr)(H, h)octa 3 (Zr)(H, h)tetra 2 (Zr)(H, h)tetra 2
bZr d-ZrH2 e-ZrH2 c-ZrH
Ukita et al. [5]
octa
(Zr)(H, h) (Zr)(H, h)octa 1.5 (Zr)(H, h)tetra 2
(Zr)(H, (Zr)(H, (Zr)(H, (Zr)(H, (Zr)(H,
h)tetra 2 h)octa 6 h)tetra 2 h)tetra 2 h)tetra 1
Table 6 Comparison of the models used in the different binary descriptions (h stands for vacancy). Binary system
Phase
Space group
Structure type
Description name
Model used
Er–H [7]
aEr
P63/mmc
b-ErH2
Fm3m
Mg CaF2
HCP_A3 FCC_C1
(Er)(H, h)octa(H, h)tetra 2 (Er)(H, h)octa(H, h)tetra 2
c-ErH3
P3c1
HoH3
HCP_A3
(Er)(H, h)tri(H, h)tetra 2
aZr
P63/mmc
bZr
Im3m
Mg W
HCP_A3 BCC_A2
(Zr)(h)octa(H, h)tetra (Zr)(H, h)octa 3
d-ZrH2
Fm3m I4/mmm
CaF2
FCC_C1
(Zr)(H, h)tetra 2
ThH2
ZRH2_EPSILON
(Zr)(H, h)tetra 2
Im3m P63/mmc
W
BCC_A2
(Er, Zr)(h)octa 3
Mg
HCP_A3
(Er, Zr)(h)octa
Zr–H [3]
e-ZrH2 Er–Zr [8]
bZr
aZr
5.2.2. ZRH2_EPSILON (e-ZrH2) This phase is present only in the H–Zr binary system. The model used is as follows: (Er, Zr)(H, h)tetra to allow ternary solubility of 2 erbium (h stands for vacancy). Thus, the e-ErH2 end-member (space group I4/mmm and structure type ThH2) has to be introduced and its enthalpy value has been taken from the DFT calculations of this work. 5.2.3. BCC_A2. (bcc) This phase appears in both H–Zr [3] and Er–Zr [8] phase diagrams. If we combine both models (Zr)(H, h)octa and (Er, Zr)(h)octa , 3 3 octa the new model obtained is (Er, Zr)(H, h)3 . For the enthalpy of formation of the end-member ErHocta (bcc) as a first approximation, 3 the value of the ErH3 fcc phase has been used, i.e. DHfor ErH3 bcc = 231,708 J mol1. 5.2.4. FCC_C1. (b-ErH2, d-ZrH2) This FCC_C1 model describes the two hydrides b-ErH2 and dZrH2 which have the same crystal structure type, CaF2. However in the H–Zr phase diagram this phase is described with two sublattices whereas three are needed in the Er–H phase diagram (in order to describe the hyper-stoichiometric side of the hydride b-ErH2). Adding a sublattice describing the octahedral interstitial sites in the fcc phase yields the model (Er, Zr)(H, h)2(H, h). New end-members are created which have been assigned the enthalpies of formation calculated by DFT. On the other hand, the defined phase shows an existence range in the binary Er–Zr system in which the fcc phase was not optimized. It was assumed that the binary interaction in fcc was similar to the one in the hcp phase, as suggested by the SQS calculations in Fig. 6. This is sufficient to avoid the unrealistic presence of a stable fcc phase in the calculation of the binary Er–Zr system. 5.2.5. HCP_A3. (hcp, c-ErH3) In the H–Zr optimization, the HCP_A3 phase is described by two sublattices, one for the metallic atoms and the second one for half of the tetrahedral interstitial sites. In fact, the multiplicity of this site is 1 in the H–Zr binary system [3] instead of 2 in the Er–H optimization, in order to describe the c-ErH3 phase which also needs the third sublattice describing the octahedral sites. To combine the H–Zr optimization with the other binaries, the tetrahedral sub-
lattice multiplicity has to be doubled and the octahedral sublattice has to be introduced to yield the following model: (Er, Zr)(H, h)2(H, h). The procedure will be described hereunder. 5.3. Modification of H–Zr assessment 5.3.1. Modification of the tetrahedral multiplicity In order to make the three binary systems compatible, the description of the H–Zr system obtained by Dupin et al. [3] (called hereafter model 1) had to be adapted. Changing the multiplicity of the tetrahedral interstitial sublattice in the HCP_A3 description from 1 to 2 (in the so-called model 2) yields a change of end-member from ZrH to ZrH2. The development of the equations of the two models shows that identity is obtained if the reference term (Eq. (1))
GZrH ¼ 45; 965 þ 41:6T þ GHSERZR þ GHSERH
ð1Þ
in model 1, is changed to
GZrH2 ¼ 2ð45; 965 þ 41:6 TÞ þ GHSERZR þ 2GHSERH
ð2Þ
in model 2. However, we have to consider that the terms related to configurational entropies are different. This can be inferred from Fig. 8 in which the ideal contribution to the Gibbs energy has been plotted in the two models. Because of higher multiplicity of the insertion site in model 2, the configurational contribution is larger. In particular for xH = 0.5, the configurational term is zero in model 1 since all the interstitial sites are occupied while it is at its maximum in model 2 and is equal to 2RTln(0.5). There is no simple analytical relation allowing the correction of the difference between the models. Therefore we used an approximation equal to 4yHRTln(1/ 2) where y is the site fraction that allows having the same Gibbs energy in both models for xH = 0 and xH = 0.5. This correction has also been plotted in Fig. 8 and it can be seen that the difference is minimal, in particular at low hydrogen content corresponding to the domain in which the phase is stable. At a composition higher than xH = 0.5, where the phase was not defined in model 1, the contribution destabilizes the phase. It is also worth mentioning that the configurational contribution is relatively small compared to the reference terms at temperatures below 1100 K where the phase is stable. To confirm this point, the binary H–Zr system
14
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
gas phase are taken from Ref. [31]. All the solid phases were modelled using the sublattice model [29]. The Gibbs energy of each phase u per mole of formula unit is expressed as follows:
Gu ¼ ref Gu þ id Gu þ ex Gu
ð4Þ
For u = bcc (k = 3) and e (k = 2), where only one interstitial lattice of multiplicity k is present: u u 0 00 0 00 u 0 00 Gu ¼ y0Er y00H Gu Er:H þ yEr yVa GEr:Va þ yZr yH GZr:H þ yZr yVa GZr:Va
ð5Þ
Gu ¼ RTððy0Er ln y0Er þ y0Zr ln y0Zr Þ þ kðy00H ln y00H þ y00Va ln y00Va ÞÞ
ð6Þ
0 00 00 u Gu ¼ y0Er y0Zr y00Va Lu Er;Zr:Va þ yZr yH yVa LZr:H;Va
ð7Þ
ref
id
ex
Fig. 8. Gibbs energies of the hcp phase at 1000 K showing the configurational terms in the H–Zr model (model 1) and in the Er–H–Zr ternary database (model 2) and the Gibbs energy after correction (model 2 corrected).
has been plotted with model 2 and no visible modification is observed. Technically, the correction term for the change of the configurational entropy, since it is linear as a function of the site fraction, can be introduced in the reference term as follows:
where y represents the site fraction of the given element in the given sublattice. For u = hcp and fcc, where two interstitial lattices represent tetrahedral and octahedral sites: ref
u 0 00 000 u 0 00 000 u Gu ¼ y0Er y00Va y000 Va GEr:Va:Va þ yZr yVa yVa GZr:Va:Va þ yEr yH yVa GEr:H:Va u 0 00 000 u 0 00 000 u þ y0Zr y00H y000 Va GZr:H:Va þ yEr yVa yH GEr:Va:H þ yZr yVa yH GZr:Va:H u 0 00 000 u þ y0Er y00H y000 H GEr:H:H þ yZr yH yH GZr:H:H
id
ð8Þ
Gu ¼ RTððy0Er ln y0Er þ y0Zr ln y0Zr Þ þ 2ðy00H ln y00H þ y00Va ln y00Va Þ 000 000 000 þ ðy000 H ln yH þ yVa ln yVa ÞÞ
GZrH2 ¼ 2ð45; 965 þ 41:6T þ 2RT lnð1=2ÞÞ þ GHSERZR þ 2GHSERH
ð3Þ
ex
ð9Þ
u 0 00 00 000 u Gu ¼ y0Er y0Zr y00Va y000 Va LEr;Zr:Va:Va þ yEr yH yVa yVa LEr:H;Va:Va u
u
0 00 000 000 þ y0Er y00H y00Va y000 H LEr:H;Va:H þ yEr yH yH yVa LEr:H:H;Va
5.3.2. DFT calculations in the H–Zr binary system Enthalpies of formation of the new end-members generated by the new model for hcp and fcc phases and the tetragonal e-ZrH2 have been calculated by DFT and presented in Section 3 (Fig. 5, Table 4). Not all of them were used in the description since we decided to keep the description by Dupin et al. [3]. So, for the end-members already existing or adapted (ZrH2 in fcc, ZrH in hcp transformed into ZrH2, e ZrH2), the assessed values have been conserved. It is important to note that they are in excellent agreement with the DFT values for the stable phases (d-ZrH2 and e-ZrH2). The difference is larger for hcp ZrH2 which has been transformed from the assessed value of ZrH in model 1. This phase is metastable and therefore much more difficult to assess. The enthalpies of the new compounds generated by the presence of the octahedral site have been assigned their DFT values (see Table 7). For the entropies of formations, either the assessed values have been kept or ideal values have been chosen (65 J mol1 K1 per hydrogen atom corresponding to half of the entropy of formation of an H2 molecule). 5.4. Thermodynamic equations The equations for the Gibbs energies of pure Er and Zr in fcc, hcp and bcc structure and liquid as well as molecular hydrogen in the
000 u þ y0Er y00Va y000 H yVa LEr:Va:H;Va
ð10Þ
The end-members and interaction parameters are taken from the three papers [3,7,8] unless they have been modified as explained above. The values for the different end-members are summarized in Table 7. The thermodynamic database file is supplied as Supplementary material to this paper. 5.5. Results Equilibrium has been obtained by Gibbs energy minimization using Thermo-Calc. Several Er–H–Zr isothermal sections at 350 °C, 600 °C and 1100 °C have been calculated from the three binaries made consistent. They are presented in Figs. 9–11. At 350 °C (Fig. 9), six single phase regions are present and five three phase equilibria have been identified. A miscibility gap can be observed between the two CaF2 hydrides b-ErH2 and d-ZrH2. At 600 °C (Fig. 10), the two allotropic forms of the zirconium can be observed (bZr is nearly restricted to H–Zr binary border). e-ZrH2 is still stable under 105 Pa contrary to c-ErH3. The miscibility gap between b-ErH2 and d-ZrH2 closes above 447 °C and is replaced by a complete solubility range. One may note that this temperature is located just between the two TC estimated from the SQS calcula-
Table 7 Enthalpies and entropies of formation used in the H–Zr description (per mole of compound). Composition
Zr ZrH ZrH2 ZrH3 a
HCP
FCC
Tetragonal
DHfor (J mol1)
DSfor (J mol1 K1)
DHfor (J mol1)
DSfor (J mol1 K1)
DHfor (J mol1)
DSfor (J mol1 K1)
0 53,498 91,930a 168,834
0 65 47.4a 195
7600a 61,453 170,490a 91,710
0.9a 65 208.2a 195
– – 168,215a –
– – 110.5a –
From Dupin et al. [3] or adapted from Dupin et al.
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
15
5.6. Discussion
Fig. 9. Er–H–Zr isothermal section at 350 °C calculated by projection of the three binaries.
The 350 °C calculated and experimental isothermal sections can be compared (Figs. 4 and 9). All the equilibria evidenced experimentally are well reproduced by the calculation. The calculation reproduces as well, without the introduction of any ternary interaction parameter, the miscibility gap between the two CaF2 hydrides. The shape of the aEr homogeneity domain is not so well reproduced. We did not want to introduce ternary interaction parameters to obtain a better agreement since we are not certain that the experimental data close to the metallic border represent equilibrium at this very low temperature for a metallic system. Given the synthesis technique used (hydrogenation of alloys annealed at 800 °C), several samples may have remained in a paraequilibrium state (equilibrium of the hydride phases with frozen quenched solid solution). This is one of the major outcomes of Calphad to be able to predict equilibrium at temperatures at which it is impossible to reach experimentally. 600 °C is an incidental temperature in PWRs. The 600 °C isothermal section shows the bZr phase and a complete homogeneity domain between the two CaF2 hydrides. In case of incident, the chemistry of the hydride would be changed due to erbium solution in the d-ZrH2 phase. Finally, 1100 °C is an accidental temperature for PWRs. The result shows that at this point, the hydrogen can be trapped in the form of b-ErH2 hydrides. This can limit the di-hydrogen gas formation.
6. Conclusion
Fig. 10. Er–H–Zr isothermal section at 600 °C calculated by projection of the three binaries.
The erbium–hydrogen–zirconium ternary system has been studied experimentally. Different and complementary experimental techniques such as XRD and a combination of ERDA and RBS have been used in order to find the equilibria and phase compositions. A first evaluation of this ternary system has been proposed at 350 °C. To model this ternary system, the three associated binaries have been made compatible with each other. The calculation at 350 °C shows a fair agreement with the experimental data without the use of any ternary parameter. A miscibility gap has been evidenced at 350 °C between the two hydrides both experimentally and by calculations. This miscibility gap is expected from the calculation to disappear at high temperatures. From the DFT approach, heats of formation of the new end-members generated by the model in the ternary system have been calculated. Even if the SQS results have not been directly considered in the assessment of the present work, SQS mixing energies show reliable agreement with the assessment, but still need to be tested on other systems before a systematic use. Finally, extrapolations using the Calphad technique allow for a good approximation of behavior at the temperatures which experiments become unfeasible.
Acknowledgements
Fig. 11. Er–H–Zr isothermal section at 1100 °C calculated by projection of the three binaries.
tions on (Er, Zr)H2 in CaF2 (201 or 681 °C, see Section 4.4). At 1100 °C (Fig. 11), a large homogeneity domain of the aEr phase can be noticed. Zirconium exists only in the b form and the only hydride stable at this high temperature is the under-stoichiometric b-ErH2.
The financial support from CEA is acknowledged. The authors wish to thank the nuclear microprobe analysis team and Didier Hamon for the EPMA measurements. DFT calculations were performed using HPC resources from GENCI-IDRIS (Grants 2012096175 and 2013-096175).
Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jnucmat.2014. 09.015.
16
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
References [1] J.-C. Brachet, C. Chabert, P. Olier, S. Urvoy, French Patent, BD 1725, 2006. [2] J.-C. Brachet, P. Olier, S. Urvoy, V. Vandenberghe, C. Chabert (Eds.), in: TopFuel 2009 Conference, Paris, 2009 (Paper 2189). [3] N. Dupin, I. Ansara, C. Servant, C. Toffolon, C. Lemaignan, J.-C. Brachet, J. Nucl. Mater. 275 (1999) 287–295. [4] E. Königsberger, G. Eriksson, W.A. Oates, J. Alloys Compd. 299 (2000) 148–152. [5] Shusuke Ukita, Hiroshi Ohtani, Mitsuhiro Hasebe, J. Jpn. Inst. Met. 71 (9) (2007) 721–729. [6] Yu Zhong, D.D. Macdonald, J. Nucl. Mater. 423 (2012) 87–92. [7] A. Mascaro, C. Toffolon-Masclet, J.-M. Joubert, Coupling Phase Diagrams Thermochem. 41 (2013) 50–59. [8] J. Jourdan, C. Toffolon-Masclet, J.-M. Joubert, J. Nucl. Mater. 402 (2010) 102– 107. [9] T.B. Flanagan, C.-N. Park, J. Alloys Compd. 293–295 (1999) 161–168. [10] H.M. Rietveld, J. Appl. Crystallogr. 2 (1969) 65–71. [11] J. Rodríguez-Carvajal, Newsletter (26) (2001) 12–19. [12] H. Khodja, E. Berthoumieux, L. Daudin, J.-P. Gallien, Nucl. Instrum. Meth. B 181 (2001) 83–86. [13] Z.B. Alfassi, M. Peisach (Eds.), Elemental Analysis by Particle Accelerators, CRC Press, 1992, pp. 179–278. [14] L. Daudin, H. Khodja, J.-P. Gallien, Nucl. Instrum. Meth. B 210 (2003) 153–158. [15] M. Mayer (Ed.), SIMNRA User’s Guide. Tech. Rep. IPP 9/113, Max-PlanckInstitut für Plasmaphysik, Garching, 1997. [16] V.I. Shcherbak, V.N. Bykov, B.P. Dyakonov, S. Kolesnik, Zh. Neorganich. Khim. 17 (1972) 1156–1158. [17] V.N. Fadeyev, L.F. Eremina, L.A. Izhanov, Russ. Metall. (1977) 188–191. [18] K.N. Semenenko, V.N. Verbetskii, E.A. Movlaev, A.A. Garibov, Zh. Neorganich. Khim. 34 (1989) 795–797.
[19] W. Kohn, L. Sham, Phys. Rev. 140 (1965) A1133–A1140. [20] A. Zunger, S.-H. Wei, L.G. Ferreira, J.E. Bernard, Phys. Rev. Lett. 65 (3) (1990) 353–356. [21] G. Kresse, D. Joubert, Phys. Rev. B 59 (3) (1999) 1758–1775. [22] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169–11186. [23] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (18) (1996) 3865–3868. [24] C. Wolverton, Acta Mater. 49 (2001) 3129–3142. [25] C. Jiang, C. Wolverton, J. Sofo, L.-Q. Chen, Z.-K. Liu, Phys. Rev. B69 (2004) 214202. [26] D. Shin, R. Arróyave, Z.-K. Liu, A. Van de Walle, Phys. Rev. B74 (2006) 024204. [27] J.-M. Joubert, J.-C. Crivello, Int. J. Hydrogen Energy 37 (2012) 4246–4253. [28] B. Sundman, B. Jansson, J.O. Andersson, Calphad 9 (2) (1985) 153–190. [29] B. Sundman, J. Ågren, J. Phys. Chem. Solids 42 (1981) 297–301. [30] J.-M. Joubert, JOM 64 (12) (2012) 1438–1447. [31] A.T. Dinsdale, Calphad 15 (4) (1991) 317–425. [32] H.E. Swanson, R.K. Fuyat, NBS Circular 539 (1953) 11–12. [33] K. Yasohama, T. Ogasawara, J. Phys. Soc. Jpn. 36 (1974) 1349–1355. [34] I.O. Bashkin, A.I. Latynin, V.Y. Malyshev, Phys. Solid State 37 (1995) 1146– 1151. [35] R.L. Beck, in: W.M. Mueller (Ed.), Metal Hydrides, Academic Press, New York, 1968, pp. 241–335. [36] R.E. Rundle, C.G. Shull, E.O. Wollan, Acta Crystallogr. 5 (1952) 22–26. [37] F.H. Spedding, A.H. Daane, K.W. Herrmann, Acta Crystallogr. 9 (1956) 559–563. [38] C.E. Lundin, Trans. Metall. Soc. AIME 242 (1968) 903–907. [39] Z.M. Azarkh, P.I. Gavrilov, Sov. Phys. Crystallogr. 12 (1968) 932–934. [40] J.E. Bonnet, J.N. Daou, J. Appl. Phys. 48 (1977) 964–968. [41] A. Pebler, W.E. Wallace, J. Phys. Chem. 66 (1962) 148–151. [42] M. Mansmann, W.E. Wallace, J. Phys. 25 (1964) 454–459.
Contents lists available at ScienceDirect
Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat
Experimental study and thermodynamic description of the erbium–hydrogen–zirconium ternary system Aurore Mascaro a,b, Caroline Toffolon-Masclet a, Caroline Raepsaet c, Jean-Claude Crivello b, Jean-Marc Joubert b,⇑ a b c
CEA-Saclay, Nuclear Energy Division, Nuclear Materials Department, SRMA, LA2M, 91191 Gif-Sur-Yvette, France Chimie Métallurgique des Terres Rares, Institut de Chimie et des Matériaux Paris-Est, CNRS, Université Paris-Est Créteil, 2-8 rue H. Dunant, 94320 Thiais, France CEA-Saclay, DSM/IRAMIS/NIMBE/LEEL, 91191 Gif-Sur-Yvette, France
a r t i c l e
i n f o
Article history: Received 26 February 2014 Accepted 6 September 2014 Available online 16 September 2014
a b s t r a c t The erbium–hydrogen–zirconium (Er–H–Zr) ternary system has been investigated experimentally at 350 °C using high purity materials. The extent of the ternary homogeneity domains have been measured using two combined experimental techniques: X-ray diffraction and ion beam analysis. An isothermal section is proposed according to these measurements. The three binary systems Er–H, Er–Zr and H–Zr were already assessed using the Calphad method. After making them compatible with each other and assigning the enthalpy of formation of the new generated end-members (including in H–Zr system) to the results of DFT calculations, the ternary system has been calculated without using any ternary parameter. The calculated isothermal section at 350 °C shows a fair agreement with the experimental data and the behavior at higher temperature is predicted. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction In order to increase the cycle length and the fuel burn up of light water reactors such as PWR (Pressurized Water Reactors), new cladding concepts are being developed. A solution currently studied at CEA consists of inserting solid burnable poisons, such as gadolinium or erbium, inside the cladding [1,2]. This new cladding tube is constituted by an internal layer made of zirconium alloy enriched in erbium, which is inserted between two regular zirconium base alloy layers. In PWRs, the cladding is surrounded by pressurized water (350 °C, 155 bars). Under these conditions, the water molecules dissociate at the surface and a part of the hydrogen released diffuses inside the cladding. Thus, it is interesting to have a precise knowledge of the interactions between hydrogen and the Zr(Er) inner layer. In the present study, the ternary system Er–H–Zr has been studied experimentally at the service temperature and described thermodynamically from the three associated binaries after making them compatible with each other. A literature survey on the present system is given in Section 2. In Section 3, the experimental work is described. DFT investigation is detailed ⇑ Corresponding author. Tel.: +33 1 49 78 13 44; fax: +33 1 49 78 12 03. E-mail address: [email protected] (J.-M. Joubert). http://dx.doi.org/10.1016/j.jnucmat.2014.09.015 0022-3115/Ó 2014 Elsevier B.V. All rights reserved.
in Section 4, followed by the thermodynamic calculations presented in Section 5. 2. Literature survey 2.1. The H–Zr binary system This system has been studied experimentally several times. It has also been thermodynamically assessed by four different authors [3–6]. The reported phases are the two allotropic forms of zirconium aZr and bZr, three different hydrides, c-ZrH, d-ZrH2 and e-ZrH2, and the H2 gas phase. The crystal structures of the solid phases are detailed in Table 1. Four invariant reactions can be observed in this system: a peritectoid reaction around 277 °C, a eutectoid reaction at 549 °C and two gas-peritectoid reactions at 797 °C and 867 °C. 2.2. The Er–H binary system The Er–H binary system has been re-evaluated recently and optimized thermodynamically [7]. This system is constituted by an aEr solid solution, two hydrides: b-ErH2 and c-ErH3 obtained by hydrogen occupancy of the interstitial sites of fcc and hcp
8
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
structures, respectively, and the H2 gas phase. The crystal structures of the solid phases can be found in Table 2. This system also shows two gas-peritectoid reactions at 433 °C and 1161 °C. 2.3. The Er–Zr binary system The Er–Zr binary system has been recently re-determined and optimized thermodynamically [8]. This system is constituted by two terminal hcp solid solutions aEr and aZr, separated by a miscibility gap, the bcc solution based on Zr at higher temperature and the liquid phase. The crystal structures of all the phases of this system can be found in Tables 1 and 2. Two invariant reactions can be observed in this system: a eutectoid reaction at 1045 °C and a eutectic reaction at 1380 °C. 3. Experimental work 3.1. Synthesis of the samples For the synthesis of the samples, distilled erbium (purity of 99.95%, China Rare Metals) and distilled zirconium (Van Arkel, purity of 99.98%) have been used as starting metals. Pure hydrogen (99.9999%) has been used for the hydrogenation. The raw metals were conserved in a glove box under argon atmosphere, to avoid oxidation in air. Just before synthesis, the zirconium was filed to remove the surface layer which could have been contaminated. Due to irregular shapes, the erbium could not be filed. Er–Zr samples of 2–3 g have been synthesized by arc melting under argon atmosphere (U grade, 800 mbar) purified by melting a zirconium getter. The samples have always been melted three times without important weight losses and turned upside down to homogenize them. Then, the samples were annealed over 6 weeks (1000 h) at 800 °C in order to reach thermodynamic equilibrium at this temperature. At this step, the samples were checked by X-ray diffraction (XRD) and Electron Probe Micro Analysis (EPMA). Then, they were cut into small pieces and introduced into stainless steel sample holders which were placed in a resistance furnace at 350 °C for the hydrogenation. The container was connected to a Sieverts’ apparatus working in a hydrogen atmosphere. The hydrogen pressure in the different volumes allows for monitoring of the chemical composition of the samples. To reach thermodynamic equilibrium, the ternary samples were kept inside the furnace at 350 °C during at least 3 days (72 h). Samples with higher hydrogen content (more than approximately 30 at.%) did not show any change after 3 days. The samples with lower hydrogen content were kept seven days. Note that equilibrium between hydrogen and alloys is reached much faster than between the metallic elements themselves. This behavior has already been observed in the case of the hydrogenation of Pd–Rh alloys [9]. These later alloys decompose according to the low temperature Pd–Rh miscibility gap in the presence of hydrogen at a temperature at which they would never reach equilibrium without the presence of hydrogen. However, it is possible that, very close to the Er–Zr binary border, the equilibrium can never be reached at 350 °C. Finally, the samples were air quenched. After the synthesis, the stainless steel sample holder can be opened
Table 2 Crystal structure of the phases of the Er–H binary system. Data
aEr
b-ErH2
c-ErH3
Space group
P63/mmc
Phase prototype Lattice parameters
Mg a = 3.559 Å c = 5.587 Å [37]
Fm3m CaF2 a = 5.123 Å
P3c1 HoH3 a = 6.272 Å c = 6.526 Å [38,41,42]
References
[38–41]
under ambient atmosphere due to the high stability of the hydride phases in air. 3.2. Phase structure characterization and chemical composition investigation In order to determine the phases involved in the different equilibria, each sample has been characterized by XRD at room temperature on a Bruker D8 Advance diffractometer (copper radiation, 40 kV, 40 mA, Bragg–Brentano geometry, h–h mode, step-by-step scan). The samples with high hydrogen content are powders and can be measured without any preparation. The samples with low hydrogen content that cannot be reduced into powder have been measured in the massive form. The XRD patterns have been processed by Rietveld refinement [10] using the Fullprof program [11], to refine the cell parameters and obtain the mass fraction of each phase. Hydrogen composition in the different phases cannot be determined by usual means. To determine the chemical composition of each phase, ion beam analysis has been used at the nuclear microprobe of DSM/IRAMIS/SIS2M/LEEL [12], CEA Saclay, France. For these measurements, combined RBS (Rutherford Back-Scattering) and ERDA (Elastic Recoil Detection Analysis) has been used [13]. RBS is sensitive to the heavy elements, such as Er, Zr or Au coating and allows the quantification of Er and Zr, while ERDA quantifies exclusively the H content. Before the analysis, the samples have been prepared in small brass tubes filled with resin, polished, joined together and then metalized with a gold coating of roughly 10 nm. For the analysis, a 3 lm 3 lm alpha beam of 3 MeV has been used. Due to the grazing angle incidence of the ERDA experimental configuration, it corresponds to a 12 lm 3 lm beam at the surface of the sample which may limit the analysis of small precipitates. Counting time was between half an hour for the samples with higher hydrogen content and few hours for those with low hydrogen content. After the analysis, the raw data were sorted with the RISMIN software [14] in order to obtain the different cartographies and spectra. Then, the SIMNRA software [15] was used to determine the elemental composition from the ERDA and RBS spectra. 3.3. Results 20 ternary samples were synthesized in the whole composition range at 350 °C and analyzed by XRD at room temperature. The results of the characterization of these samples is presented in Table 3. An example of a diffraction pattern analyzed with the Riet-
Table 1 Crystal structure of the phases of the H–Zr binary system. Data
aZr
bZr
c-ZrH
d-ZrH2
e-ZrH2
Space group
P63/mmc
Fm3m CaF2 a = 4.777 Å
I4/mmm
Mg a = 3.233 Å c = 5.148 Å [32]
Im3m W a = 3.610 Å
P42/n
Phase prototype Lattice parameters References
[33]
ZrH a = 4.586 Å c = 4.948 Å [34]
[35]
ThH2 a = 3.495 Å c = 4.463 Å [36]
Table 3 Lattice parameters of the different samples determined by XRD and their chemical composition measured by ERDA + RBS. Sample composition
Phases
at.%
H/M
Er1Zr27H72
Er0.05Zr0.95H2.57
e-ZrH2
Er1Zr95H4
Er0.01Zr0.99H0.04
d-ZrH2
Er2Zr29H69
Er0.05Zr0.95H2.23
Er2Zr94H4
Er0.025Zr0.975H0.04
Er2.3Zr38.7H59
Er0.05Zr0.95H1.43
Mass fraction (%)
4.507
Er2.2Zr43.5H63.3
Er0.05Zr0.95H1.38
aZr
4.783 3.247
5.190
/ Er1.0Zr98.2H0.8
/ Er0.01Zr0.99H0.01
e-ZrH2
99
3.513
4.512
Er1.9Zr35.2H62.9
Er0.05Zr0.95H1.70
d-ZrH2
1 99
4.785 3.239
5.163
/ Er2.5Zr96.8H0.7
/ Er0.025Zr0.975H0.01
93 7
4.787 3.248
5.212
Er2.1Zr35.9H62.0 /
Er0.06Zr0.94H1.63 /
27 12 61
4.786 5.157 3.242
5.159
/ / Er4.2Zr89.7H6.1
/ / Er0.04Zr0.96H0.06
1 99
4.781 3.242
5.164
/ Er6.5Zr92.9H0.6
/ Er0.07Zr0.93H0.01
1 98 1
4.782 3.243 5.140
5.160
/ Er6.5Zr92.9H0.6 /
/ Er0.07Zr0.93H0.01 /
39 57 4
4.803 3.257 5.172
5.181
/ Er14.6Zr82.9H2.5 /
/ Er0.15Zr0.85H0.03 /
b-ErH2
1 98 1 1 98 1
4.789 3.250 5.140 4.802 3.260 5.163
/ Er7.9Zr90.9H1.2 / / Er9.6Zr89.1H1.3 /
/ Er0.08Zr0.92H0.01 / / Er0.10Zr0.90H0.01 /
/ / Er22.1Zr7.3H70.6
/ / Er0.75Zr0.25H2.40
Er13.2Zr27.5H59.3 Er19.65Zr19.65H60.7
Er0.32Zr0.68H1.46 Er0.50Zr0.50H1.54
Er16.8Zr20.6H62.6 Er22.6Zr15.1H62.3
Er0.45Zr0.55H1.63 Er0.60Zr0.40H1.65
d-ZrH2 d-ZrH2 b-ErH2
Er0.05Zr0.95H0.11
d-ZrH2
aZr Er5Zr91H4
Er0.05Zr0.95H0.04
d-ZrH2
aZr b-ErH2 Er5.5Zr67H27.5
Er0.075Zr0.925H0.38
d-ZrH2
aZr b-ErH2 Er7Zr89H4
Er0.075Zr0.925H0.04
d-ZrH2
aZr Er9.5Zr85H5.5
Er0.1Zr0.9H0.06
b-ErH2 d-ZrH2
aZr
5.164
5.168
Er16.5Zr13.5H70
Er0.55Zr0.45H2.33
e-ZrH2 b-ErH2 c-ErH3
27 1 72
3.500 5.092 6.244
Er18.3Zr20.6H61.1
Er0.47Zr0.53H1.57
d-ZrH2 b-ErH2
28 72
4.822 5.091
Er19Zr15H66
Er0.55Zr0.45H1.94
e-ZrH2 b-ErH2
39 61
3.497 5.096
b-ErH2 c-ErH3
1 99
5.111 6.255
6.497
/ Er25.4Zr1.2H73.4
/ Er0.95Zr0.05H2.76
b-ErH2 c-ErH3
96 4
5.105 6.252
6.493
Er32.0Zr1.8H66.2 Er30.5Zr1.8H67.7
Er0.95Zr0.05H1.96 Er0.93Zr0.07H2.06
Er25Zr1.5H73.5 Er29Zr2H69
Er0.95Zr0.05H2.80 Er0.95Zr0.05H2.23
4.630 6.469
4.631
Er31Zr8.5H60.5
Er0.78Zr0.22H1.53
b-ErH2
100
5.050
Not analyzed
Not analyzed
Er45Zr12.5H42.5
Er0.78Zr0.22H0.74
aZr aEr
/ / /
3.257 3.567 5.051
5.127 5.579
/ Er59.0Zr16.6H24.4 Er27.3Zr7.7H65.0
/ Er0.78Zr0.22H0.32 Er0.78Zr0.22H1.86
Er47Zr2H51
Er0.95Zr0.05H1.04
2 98
3.548 5.107
5.562
Er76.3Zr3.2H20.5 Er35.8Zr1.5H62.7
Er0.96Zr0.04H0.26 Er0.96Zr0.04H1.68
1 49 50
3.196 3.536 5.096
5.294 5.546
/ Er82.8Zr10.2H7.0 Er33.6Zr4.1H62.3
/ Er0.89Zr0.11H0.08 Er0.89Zr0.11H1.65
b-ErH2
aEr b-ErH2
Er51Zr6H43
Er0.9Zr0.1H0.75
aZr aEr b-ErH2
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
3.506
3 97
aZr Er4.5Zr85.5H10
Composition measured by ERDA H/M
100
aZr Er0.05Zr0.95H0.16
Composition measured by ERDA at.%
c (Å)
aZr
Er4Zr82H14
Lattice parameters a (Å)
9
10
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
Intensity (counts)
20000
10000
0
δ-ZrH 2 β-ErH 2
Fig. 4. This isothermal section presents two solid solutions (aEr and aZr) and four hydrides (b-ErH2, c-ErH3, d-ZrH2 and e-ZrH2). aEr, contrary to aZr, has a large ternary extension. c-ErH3 and eZrH2 have small ternary extensions while d-ZrH2 and b-ErH2 have important extensions into the phase diagram. Nevertheless, a miscibility gap has been evidenced between these two hydrides with the same CaF2 structure type. Finally, the isothermal section is characterized by the presence of a large field of three-phase equilibrium between aEr, aZr and b-ErH2 that has been evidenced in several samples. 3.4. Discussion
30
40
50
60
70
80
90
100
110
120
2 (°) Fig. 1. X-ray diffraction pattern of sample Er18.3Zr20.6H61.1 with the calculated pattern involving the two phases d-ZrH2 and b-ErH2. The difference is shown below. This sample is characteristic of the presence of a miscibility gap in the phase with CaF2 structure.
Fig. 2. ERDA H mapping showing hydrides (in blue and red) in Er9.5Zr85H5.5 sample.
veld method for the phase characterization is presented in Fig. 1. With ion beam analysis, we obtain element mapping as shown in Fig. 2. RBS and ERDA spectra are extracted with the SIMNRA software for H-rich (blue1 and red in Fig. 2) and H-poor (white and light blue in Fig. 2) regions (Fig. 3). The RBS spectrum gives the Er and Zr contribution. The Au coating can be seen as a thin peak at high energies. In the ERDA spectrum an important difference can be observed between the hydride region and the solid solution. Indeed, hydrides give rise to a much larger signal than solid solutions. Thanks to the analysis of each sample with XRD and combined RBS-ERDA, a 350 °C isothermal section of the ternary phase diagram may be plotted (Fig. 4). Note that, due to slight composition deviations, the point representative of the composition of several samples may not exactly fall in the corresponding equilibrium evidenced in Table 3. Also, in some cases, the ERDA hydrogen concentration measurement in precipitates of a minor phase may be biased by the presence of the surrounding matrix. For this reason, the same equilibrium (e.g. aEr–aZr–b-ErH2) may be measured differently in different samples. We chose to leave all the different measurements in Table 3 to show the scatter and the drawing may result from the analysis of different samples showing the same equilibrium but with different phase amounts. From this analysis, we drew the isothermal section as the most probable in
1 For interpretation of color in Fig. 2, the reader is referred to the web version of this article.
All the crystal structures and the lattice parameters found in this study using XRD measurements followed by Rietveld refinement are consistent with the literature. The spatial resolution of ERDA combined with RBS analysis (12 lm 3 lm) is not sufficient to resolve small precipitates or fine microstructure of solid solutions. No valid chemical composition can be obtained for these individual small areas. This explains the unmeasured phases in Table 3. The 350 °C experimental isothermal section only contains already known phases and is consistent with the reported binary borders. No ternary compound has been evidenced. Yet, a very large extension of both CaF2-type hydrides is observed leaving a tiny miscibility gap between them. No data is available in the literature on the Er–H–Zr ternary system. However, two other rare earth–H–Zr ternary systems have been investigated so far. The Y–H–Zr has been studied by Shcherbak et al. [16] and Fadeyev et al. [17] and presents a miscibility gap between the CaF2 hydrides (d-ZrH2 and YH2) from 25 °C to 900 °C with no reported mutual solubilities. In contrast, the Sc–H–Zr ternary system studied by Semenenko et al. [18] shows a complete homogeneity domain between the two CaF2 structures. The Er–H–Zr system stands between these two opposite behaviors with a CaF2 phase presenting both a miscibility gap at 350 °C and extended solubility ranges on its two sides. 350 °C corresponds to the service temperature in a PWR. The present results show that, for the amount of erbium foreseen in our application that is 3–6 wt% Er (1.5–3 at.% Er), hcp phase is in equilibrium with d-ZrH2, which is the usual hydride formed in PWR reactors. 4. DFT investigation The heats of formation of hydrides and enthalpies of mixing of several solutions were calculated in the frame of the Density Functional theory (DFT) [19]. For the solutions (Er, Zr) and (Er, Zr)H2, we used the Special Quasi-Random Structures (SQS) [20] technique. 4.1. Methodology The DFT calculations were carried out using the Vienna ab initio simulation package (VASP) [21,22]. The generalized gradient approximation was used for the exchange and correlation energy included in the PBE functional [23]. An energy cutoff of 400 and 800 eV was used for the plane-wave basis set for calculations using SQS procedure and determination of heat of formation, respectively. Both the internal cell parameters and atomic coordinates were relaxed, carefully preserving the original crystal symmetries for the SQS structures. For the heat of formation of the ordered hydrides, the contributions from zero-point energies (ZPE) of the H atoms were estimated within the Einstein model. The SQS structures at 3 compositions (0.25, 0.5, 0.75) of binary (Er, Zr) solutions have been taken from the literature in fcc [24], bcc [25] and hcp [26] structures within the 16-atom description. In addition, infinite
11
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
Δ
Fig. 3. RBS (a) and ERDA (b) spectra of the Er47Zr2H51 sample.
ε
Fig. 4. Er–H–Zr experimental isothermal section at 350 °C.
dilution is modelled by the calculation at 1/16 and 15/16 compositions for all solid solutions using a supercell. For the SQS of (Er, Zr)H2, we have used a fcc based SQS cell with additional hydrogen atoms in the tetragonal interstitial sites in order to reproduce the CaF2 structure type. 4.2. Heat of formation of hydrides As described in the following section (5. Thermodynamic modelling), the model used for both hcp and fcc phases in the Er–H system generates new end-members in the Zr–H system with hydrogen in octahedral or triangular and/or tetrahedral sites. The heat of formation of these metastable compounds in the Zr–H system has been calculated with a procedure similar to that used for the Er–H system [27]. The tetragonal e-ZrH2 phase has also been calculated for both ZrH2 and ErH2 compositions. Fig. 5 presents the results obtained for the different configurations in Zr–H system. The ground state represented as a solid line is in agreement with the experimental observation. Table 4 presents the numerical results of all the calculations. The enthalpies of formation of both d and e phases compare very well with recent DFT calculations [6]. The small difference observed (3–6 kJ mol1 f.u.) may be explained by a different choice of pseudo-potentials. 4.3. Enthalpies of mixing of (Er, Zr) solutions Fig. 6 shows the enthalpies of mixing in fcc, bcc and hcp phases of the Er–Zr system. Whatever the structure, these energies are positive, including in hcp, the stable structure of both elements at 0 K. As observed in other systems, the magnitude of the enthalpy
Fig. 5. DFT calculated enthalpies of formation per mole of compound of the ZrHx compounds.
of mixing is similar for fcc and hcp. The repulsive character is more pronounced in the bcc phase. The SQS structure relaxation has been done in 2 steps. First, only the cell volume is allowed to relax, then, the internal parameters are optimized keeping the obtained volume fixed. The results at both steps are presented in Fig. 6. Those obtained at the second step are in better agreement with the enthalpies deduced from the thermodynamic assessment of the system [8]. In spite of this result, it is still not clear which kind of relaxation best describes the actual thermodynamic properties. This kind of comparison needs to be extended to a larger number of systems before hasty use of SQS results in thermodynamic assessments.
4.4. Enthalpies of mixing of (Er, Zr)H2 hydride As described in Section 3, a miscibility gap has been evidenced between the two CaF2 hydrides (d-ZrH2 and b-ErH2), and was the motivation to estimate the enthalpies of mixing in (Er, Zr)H2. The calculated results with the two relaxation schemes are illustrated in Fig. 7. Both result sets present positive and symmetric mixing energies which gives rise to a symmetric miscibility gap at low temperature as evidenced experimentally. The critical temperature TC could be roughly estimated considering that at TC, the excess mixing energy compensates the configurational energy in the middle of the miscibility gap, i.e. TC = DHmix/(R ln ½) = 474 or 954 K with the first or second relaxation scheme, respectively.
12
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
Table 4 DFT calculation results on the binary systems, ZPE contribution included. Composition Zr ZrH ZrH2 ZrH3 ErH2 a
HCP-trian DHfor (J mol1) a
0 25,857 132,895 168,834 See [27]
HCP-octa DHfor (J mol1) a
0 53,498 132,895 97,500
FCC DHfor (J mol1)
Tetragonal DHfor (J mol1)
3902 57,566 158,335 119,159
None None 164,529 None 205,126
a
a
Stable phase.
Fig. 6. SQS calculated enthalpies of mixing of (Er, Zr) binary system in (a) fcc, (b) bcc and (c) hcp with 2-step structure relaxation scheme: volume () and internal parameters (N). Solid line corresponds to the energy assessed in [8] (the fcc value has been taken equal to hcp).
Fig. 7. SQS calculated enthalpies of mixing of (Er, Zr)H2 hydrides in CaF2 structure within the 2-step structure relaxation scheme: volume () and internal parameters (N).
5. Thermodynamic modelling The Er–H–Zr phase diagram has been obtained by the projection of the three associated binaries using Thermo-Calc software [28]. The two binary systems Er–H and Er–Zr have been thermodynamically described only once in the literature [7,8] and both descriptions have been accepted. The choice made for the H–Zr system is justified hereunder. Finally, the models have been made compatible between the three binaries in order to perform the calculation of the ternary system.
5.1. Different H–Zr optimizations The H–Zr binary system has been assessed by Dupin et al. [3], Königsberger et al. [4] and Ukita et al. [5]. In none of the assessments has the liquid phase been considered. Differences are noted concerning the number of solid phases considered and the choice
of the model for interstitial solutions. Königsberger et al. considered only one of the three hydrides (d-ZrH2), Dupin et al. only two (d-ZrH2 and e-ZrH2) while Ukita et al. considered all of them (d-ZrH2, e-ZrH2 and c-ZrH). As shown in Table 5, all the phases are described using the sublattice model [29]. From this Table, one may also observe the differences concerning the choice of the multiplicity of the interstitial sites. Königsberger et al. and Dupin et al. use the same multiplicity for HCP_A3 (aZr) solid solution though they do not consider the same sites (octahedral in one case, half of the tetrahedral sites in the other case). Ukita et al. on the contrary, considered a multiplicity of 2 corresponding to the tetrahedral sites. In the BCC_A2 phase (bZr), the multiplicities are also different: 1.5, 3 and 6 for the different authors. For a deeper discussion about these different assumptions, see Ref. [30]. For our calculation, the description of Dupin et al. was preferred because it used much less optimized parameters than Ukita et al. and because it described the e-ZrH2 phase contrary to Königsberger et al. The absence of the c-ZrH phase is not an issue since it is a low temperature phase, stable far below the investigated temperatures. It may be easily added to the description of Dupin et al. as shown recently by Zhong and Macdonald [6]. 5.2. Comparison of the models used in the three binaries In order to combine the three binaries, each similar phase has to be described by the same model. The models used for each phase of the Er–H, Er–Zr and H–Zr binary systems are compared in Table 6. 5.2.1. Gas and liquid phases The only species considered in the gas phase is the di-hydrogen H2 in the Er–H binary system. In the H–Zr binary system, the considered gaseous species are H, H2, Zr and Zr2. The gas phase is described as an ideal gas with ideal mixing of the different species. The liquid phase has not been described in either of the two binary metal-hydrogen systems and is only described in the Er–Zr binary system. A substitutional solution model has been used and no hydrogen solubility was considered [8]. It is, regardless, extremely low at the temperatures at which the liquid appears.
13
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16 Table 5 Comparison of the models used for the H–Zr assessments (h stands for vacancy). Phase
Phase name
Dupin et al. [3] octa
aZr
HCP_A3 BCC_A2 FCC_C1 ZRH2_EPSILON ZRH_GAMMA
Königsberger et al. [4] tetra
(Zr)(h) (H, h) (Zr)(H, h)octa 3 (Zr)(H, h)tetra 2 (Zr)(H, h)tetra 2
bZr d-ZrH2 e-ZrH2 c-ZrH
Ukita et al. [5]
octa
(Zr)(H, h) (Zr)(H, h)octa 1.5 (Zr)(H, h)tetra 2
(Zr)(H, (Zr)(H, (Zr)(H, (Zr)(H, (Zr)(H,
h)tetra 2 h)octa 6 h)tetra 2 h)tetra 2 h)tetra 1
Table 6 Comparison of the models used in the different binary descriptions (h stands for vacancy). Binary system
Phase
Space group
Structure type
Description name
Model used
Er–H [7]
aEr
P63/mmc
b-ErH2
Fm3m
Mg CaF2
HCP_A3 FCC_C1
(Er)(H, h)octa(H, h)tetra 2 (Er)(H, h)octa(H, h)tetra 2
c-ErH3
P3c1
HoH3
HCP_A3
(Er)(H, h)tri(H, h)tetra 2
aZr
P63/mmc
bZr
Im3m
Mg W
HCP_A3 BCC_A2
(Zr)(h)octa(H, h)tetra (Zr)(H, h)octa 3
d-ZrH2
Fm3m I4/mmm
CaF2
FCC_C1
(Zr)(H, h)tetra 2
ThH2
ZRH2_EPSILON
(Zr)(H, h)tetra 2
Im3m P63/mmc
W
BCC_A2
(Er, Zr)(h)octa 3
Mg
HCP_A3
(Er, Zr)(h)octa
Zr–H [3]
e-ZrH2 Er–Zr [8]
bZr
aZr
5.2.2. ZRH2_EPSILON (e-ZrH2) This phase is present only in the H–Zr binary system. The model used is as follows: (Er, Zr)(H, h)tetra to allow ternary solubility of 2 erbium (h stands for vacancy). Thus, the e-ErH2 end-member (space group I4/mmm and structure type ThH2) has to be introduced and its enthalpy value has been taken from the DFT calculations of this work. 5.2.3. BCC_A2. (bcc) This phase appears in both H–Zr [3] and Er–Zr [8] phase diagrams. If we combine both models (Zr)(H, h)octa and (Er, Zr)(h)octa , 3 3 octa the new model obtained is (Er, Zr)(H, h)3 . For the enthalpy of formation of the end-member ErHocta (bcc) as a first approximation, 3 the value of the ErH3 fcc phase has been used, i.e. DHfor ErH3 bcc = 231,708 J mol1. 5.2.4. FCC_C1. (b-ErH2, d-ZrH2) This FCC_C1 model describes the two hydrides b-ErH2 and dZrH2 which have the same crystal structure type, CaF2. However in the H–Zr phase diagram this phase is described with two sublattices whereas three are needed in the Er–H phase diagram (in order to describe the hyper-stoichiometric side of the hydride b-ErH2). Adding a sublattice describing the octahedral interstitial sites in the fcc phase yields the model (Er, Zr)(H, h)2(H, h). New end-members are created which have been assigned the enthalpies of formation calculated by DFT. On the other hand, the defined phase shows an existence range in the binary Er–Zr system in which the fcc phase was not optimized. It was assumed that the binary interaction in fcc was similar to the one in the hcp phase, as suggested by the SQS calculations in Fig. 6. This is sufficient to avoid the unrealistic presence of a stable fcc phase in the calculation of the binary Er–Zr system. 5.2.5. HCP_A3. (hcp, c-ErH3) In the H–Zr optimization, the HCP_A3 phase is described by two sublattices, one for the metallic atoms and the second one for half of the tetrahedral interstitial sites. In fact, the multiplicity of this site is 1 in the H–Zr binary system [3] instead of 2 in the Er–H optimization, in order to describe the c-ErH3 phase which also needs the third sublattice describing the octahedral sites. To combine the H–Zr optimization with the other binaries, the tetrahedral sub-
lattice multiplicity has to be doubled and the octahedral sublattice has to be introduced to yield the following model: (Er, Zr)(H, h)2(H, h). The procedure will be described hereunder. 5.3. Modification of H–Zr assessment 5.3.1. Modification of the tetrahedral multiplicity In order to make the three binary systems compatible, the description of the H–Zr system obtained by Dupin et al. [3] (called hereafter model 1) had to be adapted. Changing the multiplicity of the tetrahedral interstitial sublattice in the HCP_A3 description from 1 to 2 (in the so-called model 2) yields a change of end-member from ZrH to ZrH2. The development of the equations of the two models shows that identity is obtained if the reference term (Eq. (1))
GZrH ¼ 45; 965 þ 41:6T þ GHSERZR þ GHSERH
ð1Þ
in model 1, is changed to
GZrH2 ¼ 2ð45; 965 þ 41:6 TÞ þ GHSERZR þ 2GHSERH
ð2Þ
in model 2. However, we have to consider that the terms related to configurational entropies are different. This can be inferred from Fig. 8 in which the ideal contribution to the Gibbs energy has been plotted in the two models. Because of higher multiplicity of the insertion site in model 2, the configurational contribution is larger. In particular for xH = 0.5, the configurational term is zero in model 1 since all the interstitial sites are occupied while it is at its maximum in model 2 and is equal to 2RTln(0.5). There is no simple analytical relation allowing the correction of the difference between the models. Therefore we used an approximation equal to 4yHRTln(1/ 2) where y is the site fraction that allows having the same Gibbs energy in both models for xH = 0 and xH = 0.5. This correction has also been plotted in Fig. 8 and it can be seen that the difference is minimal, in particular at low hydrogen content corresponding to the domain in which the phase is stable. At a composition higher than xH = 0.5, where the phase was not defined in model 1, the contribution destabilizes the phase. It is also worth mentioning that the configurational contribution is relatively small compared to the reference terms at temperatures below 1100 K where the phase is stable. To confirm this point, the binary H–Zr system
14
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
gas phase are taken from Ref. [31]. All the solid phases were modelled using the sublattice model [29]. The Gibbs energy of each phase u per mole of formula unit is expressed as follows:
Gu ¼ ref Gu þ id Gu þ ex Gu
ð4Þ
For u = bcc (k = 3) and e (k = 2), where only one interstitial lattice of multiplicity k is present: u u 0 00 0 00 u 0 00 Gu ¼ y0Er y00H Gu Er:H þ yEr yVa GEr:Va þ yZr yH GZr:H þ yZr yVa GZr:Va
ð5Þ
Gu ¼ RTððy0Er ln y0Er þ y0Zr ln y0Zr Þ þ kðy00H ln y00H þ y00Va ln y00Va ÞÞ
ð6Þ
0 00 00 u Gu ¼ y0Er y0Zr y00Va Lu Er;Zr:Va þ yZr yH yVa LZr:H;Va
ð7Þ
ref
id
ex
Fig. 8. Gibbs energies of the hcp phase at 1000 K showing the configurational terms in the H–Zr model (model 1) and in the Er–H–Zr ternary database (model 2) and the Gibbs energy after correction (model 2 corrected).
has been plotted with model 2 and no visible modification is observed. Technically, the correction term for the change of the configurational entropy, since it is linear as a function of the site fraction, can be introduced in the reference term as follows:
where y represents the site fraction of the given element in the given sublattice. For u = hcp and fcc, where two interstitial lattices represent tetrahedral and octahedral sites: ref
u 0 00 000 u 0 00 000 u Gu ¼ y0Er y00Va y000 Va GEr:Va:Va þ yZr yVa yVa GZr:Va:Va þ yEr yH yVa GEr:H:Va u 0 00 000 u 0 00 000 u þ y0Zr y00H y000 Va GZr:H:Va þ yEr yVa yH GEr:Va:H þ yZr yVa yH GZr:Va:H u 0 00 000 u þ y0Er y00H y000 H GEr:H:H þ yZr yH yH GZr:H:H
id
ð8Þ
Gu ¼ RTððy0Er ln y0Er þ y0Zr ln y0Zr Þ þ 2ðy00H ln y00H þ y00Va ln y00Va Þ 000 000 000 þ ðy000 H ln yH þ yVa ln yVa ÞÞ
GZrH2 ¼ 2ð45; 965 þ 41:6T þ 2RT lnð1=2ÞÞ þ GHSERZR þ 2GHSERH
ð3Þ
ex
ð9Þ
u 0 00 00 000 u Gu ¼ y0Er y0Zr y00Va y000 Va LEr;Zr:Va:Va þ yEr yH yVa yVa LEr:H;Va:Va u
u
0 00 000 000 þ y0Er y00H y00Va y000 H LEr:H;Va:H þ yEr yH yH yVa LEr:H:H;Va
5.3.2. DFT calculations in the H–Zr binary system Enthalpies of formation of the new end-members generated by the new model for hcp and fcc phases and the tetragonal e-ZrH2 have been calculated by DFT and presented in Section 3 (Fig. 5, Table 4). Not all of them were used in the description since we decided to keep the description by Dupin et al. [3]. So, for the end-members already existing or adapted (ZrH2 in fcc, ZrH in hcp transformed into ZrH2, e ZrH2), the assessed values have been conserved. It is important to note that they are in excellent agreement with the DFT values for the stable phases (d-ZrH2 and e-ZrH2). The difference is larger for hcp ZrH2 which has been transformed from the assessed value of ZrH in model 1. This phase is metastable and therefore much more difficult to assess. The enthalpies of the new compounds generated by the presence of the octahedral site have been assigned their DFT values (see Table 7). For the entropies of formations, either the assessed values have been kept or ideal values have been chosen (65 J mol1 K1 per hydrogen atom corresponding to half of the entropy of formation of an H2 molecule). 5.4. Thermodynamic equations The equations for the Gibbs energies of pure Er and Zr in fcc, hcp and bcc structure and liquid as well as molecular hydrogen in the
000 u þ y0Er y00Va y000 H yVa LEr:Va:H;Va
ð10Þ
The end-members and interaction parameters are taken from the three papers [3,7,8] unless they have been modified as explained above. The values for the different end-members are summarized in Table 7. The thermodynamic database file is supplied as Supplementary material to this paper. 5.5. Results Equilibrium has been obtained by Gibbs energy minimization using Thermo-Calc. Several Er–H–Zr isothermal sections at 350 °C, 600 °C and 1100 °C have been calculated from the three binaries made consistent. They are presented in Figs. 9–11. At 350 °C (Fig. 9), six single phase regions are present and five three phase equilibria have been identified. A miscibility gap can be observed between the two CaF2 hydrides b-ErH2 and d-ZrH2. At 600 °C (Fig. 10), the two allotropic forms of the zirconium can be observed (bZr is nearly restricted to H–Zr binary border). e-ZrH2 is still stable under 105 Pa contrary to c-ErH3. The miscibility gap between b-ErH2 and d-ZrH2 closes above 447 °C and is replaced by a complete solubility range. One may note that this temperature is located just between the two TC estimated from the SQS calcula-
Table 7 Enthalpies and entropies of formation used in the H–Zr description (per mole of compound). Composition
Zr ZrH ZrH2 ZrH3 a
HCP
FCC
Tetragonal
DHfor (J mol1)
DSfor (J mol1 K1)
DHfor (J mol1)
DSfor (J mol1 K1)
DHfor (J mol1)
DSfor (J mol1 K1)
0 53,498 91,930a 168,834
0 65 47.4a 195
7600a 61,453 170,490a 91,710
0.9a 65 208.2a 195
– – 168,215a –
– – 110.5a –
From Dupin et al. [3] or adapted from Dupin et al.
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
15
5.6. Discussion
Fig. 9. Er–H–Zr isothermal section at 350 °C calculated by projection of the three binaries.
The 350 °C calculated and experimental isothermal sections can be compared (Figs. 4 and 9). All the equilibria evidenced experimentally are well reproduced by the calculation. The calculation reproduces as well, without the introduction of any ternary interaction parameter, the miscibility gap between the two CaF2 hydrides. The shape of the aEr homogeneity domain is not so well reproduced. We did not want to introduce ternary interaction parameters to obtain a better agreement since we are not certain that the experimental data close to the metallic border represent equilibrium at this very low temperature for a metallic system. Given the synthesis technique used (hydrogenation of alloys annealed at 800 °C), several samples may have remained in a paraequilibrium state (equilibrium of the hydride phases with frozen quenched solid solution). This is one of the major outcomes of Calphad to be able to predict equilibrium at temperatures at which it is impossible to reach experimentally. 600 °C is an incidental temperature in PWRs. The 600 °C isothermal section shows the bZr phase and a complete homogeneity domain between the two CaF2 hydrides. In case of incident, the chemistry of the hydride would be changed due to erbium solution in the d-ZrH2 phase. Finally, 1100 °C is an accidental temperature for PWRs. The result shows that at this point, the hydrogen can be trapped in the form of b-ErH2 hydrides. This can limit the di-hydrogen gas formation.
6. Conclusion
Fig. 10. Er–H–Zr isothermal section at 600 °C calculated by projection of the three binaries.
The erbium–hydrogen–zirconium ternary system has been studied experimentally. Different and complementary experimental techniques such as XRD and a combination of ERDA and RBS have been used in order to find the equilibria and phase compositions. A first evaluation of this ternary system has been proposed at 350 °C. To model this ternary system, the three associated binaries have been made compatible with each other. The calculation at 350 °C shows a fair agreement with the experimental data without the use of any ternary parameter. A miscibility gap has been evidenced at 350 °C between the two hydrides both experimentally and by calculations. This miscibility gap is expected from the calculation to disappear at high temperatures. From the DFT approach, heats of formation of the new end-members generated by the model in the ternary system have been calculated. Even if the SQS results have not been directly considered in the assessment of the present work, SQS mixing energies show reliable agreement with the assessment, but still need to be tested on other systems before a systematic use. Finally, extrapolations using the Calphad technique allow for a good approximation of behavior at the temperatures which experiments become unfeasible.
Acknowledgements
Fig. 11. Er–H–Zr isothermal section at 1100 °C calculated by projection of the three binaries.
tions on (Er, Zr)H2 in CaF2 (201 or 681 °C, see Section 4.4). At 1100 °C (Fig. 11), a large homogeneity domain of the aEr phase can be noticed. Zirconium exists only in the b form and the only hydride stable at this high temperature is the under-stoichiometric b-ErH2.
The financial support from CEA is acknowledged. The authors wish to thank the nuclear microprobe analysis team and Didier Hamon for the EPMA measurements. DFT calculations were performed using HPC resources from GENCI-IDRIS (Grants 2012096175 and 2013-096175).
Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jnucmat.2014. 09.015.
16
A. Mascaro et al. / Journal of Nuclear Materials 456 (2015) 7–16
References [1] J.-C. Brachet, C. Chabert, P. Olier, S. Urvoy, French Patent, BD 1725, 2006. [2] J.-C. Brachet, P. Olier, S. Urvoy, V. Vandenberghe, C. Chabert (Eds.), in: TopFuel 2009 Conference, Paris, 2009 (Paper 2189). [3] N. Dupin, I. Ansara, C. Servant, C. Toffolon, C. Lemaignan, J.-C. Brachet, J. Nucl. Mater. 275 (1999) 287–295. [4] E. Königsberger, G. Eriksson, W.A. Oates, J. Alloys Compd. 299 (2000) 148–152. [5] Shusuke Ukita, Hiroshi Ohtani, Mitsuhiro Hasebe, J. Jpn. Inst. Met. 71 (9) (2007) 721–729. [6] Yu Zhong, D.D. Macdonald, J. Nucl. Mater. 423 (2012) 87–92. [7] A. Mascaro, C. Toffolon-Masclet, J.-M. Joubert, Coupling Phase Diagrams Thermochem. 41 (2013) 50–59. [8] J. Jourdan, C. Toffolon-Masclet, J.-M. Joubert, J. Nucl. Mater. 402 (2010) 102– 107. [9] T.B. Flanagan, C.-N. Park, J. Alloys Compd. 293–295 (1999) 161–168. [10] H.M. Rietveld, J. Appl. Crystallogr. 2 (1969) 65–71. [11] J. Rodríguez-Carvajal, Newsletter (26) (2001) 12–19. [12] H. Khodja, E. Berthoumieux, L. Daudin, J.-P. Gallien, Nucl. Instrum. Meth. B 181 (2001) 83–86. [13] Z.B. Alfassi, M. Peisach (Eds.), Elemental Analysis by Particle Accelerators, CRC Press, 1992, pp. 179–278. [14] L. Daudin, H. Khodja, J.-P. Gallien, Nucl. Instrum. Meth. B 210 (2003) 153–158. [15] M. Mayer (Ed.), SIMNRA User’s Guide. Tech. Rep. IPP 9/113, Max-PlanckInstitut für Plasmaphysik, Garching, 1997. [16] V.I. Shcherbak, V.N. Bykov, B.P. Dyakonov, S. Kolesnik, Zh. Neorganich. Khim. 17 (1972) 1156–1158. [17] V.N. Fadeyev, L.F. Eremina, L.A. Izhanov, Russ. Metall. (1977) 188–191. [18] K.N. Semenenko, V.N. Verbetskii, E.A. Movlaev, A.A. Garibov, Zh. Neorganich. Khim. 34 (1989) 795–797.
[19] W. Kohn, L. Sham, Phys. Rev. 140 (1965) A1133–A1140. [20] A. Zunger, S.-H. Wei, L.G. Ferreira, J.E. Bernard, Phys. Rev. Lett. 65 (3) (1990) 353–356. [21] G. Kresse, D. Joubert, Phys. Rev. B 59 (3) (1999) 1758–1775. [22] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169–11186. [23] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (18) (1996) 3865–3868. [24] C. Wolverton, Acta Mater. 49 (2001) 3129–3142. [25] C. Jiang, C. Wolverton, J. Sofo, L.-Q. Chen, Z.-K. Liu, Phys. Rev. B69 (2004) 214202. [26] D. Shin, R. Arróyave, Z.-K. Liu, A. Van de Walle, Phys. Rev. B74 (2006) 024204. [27] J.-M. Joubert, J.-C. Crivello, Int. J. Hydrogen Energy 37 (2012) 4246–4253. [28] B. Sundman, B. Jansson, J.O. Andersson, Calphad 9 (2) (1985) 153–190. [29] B. Sundman, J. Ågren, J. Phys. Chem. Solids 42 (1981) 297–301. [30] J.-M. Joubert, JOM 64 (12) (2012) 1438–1447. [31] A.T. Dinsdale, Calphad 15 (4) (1991) 317–425. [32] H.E. Swanson, R.K. Fuyat, NBS Circular 539 (1953) 11–12. [33] K. Yasohama, T. Ogasawara, J. Phys. Soc. Jpn. 36 (1974) 1349–1355. [34] I.O. Bashkin, A.I. Latynin, V.Y. Malyshev, Phys. Solid State 37 (1995) 1146– 1151. [35] R.L. Beck, in: W.M. Mueller (Ed.), Metal Hydrides, Academic Press, New York, 1968, pp. 241–335. [36] R.E. Rundle, C.G. Shull, E.O. Wollan, Acta Crystallogr. 5 (1952) 22–26. [37] F.H. Spedding, A.H. Daane, K.W. Herrmann, Acta Crystallogr. 9 (1956) 559–563. [38] C.E. Lundin, Trans. Metall. Soc. AIME 242 (1968) 903–907. [39] Z.M. Azarkh, P.I. Gavrilov, Sov. Phys. Crystallogr. 12 (1968) 932–934. [40] J.E. Bonnet, J.N. Daou, J. Appl. Phys. 48 (1977) 964–968. [41] A. Pebler, W.E. Wallace, J. Phys. Chem. 66 (1962) 148–151. [42] M. Mansmann, W.E. Wallace, J. Phys. 25 (1964) 454–459.