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Compressibility and thermal expansion study of δ-UZr2 at high pressure and high temperature
Journal of Alloys and Compounds 813 (2020) 152214
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Compressibility and thermal expansion study of d-UZr2 at high pressure and high temperature Balmukund Shukla a, *, N.R. Sanjay Kumar a, Gurpreet Kaur b, N.V. Chandra Shekar a, A.K. Sinha c, d a
High Pressure Physics Section, Condensed Matter Physics Division, Materials Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, 603102, Tamil Nadu, India Materials Physics Division, Materials Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, 603102, Tamil Nadu, India c Synchrotron Utilization Section, Raja Ramanna Center for Advanced Technology, Indore, 452013, India d Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400094, India b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 May 2019 Received in revised form 29 August 2019 Accepted 9 September 2019 Available online 9 September 2019
UZr2 has been synthesized using the arc-melting technique. At ambient the compound is found to crystallize in a modified C32, AlB2 type structure, called d-structure and it remains stable up to 20 GPa. However, an anomalous decrease of c/a ratio has been observed in different pressure intervals at ambient temperature. At elevated temperature c/a ratio, shows a marginal increase with pressure. The bulk modulus and its pressure derivative at ambient temperature are found to be 108.3 GPa and 5.0, respectively. High-pressure and high-temperature studies reveal a softening in the material at higher temperatures. The thermal expansion coefficients are found to decrease from 4.6 105 K1 at 1.2 GPa to 2.7 105 K1 at 6.6 GPa in the temperature range 300 Ke473 K. © 2019 Elsevier B.V. All rights reserved.
Keywords: High pressure Bulk modulus DFT calculation Density of state Fermi energy Charge density
1. Introduction U-Pu-Zr alloy is a candidate fuel material for the metallic fuel based fast reactors [1]. A typical fuel contains 23% of zirconium. Due to thermal gradient generated in the fuel pin during the burnup, redistribution of uranium and zirconium takes place. Zirconium is enriched at the center of the fuel pin and uranium concentration decreases at the center [2,3]. At a higher burnup of the fuel, gamma (bcc) and d phases of UZr2 may form inside the fuel pin at homogeneity range 63e78 at% Zr [3]. The UeZr binary phase diagram shows the existence of only d phase in the homogeneity range 64.2e78.2 at%Zr [4e6]. This phase forms on cooling below 908 K from the high-temperature bcc UeZr solid solution. Basak et al. established the formation of the UZr2 phases through various quenching rates. It states that cooling/quenching has to be done below 823 K to arrive at the d phase, failing which a mixture of d and bcc phase would be obtained [4]. The enthalpy of formation
* Corresponding author. E-mail address: [email protected] (B. Shukla). https://doi.org/10.1016/j.jallcom.2019.152214 0925-8388/© 2019 Elsevier B.V. All rights reserved.
and phase transition temperatures are reported in the literature [7e11]. High-temperature gamma phase transforms to d phase by u phase transformation mechanism where alternate (111) planes of gamma phase collapse and form AlB2 type (C32) hexagonal crystal structure, which is related to the u structure [4]. T. Ogawa et al. explained that u phase stabilizes due to increase in the d-band occupancy of zirconium wherein a significant mixing of the valence shell of uranium with d band of zirconium is seen [12]. Therefore, uranium acts as a chemical pressure to stabilize UZr2 in u structure as it happens in the case of zirconium wherein external pressure transforms the ambient hcp phase to u phase through interband electron transfer. Moreover, Zr metal goes to bcc structure with large atomic cell volume at ~33 GPa [13]. It has been reported that the transition pressure for u to bcc phase transition in Zr decreases with increase in temperature and the decrease is quite significant such that the material changes phase at a much lower pressure of ~6 GPa at 973 K [12]. Therefore, the fascinating properties of d-UZr2 such as better mechanical properties of u phase [14e17], similarity in the structural phase transition with Zr at high temperature [12,18] along with the observation of a series of structural phase transitions [19,20] in AlB2 type UX2 (X ¼ transition metal)
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compounds [19] make this study relevant and interesting. The unit cell of d-UZr2 is AlB2 type hexagonal cell wherein Zr occupies corner (0,0,0) position and U & Zr randomly occupy (1/3, 2/3, 1/2) & (2/3, 1/3, 1/2) positions [3e5,18,21,22]. X-ray diffraction study by Boyko et al. [1957] found intensity differences between various Bragg peaks of the observed & calculated patterns and attributed it to the randomness in the uranium & zirconium positions [21]. Density functional study on the compound also confirms that partially ordered structure is energetically favorable [3,23]. Earlier, neutron diffraction study on d-UZr2 describes the variation of lattice parameter at high temperatures wherein c/a ratio is found to decrease with increase in the temperature [18]. However, the decrease in not significant in the lower temperature range. Several other studies on d-UZr2 such as microstructure evolution upon ion irradiation [24], phase transformations in UeZr alloy using differential thermal analysis [25], evolution of microstructure and thermal expansion studies in U-rich UeZr alloys [26] have been reported in the literature. As discussed earlier, the formation of UZr2 is probable in metallic fuel reactors, therefore, it is interesting to study the structural stability of UZr2 at High Pressure-High Temperature (HP-HT) and thermal expansion behavior at high pressure. It is also interesting to observe whether phase transition, similar to Zr, is seen in UZr2 at high pressure and high temperature. In this paper, we have carried out High-Pressure X-Ray Diffraction (HP-XRD) of UZr2 at synchrotron source. Also, we report in-situ HPHT XRD study on d-UZr2. 2. Experimental methods & computational details 2.1. Preparation of materials The sample was prepared using the arc-melting technique. Ingots of both uranium (99.98% pure) and zirconium (99.99% pure) were rubbed using emery sheet to remove the oxide layer on the surface. The ingots were then etched using dilute HNO3 and thoroughly cleaned using HF. Uranium and zirconium were taken in a stoichiometric ratio of ~70.7 atom% Zr and arc-melted several times until a homogenous ingot was achieved. Proper care was taken to remove atmospheric gases as the preparation is chemically sensitive to nitrogen and oxygen presence [12]. The obtained ingot was vacuum-sealed in a quartz tube and annealed at 773 K for 2 weeks. The temperature was slowly reduced to ambient. The X-ray diffraction pattern of the powder sample confirms the formation of a single phase d-UZr2 with lattice parameters a ¼ 5.032 Å and c ¼ 3.081 Å [22]. 2.2. High-pressure measurement at room temperature (HP-RT) HP-XRD study on d-UZr2 was carried out up to 20 GPa. Indigenously designed Mao-Bell type Diamond Anvil Cell (DAC) was used to achieve high pressure [27]. Sample (UZr2) along with silver (pressure calibrant) and Methanol: Ethanol: Water T 16:3:1 (pressure transmitting medium) were loaded in a Stainless Steel (SS) chamber of dia ~200 mm [28]. Silver was used as its Bragg reflections do not overlap with the sample peaks. High-pressure experiments were carried out at Angle Dispersive X-ray Diffraction (ADXRD) Beamline (BL-12) Indus-2 synchrotron Source, RRCAT [29]. The incident X-ray beam of dia ~100 mm and wavelength of 0.6061 Å was used for the high-pressure diffraction studies. The wavelength was accurately calibrated using the XRD pattern of NIST standard LaB6. The diffraction data were collected for 20 min at each pressure using mar345 IP detector. The obtained image from the detector was analyzed using Fit2D software [30]. NIST*AIDS-83 software was used to obtain lattice parameter at each pressure [31]. UZr2 was pressurized in several steps up to a pressure of 20 GPa at
ambient temperature. In the reverse cycle, pressure was decreased slowly in steps and diffraction patterns were collected after a relaxation time of 15 min. 2.3. High-pressure measurements in the temperature range 373e673 K (HP-HT) Static HP-HT was achieved by Helios membrane Diamond Anvil Cell (of M/s Almax easyLab). The DAC is designed to achieve 25 GPa and 1273 K simultaneously. It employs a pair of diamonds to achieve high pressure wherein the sample is squeezed between the culets of the diamonds. A circular form of resistive heater around the diamonds is used to realize high temperature. Temperature is estimated using a NiCreNiAl thermocouple which is in contact with the diamond girdle. Diamond, being a good thermal conductor, has negligible thermal gradient across it, therefore, the temperature at the culet, where sample sits, is found to be the same to that of the girdle. The temperature reading of the thermocouple was confirmed using Equation of State (EOS) of NaCl and also by measuring the melting point of NH4Cl and AgCl [32]. HP-HT XRD studies were carried out using a novel custom-designed combination of membrane cell DAC coupled to a high flux micro-focus X-ray machine (of M/s XENOCS, France). The multi-layered mirror optics focuses intense monochromatic beam at the focal spot (FWHM-130 mm). Molybdenum target of the X-ray generator gives a beam of wavelength 0.711 Å. The flux obtained was 15.5 106 photon/sec at 50 kV and 1 mA [33]. To perform HP-HT experiment Stainless Steel (SS) gasket of thickness 250 mm was used to contain the sample as well as pressure transmitting medium. A hole of ~250 mm was drilled at the center of the pre-indented region of the gasket. The gasket was mounted on the cylinder of the DAC that has a diamond of culet dia ~600 mm. The SS gasket chamber was filled with NaCl which acts as pressure transmitting medium as well as pressure and temperature calibrant [32]. A pelletized chip of size ~150 mm of the sample (UZr2) was placed at the center of the chamber of the gasket and topped up with NaCl to realize better hydrostatic pressure conditions around the sample. Nitrogen gas in a controlled fashion was supplied to the membrane inside the DAC which in turn pushes the piston thereby increasing the pressure on the sample. During the heating of the sample, gas mixture of argon (inert) and 2% hydrogen (reducing) is allowed to flow around the sample region in the DAC at a very low flow rate of ~15e18 sccm to avoid tarnishing and oxidation of the DAC surface due to heating. Mica sheets on both the sides of the DAC, in the path of X-ray, were placed to insulate the diamonds from the atmospheric gases and also to provide insulation of the hot zone. The details of the HP-HT experiment are described by Shukla et al. [33]. HP-HT studies were carried out up to ~6 GPa and 473 K in the temperature interval of 100 K. XRD patterns were collected for 30 min at each pressure and temperature. The relaxation time of 30 min was given between successive temperature intervals. Data was collected using a mar345 image plate based detector and analyzed using Fit2D software. Lattice parameter was obtained using NIST*AIDS-83 at various pressure and temperature. 2.4. Computational details First-principle based calculations were carried out to understand the bonding and charge density distribution using the density functional theory as implemented in Vienna Ab-Initio Simulation Package (VASP) [34e36]. The interaction between the valence electrons and the ionic core was described by Projector Augmented Wave (PAW) based pseudopotential [37]. Generalized Gradient Approximation as parametrized by Perdew, Burke, and
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Ernzerhof (PBE) [38] was used for exchange-correlation functional. The pseudopotentials used for U and Zr treat 6s2 6p6 7s2 5f3 6d1 and 4s2 4p6 5s2 4d2, respectively, as valence electrons. All the calculations are scalar relativistic and non-spin polarized. The calculations were carried out with random occupancy of U and Zr at (1/3, 2/3, 1/ 2) & (2/3, 1/3, 1/2) position, respectively. A plane wave energy cutoff of 450 eV and brillouin zone sampling using a 9 9 15 gamma centered mesh were used to ensure energy convergence of better than 1 meV/atom. Calculations were done for different volumes which were fitted to Birch-Murnagan EOS (B-M EOS) [39] to obtain equilibrium volume, bulk modulus, and its pressure derivative. To see the effect of pressure both unit cell shape and volume were relaxed at different pressures to get equilibrium structure corresponding to each pressure.
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Rietveld refinement. Hence, random occupancy factor of 50:50, as established in the literature, was considered for first principle calculations. 3.2. High-pressure studies at ambient temperature Fig. 2 shows HP-XRD patterns at various pressures. It is seen from the diffraction patterns that the parent phase reflections are traceable up to the highest pressure studied indicating the stability of the parent d-UZr2 phase up to 20 GPa. The lattice parameters obtained at various pressures are shown in Fig. 3. The volume of the unit cell at different pressures are shown in Fig. 4. The pressurevolume data was fitted with 3rd order Birch Murnaghan (BM) EOS resulting in the bulk modulus and its pressure derivative to be 108.3 GPa and 5.0, respectively. Density Functional Theory (DFT)
3. Results and discussion 3.1. Characterization of arc-melted UZr2 compound The arc-melted & annealed sample was finely powdered and characterized using synchrotron X-ray radiation. XRD pattern was collected for 10 min in an angle dispersive mode wherein the sample was on a fixed stage. The obtained data was analyzed using GSAS Rietveld refinement software [40]. It has been reported in the literature that in the unit cell of UZr2, as shown in Fig. 1 (a), Zr atom occupies corner (0,0,0) position and one U atom & one Zr atom randomly occupies (1/3, 2/3, 1/2) & (2/3, 1/3, 1/2) position [3e5,18,21,22]. It is interesting to note that with 50% randomness at U & Zr positions in UZr2, calculated Bragg peaks have a mismatch in the intensities compared to those of observed pattern. Refinement in the occupancy factor of U & Zr at (1/3, 2/3, 1/2) and (2/3, 1/3, 1/2) positions results in a better match [Fig. 1b]. The occupancy factor of 0.84 at Zr position (1/3, 2/3, 1/2) turns out to be a better match of the observed and calculated Bragg reflections. Further, XRD experiment with sample rotation in angle dispersive mode is required to avoid any possibility of preferred orientation in the lattice that may affect the determination of occupancy factor during
Fig. 2. HP-XRD plots of d-UZr2 at various pressures.
Fig. 1. (a) A unit cell of UZr2 (b) Rietveld Refined X-ray diffraction pattern. The bottom plot shows mismatch in the observed and calculated intensity with random occupancies at (1/ 3, 2/3, 1/2) & (2/3, 1/3, 1/2) sites. The top plot shows better fitting after occupancy factor refinement.
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Fig. 5. Energy vs volume plot of d-UZr2 obtained from DFT calculation.
Fig. 3. Variation of a, c and c/a variation with pressure, the bottom curve shows computed c/a ratio.
Fig. 4. Normalized unit cell volume vs pressure plot of d-UZr2 at ambient temperature.
calculations have also been carried out and the plot of Energy vs Volume is shown in Fig. 5. The BM EOS fitting yields the bulk modulus to be 100.4 GPa, which is in good agreement with the observed value (108.3 GPa). From Fig. 3, it can be seen that the lattice parameters ‘a’ and ‘c’ decrease with increasing pressure. The c/a vs pressure plot shows very interesting behavior wherein a different rate of decrease in c/a have been observed in different pressure intervals. Up to 10 GPa, c/a decreases slowly and as the pressure is increased further, the rate of decrease in c/a increases sharply. Therefore, the c/a variation can be classified into two regions, one below 10 GPa and another above 10 GPa. The same trend of variation has also been seen in the c/a ratio estimated from DFT calculation as shown in Fig. 3. Variations
in the rate of change in c/a with pressure can be understood from the bonding nature between the U & Zr atoms at (1/3, 2/3, 1/2) and (2/3, 1/3, 1/2) positions. Difference charge density has been calculated along (110) and (001) planes at various pressures and is shown in Fig. 6a and b. It can be seen that corner ZreZr bonds have metallic nature and U (1/3,2/3,1/2)-Zr (2/3, 1/3, 1/2) bond have metallic as well as covalent character. To quantify the bonding nature between atoms, line charge density along the bonds Zr (0,0,0)/ U(1/3,2/3,1/2)/ Zr(2/3,1/3,1/2)/Zr (1,1,1)/Zr (0,1,1) have been plotted at various pressures and are shown in Fig. 7. The plot shows that charge density between bond U(1/3,2/3,1/2)/ Zr(2/3,1/3,1/2) increases with increasing pressure. The increase is from 0.0109 e/Å3 at 0 GPa to 0.0155 e/Å3 at 15 GPa indicating an increase in the covalent nature of bonding. Therefore, it can be concluded that at lower pressures U (1/3, 2/3, 1/2) / Zr (2/3, 1/3, 1/ 2) bond is weaker hence fast decrease in ‘a’ lattice parameter up to 10 GPa, beyond which the bond is strongest leading to a resistance in compression along ‘a’ axis at higher pressures. These changes in lattice parameter ‘a’, reflects in the c/a ratio. Another interesting point which comes out from the charge density plot is that charge gets concentrated on each atom with increasing pressure i.e. charges get more localized at a higher pressure and hence the overall metallicity of UZr2 decreases which is in contradiction to the usual trends. In general, the metallicity of the system increases with pressure, however, UZr2 shows opposite behavior and it becomes less metallic at high pressures. In addition to the charge density plot, electron Density of States (DOS) plot also indicates a similar decrease in the metallicity of the system. DOS plot with increasing pressure, as shown in Fig. 8a, reflects a decrease in the total density of state at the Fermi level indicating localization of electrons. However, after a certain pressure, the decrease in the DOS saturates [Fig. 8b] implying no further localization i.e. metallicity of UZr2 does not decrease further. Since U-f electrons and then Zr-d electrons contribute majorly to the total DOS [Fig. 8c], U-f and Zr-d orbitals are responsible for a possible decrease in the metallicity of the system. This conclusion of decrease in metallicity of UZr2 under pressure is arrived at from first principle calculations and can be verified through resistivity measurements at high pressures. 3.3. High-pressure studies at 293e673 K High-temperature study on d-UZr2 has been reported earlier [18] where temperature dependence of the lattice parameters is
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Fig. 7. Line profile charge density along Zr (0,0,0)/ U(1/3,2/3,1/2)/ Zr(2/3,1/3,1/2)/ Zr (1,1,1)/Zr (0,1,1) bonds.
Fig. 6. Difference Charge density along (a) (110) plane (b) (001) plane; Same scale (linear) have been used in the charge density plots.
described up to 880 K. With the increase in temperature, the c/a ratio decreases, however, the decrease is not significant in the lower temperature range. Above 500 K, it drops below the ideal value of the hexagonal cell which is 0.612. Beyond 885 K, the d phase is reported to transform to bcc phase which has higher atomic volume. The bcc and d phases have Bragg reflection at the same 2-theta values, except for the (001) and (111) peak, through which the presence of d phase can be identified. We have carried out in-situ HP-HT XRD study up to ~6 GPa and 673 K to study the structural behavior at high pressures and high temperatures. The XRD plots at different pressures and temperatures are shown in Fig. 9. It is observed from the HP-HT XRD plots that reflections (001) and (111), which particularly belong to d phase of UZr2, continue to appear and the relative intensities with the high intense reflection (101) do not alter up to the highest pressure and temperature studied. Therefore, it can be concluded that the d phase remains stable up to 6 GPa and 673 K. Diffraction data at 373 K and 473 K have been analyzed and lattice parameters as a function of pressure at each temperature are plotted in Fig. 10. As usual, the lattice parameters are seen to decrease with pressure at higher temperatures. However, c/a ratio is found to increase marginally in HP-HT experiments as compared to near-constant c/a in HP experiments and this may be ascribed to the weakening of U(1/3, 2/3, 1/2) -Zr(2/3, 1/3, 1/2) bond along a-axis of the lattice. The bond between U & Zr is covalent as well as metallic in nature and it is known that temperature causes the material to be more metallic leading to the weakening of the U(1/ 3,2/3,1/2) - Zr(2/3,1/3,1/2) covalent bond. The weakening of UeZr bond at high temperature may lead to the observed trend in c/a. However, it needs further confirmation through experiments at even higher temperatures. The pressure versus volume data is fitted with the 3rd order BM EOS [Fig. 11] resulting in the bulk moduli of the materials to be 104.8 GPa and 101.6 GPa at 373 K and 473 K, respectively. A drop in the bulk modulus, observed at high temperature, signifies softening of the material. Reduced bulk modulus is due to softening of the lattice modes at high temperature. Apart from the compressibility study, thermal expansion behavior of the material has also been studied. In the present study, the volume of the unit cell is found to increase with temperature at higher pressure, showing the expected lattice expansion behavior. Thermal expansion coefficients have been calculated as a function of pressure and found to be 4.6 105 K1, 3.7 105 K1, 2.7 105 K1 at 1.2 GPa, 4.8 GPa and 6.6 GPa, respectively, in the temperature range 300 Ke473 K. A
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Fig. 8. (a) DOS plot at high pressures, (b) part of DOS around Fermi Energy (c) Partial DOS at ambient pressure.
decrease in the thermal expansion coefficient as a function of pressure is expected because pressure causes hindrance in the expansion of the material. 4. Conclusions
Fig. 9. In-situ HP-HT XRD plots at various pressures and temperatures.
d-UZr2 was synthesized by arc melting technique and found to be in the d phase. High-pressure study at ambient temperature on d-UZr2 reveals that d phase of UZr2 is stable up to 20 GPa and the bulk modulus is found to be 108.3 GPa at ambient temperature. Up to a pressure of 10 GPa, the c/a ratio was found to decrease slowly, after which the reduction rate increases sharply. It is attributed to the strengthening of U(1/3,2/3,1/2) - Zr(2/3,1/3,1/2) covalent bond along ‘a’ axis at higher pressures. DFT computation also reveals that the localization of charge density across the lattice which may lead to a drop in the metallization of the material. In-situ high pressure and high-temperature study on UZr2 shows that the structure is stable up to ~6 GPa and 473 K simultaneously. Bulk modulus value of 101.6 GPa at 473 K indicates a softening in the material at high temperature. The lattice parameter
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4.6 105 K1, 3.7 105 K1, 2.7 105 K1 at 1.2 GPa, 4.8 GPa and 6.6 GPa, respectively, in the temperature range 300 Ke473 K. Acknowledgment The authors thank Dr. S Kalavathi for her valuable suggestions and the members of High-Pressure Physics Section for help at various stages of the experiments. We would like to acknowledge Mr. L Meenakshi Sundaram for his help during the synthesis of material and the members of the synchrotron beamline-12, Indus2, RRCAT, Indore for their support during the experiment. We thank IGCAR management for their encouragement and support. References
Fig. 10. Variation of a & c variation with pressure at 373K and 473K [top], c/a ratio variation with pressure at 473 K [bottom].
Fig. 11. Pressure vs volume d-UZr2 at 473K
decreases with pressure at high temperature, however, c/a is found to increase marginally. It may be due to the weakening of the covalent bonds between uranium and zirconium. A usual decrease in the thermal expansion coefficient has been observed, which are
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Compressibility and thermal expansion study of d-UZr2 at high pressure and high temperature Balmukund Shukla a, *, N.R. Sanjay Kumar a, Gurpreet Kaur b, N.V. Chandra Shekar a, A.K. Sinha c, d a
High Pressure Physics Section, Condensed Matter Physics Division, Materials Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, 603102, Tamil Nadu, India Materials Physics Division, Materials Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, 603102, Tamil Nadu, India c Synchrotron Utilization Section, Raja Ramanna Center for Advanced Technology, Indore, 452013, India d Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400094, India b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 May 2019 Received in revised form 29 August 2019 Accepted 9 September 2019 Available online 9 September 2019
UZr2 has been synthesized using the arc-melting technique. At ambient the compound is found to crystallize in a modified C32, AlB2 type structure, called d-structure and it remains stable up to 20 GPa. However, an anomalous decrease of c/a ratio has been observed in different pressure intervals at ambient temperature. At elevated temperature c/a ratio, shows a marginal increase with pressure. The bulk modulus and its pressure derivative at ambient temperature are found to be 108.3 GPa and 5.0, respectively. High-pressure and high-temperature studies reveal a softening in the material at higher temperatures. The thermal expansion coefficients are found to decrease from 4.6 105 K1 at 1.2 GPa to 2.7 105 K1 at 6.6 GPa in the temperature range 300 Ke473 K. © 2019 Elsevier B.V. All rights reserved.
Keywords: High pressure Bulk modulus DFT calculation Density of state Fermi energy Charge density
1. Introduction U-Pu-Zr alloy is a candidate fuel material for the metallic fuel based fast reactors [1]. A typical fuel contains 23% of zirconium. Due to thermal gradient generated in the fuel pin during the burnup, redistribution of uranium and zirconium takes place. Zirconium is enriched at the center of the fuel pin and uranium concentration decreases at the center [2,3]. At a higher burnup of the fuel, gamma (bcc) and d phases of UZr2 may form inside the fuel pin at homogeneity range 63e78 at% Zr [3]. The UeZr binary phase diagram shows the existence of only d phase in the homogeneity range 64.2e78.2 at%Zr [4e6]. This phase forms on cooling below 908 K from the high-temperature bcc UeZr solid solution. Basak et al. established the formation of the UZr2 phases through various quenching rates. It states that cooling/quenching has to be done below 823 K to arrive at the d phase, failing which a mixture of d and bcc phase would be obtained [4]. The enthalpy of formation
* Corresponding author. E-mail address: [email protected] (B. Shukla). https://doi.org/10.1016/j.jallcom.2019.152214 0925-8388/© 2019 Elsevier B.V. All rights reserved.
and phase transition temperatures are reported in the literature [7e11]. High-temperature gamma phase transforms to d phase by u phase transformation mechanism where alternate (111) planes of gamma phase collapse and form AlB2 type (C32) hexagonal crystal structure, which is related to the u structure [4]. T. Ogawa et al. explained that u phase stabilizes due to increase in the d-band occupancy of zirconium wherein a significant mixing of the valence shell of uranium with d band of zirconium is seen [12]. Therefore, uranium acts as a chemical pressure to stabilize UZr2 in u structure as it happens in the case of zirconium wherein external pressure transforms the ambient hcp phase to u phase through interband electron transfer. Moreover, Zr metal goes to bcc structure with large atomic cell volume at ~33 GPa [13]. It has been reported that the transition pressure for u to bcc phase transition in Zr decreases with increase in temperature and the decrease is quite significant such that the material changes phase at a much lower pressure of ~6 GPa at 973 K [12]. Therefore, the fascinating properties of d-UZr2 such as better mechanical properties of u phase [14e17], similarity in the structural phase transition with Zr at high temperature [12,18] along with the observation of a series of structural phase transitions [19,20] in AlB2 type UX2 (X ¼ transition metal)
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compounds [19] make this study relevant and interesting. The unit cell of d-UZr2 is AlB2 type hexagonal cell wherein Zr occupies corner (0,0,0) position and U & Zr randomly occupy (1/3, 2/3, 1/2) & (2/3, 1/3, 1/2) positions [3e5,18,21,22]. X-ray diffraction study by Boyko et al. [1957] found intensity differences between various Bragg peaks of the observed & calculated patterns and attributed it to the randomness in the uranium & zirconium positions [21]. Density functional study on the compound also confirms that partially ordered structure is energetically favorable [3,23]. Earlier, neutron diffraction study on d-UZr2 describes the variation of lattice parameter at high temperatures wherein c/a ratio is found to decrease with increase in the temperature [18]. However, the decrease in not significant in the lower temperature range. Several other studies on d-UZr2 such as microstructure evolution upon ion irradiation [24], phase transformations in UeZr alloy using differential thermal analysis [25], evolution of microstructure and thermal expansion studies in U-rich UeZr alloys [26] have been reported in the literature. As discussed earlier, the formation of UZr2 is probable in metallic fuel reactors, therefore, it is interesting to study the structural stability of UZr2 at High Pressure-High Temperature (HP-HT) and thermal expansion behavior at high pressure. It is also interesting to observe whether phase transition, similar to Zr, is seen in UZr2 at high pressure and high temperature. In this paper, we have carried out High-Pressure X-Ray Diffraction (HP-XRD) of UZr2 at synchrotron source. Also, we report in-situ HPHT XRD study on d-UZr2. 2. Experimental methods & computational details 2.1. Preparation of materials The sample was prepared using the arc-melting technique. Ingots of both uranium (99.98% pure) and zirconium (99.99% pure) were rubbed using emery sheet to remove the oxide layer on the surface. The ingots were then etched using dilute HNO3 and thoroughly cleaned using HF. Uranium and zirconium were taken in a stoichiometric ratio of ~70.7 atom% Zr and arc-melted several times until a homogenous ingot was achieved. Proper care was taken to remove atmospheric gases as the preparation is chemically sensitive to nitrogen and oxygen presence [12]. The obtained ingot was vacuum-sealed in a quartz tube and annealed at 773 K for 2 weeks. The temperature was slowly reduced to ambient. The X-ray diffraction pattern of the powder sample confirms the formation of a single phase d-UZr2 with lattice parameters a ¼ 5.032 Å and c ¼ 3.081 Å [22]. 2.2. High-pressure measurement at room temperature (HP-RT) HP-XRD study on d-UZr2 was carried out up to 20 GPa. Indigenously designed Mao-Bell type Diamond Anvil Cell (DAC) was used to achieve high pressure [27]. Sample (UZr2) along with silver (pressure calibrant) and Methanol: Ethanol: Water T 16:3:1 (pressure transmitting medium) were loaded in a Stainless Steel (SS) chamber of dia ~200 mm [28]. Silver was used as its Bragg reflections do not overlap with the sample peaks. High-pressure experiments were carried out at Angle Dispersive X-ray Diffraction (ADXRD) Beamline (BL-12) Indus-2 synchrotron Source, RRCAT [29]. The incident X-ray beam of dia ~100 mm and wavelength of 0.6061 Å was used for the high-pressure diffraction studies. The wavelength was accurately calibrated using the XRD pattern of NIST standard LaB6. The diffraction data were collected for 20 min at each pressure using mar345 IP detector. The obtained image from the detector was analyzed using Fit2D software [30]. NIST*AIDS-83 software was used to obtain lattice parameter at each pressure [31]. UZr2 was pressurized in several steps up to a pressure of 20 GPa at
ambient temperature. In the reverse cycle, pressure was decreased slowly in steps and diffraction patterns were collected after a relaxation time of 15 min. 2.3. High-pressure measurements in the temperature range 373e673 K (HP-HT) Static HP-HT was achieved by Helios membrane Diamond Anvil Cell (of M/s Almax easyLab). The DAC is designed to achieve 25 GPa and 1273 K simultaneously. It employs a pair of diamonds to achieve high pressure wherein the sample is squeezed between the culets of the diamonds. A circular form of resistive heater around the diamonds is used to realize high temperature. Temperature is estimated using a NiCreNiAl thermocouple which is in contact with the diamond girdle. Diamond, being a good thermal conductor, has negligible thermal gradient across it, therefore, the temperature at the culet, where sample sits, is found to be the same to that of the girdle. The temperature reading of the thermocouple was confirmed using Equation of State (EOS) of NaCl and also by measuring the melting point of NH4Cl and AgCl [32]. HP-HT XRD studies were carried out using a novel custom-designed combination of membrane cell DAC coupled to a high flux micro-focus X-ray machine (of M/s XENOCS, France). The multi-layered mirror optics focuses intense monochromatic beam at the focal spot (FWHM-130 mm). Molybdenum target of the X-ray generator gives a beam of wavelength 0.711 Å. The flux obtained was 15.5 106 photon/sec at 50 kV and 1 mA [33]. To perform HP-HT experiment Stainless Steel (SS) gasket of thickness 250 mm was used to contain the sample as well as pressure transmitting medium. A hole of ~250 mm was drilled at the center of the pre-indented region of the gasket. The gasket was mounted on the cylinder of the DAC that has a diamond of culet dia ~600 mm. The SS gasket chamber was filled with NaCl which acts as pressure transmitting medium as well as pressure and temperature calibrant [32]. A pelletized chip of size ~150 mm of the sample (UZr2) was placed at the center of the chamber of the gasket and topped up with NaCl to realize better hydrostatic pressure conditions around the sample. Nitrogen gas in a controlled fashion was supplied to the membrane inside the DAC which in turn pushes the piston thereby increasing the pressure on the sample. During the heating of the sample, gas mixture of argon (inert) and 2% hydrogen (reducing) is allowed to flow around the sample region in the DAC at a very low flow rate of ~15e18 sccm to avoid tarnishing and oxidation of the DAC surface due to heating. Mica sheets on both the sides of the DAC, in the path of X-ray, were placed to insulate the diamonds from the atmospheric gases and also to provide insulation of the hot zone. The details of the HP-HT experiment are described by Shukla et al. [33]. HP-HT studies were carried out up to ~6 GPa and 473 K in the temperature interval of 100 K. XRD patterns were collected for 30 min at each pressure and temperature. The relaxation time of 30 min was given between successive temperature intervals. Data was collected using a mar345 image plate based detector and analyzed using Fit2D software. Lattice parameter was obtained using NIST*AIDS-83 at various pressure and temperature. 2.4. Computational details First-principle based calculations were carried out to understand the bonding and charge density distribution using the density functional theory as implemented in Vienna Ab-Initio Simulation Package (VASP) [34e36]. The interaction between the valence electrons and the ionic core was described by Projector Augmented Wave (PAW) based pseudopotential [37]. Generalized Gradient Approximation as parametrized by Perdew, Burke, and
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Ernzerhof (PBE) [38] was used for exchange-correlation functional. The pseudopotentials used for U and Zr treat 6s2 6p6 7s2 5f3 6d1 and 4s2 4p6 5s2 4d2, respectively, as valence electrons. All the calculations are scalar relativistic and non-spin polarized. The calculations were carried out with random occupancy of U and Zr at (1/3, 2/3, 1/ 2) & (2/3, 1/3, 1/2) position, respectively. A plane wave energy cutoff of 450 eV and brillouin zone sampling using a 9 9 15 gamma centered mesh were used to ensure energy convergence of better than 1 meV/atom. Calculations were done for different volumes which were fitted to Birch-Murnagan EOS (B-M EOS) [39] to obtain equilibrium volume, bulk modulus, and its pressure derivative. To see the effect of pressure both unit cell shape and volume were relaxed at different pressures to get equilibrium structure corresponding to each pressure.
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Rietveld refinement. Hence, random occupancy factor of 50:50, as established in the literature, was considered for first principle calculations. 3.2. High-pressure studies at ambient temperature Fig. 2 shows HP-XRD patterns at various pressures. It is seen from the diffraction patterns that the parent phase reflections are traceable up to the highest pressure studied indicating the stability of the parent d-UZr2 phase up to 20 GPa. The lattice parameters obtained at various pressures are shown in Fig. 3. The volume of the unit cell at different pressures are shown in Fig. 4. The pressurevolume data was fitted with 3rd order Birch Murnaghan (BM) EOS resulting in the bulk modulus and its pressure derivative to be 108.3 GPa and 5.0, respectively. Density Functional Theory (DFT)
3. Results and discussion 3.1. Characterization of arc-melted UZr2 compound The arc-melted & annealed sample was finely powdered and characterized using synchrotron X-ray radiation. XRD pattern was collected for 10 min in an angle dispersive mode wherein the sample was on a fixed stage. The obtained data was analyzed using GSAS Rietveld refinement software [40]. It has been reported in the literature that in the unit cell of UZr2, as shown in Fig. 1 (a), Zr atom occupies corner (0,0,0) position and one U atom & one Zr atom randomly occupies (1/3, 2/3, 1/2) & (2/3, 1/3, 1/2) position [3e5,18,21,22]. It is interesting to note that with 50% randomness at U & Zr positions in UZr2, calculated Bragg peaks have a mismatch in the intensities compared to those of observed pattern. Refinement in the occupancy factor of U & Zr at (1/3, 2/3, 1/2) and (2/3, 1/3, 1/2) positions results in a better match [Fig. 1b]. The occupancy factor of 0.84 at Zr position (1/3, 2/3, 1/2) turns out to be a better match of the observed and calculated Bragg reflections. Further, XRD experiment with sample rotation in angle dispersive mode is required to avoid any possibility of preferred orientation in the lattice that may affect the determination of occupancy factor during
Fig. 2. HP-XRD plots of d-UZr2 at various pressures.
Fig. 1. (a) A unit cell of UZr2 (b) Rietveld Refined X-ray diffraction pattern. The bottom plot shows mismatch in the observed and calculated intensity with random occupancies at (1/ 3, 2/3, 1/2) & (2/3, 1/3, 1/2) sites. The top plot shows better fitting after occupancy factor refinement.
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Fig. 5. Energy vs volume plot of d-UZr2 obtained from DFT calculation.
Fig. 3. Variation of a, c and c/a variation with pressure, the bottom curve shows computed c/a ratio.
Fig. 4. Normalized unit cell volume vs pressure plot of d-UZr2 at ambient temperature.
calculations have also been carried out and the plot of Energy vs Volume is shown in Fig. 5. The BM EOS fitting yields the bulk modulus to be 100.4 GPa, which is in good agreement with the observed value (108.3 GPa). From Fig. 3, it can be seen that the lattice parameters ‘a’ and ‘c’ decrease with increasing pressure. The c/a vs pressure plot shows very interesting behavior wherein a different rate of decrease in c/a have been observed in different pressure intervals. Up to 10 GPa, c/a decreases slowly and as the pressure is increased further, the rate of decrease in c/a increases sharply. Therefore, the c/a variation can be classified into two regions, one below 10 GPa and another above 10 GPa. The same trend of variation has also been seen in the c/a ratio estimated from DFT calculation as shown in Fig. 3. Variations
in the rate of change in c/a with pressure can be understood from the bonding nature between the U & Zr atoms at (1/3, 2/3, 1/2) and (2/3, 1/3, 1/2) positions. Difference charge density has been calculated along (110) and (001) planes at various pressures and is shown in Fig. 6a and b. It can be seen that corner ZreZr bonds have metallic nature and U (1/3,2/3,1/2)-Zr (2/3, 1/3, 1/2) bond have metallic as well as covalent character. To quantify the bonding nature between atoms, line charge density along the bonds Zr (0,0,0)/ U(1/3,2/3,1/2)/ Zr(2/3,1/3,1/2)/Zr (1,1,1)/Zr (0,1,1) have been plotted at various pressures and are shown in Fig. 7. The plot shows that charge density between bond U(1/3,2/3,1/2)/ Zr(2/3,1/3,1/2) increases with increasing pressure. The increase is from 0.0109 e/Å3 at 0 GPa to 0.0155 e/Å3 at 15 GPa indicating an increase in the covalent nature of bonding. Therefore, it can be concluded that at lower pressures U (1/3, 2/3, 1/2) / Zr (2/3, 1/3, 1/ 2) bond is weaker hence fast decrease in ‘a’ lattice parameter up to 10 GPa, beyond which the bond is strongest leading to a resistance in compression along ‘a’ axis at higher pressures. These changes in lattice parameter ‘a’, reflects in the c/a ratio. Another interesting point which comes out from the charge density plot is that charge gets concentrated on each atom with increasing pressure i.e. charges get more localized at a higher pressure and hence the overall metallicity of UZr2 decreases which is in contradiction to the usual trends. In general, the metallicity of the system increases with pressure, however, UZr2 shows opposite behavior and it becomes less metallic at high pressures. In addition to the charge density plot, electron Density of States (DOS) plot also indicates a similar decrease in the metallicity of the system. DOS plot with increasing pressure, as shown in Fig. 8a, reflects a decrease in the total density of state at the Fermi level indicating localization of electrons. However, after a certain pressure, the decrease in the DOS saturates [Fig. 8b] implying no further localization i.e. metallicity of UZr2 does not decrease further. Since U-f electrons and then Zr-d electrons contribute majorly to the total DOS [Fig. 8c], U-f and Zr-d orbitals are responsible for a possible decrease in the metallicity of the system. This conclusion of decrease in metallicity of UZr2 under pressure is arrived at from first principle calculations and can be verified through resistivity measurements at high pressures. 3.3. High-pressure studies at 293e673 K High-temperature study on d-UZr2 has been reported earlier [18] where temperature dependence of the lattice parameters is
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Fig. 7. Line profile charge density along Zr (0,0,0)/ U(1/3,2/3,1/2)/ Zr(2/3,1/3,1/2)/ Zr (1,1,1)/Zr (0,1,1) bonds.
Fig. 6. Difference Charge density along (a) (110) plane (b) (001) plane; Same scale (linear) have been used in the charge density plots.
described up to 880 K. With the increase in temperature, the c/a ratio decreases, however, the decrease is not significant in the lower temperature range. Above 500 K, it drops below the ideal value of the hexagonal cell which is 0.612. Beyond 885 K, the d phase is reported to transform to bcc phase which has higher atomic volume. The bcc and d phases have Bragg reflection at the same 2-theta values, except for the (001) and (111) peak, through which the presence of d phase can be identified. We have carried out in-situ HP-HT XRD study up to ~6 GPa and 673 K to study the structural behavior at high pressures and high temperatures. The XRD plots at different pressures and temperatures are shown in Fig. 9. It is observed from the HP-HT XRD plots that reflections (001) and (111), which particularly belong to d phase of UZr2, continue to appear and the relative intensities with the high intense reflection (101) do not alter up to the highest pressure and temperature studied. Therefore, it can be concluded that the d phase remains stable up to 6 GPa and 673 K. Diffraction data at 373 K and 473 K have been analyzed and lattice parameters as a function of pressure at each temperature are plotted in Fig. 10. As usual, the lattice parameters are seen to decrease with pressure at higher temperatures. However, c/a ratio is found to increase marginally in HP-HT experiments as compared to near-constant c/a in HP experiments and this may be ascribed to the weakening of U(1/3, 2/3, 1/2) -Zr(2/3, 1/3, 1/2) bond along a-axis of the lattice. The bond between U & Zr is covalent as well as metallic in nature and it is known that temperature causes the material to be more metallic leading to the weakening of the U(1/ 3,2/3,1/2) - Zr(2/3,1/3,1/2) covalent bond. The weakening of UeZr bond at high temperature may lead to the observed trend in c/a. However, it needs further confirmation through experiments at even higher temperatures. The pressure versus volume data is fitted with the 3rd order BM EOS [Fig. 11] resulting in the bulk moduli of the materials to be 104.8 GPa and 101.6 GPa at 373 K and 473 K, respectively. A drop in the bulk modulus, observed at high temperature, signifies softening of the material. Reduced bulk modulus is due to softening of the lattice modes at high temperature. Apart from the compressibility study, thermal expansion behavior of the material has also been studied. In the present study, the volume of the unit cell is found to increase with temperature at higher pressure, showing the expected lattice expansion behavior. Thermal expansion coefficients have been calculated as a function of pressure and found to be 4.6 105 K1, 3.7 105 K1, 2.7 105 K1 at 1.2 GPa, 4.8 GPa and 6.6 GPa, respectively, in the temperature range 300 Ke473 K. A
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Fig. 8. (a) DOS plot at high pressures, (b) part of DOS around Fermi Energy (c) Partial DOS at ambient pressure.
decrease in the thermal expansion coefficient as a function of pressure is expected because pressure causes hindrance in the expansion of the material. 4. Conclusions
Fig. 9. In-situ HP-HT XRD plots at various pressures and temperatures.
d-UZr2 was synthesized by arc melting technique and found to be in the d phase. High-pressure study at ambient temperature on d-UZr2 reveals that d phase of UZr2 is stable up to 20 GPa and the bulk modulus is found to be 108.3 GPa at ambient temperature. Up to a pressure of 10 GPa, the c/a ratio was found to decrease slowly, after which the reduction rate increases sharply. It is attributed to the strengthening of U(1/3,2/3,1/2) - Zr(2/3,1/3,1/2) covalent bond along ‘a’ axis at higher pressures. DFT computation also reveals that the localization of charge density across the lattice which may lead to a drop in the metallization of the material. In-situ high pressure and high-temperature study on UZr2 shows that the structure is stable up to ~6 GPa and 473 K simultaneously. Bulk modulus value of 101.6 GPa at 473 K indicates a softening in the material at high temperature. The lattice parameter
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4.6 105 K1, 3.7 105 K1, 2.7 105 K1 at 1.2 GPa, 4.8 GPa and 6.6 GPa, respectively, in the temperature range 300 Ke473 K. Acknowledgment The authors thank Dr. S Kalavathi for her valuable suggestions and the members of High-Pressure Physics Section for help at various stages of the experiments. We would like to acknowledge Mr. L Meenakshi Sundaram for his help during the synthesis of material and the members of the synchrotron beamline-12, Indus2, RRCAT, Indore for their support during the experiment. We thank IGCAR management for their encouragement and support. References
Fig. 10. Variation of a & c variation with pressure at 373K and 473K [top], c/a ratio variation with pressure at 473 K [bottom].
Fig. 11. Pressure vs volume d-UZr2 at 473K
decreases with pressure at high temperature, however, c/a is found to increase marginally. It may be due to the weakening of the covalent bonds between uranium and zirconium. A usual decrease in the thermal expansion coefficient has been observed, which are
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