Ab initio calculation of mechanical and thermodynamic properties of Gd2Zr2O7 pyrochlore

Journal Pre-proof Ab initio calculation of mechanical and thermodynamic properties of Gd2Zr2O7 pyrochlore

Fen Luo, Bingsheng Li, Zhicheng Guo, Yi Xie, Linyan Li, Dadong Shao, Haibin Zhang, Xirui Lu PII:

S0254-0584(19)31375-6

DOI:

https://doi.org/10.1016/j.matchemphys.2019.122565

Reference:

MAC 122565

To appear in:

Materials Chemistry and Physics

Received Date:

13 August 2019

Accepted Date:

16 December 2019

Please cite this article as: Fen Luo, Bingsheng Li, Zhicheng Guo, Yi Xie, Linyan Li, Dadong Shao, Haibin Zhang, Xirui Lu, Ab initio calculation of mechanical and thermodynamic properties of Gd2Zr2 O7 pyrochlore, Materials Chemistry and Physics (2019), https://doi.org/10.1016/j.matchemphys. 2019.122565

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Journal Pre-proof

Ab initio calculation of mechanical and thermodynamic properties of Gd2Zr2O7 pyrochlore Fen Luoa, b, Bingsheng Lia, b, Zhicheng Guoa, Yi Xiec, Linyan Lid, Dadong Shaoe, Haibin Zhangf, Xirui Lua, b, a State

*

Key Laboratory of Environmental-friendly Energy Materials, Southwest University of Science and Technology, Mianyang Sichuan 621010, PR China

b

Fundamental Science on Nuclear Wastes and Environmental Safety Laboratory, Southwest University of Science and Technology, Mianyang Sichuan 621010, PR China

c Institute d

of Plasma Physics, Chinese Academy of Sciences, Hefei Anhui 230031, PR China

Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, PR China e

Jiangsu Key Laboratory of Chemical Pollution Control and Resources Reuse, School of Environmental and Biological Engineering, Nanjing University of Science and Technology, Nanjing 210094, PR China

f Institute

of Materials, China Academy of Engineering Physics, Mianyang Sichuan 621700, PR China

Abstract: Using density functional theory with GGA+U method, the mechanical, thermodynamic properties and minimum thermal conductivity of Gd2Zr2O7 pyrochlore are investigated. The obtained lattice parameters and density with GGA+U method are consistent with other experimental and theoretical results. The calculated elastic constants reveal that Gd2Zr2O7 pyrochlore is mechanically stable and ductile material under high pressure. From the direction dependence Young’s modulus and Zener ratio analysis, it is shown that Gd2Zr2O7 pyrochlore is weak anisotropy at 0 GPa and 10 GPa. In addition, the pressure effect on the Young’s modulus, bulk modulus, sound wave velocity, shear modulus and minimum thermal conductivity of Gd2Zr2O7 pyrochlore are analyzed. Subsequently, the thermodynamic properties such

Corresponding author at: State Key Laboratory of Environmental Friendly Energy Materials, Southwest University of Science and Technology, Mianyang, Sichuan 621010, PR China. E-mail address: [email protected] (X. Lu). 1

Journal Pre-proof as the constant volume heat capacity, thermal expansion coefficient, Debye temperature, thermal expansion coefficient and entropy under high pressure and temperature are also estimated with the quasi-harmonic Debye model. Keywords: Gd2Zr2O7 ceramic; Mechanical properties; Density functional theory; Thermodynamic properties;

1 Introduction With the development of nuclear industry, it is always a great challenge to get rid of high level radioactive waste (HLW) up to now. Actinides as a primary concern for HLW should be properly handled as a result of high radiotoxicity and long half-life[1]. For the immobilization of nuclear waste, the modern and safe technology has been developed[2-4]. The pyrochlore structure-type compounds have gained considerable interest owing to their outstanding chemical and physical properties, which has been proposed as a potential matrix to solidify the nuclear waste[5,6]. Pyrochlore oxides have the general formula of A2B2O6O'(A2B2O7), where the cations including trivalent and tetravalent metal atoms occupied the 8 coordinate A site and 6 coordinate B site, respectively. The anions oxygen of O and O' are deposited at the 48f (x, 0.125, 0.125) and 8b (0.375, 0.375, 0.375) positions, where x is the internal free coordinate[7-9]. The 16d (0,0,0) and 16c (0.5,0.5,0.5) sites are occupied by A and B cations, respectively. The relationship between pyrochlore structure stability and ionic radius ratio of A and B site cations(rA/rB) can be described as[10]: the pyrochlore structure is stable when rA/rB is between 1.46 and 1.78, while the disordered fluorite structure forms as rA/rB below 1.46. Due to the flexible crystal structure of typical A2B2O7 stoichiometry, the A and B positions can be occupied by the actinides such as U, Np, Th and so on[1,11]. Gd2Zr2O7, as a family of pyrochlore type compounds, has attracted significant attention among experimental and theoretical researches because of its remarkable irradiation resistance, chemical endurance, and thermal stability[12,13]. Wang et al.[14] showed that the Gd2(ZrxTi1-x)2O7 system became more radiation-resistant as zirconium content increase under 1 MeV Kr+ irradiation. Weber et al.[15] indicated that 2

Journal Pre-proof Gd2Zr2O7 exhibited better irradiation resistance than Gd2Ti2O7. In our previous study, Gd2Zr2O7 ceramic was synthesized for the first time by spark plasma sintering (SPS)[16]. Compared to the conventional method, the high densified Gd2Zr2O7 ceramic was produced at 1700ºC for 3 min under 80 MPa. With self-propagating chemical furnace synthesis plus quick pressing, the single Gd2Zr2O7 nanocrystalline ceramic was prepared with the density over 94%[17]. Shimamura et al.[18] measured the thermophysical properties of A2Zr2O7 (A=Gd, Sm, La, Nd, Y, Dy) by ultrasound pulse-echo and X-ray diffractometry method. Zhang et al.[19] studied the high pressure phase transformation of Gd2Zr2O7 using Raman scattering and synchrotron x-ray diffraction measurements. In their work, the ordered pyrochlore Gd2Zr2O7 became instable and changed to defect fluorite structure at a pressure above 15.3 GPa. Furthermore, x-ray-diffraction (XRD) experiment results[20] showed that the pyrochlore Gd2Zr2O7 is stable below 23 GPa. Theoretically[21], the structural phase transformation pressure for Gd2Zr2O7 was predicted 13 GPa, which are in good agreement with experiment results[19,20]. The structural, elastic and thermal properties as a function of composition in 25 different pyrochlore compounds were investigated by using molecular dynamics methods[22]. However, there has been little focus on the mechanical and thermodynamic properties of Gd2Zr2O7 pyrochlore at high pressures by using theoretical methods. In our work, using the density functional theory with GGA+U method, the mechanical, thermodynamic properties and minimum thermal conductivity of Gd2Zr2O7 pyrochlore have been investigated. Firstly, the structural and elastic constants of Gd2Zr2O7 pyrochlore as a function of pressure have been discussed. In the light of the calculated elastic constants, the mechanical properties and minimum thermal conductivity of Gd2Zr2O7 pyrochlore under high pressures have been obtained. With the quasi-harmonic Debye model[23], pressure and temperature dependence of the thermodynamic properties of Gd2Zr2O7 pyrochlore have been systematically studied. 2 Computational details 2.1 Computational details 3

Journal Pre-proof All of our calculations are implemented in VASP (Vienna ab initio simulation package) soft, which based on the density functional theory (DFT)[24,25]. In order to describe the electronic exchange-correlation interactions, the generalized gradient approximation (GGA) with the PBE (Perdew-Burke-Ernzerhof)[25]form is used. Projector augmented wave (PAW) method[26] is chosen to depict the interplay between electrons and ions. For the purpose of adequate description of strong Coulomb repulsion between f electrons, the Hubbard U correction method[27] is introduced for Gd 4f electrons. In this regime, based on the definition of exchange energy J and Coulomb energy U, the parameter Ueff is defined as Ueff=U-J. In the GGA+U calculations, the Ueff=6.9 eV is employed for Gd 4f electrons, which is proposed by Losovyj et al.[28] Monkhorst-Pack grids with 4 × 4 × 4 for sampling Brillouin zone and the plane wave cut-off energy of 500 eV are selected for Gd2Zr2O7 pyrochlore. 2.2 Mechanical properties To determine the mechanical properties of Gd2Zr2O7 pyrochlore, the elastic constants should be investigated. Because of the lattice symmetry of Gd2Zr2O7, three independent elastic constants (C11, C12, C44) need to be considered. Elastic constants are related to bulk modulus (B) and pressure (P), which can be expressed as follow[29]:

B  (C11  2C12  P) / 3.

(1)

The C11 and C12 can be obtained based on the volume conserving strain matrix ε(δ)[29]: 0 δ 0    ε (δ )   0 δ 0 ,  0 0 (1  δ ) 2  1  

(2)

where δ represents the small strain magnitude. Therefore, the relationship between strain energy E(δ) and strain is expressed as[29]

E (δ )  E (0)  3(C11  C12  2 P)Vδ 2  O(δ 3 ),

(3)

where E(0) is the energy of the unstrained unit cell and V is the corresponding volume, respectively. Similarly, in the light of the following volume-conserving strain matrix[29] and corresponding strain energy, C44 is also obtained. 4

Journal Pre-proof 0 0 δ    ε (δ )   δ 0 0 ,  0 0 δ 2 (1  δ 2 )   

E (δ )  E (0)  2(C44  P)Vδ 2  O(δ 4 ).

(4)

(5)

Subsequently, the Voigt and Reuss modulus can be calculated from the obtained elastic constants. The corresponding modulus can be written as[30]:

1 GV  (C11  C12  3C44 ), 5

(6)

5(C11  C12 )C44 , 4C44  3(C11  C12 )

(7)

GR 

BV  BR  B.

(8)

Then the polycrystalline modulus are given by the following average values of Voigt and Reuss modulus[31],

B  ( BV  BR ) / 2, G  (GV  GR ) / 2.

(9)

Therefore, the Young’s modulus E can be calculated by

E

9 BG . 3B  G

(10)

To further evaluate the elastic anisotropy of Gd2Zr2O7 pyrochlore, the direction-dependent Young’s modulus can be written as follow[32]:

1/ E  S11  (2 S11  2 S12  S 44 )(l12l22  l12l32  l22l32 ),

(11)

where Sij indicates the elastic compliance constant, l1, l2, and l3 represent the direction cosines with respect to the θ and φ (l1=sinθcosφ, l2=sinθsinφ, l3=cosθ), respectively. The velocities of longitudinal and transverse wave Vl and Vt, and the average acoustic velocity Vm can be written as[33]:

Vm  [(2 / Vt 3  1/ Vl 3 ) / 3]1/3 , Vl   B  4 / 3G  / ρ  , Vt  (G / ρ)1/2 . 1/2

(12)

2.3. Thermodynamic properties With the quasi-harmonic Debye model[23], the Gibbs free energy G * (V ; P, T ) as a function of pressure (P), temperature (T) and volume (V) can be written in the form 5

Journal Pre-proof of:

G* (V ; P, T )  E (V )  PV  AVib (Θ(V ); T ),

(13)

where Θ(V) is the Debye temperature, PV corresponds to the constant hydrostatic pressure condition, E(V) represents the total energy, Avib is the vibrational Helmholtz free energy and can be written by: 9 Θ  AVib (Θ; T )  nkT   3ln(1  e  Θ/T )  D(Θ / T )  , 8 T 

(14)

Where k is the Boltzmann constant, n represents the number of atoms in unit cell. D(Θ/T) is the Debye integral and Θ can be written as a function of adiabatic bulk modulus BS and the molecular mass per unit cell M:

B  Θ  [6π 2V 1/2 n]1/3 f (σ ) S , k M

(15)

where σ is Poisson ratio, and f(σ) is given by:

f (σ )  {3[2(

2 1  σ 3 2 1 1  σ 3 2 1 1 3 ) ( ) ] } , 3 1  2σ 3 1 σ

(16)

By solving the following equation to obtain the thermal equation of state V(P,T).

 G * (V ; P, T )     0, V   P ,T

(17)

Furthermore, the thermodynamic properties, such as volume thermal expansion coefficient α, entropy S and heat capacity CV can be derived as: α

γCV , BT V

(18)

S  nk[4 D( / T )  3ln(1  e  /T )],

(19)

3Θ / T   CV  3nk  4 D(Θ / T )  Θ/T , e  1  

(20)

where γ is Grüneisen parameter, and can be expressed as: γ

d ln Θ(V ) . d ln V

3. Results and discussions 3.1 Structural properties 6

(21)

Journal Pre-proof At ambient pressure, Gd2Zr2O7 pyrochlore crystallizes in the cubic structure with the Fd-3m space group. The unit cell of Gd2Zr2O7 pyrochlore contains 88 atoms, as shown in Fig 1. Through the full structure optimization of Gd2Zr2O7 pyrochlore, the structural parameters are obtained in Table 1. In our previous work, the experimental data shows that the Gd2Zr2O7 sample is pyrochlore structure and the lattice parameter is 10.51 Å[34]. The density of Gd2Zr2O7 pyrochlore 6.80 g/cm3 is obtained in our previous experiment[35]. The lattice parameter and density with GGA+U method are consistent with our experimental data[34,35], which deviate no more than 3%. Furthermore, the calculated lattice parameter and internal free coordinate agree well with the experimental results of Mandal et al.[36]. Our calculated results are in accord with the experimental and theoretical data[22,34-36], which indicate the accuracy of our calculation method.

Fig. 1 Gd2Zr2O7 pyrochlore crystal structure. Different colours represent corresponding atoms, such as the red is O, green is Zr and purple is Gd atom.

The energy-volume relations are fitted to the Birch-Murnaghan equation of state[37], and then the bulk modulus B and its pressure derivative B' are obtained, as shown in Table 1. The bulk modulus B is 175.87 GPa, which is agreement with the corresponding experimental data 174 GPa[19]. In Fig. 2, it shows the pressure dependences of density ρ of Gd2Zr2O7 pyrochlore at 0 K. The density ρ of Gd2Zr2O7 pyrochlore increases when the pressure increases. As presented in Fig 2, the density ρ increases from 6.629 g/cm3 at 0 GPa to 6.808 g/cm3 at 5 GPa, with an increase of 7

Journal Pre-proof about 2.7%. The density as a function of pressure can be described as a second polynomial:   6.628  0.0375 P  2.8881104 P 2 . Table 1 Calculated lattice constants a (Å) and crystal density ρ (g/cm3), internal free coordinate z, bulk modulus B (GPa) and its pressure derivative B', together with the experiments and theoretical results. a

ρ

z

B

B'

present

10.682

6.629

0.338

175.87

4.25

exp.

10.501 [33]

6.80 [34] 0.344 [35]

174 [19]

10.54 [35] Calc.

10.589 [20]

214.0659 [20]

Fig. 2 The density ρ as a function of pressure for Gd2Zr2O7 pyrochlore at 0K.

3.2 Mechanical properties and Thermal conductivity To knowledge the mechanical stability of Gd2Zr2O7 pyrochlore under high pressure, the pressure dependent of elastic constants are investigated with the above discussed method. As shown in Table 2, the elastic constants, Bulk modulus B, shear modulus G and Young’s modulus E of Gd2Zr2O7 pyrochlore under different pressures are obtained. Based on the elastic constants, it is shown that the mechanical stability of cubic structure under high pressure satisfied the Born criteria[29] C44  P  0, C11  C12  P  P  0, C11  2C12  P  0.

From Table 2, it can be seen that our

calculated elastic constants satisfy the conditions of Born criteria, which implies that 8

Journal Pre-proof Gd2Zr2O7 pyrochlore is mechanically stable as the pressure increases.

Table 2 Calculated elastic constants Cij (GPa), Bulk modulus B (GPa) , Young’s modulus E (GPa), shear modulus G (GPa) and Zener ratio Z under different pressures P (GPa). P

E

C11-|C12+P|-

C11+2C12+

P

P

54.5

93.1

527.5

1.17

59.6

58.9

107.5

590.1

1.19

67.9

64.8

117.3

657.1

1.28

C11

C12

C44

B

G

C44-P

0

237.9

144.8

54.5

175.9

139.9

51.1

5

266.7

159.2

63.9

195.0

162.4

10

293.9

176.6

74.8

215.7

184.3

Z

The pressure dependent of elastic constants of Gd2Zr2O7 pyrochlore are shown in Table 2 and Fig. 3. All elastic constants increase linearly when the pressure increases. For all elastic constants, C11 is most sensitive to the pressure, but C44 is the least sensitive one. Under different pressures, elastic modulus containing the shear modulus G, bulk modulus B and Young’s modulus E can be calculated based on the corresponding elastic constants as shown in Table 2. Shear modulus G and bulk modulus B reflect the resistance of shape deformation and volume change in a material, while the resistance against the uniaxial compressions is represented by Young’s modulus E. With increasing pressure, it is shown that shear modulus G, bulk modulus B and Young’s modulus E increase simultaneously.

Fig 3 Elastic constants Cij as a function of pressure P. 9

Journal Pre-proof The direction dependence Young’s modulus E of Gd2Zr2O7 pyrochlore under different pressures are listed in Fig 4. It can be seen from Fig 4 that 3D figure of Gd2Zr2O7 pyrochlore at 0GPa and 10 GPa are not perfect sphere, indicating weak anisotropy. The Zener ratio[38] was used to quantify the degree of anisotropy in the elastic constants for a cubic crystal, which can be defined as Z  2C44 / (C11  C12 ) . Generally, if Z is equal to unity, the material is isotropic; otherwise, the material is anisotropic. The relation between Zener ratio and pressure are presented in Table 2. The calculated Zener ratios are 1.17 at 0 GPa and 1.28 at 10 GPa, and are little larger than 1, which suggest that Gd2Zr2O7 pyrochlore is weak anisotropic.

Fig 4 Direction dependence Young’s modulus E (GPa) of Gd2Zr2O7 pyrochlore at 0 GPa (a) and 10 GPa, respectively.

Pugh[39] proposed a criterion about the relation between brittle or ductile manner of material and the ratio of B/G. If B/G > 1.75, a material manifests a ductile manner; On the contrary, it displays a brittle manner. The ratios B/G of Gd2Zr2O7 pyrochlore under high pressures are shown in Table 3. Gd2Zr2O7 pyrochlore is a ductile material at 0 GPa as the ratio of B/G is 3.44. As shown in Table 3, it found that the values of B/G decrease with increasing pressure. In addition, all the values of B/G are higher than 1.75 in the pressure ranges from 0 GPa to 10 GPa, implying that Gd2Zr2O7 pyrochlore is still ductile under high pressure. The average sound wave velocity Vm, transverse sound wave velocity Vt and longitudinal sound wave velocity Vl are also predicted in Table 3. As pressure 10

Journal Pre-proof increase, all sound wave velocity increase monotonously. Additionally, the minimum thermal conductivity kClarke Clarke’s[40] cahill kmin 

and

Cahill’s[41]

minand kCahill min can be estimated by the model,

i.e.,



2

1

1

clark kmin  0.87 M a 3 E 2  6

and

k n 23 ( ) (vl  2vt ) . The minimum thermal conductivity of Gd2Zr2O7 2.48 V

pyrochlore under different pressures are summarized in Table 3. At 0 GPa, the minimum thermal conductivity of Gd2Zr2O7 pyrochlore are calculated to be 0.96 W/(m∙K) and 1.12 W/(m∙K) by Clarke’s and Cahill’s model, which agree well with the experiment range of 1.0-1.6 W/(m∙K)[42-44]. The minimum thermal conductivity of Gd2Zr2O7 pyrochlore increases with increasing pressure. The Gd2Zr2O7 pyrochlore has been proposed as a potential matrix to solidify the nuclear waste owing to their outstanding chemical and physical properties[12,13]. According to the obtained mechanical properties and thermal conductivity, the Gd2Zr2O7 pyrochlore exhibit mechanically stable and low thermal conductivities. It is helpful to provide physical property information when Gd2Zr2O7 pyrochlore has been considered as a potential candidate in immobilizing radionuclides. Table 3 The B/G, average sound wave velocity Vm (km/s), transverse sound wave velocity Vt (km/s), longitudinal sound wave velocity Vl (km/s) and minimum thermal conductivity k (W/(m∙K)) under different pressures P (GPa). P

B/G

Vl

Vt

Vm

kClarke

kCahill

min

min

0

3.44

6.07

2.78

3.78

0.96

1.12

5

3.27

6.35

2.96

4.01

1.03

1.21

10

3.18

6.62

3.12

4.22

1.11

1.28

3.3 Thermodynamic properties The quasi-harmonic Debye model is applied to gain deeper insights into the thermodynamic properties of Gd2Zr2O7 pyrochlore. The temperature and pressure effects of the constant volume heat capacity CV of Gd2Zr2O7 pyrochlore are investigated. As shown in Fig 5, under different pressures, the constant volume heat 11

Journal Pre-proof capacity Cv influenced by the temperature T are probed. At zero pressure and ambient temperature, the calculated constant volume heat capacity of Gd2Zr2O7 pyrochlore is 235.06 J mol-1K-1. At 0 GPa, the relation between CV and T3 at low temperature are presented in the inset of Fig 5. It is shown that the CV is proportional to T3[45]. At a given pressure, the CV increases with increasing temperature and then approaches the Dulong-Petit limit[46] of 274.37 J mol-1K-1 at high temperature region.

Fig. 5. The constant volume heat capacity CV of Gd2Zr2O7 pyrochlore versus temperature under different pressures. The relation between CV and T3 at 0 GPa and low temperature are shown in the inset.

The Debye temperature Θ plays an important role in thermodynamic properties, which is closely associated with the heat capacity and melting temperature and so on. The temperature and pressure dependences of the Debye temperature Θ of Gd2Zr2O7 pyrochlore are illustrated in Fig 6. Along the isobar, it is shown that Θ decreases with temperature increases. At ambient temperature, the value of Θ at 10 GPa decreases to about 10.8% of the value at 0 GPa.

12

Journal Pre-proof

Fig. 6. The Debye temperature Θ of Gd2Zr2O7 pyrochlore versus temperature under different pressures.

Under different pressure regions (from 0 GPa to 10 GPa), the volume thermal expansion coefficient α of Gd2Zr2O7 pyrochlore as a function of temperature, which is shown in Fig 7. It is shown that the volume thermal expansion coefficient of Gd2Zr2O7 pyrochlore increases rapidly when temperature below 400 K. With further increase of temperature, thermal expansion coefficient increases slowly.

Fig. 7. The volume thermal expansion coefficient α of Gd2Zr2O7 pyrochlore versus temperature under different pressures.

The entropy S of Gd2Zr2O7 pyrochlore as a function of temperature up to 1000 K at pressures of 0, 2, 4, 6, 8 and 10 GPa are plotted in Fig 8. It can be seen that the entropy increases from 227.11 J mol-1K-1 to 552.73 J mol-1K-1 at 0 GPa as temperature increases from 298 K to 1000 K. Furthermore, it is found that the entropy increases 13

Journal Pre-proof with increasing temperature at fixed pressure. At a given temperature, the entropy decreases slightly as the pressure increases.

Fig. 8. The entropy S of Gd2Zr2O7 pyrochlore versus temperature under different pressures.

4. Conclusions The mechanical, thermodynamic properties and minimum thermal conductivity of Gd2Zr2O7 pyrochlore have been studied by using density functional theory with GGA+U method. The lattice parameter and density with GGA+U method are agreement with experimental and theoretical data. The pressure effect on the elastic constants, shear modulus, bulk modulus, Young’s modulus, sound wave velocity and minimum thermal conductivity of Gd2Zr2O7 pyrochlore are successfully obtained. The results show that the Gd2Zr2O7 pyrochlore exhibit mechanically stable and ductile properties under applied pressure. The minimum thermal conductivity, shear modulus, bulk modulus, Young’s modulus and sound wave velocity of Gd2Zr2O7 pyrochlore increase with increasing pressure. The results of direction dependence Young’s modulus and Zener ratio show that Gd2Zr2O7 pyrochlore is weak anisotropy at 0 GPa and 10 GPa. Based on the quasi-harmonic Debye model, the thermodynamic properties, such as the constant volume heat capacity, Debye temperature, thermal expansion coefficient and entropy at high temperature and pressure are also investigated. This work provides physical property information when Gd2Zr2O7 pyrochlore has been considered as a potential host material for the immobilization of radionuclides. 14

Journal Pre-proof Acknowledgments The authors acknowledge the financial support of the National Natural Science Foundation of China (No. 21507105, 21471088), Project of State Key Laboratory of Environment-friendly Energy Materials, Southwest University of Science and Technology（No. 17FKSY0118）and the Doctor Research Foundation of Southwest University of Science and Technology (No. 18zx7141). References [1] R.C. Ewing, W.J. Weber, J. Lian, J. Appl. Phys. 95 (2004) 5949. [2] A.R. Boccaccini, T. Berthier, S. Seglem, Ceram. Int. 33 (2007) 1231. [3] A. Salama, M.F. El Amin, S.Y. Sun, Prog. Nucl. Energ. 85 (2015) 747. [4] R.C. Ewing, W. Lutze, Ceram. Int. 17 (1991) 287. [5] S.J. Patwe, A.K. Tyagi, Ceram. Int. 32 (2006) 545. [6] B.P. Mandal, M. Pandey, A.K. Tyagi, J. Nucl. Mater. 406 (2010) 238. [7] M. Lang, J. Lian, J.M. Zhang, F.X. Zhang, W.J. Weber, C. Trautmann, R.C. Ewing, Phys. Rev. B 79 (2009) 224105. [8] J. Lian, S.V. Yudintsev, S.V. Stefanovsky, L.M. Wang, R.C. Ewing, J. Alloy. Compd. 444 (2007) 429. [9] A.N. Radhakrishnan, P.P. Rao, K.S. Sibi, M. Deepa, P. Koshy, J. Solid State Chem. 182 (2009) 2312. [10] L. Minervini, R.W. Grimes, K.E. Sickafus, J. Am. Ceram. Soc. 83 (2000) 1873. [11] B.C. Chakoumakos, J. Solid State Chem. 53 (1984) 120. [12] X.R. Lu, Y. Ding, H. Dan, M.F. Wen, X.L. Mao, Y.L. Wu, X.L. Wang, Mater. Lett. 136 (2014) 1. [13] X.Y. Shu, L. Fan, X.R. Lu, Y. Xie, Y. Ding, J. Eur. Ceram. Soc. 35 (2015) 3095. [14] S.X. Wang, B.D. Begg, L.M. Wang, R.C. Ewing, W.J. Weber, K.V.G. Kutty, J. Mater. Res. 14 (1999) 4470. [15] W.J. Weber, R.C. Ewing, Science 289 (2000) 2051. [16] L. Wang, X.Y. Shu, X.R. Lu, Y.L. Wu, Y. Ding, S. Zhang, Mater. Lett. 196 (2017) 403. [17] Z.S. He, K.B. Zhang, J.L. Xue, W.W. Zhao, H.B. Zhang, J. Nucl. Mater. 512 (2018) 385. [18] K. Shimamura, T. Arima, K. Idemitsu, Y. Inagaki, Int. J. Thermophys. 28 (2007) 1074. [19] F.X. Zhang, J. Lian, U. Becker, R.C. Ewing, J.Z. Hu, S.K. Saxena, Phys. Rev. B 76 (2007) 214104. [20] F.X. Zhang, J.W. Wang, J. Lian, M.K. Lang, U. Becker, R.C. Ewing, Phys. Rev. Lett. 100 (2008). [21] H.Y. Xiao, W.J. Weber, J. Phys. Condens. Matter 23 (2011) 035501. [22] L.Y. Dong, Y.H. Li, R. Devanathan, F. Gao, RSC Adv. 6 (2016) 41410. [23] M.A. Blanco, E. Francisco, V. Luaña, Comput. Phys. Commun. 158 (2004) 57. [24] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [25] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [26] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953. [27] S.L. Dudarev, G.A. Botton, S.Y. Savrasov, C.J. Humphreys, A.P. Sutton, Phys. Rev. B 57 (1998) 1505. [28] Y.B. Losovyj, D. Wooten, J.C. Santana, J.M. An, K.D. Belashchenko, N. Lozova, J. Petrosky, A. 15

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Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Journal Pre-proof 1. Gd2Zr2O7 pyrochlore is mechanically stable and ductile under high pressures. 2. Gd2Zr2O7 pyrochlore is weak anisotropy at 0 GPa and 10 GPa. 3. The thermodynamic properties of Gd2Zr2O7 pyrochlore have been investigated.