- Email: [email protected]
First-principles investigation on thermodynamic phase stability of jadeite under high temperature and high pressure
Physica B: Condensed Matter 567 (2019) 55–60
Contents lists available at ScienceDirect
Physica B: Condensed Matter journal homepage: www.elsevier.com/locate/physb
First-principles investigation on thermodynamic phase stability of jadeite under high temperature and high pressure
T
Taiqiao Liua,1, Mingyu Hua,b,1, Wenting Luc, Jianxiang Zhana, Xiaoying Cuid, Xianghao Zhana, Jie Yua,∗ a
Faculty of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, China School of Materials Engineering, Brown University, 184 Hope Street, Barus & Holley Providence, RI 02912, USA c National Gemstone Testing Center, Yunnan Lab., Kunming 650000, China d Research Center for Analysis and Measurement, Kunming University of Science and Technology, Kunming 650106, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Jadeite First-principles calculation Thermodynamics Gibbs free energy Phase transition HTHP
In this paper, the functions of enthalpy, entropy, free energy and heat capacity with temperature from 0 to 1800K and pressure from normal (101.325 KPa) to 80Gpa are obtained by the calculation of CASTEP module based on density functional theory (DFT) and compared with the corresponding values from manual thermodynamics data. Besides, the thermodynamic parameters such as enthalpy changes, entropy of various phases at different pressures and temperatures for the reaction of 2NaAlSi2O6 → NaA1Si3O8 + NaAlSiO4 are calculated and the Gibbs free energy of the reaction is gotten. Furthermore, the Gibbs free energy as a function of both temperature and pressure is presented with the three-dimensional graph by surface fitting. The calculation results show that the calculated values of the thermodynamic parameters are consistent with the data in the manual and the error values of that are less than or equal to 1%. In addition, there is a transition between endothermic and exothermic at 450 K under normal pressure. Compared with high temperature and low pressure or high temperature and high pressure, ΔrG is closer to zero at low temperature and high pressure (60 Gpa, near 400 k), at the same time, the phase stability is better.
1. Introduction One of an important form of Na element accumulation in the mantle is Jadeite (NaAlSi2O6, monoclinic pyroxene). The researches about thermodynamic phase stability of the compounds in high temperature and high pressure (HTHP) can be a significant meaning of understanding the fate of subducted crusts and the material formation in deep mantle [1]. Jadeite is formed by the metamorphism of albite (NaA1Si3O8) and nepheline (NaAlSiO4) in high-pressure solid-phase reaction, which means the reaction of NaA1Si3O8+NaAlSiO4→ 2NaAlSi2O6 occurs [2]. So, it is also used as a pressure gauge to indicate the pressure in the location of the mineral as well as the geological environment of the mineral formation process. However, the thermodynamic parameters of it, especially under various temperatures and pressures, are unsure yet. The thermodynamics works of jadeite, such as heat capacity, enthalpy, entropy, molar volume, thermal expansion at low temperature and high pressure were developed by Yoder et al. [3]. The phase
∗
Corresponding author. E-mail address: [email protected] (J. Yu). 1 Both authors contributed equally to this paper. https://doi.org/10.1016/j.physb.2019.04.032 Received 20 March 2019; Accepted 28 April 2019 Available online 12 May 2019 0921-4526/ © 2019 Elsevier B.V. All rights reserved.
diagram of the pressure-temperature stable region of the jadeite was determined by Adams et al. [4] with computational and experimental methods. They all provided vital theoretical support for jadeite thermodynamic parameters. Therefore, jadeite is the intermediate phase of albite and nepheline in composition [5]. The increasing volume heatcaused is about 21%, thus jadeite is a metastable substance at normal pressure [2]. Phase transition of jadeite, NaAlSi2O6→NaAlSiO4(CFtype)+SiO2(St,Stishovite), was assured at pressure larger than 23.4 GPa and temperature larger than 1800 K by Kenji Kawai and Taku Tsuchiya [6] with first-principles calculations. Crystal structure of jadeite at different pressures was researched by Jin Yang et al. [7] and its electronic structure, optical properties, mechanical properties and thermodynamic properties were predicted. It is found that jadeite transforms into garnet and ilmenite type structures at pressure over 60Gpa through shock wave experiment by E.Takazaw et al. [8]. The crystal structures, electronic, elastic properties, hardness and phase transition of jadeite under various pressures from 0 to 70 GPa were investigated with the first-principles calculations by Jin Yang et al. [1]
Physica B: Condensed Matter 567 (2019) 55–60
T. Liu, et al.
Fig. 1. The crystal structures of jadeite (a), low albite (b) and nepheline (c).
Fig. 2. Comparison of cell parameters between experiment and simulation of different pseudo potentials: (a) V, (b) a-axis, (c) b-axis, (d) c-axis.
compensate for the lacking of thermodynamic data in handbook.
whose results presented phase transition of jadeite occurs above 60 GPa. These studies offered phase transition data for jadeite at certain temperature and pressure. In this article, the related thermodynamic parameters of the jadeite phase were calculated by the first-principles phonon spectrum calculation [9,10]. A method that compared the thermodynamic calculation data of first-principles with the data of thermodynamic handbook was adopted to verify the calculation errors and feasibility in order to provide new research methods and means for the stability of materials at high temperature and high pressure. Meanwhile, both temperature and pressure were taken as a function of Gibbs free energy and rendered in three dimensions in order to
2. Calculation methods The first-principles calculations are finished with the Materials Studio 8.0 software CASTEP package. All models are subjected to Geometry Optimization via pressure setting, and the thermodynamic properties are calculated on the structure of the successfully optimized unit cell model. The calculation accuracy is set to Ultra-fine. The geometric optimization algorithm adopts BFGS algorithm, and the convergence error precision is as follows: energy within 5.0*10−6, and the 56
Physica B: Condensed Matter 567 (2019) 55–60
T. Liu, et al.
maximum force, maximum stress, maximum atomic displacement distance, maximum number of iteration calculations are 0.01 V/Å, 0.02 GPa, 5.0*10−4, 500 times, respectively. The Perdew–Burke–Ernzerh of functionals (PBE) of generalized gradient approximation (GGA) is utilized by electron exchange correlation function [11]. The norm conserving pseudo potentials representing as reciprocal space are adopted. Besides, the k-points precision is set to fine. The SCF self-consistent loops convergence precision is 5.0 × 10−7 eV/atom, and the number of self-consistent calculation iterations is 500. The calculated crystal structure models of different phases in this paper are presented in Fig. 1. 3. Results and discussions 3.1. Reliability verification of calculation X-ray diffraction experimental data of jadeite come from McCarthy et al. [12]. The cell parameters of jadeite at different pressures are given in Table 1. The simulation of this study is carried out under the CASTEP module of the MS software after comparing PDF card thus confirming the correctness of the model. Geometric optimizations of crystals at different pressures are completed under ultra-soft and norm conserving pseudo potentials, respectively. As illustrated in Tables 2 and 3 (Table 1, 2 and 3 are shown in the file of support information), the errors of the cell parameters of the crystal model obtained by the ultra-soft pseudo potentials are 1.12%–1.54% for the a-axis, 1.05%–1.11% for the b-axis, 1.13%–1.19% for the c-axis and 3.15%–3.73% for the unit cell volume V. While the errors of the cell parameters of the model acquired by the norm conserving pseudo potentials are as follows: 0.03%–0.54% for the a-axis, 0.18%–0.33% for the b-axis, 0.17%–0.40% for the c-axis and 0.04–0.44% for the unit cell volume V, which demonstrates the simulation of the jadeite cell is in accordance with the actual crystal condition. Moreover, the comparisons of cell parameters and cell volume between experiment and simulation of ultra-soft pseudo potentials and norm conserving pseudo potentials respectively are shown in Fig. 2. It illustrates that simulating the unit cell with norm conserving pseudo potentials has the advantage of slight errors. Under the normal pressure, the phonon spectra of jadeite and low albite are calculated by first-principles. The functions of enthalpy, entropy, free energy and heat capacity within temperature are shown in Figs. 3–6. The calculation results of the CASTEP phonon spectrum calculation are in good agreement with the data of the Manual of Practical Inorganic Thermodynamics [13], however, the heat capacity has relatively large errors when the temperature is larger than 800 K, and the maximum errors are 5.88% and 6.21% (errors are shown in Table 4). The vibration free energy in CASTEP calculation is gotten by the quasi-harmonic approximation (QHA), so the approximation method has higher accuracy only below the melting point of the crystal. Hence, the higher the temperature is, the larger errors of the heat capacity are [14]. This is also the reason why the errors of entropy, enthalpy and free energy are bigger and bigger with the increase of temperature.
Fig. 3. Comparison of jadeite thermodynamic data between manual value and computer simulation: ΔU(or H)-Hf,298, T·S, ΔG(or A)-Hf,298.
Fig. 4. Comparison of jadeite thermodynamic data between manual value and computer simulation: CV(or p).
3.2. Calculation of thermodynamic parameters of various phases in jadeite The T*S-temperature functions of jadeite, nepheline and albite under pressures of normal pressure, 3.00, 4.50 and 5.00Gpa are presented in Fig. 7. The graphics are almost the same under the four pressures. For the three involved substances in phase transition reaction of jadeite, the values of T*S are always albite > jadeite > nepheline. Consequently, at normal pressure to 5.00 GPa, the stability is low albite > jadeite > nepheline. Further more, the stability was tested by Kracek and Kelley et al. [15] through the calculation of the reaction heat and entropy respectively. It also proved that at normal
Fig. 5. Comparison of low albite thermodynamic data between manual value and computer simulation: ΔU(or H)-Hf,298, T∙S, ΔG(or A)-Hf,298.
57
Physica B: Condensed Matter 567 (2019) 55–60
T. Liu, et al.
2NaAlSi2O6 (jadeite)→NaA1Si3O8 (albite) + NaAlSiO4 (nepheline). (1) The values of enthalpy changes of the reaction at different temperatures can be calculated by the following formula: Δr H(T) = H298(T)(low-albite) deite).
+
H298(T)(nepheline)-2H298(T)(ja(2)
The calculation result is shown in Fig. 8. In Fig. 8, the values of enthalpy changes calculated by CASTEP decline gradually with the increase of temperature. For the isobaric process, the thermal effect Qp of the reaction is numerically equal to ΔH. Therefore, at normal pressure, it is an endothermic reaction at 450 K but an exothermic reaction above 450 K. 3.3. The thermodynamic calculation of reaction Due to the Gibbs free energy is equivalent to the solid Helmholtz free energy, the Gibbs free energy difference can be known by the measurement sum of the calculated Helmholtz free energy of the products (i.e., albite and nepheline) that subtracts the Helmholtz free energy of the reactant(jadeite), which can be expressed as:
Fig. 6. Comparison of low albite thermodynamic data between manual value and computer simulation: CV(or p).
temperature and normal pressure, jadeite is more stable than albite and nepheline. According to the study of Tinghe Zhao et al. [16], there is a reaction in jadeite under normal pressure which is as follows:
ΔrG(T) = G298(T)(low albite) + G298(T)(nepheline)-2G298(T)(jadeite). (3) It can be drawn a conclusion that, at normal pressure, the free
Fig. 7. T*S of jadeite, nepheline and albite on different pressure: (a) normal pressure, (b) 3.00 GPa, (c) 4.50 GPa, (d) 5.00 GPa. 58
Physica B: Condensed Matter 567 (2019) 55–60
T. Liu, et al.
energy difference in the phase transition reaction (as shown in Eq. (1)) is always less than zero. The above phase transition tendency will always occur when the temperature is larger than or equal to 298 K. Moreover, the higher the temperature is, the more likely the phase transition reaction occurs. In other words, the jadeite phase is always in a thermodynamically unstable state. As is exhibited in Fig. 9, the free energy of the reaction is always negative at normal pressure to 5Gpaand 298 K–1800K, namely, the reaction always tends to occur. This result proves the previous conclusion [2] that jadeite is a semi-stable substance at normal temperature and pressure. The pressure-temperature stability curve of jadeite at normal pressure to 5.0Gpa were given by Tinghe Zhao et al. [16]. It can be learned that the stability of jadeite increases with pressure in the range of pressure. From Fig. 9, the free energy difference gradually decreases as the pressure increases, which is in agreement with the experimental results. Through the surface fitting for all the free energy of reaction at pressure from normal to 80 GPa and temperature from 0 to 1800K, the binary function of the Gibbs free energy with the temperature and pressure ΔG(P,T) is gotten. The function data is fitted by the original 8.6 data processing software. In the three-dimensional images, the changes of ΔG at a certain temperature and pressure can be intuitively seen, as shown in Figs. 10–12. For the jadeite phase transition reaction in the temperature range from 298 K to 1800K and the pressure range from the normal pressure to 80 GPa, the surface presented in figures are all below the ΔG = 0 plane, that is, the free energy is less than zero, which means there is always a tendency of the phase transition reaction. As is presented in Fig. 11, for any pressures given in the scope, the whole Gibbs free energy change has a tendency to drop with the increase of temperature (i.e., the absolute values increase). That indicates a single increase in temperature is always beneficial to the decomposition reaction of jadeite and it may be formed at a relative low temperature. When the temperature is constant in Fig. 12, the free energy decreases with the increase of pressure at the normal pressure to 7 GPa, increases with the increase of pressure within the range of 7Gpa–60 GPa, but decreases again at 60Gpa–80 GPa. It can be seen that, in thermodynamics, increasing pressure blindly at least within7 GPa is not conducive to suppressing the tendency of the reaction. In fact, in the range from 7 Gpa to 80 GPa, it is apparent that the absolute values of the free energy difference are smaller than the values of other pressures at 60 GPa. Relatively speaking, the reaction is difficult to occur. As a result, compared with high temperature and low pressure or high temperature and high pressure, ΔrG is closer to zero and the thermodynamic stability of jadeite is better at low temperature and high pressure. It also verifies that jadeite has high thermodynamic stability at low temperature and high pressure. The result is similar to the first-principles investigation of Jin Yang et al. [1] and the Hugoniot equation of state of jadeite by E. Takzawa et al. [7] showing that the jadeite has a phase transition reaction above 60 Gpa. It's hard to synthesize jadeite because of its low pressure instability and special fiber interweaving structure. Although it has been able to synthesize gem-quality jadeite with high temperature and high pressure (HTHP), the cost is too high. Based on previous studies, the first principle is used to simulate the phase stability region of jadeite, which provides a theoretical basis for synthetic jadeite of ultrahigh pressure in the future.
Fig. 8. ΔHr of decomposition reaction about jadeite on different temperature
Fig. 9. ΔG(T) of the reaction on different pressure.
4. Conclusions The reliability of the jadeite thermodynamic properties based on density functional theory (DFT) was verified by comparing thermodynamic calculation data of the first-principles with the data of thermodynamics manual. The stability of the three kind of phases in the jadeite decomposition reaction is low albite > jadeite > nepheline. The jadeite is a semi-stable state substance at normal pressure. The calculation results reveal that the Gibbs free energy of jadeite is lower
Fig. 10. ΔG(P,T) of the phase transition reaction for jadeite on different pressures and temperatures.
59
Physica B: Condensed Matter 567 (2019) 55–60
T. Liu, et al.
than zero at normal pressure to 5Gpa. And at 0–1800K, normal pressure to 80Gpa, the decomposition reaction has a tendency to occur in thermodynamics. Actually, the thermodynamic stability is better at low temperature and high pressure(near 60Gpa and400 K), which is in accordance with the theory that jadeite is formed in the geological environment with high temperature and low pressure. Acknowledgement The authors would like to acknowledge the project supported by the fund of the Analysis and Detection of KMUST (2018T20040070) and the Introduced Talents Project Funded by the Start-up Research of KunMing University of Science and Technology (KKZ3201751043). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.physb.2019.04.032. References [1] Yang Jin, Yueting Song, Shu Zhou, Boqing Wu, Guanli Xu, Mingshun Xiang, Firstprinciples investigations of crystal structures and physical properties of jadeite under various pressures, Physic B 543 (2018) 32–37. [2] M. Akaogi, A. Tanaka, M. Kobayashi, et al., High-pressure transformations in NaAlSiO4 and thermodynamic properties of jadeite, nepheline, and calcium ferritetype phase, Phys. Earth Planet. In. 130 (1–2) (2002) 49–58. [3] H.S. Yoder, The jadeite problem, part I, Am. J. Sci. 248 (5) (1950) 312–334. [4] L.H. Adams, A note on the stability of jadeite, Am. J. Sci. 251 (1953). [5] Ying Guo, Gongbao Song, Study on the genesis and artificial synthesis of jade, J. SW. Univ. Technol. (2) (2000) 46–49. [6] K. Kawai, T. Tsuchiya, High-P , T phase relations in the NaAlSi2O6 system from first principles computation, Phys. Chem. Miner. 39 (4) (2012) 305–310. [7] J. Yang, L. Yang, J. Long, Theoretical investigation of the electronic structure, optical, elastic, hardness and thermodynamics properties of jadeite, Mater. Sci. Semicond. Process. 31 (6) (2015) 509–516. [8] E. Takazawa, T. Sekine, et al., Hugoniot equation of state and high-pressure transformation of jadeite, J. Geophys. Res. 261–12 (1998) 268. [9] Y. Pan, M. Wen, The influence of vacancy on the mechanical properties of IrAl coating: first-principles calculations, Thin Solid Films 664 (2018) 46–51. [10] Y. Pan, First-principles investigation of the new phases and electrochemical properties of MoSi2 as the electrode materials of lithium ion battery, J. Alloy. Comp. 779 (2019) 813–820. [11] B. Hammer, Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerh of functionals, Phys. Rev. B 59 (11) (1999) 7413–7421. [12] A.C. Mccarthy, R.T. Downs, R.M. Thompson, Compressibility trends of the clinopyroxenes, and in-situ high-pressure single-crystal X-ray diffraction study of jadeite, Am. Mineral. 93 (1) (2008) 198–209. [13] Yingjiao Liang, The Manual of Practical Inorganic Thermodynamics, Univ. Press, Shenyang: NE, 1993, p. 564. [14] S. Baroni, S. De Gironcoli, A. Dal Corso, et al., Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73 (2) (2008) 515–562. [15] A.M. Afifi, W.C. Kelly, E.J. Essene, Phase relations among tellurides, sulfides, and oxides; I, Thermochemical data and calculated equilibria, Econ. Geol. 83 (2) (1988) 377–394. [16] Tinghe Zhao, Xuewei Yan, Study on the synthesis, thermal behavior and thermal stability of gemstone jade, Chin. J. High Press. Phys. 6 (4) (1992) 291–296.
Fig. 11. ΔG(P,T) of the phase transition reaction for jadeite on different pressures and temperatures (from temperature).
Fig. 12. ΔG(P,T) of the phase transition reaction for jadeite on different pressures and temperatures (from pressure).
60
Contents lists available at ScienceDirect
Physica B: Condensed Matter journal homepage: www.elsevier.com/locate/physb
First-principles investigation on thermodynamic phase stability of jadeite under high temperature and high pressure
T
Taiqiao Liua,1, Mingyu Hua,b,1, Wenting Luc, Jianxiang Zhana, Xiaoying Cuid, Xianghao Zhana, Jie Yua,∗ a
Faculty of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, China School of Materials Engineering, Brown University, 184 Hope Street, Barus & Holley Providence, RI 02912, USA c National Gemstone Testing Center, Yunnan Lab., Kunming 650000, China d Research Center for Analysis and Measurement, Kunming University of Science and Technology, Kunming 650106, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Jadeite First-principles calculation Thermodynamics Gibbs free energy Phase transition HTHP
In this paper, the functions of enthalpy, entropy, free energy and heat capacity with temperature from 0 to 1800K and pressure from normal (101.325 KPa) to 80Gpa are obtained by the calculation of CASTEP module based on density functional theory (DFT) and compared with the corresponding values from manual thermodynamics data. Besides, the thermodynamic parameters such as enthalpy changes, entropy of various phases at different pressures and temperatures for the reaction of 2NaAlSi2O6 → NaA1Si3O8 + NaAlSiO4 are calculated and the Gibbs free energy of the reaction is gotten. Furthermore, the Gibbs free energy as a function of both temperature and pressure is presented with the three-dimensional graph by surface fitting. The calculation results show that the calculated values of the thermodynamic parameters are consistent with the data in the manual and the error values of that are less than or equal to 1%. In addition, there is a transition between endothermic and exothermic at 450 K under normal pressure. Compared with high temperature and low pressure or high temperature and high pressure, ΔrG is closer to zero at low temperature and high pressure (60 Gpa, near 400 k), at the same time, the phase stability is better.
1. Introduction One of an important form of Na element accumulation in the mantle is Jadeite (NaAlSi2O6, monoclinic pyroxene). The researches about thermodynamic phase stability of the compounds in high temperature and high pressure (HTHP) can be a significant meaning of understanding the fate of subducted crusts and the material formation in deep mantle [1]. Jadeite is formed by the metamorphism of albite (NaA1Si3O8) and nepheline (NaAlSiO4) in high-pressure solid-phase reaction, which means the reaction of NaA1Si3O8+NaAlSiO4→ 2NaAlSi2O6 occurs [2]. So, it is also used as a pressure gauge to indicate the pressure in the location of the mineral as well as the geological environment of the mineral formation process. However, the thermodynamic parameters of it, especially under various temperatures and pressures, are unsure yet. The thermodynamics works of jadeite, such as heat capacity, enthalpy, entropy, molar volume, thermal expansion at low temperature and high pressure were developed by Yoder et al. [3]. The phase
∗
Corresponding author. E-mail address: [email protected] (J. Yu). 1 Both authors contributed equally to this paper. https://doi.org/10.1016/j.physb.2019.04.032 Received 20 March 2019; Accepted 28 April 2019 Available online 12 May 2019 0921-4526/ © 2019 Elsevier B.V. All rights reserved.
diagram of the pressure-temperature stable region of the jadeite was determined by Adams et al. [4] with computational and experimental methods. They all provided vital theoretical support for jadeite thermodynamic parameters. Therefore, jadeite is the intermediate phase of albite and nepheline in composition [5]. The increasing volume heatcaused is about 21%, thus jadeite is a metastable substance at normal pressure [2]. Phase transition of jadeite, NaAlSi2O6→NaAlSiO4(CFtype)+SiO2(St,Stishovite), was assured at pressure larger than 23.4 GPa and temperature larger than 1800 K by Kenji Kawai and Taku Tsuchiya [6] with first-principles calculations. Crystal structure of jadeite at different pressures was researched by Jin Yang et al. [7] and its electronic structure, optical properties, mechanical properties and thermodynamic properties were predicted. It is found that jadeite transforms into garnet and ilmenite type structures at pressure over 60Gpa through shock wave experiment by E.Takazaw et al. [8]. The crystal structures, electronic, elastic properties, hardness and phase transition of jadeite under various pressures from 0 to 70 GPa were investigated with the first-principles calculations by Jin Yang et al. [1]
Physica B: Condensed Matter 567 (2019) 55–60
T. Liu, et al.
Fig. 1. The crystal structures of jadeite (a), low albite (b) and nepheline (c).
Fig. 2. Comparison of cell parameters between experiment and simulation of different pseudo potentials: (a) V, (b) a-axis, (c) b-axis, (d) c-axis.
compensate for the lacking of thermodynamic data in handbook.
whose results presented phase transition of jadeite occurs above 60 GPa. These studies offered phase transition data for jadeite at certain temperature and pressure. In this article, the related thermodynamic parameters of the jadeite phase were calculated by the first-principles phonon spectrum calculation [9,10]. A method that compared the thermodynamic calculation data of first-principles with the data of thermodynamic handbook was adopted to verify the calculation errors and feasibility in order to provide new research methods and means for the stability of materials at high temperature and high pressure. Meanwhile, both temperature and pressure were taken as a function of Gibbs free energy and rendered in three dimensions in order to
2. Calculation methods The first-principles calculations are finished with the Materials Studio 8.0 software CASTEP package. All models are subjected to Geometry Optimization via pressure setting, and the thermodynamic properties are calculated on the structure of the successfully optimized unit cell model. The calculation accuracy is set to Ultra-fine. The geometric optimization algorithm adopts BFGS algorithm, and the convergence error precision is as follows: energy within 5.0*10−6, and the 56
Physica B: Condensed Matter 567 (2019) 55–60
T. Liu, et al.
maximum force, maximum stress, maximum atomic displacement distance, maximum number of iteration calculations are 0.01 V/Å, 0.02 GPa, 5.0*10−4, 500 times, respectively. The Perdew–Burke–Ernzerh of functionals (PBE) of generalized gradient approximation (GGA) is utilized by electron exchange correlation function [11]. The norm conserving pseudo potentials representing as reciprocal space are adopted. Besides, the k-points precision is set to fine. The SCF self-consistent loops convergence precision is 5.0 × 10−7 eV/atom, and the number of self-consistent calculation iterations is 500. The calculated crystal structure models of different phases in this paper are presented in Fig. 1. 3. Results and discussions 3.1. Reliability verification of calculation X-ray diffraction experimental data of jadeite come from McCarthy et al. [12]. The cell parameters of jadeite at different pressures are given in Table 1. The simulation of this study is carried out under the CASTEP module of the MS software after comparing PDF card thus confirming the correctness of the model. Geometric optimizations of crystals at different pressures are completed under ultra-soft and norm conserving pseudo potentials, respectively. As illustrated in Tables 2 and 3 (Table 1, 2 and 3 are shown in the file of support information), the errors of the cell parameters of the crystal model obtained by the ultra-soft pseudo potentials are 1.12%–1.54% for the a-axis, 1.05%–1.11% for the b-axis, 1.13%–1.19% for the c-axis and 3.15%–3.73% for the unit cell volume V. While the errors of the cell parameters of the model acquired by the norm conserving pseudo potentials are as follows: 0.03%–0.54% for the a-axis, 0.18%–0.33% for the b-axis, 0.17%–0.40% for the c-axis and 0.04–0.44% for the unit cell volume V, which demonstrates the simulation of the jadeite cell is in accordance with the actual crystal condition. Moreover, the comparisons of cell parameters and cell volume between experiment and simulation of ultra-soft pseudo potentials and norm conserving pseudo potentials respectively are shown in Fig. 2. It illustrates that simulating the unit cell with norm conserving pseudo potentials has the advantage of slight errors. Under the normal pressure, the phonon spectra of jadeite and low albite are calculated by first-principles. The functions of enthalpy, entropy, free energy and heat capacity within temperature are shown in Figs. 3–6. The calculation results of the CASTEP phonon spectrum calculation are in good agreement with the data of the Manual of Practical Inorganic Thermodynamics [13], however, the heat capacity has relatively large errors when the temperature is larger than 800 K, and the maximum errors are 5.88% and 6.21% (errors are shown in Table 4). The vibration free energy in CASTEP calculation is gotten by the quasi-harmonic approximation (QHA), so the approximation method has higher accuracy only below the melting point of the crystal. Hence, the higher the temperature is, the larger errors of the heat capacity are [14]. This is also the reason why the errors of entropy, enthalpy and free energy are bigger and bigger with the increase of temperature.
Fig. 3. Comparison of jadeite thermodynamic data between manual value and computer simulation: ΔU(or H)-Hf,298, T·S, ΔG(or A)-Hf,298.
Fig. 4. Comparison of jadeite thermodynamic data between manual value and computer simulation: CV(or p).
3.2. Calculation of thermodynamic parameters of various phases in jadeite The T*S-temperature functions of jadeite, nepheline and albite under pressures of normal pressure, 3.00, 4.50 and 5.00Gpa are presented in Fig. 7. The graphics are almost the same under the four pressures. For the three involved substances in phase transition reaction of jadeite, the values of T*S are always albite > jadeite > nepheline. Consequently, at normal pressure to 5.00 GPa, the stability is low albite > jadeite > nepheline. Further more, the stability was tested by Kracek and Kelley et al. [15] through the calculation of the reaction heat and entropy respectively. It also proved that at normal
Fig. 5. Comparison of low albite thermodynamic data between manual value and computer simulation: ΔU(or H)-Hf,298, T∙S, ΔG(or A)-Hf,298.
57
Physica B: Condensed Matter 567 (2019) 55–60
T. Liu, et al.
2NaAlSi2O6 (jadeite)→NaA1Si3O8 (albite) + NaAlSiO4 (nepheline). (1) The values of enthalpy changes of the reaction at different temperatures can be calculated by the following formula: Δr H(T) = H298(T)(low-albite) deite).
+
H298(T)(nepheline)-2H298(T)(ja(2)
The calculation result is shown in Fig. 8. In Fig. 8, the values of enthalpy changes calculated by CASTEP decline gradually with the increase of temperature. For the isobaric process, the thermal effect Qp of the reaction is numerically equal to ΔH. Therefore, at normal pressure, it is an endothermic reaction at 450 K but an exothermic reaction above 450 K. 3.3. The thermodynamic calculation of reaction Due to the Gibbs free energy is equivalent to the solid Helmholtz free energy, the Gibbs free energy difference can be known by the measurement sum of the calculated Helmholtz free energy of the products (i.e., albite and nepheline) that subtracts the Helmholtz free energy of the reactant(jadeite), which can be expressed as:
Fig. 6. Comparison of low albite thermodynamic data between manual value and computer simulation: CV(or p).
temperature and normal pressure, jadeite is more stable than albite and nepheline. According to the study of Tinghe Zhao et al. [16], there is a reaction in jadeite under normal pressure which is as follows:
ΔrG(T) = G298(T)(low albite) + G298(T)(nepheline)-2G298(T)(jadeite). (3) It can be drawn a conclusion that, at normal pressure, the free
Fig. 7. T*S of jadeite, nepheline and albite on different pressure: (a) normal pressure, (b) 3.00 GPa, (c) 4.50 GPa, (d) 5.00 GPa. 58
Physica B: Condensed Matter 567 (2019) 55–60
T. Liu, et al.
energy difference in the phase transition reaction (as shown in Eq. (1)) is always less than zero. The above phase transition tendency will always occur when the temperature is larger than or equal to 298 K. Moreover, the higher the temperature is, the more likely the phase transition reaction occurs. In other words, the jadeite phase is always in a thermodynamically unstable state. As is exhibited in Fig. 9, the free energy of the reaction is always negative at normal pressure to 5Gpaand 298 K–1800K, namely, the reaction always tends to occur. This result proves the previous conclusion [2] that jadeite is a semi-stable substance at normal temperature and pressure. The pressure-temperature stability curve of jadeite at normal pressure to 5.0Gpa were given by Tinghe Zhao et al. [16]. It can be learned that the stability of jadeite increases with pressure in the range of pressure. From Fig. 9, the free energy difference gradually decreases as the pressure increases, which is in agreement with the experimental results. Through the surface fitting for all the free energy of reaction at pressure from normal to 80 GPa and temperature from 0 to 1800K, the binary function of the Gibbs free energy with the temperature and pressure ΔG(P,T) is gotten. The function data is fitted by the original 8.6 data processing software. In the three-dimensional images, the changes of ΔG at a certain temperature and pressure can be intuitively seen, as shown in Figs. 10–12. For the jadeite phase transition reaction in the temperature range from 298 K to 1800K and the pressure range from the normal pressure to 80 GPa, the surface presented in figures are all below the ΔG = 0 plane, that is, the free energy is less than zero, which means there is always a tendency of the phase transition reaction. As is presented in Fig. 11, for any pressures given in the scope, the whole Gibbs free energy change has a tendency to drop with the increase of temperature (i.e., the absolute values increase). That indicates a single increase in temperature is always beneficial to the decomposition reaction of jadeite and it may be formed at a relative low temperature. When the temperature is constant in Fig. 12, the free energy decreases with the increase of pressure at the normal pressure to 7 GPa, increases with the increase of pressure within the range of 7Gpa–60 GPa, but decreases again at 60Gpa–80 GPa. It can be seen that, in thermodynamics, increasing pressure blindly at least within7 GPa is not conducive to suppressing the tendency of the reaction. In fact, in the range from 7 Gpa to 80 GPa, it is apparent that the absolute values of the free energy difference are smaller than the values of other pressures at 60 GPa. Relatively speaking, the reaction is difficult to occur. As a result, compared with high temperature and low pressure or high temperature and high pressure, ΔrG is closer to zero and the thermodynamic stability of jadeite is better at low temperature and high pressure. It also verifies that jadeite has high thermodynamic stability at low temperature and high pressure. The result is similar to the first-principles investigation of Jin Yang et al. [1] and the Hugoniot equation of state of jadeite by E. Takzawa et al. [7] showing that the jadeite has a phase transition reaction above 60 Gpa. It's hard to synthesize jadeite because of its low pressure instability and special fiber interweaving structure. Although it has been able to synthesize gem-quality jadeite with high temperature and high pressure (HTHP), the cost is too high. Based on previous studies, the first principle is used to simulate the phase stability region of jadeite, which provides a theoretical basis for synthetic jadeite of ultrahigh pressure in the future.
Fig. 8. ΔHr of decomposition reaction about jadeite on different temperature
Fig. 9. ΔG(T) of the reaction on different pressure.
4. Conclusions The reliability of the jadeite thermodynamic properties based on density functional theory (DFT) was verified by comparing thermodynamic calculation data of the first-principles with the data of thermodynamics manual. The stability of the three kind of phases in the jadeite decomposition reaction is low albite > jadeite > nepheline. The jadeite is a semi-stable state substance at normal pressure. The calculation results reveal that the Gibbs free energy of jadeite is lower
Fig. 10. ΔG(P,T) of the phase transition reaction for jadeite on different pressures and temperatures.
59
Physica B: Condensed Matter 567 (2019) 55–60
T. Liu, et al.
than zero at normal pressure to 5Gpa. And at 0–1800K, normal pressure to 80Gpa, the decomposition reaction has a tendency to occur in thermodynamics. Actually, the thermodynamic stability is better at low temperature and high pressure(near 60Gpa and400 K), which is in accordance with the theory that jadeite is formed in the geological environment with high temperature and low pressure. Acknowledgement The authors would like to acknowledge the project supported by the fund of the Analysis and Detection of KMUST (2018T20040070) and the Introduced Talents Project Funded by the Start-up Research of KunMing University of Science and Technology (KKZ3201751043). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.physb.2019.04.032. References [1] Yang Jin, Yueting Song, Shu Zhou, Boqing Wu, Guanli Xu, Mingshun Xiang, Firstprinciples investigations of crystal structures and physical properties of jadeite under various pressures, Physic B 543 (2018) 32–37. [2] M. Akaogi, A. Tanaka, M. Kobayashi, et al., High-pressure transformations in NaAlSiO4 and thermodynamic properties of jadeite, nepheline, and calcium ferritetype phase, Phys. Earth Planet. In. 130 (1–2) (2002) 49–58. [3] H.S. Yoder, The jadeite problem, part I, Am. J. Sci. 248 (5) (1950) 312–334. [4] L.H. Adams, A note on the stability of jadeite, Am. J. Sci. 251 (1953). [5] Ying Guo, Gongbao Song, Study on the genesis and artificial synthesis of jade, J. SW. Univ. Technol. (2) (2000) 46–49. [6] K. Kawai, T. Tsuchiya, High-P , T phase relations in the NaAlSi2O6 system from first principles computation, Phys. Chem. Miner. 39 (4) (2012) 305–310. [7] J. Yang, L. Yang, J. Long, Theoretical investigation of the electronic structure, optical, elastic, hardness and thermodynamics properties of jadeite, Mater. Sci. Semicond. Process. 31 (6) (2015) 509–516. [8] E. Takazawa, T. Sekine, et al., Hugoniot equation of state and high-pressure transformation of jadeite, J. Geophys. Res. 261–12 (1998) 268. [9] Y. Pan, M. Wen, The influence of vacancy on the mechanical properties of IrAl coating: first-principles calculations, Thin Solid Films 664 (2018) 46–51. [10] Y. Pan, First-principles investigation of the new phases and electrochemical properties of MoSi2 as the electrode materials of lithium ion battery, J. Alloy. Comp. 779 (2019) 813–820. [11] B. Hammer, Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerh of functionals, Phys. Rev. B 59 (11) (1999) 7413–7421. [12] A.C. Mccarthy, R.T. Downs, R.M. Thompson, Compressibility trends of the clinopyroxenes, and in-situ high-pressure single-crystal X-ray diffraction study of jadeite, Am. Mineral. 93 (1) (2008) 198–209. [13] Yingjiao Liang, The Manual of Practical Inorganic Thermodynamics, Univ. Press, Shenyang: NE, 1993, p. 564. [14] S. Baroni, S. De Gironcoli, A. Dal Corso, et al., Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73 (2) (2008) 515–562. [15] A.M. Afifi, W.C. Kelly, E.J. Essene, Phase relations among tellurides, sulfides, and oxides; I, Thermochemical data and calculated equilibria, Econ. Geol. 83 (2) (1988) 377–394. [16] Tinghe Zhao, Xuewei Yan, Study on the synthesis, thermal behavior and thermal stability of gemstone jade, Chin. J. High Press. Phys. 6 (4) (1992) 291–296.
Fig. 11. ΔG(P,T) of the phase transition reaction for jadeite on different pressures and temperatures (from temperature).
Fig. 12. ΔG(P,T) of the phase transition reaction for jadeite on different pressures and temperatures (from pressure).
60