Theoretical investigation of thermodynamic properties of Samaria-doped ceria

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This study finds the dependences of the thermal expansion coefficient and heat capacities on temperature and dopant concentration. Our results are compared with experimental data.

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Nội dung Text: Theoretical investigation of thermodynamic properties of Samaria-doped ceria

TẠP CHÍ KHOA HỌC Lo Ngoc Dung* and Nguyen Thi Thuy An (2024) Khoa học Tự nhiên và Công nghệ (32): 32-37 THEORETICAL INVESTIGATION OF THERMODYNAMIC PROPERTIES OF SAMARIA-DOPED CERIA Lo Ngoc Dung* and Nguyen Thi Thuy An Tay Bac University Abstract: The thermodynamic properties of Samaria-doped Ceria (SDC) are investigated using statistical moment method. The explicit expressions of thermal expansion coefficient and heat capacities at constant pressure and volume are derived including the anharmonicity effects of lattice vibrations. This study finds the dependences of the thermal expansion coefficient and heat capacities on temperature and dopant concentration. Our results are compared with experimental data. Key words: Thermodynamic properties, Samaria-doped Ceria, Statistical moment method. 1. INTRODUCTION CeO2 increase with the increasing of dopant concentration and is larger than that of pure Ceria (CeO2) is the interesting subject due to CeO2. its application in catalysis, electrolyte materials, Previously, statistical moment method (SMM) gas sensor, and resistive random access has been used to investigate diffusion and memory [1-4]. Samaria-doped Ceria (SDC) electrical properties of SDC crystal [8,9]. In this crystal in the cubic fluorite structure (space paper, we use SMM to calculate the group Fm3m), is created by aliovalent doping thermodynamic quantities of SDC crystal. with Sm3+ ions, which substitute Ce4+ ions on Compared with other theoretical methods, the the face-centered cubic (fcc) cation lattice. SMM gives mathematically simple with Insertion of the lower valent cations Sm3+ comprehensive descriptions of the characteristic creates high concentration oxygen vacancies properties of crystal lattice. The calculated results according to Eq. (1) with the Kröger -Vink reveal the dependences of the thermal expansion notation [5] coefficient and heat capacities on temperature and Sm2O3  2Sm'Ce  3OO  VO x •• dopant concentration. Many experimental and theoretical studies have 2. THEORY been carried out on the thermodynamic properties The general formula of SDC crystals taking of SDC crystal [6,7]. G. Neilsen et al. [6] into account the presence of oxygen vacancies measured the heat capacity of CeO2 doped Nd or is Ce1-xSmxO2-x/2, where x is the concentration Sm samples with dopant concentrations x = 0.047 - of Sm3+ ions. 0.154. They reported the thermodynamic functions In the SMM, Ce1-xSmxO2-x/2 crystals are based on theoretical fits Cp,m , S m , H m , and 0 0 0 0 m charactered by the anharmonic vibrations of Ce4+, of measured data. Here, Cp,m is the heat capacity at 0 Sm3+, and O2- ions with the force constants constant pressure, S m is molar entropy, H m is 0 0 kCe , kSm , k O the vibration frequencies Ce , Sm , O , and the anharmonic parameters  ,  Ce ,  Sm , molar enthalpy, and 0 is Gibss-energy based 1 1  ,  ,  ,  ,  Sm ,  O m O Ce Sm O [8]. Massieu potential. T. Hisashige et al. [7] found the 1 2 2 2 thermal expansion and Debye temperature of pure   2 Ce,Sm,O  (1)   1   m Ce,Sm,O , j0 * 2 CeO2 and rare earth-doped CeO2 using an kCe,Sm,O ultrasonic pulse method. They showed that the 2 j  u 2   j eq thermal expansion coefficient of rare earth-doped 32
1   3 jO0  2 (2)    2 j  u j u j  u j eq ,   kO  3 O   2  Sm 2 2 1Sm Sm  3NSm   SSm  2  2 a1    kSm  3  1   4iCe,Sm,O  (3)  1Ce,Sm,O   0  2 3 a1Sm  4 Sm   2 48 j  u 4 eq  2 X Sm  kSm  3 j  4   4 jCe,Sm,O   1  X  , (4)  Ce,Sm,O 2 1   2 2  0 8 j  u j u j  eq  2  1Sm  2  2 1Sm 2 Sm Sm (8)  Ce,Sm,O  4   1Ce,Sm,O   2Ce,Sm,O  (5)  O  E0  3N O  sO  ln 1  e O  2 sO     where  = x, y or z, u j , u j are Cartesian  2  O 2 2 1O O   3N O   SO  2  2 a1   components of the ionic displacement of jth  kO  3  ion,  jo (or  jo or  jo ) is the interaction Ce Sm O 2 3 a1O  4 O   2 potential between 0th and jth Ce4+ (or Sm3+, or  2 SO  kO  3 4  O2-) ions, and m is the average ionic mass. The Helmholtz free energy of Ce1-xSmxO2-x/2 crystal is given by [8, 9]  2  1O  2  2 1O 2 O  1  S  O    CeO   Sm  NSmu0  TSc* Ce (6)    kO  2 x /2  3N O    1  where and are total Helmholtz  6 O     SmN Ln  1 energy and the number of Sm3+ ions,  2   2 O a1O  2  a1O  kO a1O     respectively, in Ce1-xSmxO2-x/2 crystals, Sc* is the   3 3  9 2   9 3   configurational entropy of this crystal, and u0Ce  k aO   (9) is the average interaction potential of a Ce4+ ion  O 31   SO  1   , in Ce1-xO2-x/2 crystal that determined through the 9 6 kO  Helmholtz free energies of Ce4+ and O2- ions Ce,Sm,O SCe,Sm,O [10]. sCe,Sm,O  , a1Ce,Sm,O  1  , 2 2 In the SMM, the Helmholtz free energies of SCe,Sm,O  sCe,Sm,O coth sCe,Sm,O , Ce4+, Sm3+ and O2- ions can be written as [8, 9] where   k BT , kB is the Boltzmann  Ce  Ce E0  3N Ce  sCe  ln 1  e   2 sCe    constant, Ce,Sm,O is the vibrational frequencies of ions, is the Planck constant and E0Ce , E0Sm ,   2  Ce 2 2 1Ce Ce  E0O are the total interaction potentials of Ce , 4+  3N Ce   SCe  2  2 a1    kCe  3  Sm3+, and O2- ions at the equilibrium position, respectively. 2 3 a1Ce  4 Ce The average ion displacements of Ce4+,   2  2 SCe  Sm3+, and O2- ions from the equilibrium kCe  3 4  position at temperature T are given by [8,9] (7)    2 Ce,Sm 2 (10)  1  SCe   , yCe,Sm T   2 2  Ce  2  Ce Ce ACe,Sm 1 1 2  3 3kCe,Sm Sm  E0  3NSm  sSm  ln 1  e Sm   2 sSm    33
2 O 2  1  6 O 2  2 Coulomb potential and Buckingham potential yO  AO   1  x including the short-range interactions as [12] 3kO3 3 O   4  q q  r C (18)  1  O 2 2  (11) mn  r   m n  Amn e Bmn  mn , x   2  X O  1  , r r 6  3 3kO 27 O kO  where qm, qn are the effective charges of the where ACe,Sm and AO are determined as in mth and nth ions, r is the separation between Refs. [10] and [11]. ions, and the potential parameters Amn, Bmn, Cmn are presented in Table 1. The average nearest-neighbor distance at temperature T can be written as Table 1. The parameters of the Buckingham potential in SDC crystal [12]. r1 (T )  r1  0   cCe yCe (T ) (12) 6  cSm ySm (T )  cO yO (T ). o o Interaction Amn (eV) Bmn ( A) Cmn (eV . A ) The definition of the thermal expansion O2- - O2- 9547,96 0,2192 32,00 coefficient enables us to derive the fomula 4+ 2- [10,11] Ce - O 1809,68 0,3547 20,40 3+ 2-  (T )  (13) Sm - O 1944,44 0,3414 21,49 cCe Ce (T )  cSm Sm (T )  cO O (T ) Fig. 1 shows the lattice constant of SDC crystal at the room temperature as a function of with cCe , cSm , cO denote the concentration of dopant concentratrion. Ce , Sm3+ and O2- ions, respectively, and 4+ k yCe,Sm,O (T ) (14)  Ce,Sm,O (T )  B r1  0   The heat capacities of Ce4+, Sm3+ and O2- ions at constant volume CV , CV , CV can be Ce Sm O defined from the partial free energies of ions Eq. (7) – Eq. (9). Then, the heat capacity at constant volume can be written as [10,11] CV  cCeCV  cSmCV  cOCV Ce Sm O (15) Figure 1. The dopant concentration dependence of lattcice constant at T = 300 K. The experimental with results [13-16] is shown for comparison.   2  Ce  Sm   2 Sm  One can see that the lattice constant is little C Ce  T  2  , CV  T  2  ,  T   T  V larger than that of CeO2 crystal (x = 0). As the dopant concentratrion increases, an increase in  2O  the lattice constant is found. The lattice expansion C  T  O 2   T  V due to doping arises from the larger radius of Sm3+ ions compared with that of Ce4+ ions. Our The heat capacity at constant pressure is theoretical calculations are in good accordance calculated based on the relation as [10,11] with experiments [13-16]. The experimental CP  CV  9 2 BTVT (16) results [15,16] increase rapidly with an increase here, BT denotes the bulk modulus of SDC in dopant concentration at x  0.2 but vary more slowly as the dopant concentration comes close to crystal. the solubility limit, x = 0.4. 3. NUMERICAL RESULTS AND The calculated results of thermal expansion DISCUSSION coefficient of SDC crystal at 600 K are presented To describe the interionic interaction in in Fig. 2. One can see that the thermal expansion doped ceria oxides, one often employs the pure coefficient increases linearly with the increasing of dopant concentration. This dependence reveals 34
the larger value of thermal expansion coefficient In Fig. 4, the calculated results of heat of SDC crystal in comparison with that of CeO2 capacities at constant volume CV and pressure crystal. The substitution Ce4+ ions by Sm3+ ions CP are presented. One can see that the heat promotes the thermal vibration of ions and capacity at constant volume CV depends weakly therefore, the ions vibrate stronger due to on temperature, but the heat capacity at temperature. The meased results using Rigaku constant pressure CP changes quickly with Thermo Plu TMA [17] is also shown in Fig. 2. temperature and becomes a nonlinear function Our obtained SMM thermal expansion of temperature. coefficients are in relatively good with the experimental data [13]. The errors are only about 3 – 5 %. Figure 4. The temperature dependence of heat Figure 2. The dopant concentration dependence of capacities in the temperature range T = 100 – 2000 thermal expansion coefficient at T = 600 K. The K at x = 0.2. experimental results [17] is shown for comparison. The strongly anharmonic lattice vibration Fig. 3 presents the SMM results of thermal under high temperture is the principal reason expansion coefficient of SDC crystal at the for the anomalous increase of the heat capacity dopant concentration x = 0.2. The thermal at constant volume CV near melting expansion coefficient is shown as a function of temperature. This property is also found in the dopant concentration. The thermal expansion metallic materials, such as Cu, Pd, Ag, … [18]. coefficient increases as the temperature increases. The heat capacities at the different dopant Notably, the thermal expansion coefficient rises concentrations (x = 0.1; x = 0.2) show the quickly in the high temperature range, T > 2000 dopant concentration dependence of the heat K. This property arises from the anharmonicity capacities. The heat capacities become larger as effects of thermal lattice vibrations. T. Hisashige the dopant concentration increases. et al. [18] measured the thermal expansion coefficient of SDC crystal at x = 0.2 using X-ray 4. CONCLUSION powder diffractometer. The obtained data is very In this paper, the SMM model is used to close with the SMM results. investigate the thermodynamic properties of SDC crystal. The thermal expansion coefficient and heat capacities are calculated as a function of dopant concentration and temperature. The anomalous increase of thermal expansion coefficient and heat capacity at constant volume near melting temperature arises from the strongly anharmonic lattice vibration. Our results are compared with the experimental data. ACKNOWLEDGMENTS Figure 3. The temperature dependence of thermal expansion at x = 0.2. The experimental results [17] This research is funded by Tay Bac is shown for comparison. Universiy. 35
REFERENCES Pressures, Comp. Mater. Sci. 49 (4), pp. S355- [1] R. Di Monte, J. Kaspar (2004), On the S358. Role of Oxygen Storage in Three-Way [11] V. V. Hung, J. Lee, K. Masuda-Jindo Catalysis, Topic in Catalysis 28, pp. 47-57. (2006), Investigation of Thermodynamic [2] M. Sugiura, O. Masakuni, S. Properties of Cerium Dioxide by Statistical Akihiko, S.Tadashi(2005), Developement of Moment Method, J. Phys. and Chem. Solids 67 Innovative Three-Way Catalysts Containing (4) , pp. 682-689. Ceria–Zirconia Solid Solutions with High [12] L. Minervini, R. W. Grimes, K. E. Oxygen Storage/Release Capacity, Catal. Surv. Sickafus (2000), Disorder in Pyrochlore Asia 78 (5), pp. 752-767. Oxides, J. Am. Ceram. Soc. 83 (8), pp. 1873- [3] S. Bernal, G. Blanco, J.J. Calvino, J.M. 1878. Gatica, J.A. Perez-Omil, J.M. Pintado (2004), [ 13] S. Zha, C. Xia, G. Meng (2003), Effect Characterisation of three-way automotive of Gd (Sm) Doping on Properties of Ceria aftertreatment catalysts and related model Electrolyte for Solid Oxide Fuel Cells, Journal systems, Top. Catal. 28 (1-4), pp. 31-45. of Power Sources 115 (1), pp. 44-48, [4]J. Kaspar, P. Fornasiero (2003), [14] Z. Fu, Q. Sun, D. Ma, N. Zhang, Y. An, Nanostructured materials for advanced Z. Yang (2017), Effects of Sm Doping Content automotive de pollution catalysts, J. Solid State on the Ionic Conduction of CeO2 in SOFCs Chem. 171, pp. 19-29. from First Principles, Appl. Phys. Lett. 111 (2), [5] M. Coduri, S. Checchia, M. Longhi, pp. 023903-1-023903-5. D.Ceresoli, M. Scavini (2018), Rare Earth [15] K. Eguchi, T. Setoguchi, T. Inoue, H. Doped Ceria: The Complex Connection Arai (1992), Electrical Properties of Ceria- Between Structure and Properties, Front. Chem. Based Oxides and Their Application to Solid 6, pp. 526-1-526-23. Oxide Fuel Cells, Solid State lonics 52 (1-3), [6] G. Neilsen, P.F. Rosen, M.S. Dickson, pp. 165-172. M. Popovic, J. Schliesser, L.D. Hansen, A. [16] Z. Zhan, T. -L. Wen, H. Tu, Z. -Y. Lu Navrotsky, B.F. Woodfield (2021), Heat (2011), AC Impedance Investigation of capacities and thermodynamic functions of Samarium-Doped Ceria, Journal of The neodymia and samaria doped ceria, J. Chem. Electrochemical Society 148, pp. A427-A432 Thermodynamics 158, pp. 106454. [17] T. Hisashige, Y. Yamamura, T. Tsuji [7] T. Hisashige, Y. Yamamura, T. Tsuji (2006), Thermal expansion and Debye (2006), Thermal expansion and Debye temperature of rare earth-doped ceria, Journal temperature of rare earth-doped ceria, Journal of Alloys and Compounds 408, pp. 1153–1156 of Alloys and Compounds 408, pp. 1153-1156. [18] K. Masuda-Jindo, Vu Van Hung, and [8] L. T. Lam (2022), Effects of temperature Pham Dinh Tam (2003), Thermodynamic on the electrical properties of samaria-doped quantities of metals investigated by an analytic ceria predicted with the statistical moment statistical moment method, Physical Review B method, Journal of Physics and Chemistry of 67, pp. 094301. Solids 170, pp. 110907. [9] D. T. Hai, V. V. Hung, P. N. Thu, L. N. Dung, L. T. T. Huong, H. T. M. Anh, L. T. Lam (2022), Structural and Electrical Properties of Samarium-doped Ceria Electrolyte, VNU Journal of Science: Mathematics – Physics 38 (1), pp. 65-75. [10] V.V. Hung, L.T.M. Thanh, K. Masuda- Jindo (2010), Study of Thermodynamic Properties of Cerium Dioxide under High 36
NGHIÊN CỨU CÁC TÍNH CHẤT NHIỆT ĐỘNG CỦA CERIA PHA TẠP SAMARIA Lò Ngọc Dũng và Nguyễn Thị Thúy An Trường Đại học Tây Bắc - UTB Tóm tắt: Các tính chất nhiệt động của Ceria pha tạp Samaria (SDC) được nghiên cứu bằng phương pháp thống kê momen. Các biểu thức giải tích của hệ số giãn nở nhiệt và nhiệt dung đẳng áp, nhiệt dung đẳng tích được suy ra bao gồm các hiệu ứng phi điều hòa trong dao động mạng tinh thể. Chúng tôi đã tìm thấy sự phụ thuộc của hệ số giãn nở nhiệt và các nhiệt dung riêng vào nhiệt độ và nồng độ tạp chất. Các kết quả tính toán được so sánh với các số liệu thực nghiệm. Từ khóa: Tính chất nhiệt động, Ceria pha tạp Samaria, Phương pháp thống kê momen. Liên lạc: Lò Ngọc Dũng; Email: longocdung@utb.edu.vn Ngày nhận bài: 7/8/2023 Ngày đăng bài: 9/11/2023 Liên lạc: longocdung@utb.edu.vn 37