Nd2-xGdxZr2O7 electrolytes: Thermal expansion and

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 4 ) 1 e1 2

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Nd2LxGdxZr2O7 electrolytes: Thermal expansion and effect of temperature and dopant concentration on ionic conductivity of oxygen M. Razmkhah a, M.T. Hamed Mosavian a, F. Moosavi b,* a b

Department of Chemical Engineering, Ferdowsi University of Mashhad, Mashhad 9177948944, Iran Department of Chemistry, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran

article info

abstract

Article history:

The effect of temperature and complex dopant composition on oxygen ion conductivity in

Received 13 January 2014

solid oxide electrolyte fuel cells was investigated by atomistic molecular dynamics simu-

Received in revised form

lation. A new electrolyte (Nd2xGdxZr2O7) was selected to study oxygen ion conductivity

14 March 2014

using three Gd compositions (x ¼ 0.8, 1.0, and 1.2) in a wide range of temperature

Accepted 23 March 2014

(T ¼ 1273 Ke1873 K). MSD results of cations showed these groups of electrolyte are stable at

Available online xxx

high operating temperature. The first composition (x ¼ 0.8) had the highest ionic conductivity that was in good agreement with the experimental data. A simple effective model

Keywords:

that works with configuration energy of the oxygen crossing plate was applied to explain

Complex dopant

the observed conductivity trend. The model illustrated the point as well. Increasing Gd

Oxygen ion conductivity

concentration decreases existence probability of easy crossing plate. Radial distribution

Solid oxide fuel cells

function analysis also confirmed results. Thermal expansion of the electrolyte has a major

Zirconia solid oxide electrolyte

effect on the selecting of the electrolyte materials; thus, this important factor was also

Molecular dynamics simulation

studied. Results showed the first composition had the greatest thermal expansion.

Structural behavior

Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

Introduction First human efforts to gain energy from fuel goes back to steam engine (with about 7% efficiency) era. Improving thermodynamic science exposed better cycles such as BraytoneRankine that was one of the best cycles for energy generation with about 45% efficiency. Today, attractive fuel cell technology converts fuel to energy directly by electrochemical reactions and gives about 80% efficiency (for pure hydrogen fuel). Low pollution and silent operation are other advantages of fuel cells [1]. One of the most important types of

fuel cells is solid oxide fuel cell (SOFC). SOFCs consist of anode, cathode, and electrolyte that work at high operating temperature. Electrolyte allows passing oxygen ions from cathode to anode (acts as a conductor). One of the main advantages of SOFCs is insensitivity to fuel impurities. Since SOFCs contain high efficiency, low emission, and fuel and module flexibility, they are remarkable choice for power generation utility [2]. Although high operating temperature improves the fuel reaction rate (without platinum catalyst) in electrodes and diffusion of oxygen ions in electrolyte, many studies have focused on reducing operating temperature below 700 C [2e17]. Low operating temperature causes lessen thermal

* Corresponding author. E-mail addresses: [email protected], [email protected] (F. Moosavi). http://dx.doi.org/10.1016/j.ijhydene.2014.03.177 0360-3199/Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

Please cite this article in press as: Razmkhah M, et al., Nd2xGdxZr2O7 electrolytes: Thermal expansion and effect of temperature and dopant concentration on ionic conductivity of oxygen, International Journal of Hydrogen Energy (2014), http://dx.doi.org/ 10.1016/j.ijhydene.2014.03.177

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stress exhaustion and operating cost, in addition to the improving slow startup from cold condition [2,11]. A technique to reduce operating temperature is finding new materials for electrolytes. At high operating temperature that reaction rate of electrodes is fast, electrolyte may limit the efficiency of fuel cell because the rate of ion transfer is lower than electrode reaction rate. Accordingly, it is necessary to study electrolyte behavior with details and investigate the effect of temperature on transfer rate of ion. Electrolytes have also many other applications such as sensors, oxygen pumps, thermal barriers, electrochemical reactors, and steam electrolysis cells [18]. Solid oxides are generally insulator materials because each ion possesses closed shell electronic structure allowing electrons to be displaced, i.e., preventing electronic conduction in the system. At high enough temperature region, the ions can be transported through these solids. This phenomenon is called ionic conductivity. Such ion conductor materials at temperatures below melting point exhibit a liquid-like motion while they are in solid phase. This unusual behavior has attracted much attention to this group of materials [19]. In recent 60 years, many types of solid oxide electrolytes have been examined for fuel cell application, most of which are stabilized zirconia and doped ceria. A good electrolyte must have high ionic conductivity, high stability in a large spectrum of temperature, and insignificant electronic conductivity [13]. Yttrium stabilized zirconia (YSZ) is the most applicable zirconia based electrolyte for SOFC. YSZ shows high conductivity at a range of temperature above 700 C with inconsiderable electronic conductivity (it becomes an electronic conductor above 1500 C) [1]. The most common one in doped ceria group is gadolinium-doped ceria. Though this electrolyte is more conductive than YSZ, it has a major problem. Ce3þ ions create electron holes at temperatures above 600 C that make ceria electronically conductive and then short-circuit takes place [1]. According to these problems, zirconia based electrolytes have attracted more attention than other oxygen-ion conductors; thus, this study focused on stabilized zirconia. Since experimental examination is based on trial and error and solid oxide electrolyte materials are expensive, it is more appropriate to apply molecular dynamics (MD) simulation technique predicting material characterization [11]. By MD simulation, molecular structure of electrolyte and oxygen ion transport within the electrolyte can be visualized [11]. In this way, scientists can interpret the molecular behavior of systems. MD simulation also enables us to studying critical conditions such as very high temperature and pressure. Previously, many researchers studied stabilized zirconia electrolytes by MD simulation, such as Okazaki et al. [12], Brinkman et al. [5], and Yamamura et al. [17] that studied YSZ. According to Devanathan et al. [2], diffusion coefficient of YSZ, at 1273 K, (8 mol% Y2O3) was 2.56 1011 m2/s while of Sc-YSZ (9 mol% Sc2O3 and 9 mol% Y2O3) was 9 109 m2/s at the same temperature, based on Tung et al. [16] study. It can be concluded that the complexity of dopant (stabilized zirconia with two dopants) improves diffusion of ions. Following this trend, the effect of complex dopant Nd2xGdx stabilized zirconia on oxygen transport was studied in the present investigation. Zirconium oxides do not have any observable ionic movement because all sites are occupied by ions. Creating some

free spaces improves ionic movement. As well, Nd3þ and Gd3þ ions were doped in zirconia structure. However, how are the free spaces created? When 4þ charge cations like Zr4þ are substituted with 3þ charge cations like Nd3þ and Gd3þ, some oxygen ions (O2) are removed to balance the charge of the system. Removed oxygen ions make free space sites. These sites are called “oxygen vacancies” and the doping of ions is named “stabilization”. Oxygen vacancies have positive charges, which attract oxygen ions, and cause their moving. The movement of oxygen ions is because of local unbalanced charges in vacancy sites. Fundamentally, free space plays a main role to improve ionic conductivity of solid oxide electrolyte and increases number of dynamic oxygen ions (DOIs). Two types of oxygen ions are in the electrolyte structure: DOIs and static oxygen ions (SOIs) [20], i.e., oxygen ions near the vacancies are DOIs and far from them are SOIs. DOIs are affected by free spaces and directly are related to free spaces. Accordingly, more free spaces cause more ionic conductivity. Also, it is known that cubic structure of zirconia (ZrO2) appears only at 2643 K because of its polymorphism [13]. When doping process is done, FCC structure appears even at room temperature. Thus, considered structure of doped zirconia is cubic. The main goal of present study can be divided into four parts: Proposing new electrolytes and investigating their ionic conductivity; Studying the effect of temperature and dopant composition on the ionic conductivity of electrolytes; Investigating the thermal expansion of the electrolytes.

Simulation method Molecular dynamics simulation was started with a 16 A 16 A 16 A cubic simulation box of zirconia developed from crystallographic unit cells [21] containing 324 ions with three dimensional periodic boundary conditions. Nd and Gd ions were doped on zirconia structure in order to construct the doped solid oxide fuel cell electrolyte with the given composition, Nd2xGdxZr2O7 with x ¼ 0.8, 1.0, and 1.2. Ewald summation (with precision of 1 105) represents long-range electrostatic interactions with full formal ion charges and BorneMayereBuckingham potential [22] illustrates shortrange interactions: rij 4 rij ¼ Aij exp rij

!

Cij r6ij

(1)

where Aij, Cij and, rij are the potential coefficients and rij demonstrates distance between i and j atoms. Table 1 lists potential parameters [23]; cationecation interactions were considered to be only Coulombic and cationeanion interactions followed BorneMayereBuckingham potential [23] in addition to the long-range electrostatic interactions [24]. Simulations at all temperatures and compositions were performed in two stages. In the first stage, isobariceisothermal (NPT) ensemble with crystallographic structure as initial



Table 1 e Potential parameters [23]. Interaction

Aij (eV)

rij ( A)

Cij (eV A6)

ZreZr OeO ZreGd ZreO NdeNd NdeO NdeGd GdeGd GdeO ZreNd

0 22,764.3 0 1453.80 0 1379.90 0 0 1336.80 0

1 0.149 1 0.3500 1 0.3601 1 1 0.3551 1

0 27.88 0 0 0 0 0 0 0 0

3

atomic movement whereas a low height peak indicates high atomic mobility [16]. Thermal expansion coefficient [30] is defined as: a¼

1 vV vln V ¼ V vT p vT p

(6)

where p is pressure. This property can be readily obtained from temperature dependence of volume by conducting constant pressure simulations at several temperatures.

Results and discussion configuration was applied. NPT simulations were carried out to control the cell volume changes with temperature and composition variation. Berendsen thermostat and barostat [25] were used to fix temperature and pressure every 0.1 ps and 1 ps, respectively. In the second stage, the final structures of the first stage were used as initial configuration for canonical ensemble (NVT) simulation to calculate mean square displacement (MSD) at each temperature and composition by applying the same thermostat. All simulations were continued until 5 ns with a time step 1 fs. MD simulation integration algorithm was Verlet and cut off distance was 7.5 A for both series of simulations (NPT and NVT), all carried out by DL_POLY 2.17 simulation package [26,27]. Diffusion coefficient, D, was calculated from MSD via Einstein’s equation [16]: N 1 X ½ri ðtÞ ri ð0Þ2 ¼ 6Dt þ B N i¼1

(2)

where ri is atomic position, t represents time, N corresponds to the total number of atoms, and B is a constant. MSD plots versus time provide diffusion coefficient values. Ionic conductivity was evaluated using NernsteEinstein relation [16]: s¼

nq2 D kHR T

(3)

s is ionic conductivity, n represents concentration of mobile ions, q is ionic charge, k is Boltzmann constant, T is temperature, and HR is Haven ratio equal to 0.65 [16,28]. Ionic conductivity as a function of temperature was obtained from Arrhenius equation: Ea s ¼ s0 exp kT

MSD analyses As mentioned in introduction section, zirconia structure does not have impressive oxygen ionic conductivity. By doping Nd and Gd to the zirconia structure, movement of oxygen ions increases. MSDs of oxygen ions for doped and non-doped zirconia can clarify ionic movement differentiation of these two solid oxides as shown in Fig. 1. The figure shows doping Nd and Gd in zirconia structure influences ionic movement of oxygen ions and significantly improves MSD of doped zirconia. Ionic conductivity can be obtained from Einstein and NernsteEinstein relations. In order to calculate this value, MSD results must be linear. MSD of oxygen ions inside the lattice structure of NdGdZr2O7 (G10) was investigated as a typical sample; Fig. 2 shows MSD of oxygen ions for G10 at different temperatures. It was observed that MSD values increased linearly with time which indicated diffusing of oxygen ions. It is clear that increasing temperature enhanced displacement of oxygen ions. As the ionic movement depends on the temperature, all ions move more and more and finally, at the melting point, solid phase alters into liquid phase. In consequence, enhancing the temperature, solid oxide tends toward liquid and displacement of ions increases considerably. Stability of electrolyte at high temperature is an important factor for fuel cell application. Stability of electrolyte depends

(4)

where Ea is the activation energy of migration and means the barrier of conductivity and s0 is pre-exponential factor related to the number of DOIs [29]. Radial distribution function, RDF, for analyzing atomic distance can be defined as: gi;j ðrÞ ¼

V Nj ðrÞ Nj 4pr2 Dr

(5)

where V is cell volume, Nj is total number of j atoms, and Nj (r) is the number of j atoms in a spherical shell of r to r þ Dr around i atoms. RDF indicates the number of atoms around a central atom in the space [11]. Sharper peak means lower

Fig. 1 e MSD of oxygen ions of doped and non-doped zirconia at 1673 K.


4


Fig. 2 e G10 MSD of oxygen ions as function of simulation time at different temperatures.

Fig. 4 e Ionic conductivity of oxygen ions as a function of x (Nd2LxGdxZr2O7) at 1073 K.

on its cation movements. Movements of cations cause crystalline structure of solid oxide tending to amorphous. In order to analyze the structural stability of studied electrolytes, MSD of cations for G10 electrolyte at high temperature region was investigated, as a typical sample, Fig. 3. The figure shows insignificant movements of cations and therefore the stability of structure. Moreover, MSD values of Nd and Gd cations were greater than Zr and MSD is affected by valance of cations as suggested by Okazaki et al. [12]. Because the ionic charge of Nd3þ and Gd3þ is lower than Zr4þ, their displacement was high, too. The particle with less ionic charge has lower Coulombic limitation noticing that Coulombic forces reduce the movement of ions. However, sometimes the MSD values of Zr4þ were actually greater than Nd3þ, the reason of this phenomenon can be explained by ionic size of Nd3þ. According to Shannon [31], ionic size of Nd3þ is greater than Gd3þ, being much more than Zr4þ. It means Nd3þ has lower lattice space than Gd3þ and Zr4þ to vibrate in its lattice sites; thus, the influence of bigger ionic size of Nd3þ may overcome on its lower ionic charge; consequently, ionic displacement reduces even lower than Zr4þ. Overall, two factors affect cation displacement of solid oxide systems: 1. ionic charge of cations and 2. ionic size of cations.

Effect of temperature and dopant composition

Fig. 3 e MSD of cations for G10 at 1773 K.

The effect of Nd and Gd composition on oxygen ion conductivity is shown in Fig. 4. x ¼ 0.8, 1.0, and 1.2 compositions of Nd2xGdxZr2O7 (NdGdSZ) are represented by G8, G10, and G12, respectively. It can be found that higher extent of Nd showed more conductivity that was in agreement with the experimental data [29]. The simulation results tend to overpredict the ionic conductivity compared with experimental results that can be explained by grain boundary. In this series of simulations, the grain boundary effect was ignored in structural configuration and the bulk ionic conductivity is under study. However, the simulation trend is the same as the experiment. A simple well-organized model providing deep insight into structure makes it possible to explain ionic conductivity trend shown in Fig. 4. This model is based on repulsive and attractive potential energies (configuration energy or Ec) of a DOI that is surrounded by cations. It is clear that the forces of the nearest neighbor cations on the anion limit oxygen movement; thus, the best pathway has the balanced repulsive and attractive potential energies that is Ec ¼ 0, pointing at the neutrality of the pathway [32]. Given target electrolytes have cubic fluorite structure, each oxygen ion is surrounded by eight cations. Hopping oxygen ion into the vacancy demands cross through the face of cube; as a result, surface faces play the main role in anion transferring. At present, the question is which cube face is the most favor for oxygen crossing. The oxygen ion crosses through the face toward which its surface energy tends zero. In order to investigate the surface side energy, a simple cubic structure was modeled from RDF results of MD simulation, Fig. 5. Coulombic and Van der Waals energies were considered for each plate. For cation stability, the total force acting on each cation must be balanced; so, we considered some negative charges for the cation sites by including the central oxygen charge. The central oxygen charge was broken up and proportionality of each cation was taken into account, i.e., each Zr4þ needs 4 negative charges while Nd3þ or Gd3þ



5

Fig. 5 e The modeled cube from RDF results at T [ 1773 K.

needs 3 negative charges to be stable; as a result, (4/(3 þ 4)) of oxygen charge is considered for Zr4þ and (3/(3 þ 4)) for dopant. Because of oxygen formal charge, the portion of Zr4þ cations is ((4/(3 þ 4)) 2) ¼ 1.14 and ((3/ (3 þ 4)) 2) ¼ 0.86 for Nd3þ and Gd3þ dopants. In addition, as Fig. 5 shows, the oxygen is surrounded by four Zr4þ, two Gdþ3, and two Nd3þ cations, it can be concluded that the portions for each Zr4þ and each Nd3þ and Gd3þ is (1.14/ 4) ¼ 0.29 and 0.86/4 ¼ 021, respectively. Accordingly, each Zr4þ needs 4 0.29 ¼ 3.71 negative static charges and each dopant needs 3 0.21 ¼ 2.79 negative static charges located on their sites to follow charge neutrality. In the whole, the following assumptions, for this simple model, were into consideration: 1. O2 ion is attracted by a vacancy and oxygen ion comes across the cube face as an entrance to the vacancy; thus, the surface energy of each face is very important. 2. The structure is fully cubic; thus, the cations on each side are at a unique plate. 3. The charges are static. 4. Some negative charges are located on cations edges in order to keep the neutrality and immobility of the system. 5. The first nearest cations in cube surfaces are more significant than the other neighbors. With all these assumptions, as Fig. 5 illustrates, the right, left, and front faces of the cube are three distinguishable plates and other plates are similar with them. Fig. 6 shows the result of configuration energy of the right, left, and front faces of the cube. These results can shed light on the unclear part of the ionic conductivity that is which cube face is more opportune to let oxygen ions cross. It was observed that configuration energy of right face of the cube, NdeZreZreNd plate, is closer to zero as shown in Fig. 6g, h, i, and j, i.e., crossing through this surface is easier rather than other plates because the higher energy points to instability of site and crossing activation energy of such instable site is the lowest. Therefore, it is, at the moment, reasonable that by increasing the concentration of Nd or decreasing number of Gd in the electrolyte, the existence probability of such plate increases. Greater

number of such plates causes higher ionic conductivity of electrolyte. In addition, observable rhombus energy area, see Fig. 6b, d, and f, may locate the most favor site for anion crossing. The angle of this rhombus energy area has stretched toward ZreZr edge; it can be deduced the oxygen ion prefers to cross through the area near Zr ion that agrees well with the previous result of other researchers [33]. Fig. 6h and i clearly shows the minimum point of each plate tends toward the ZreZr edge. The rhombus boundary with zero energy value just separates the negative and positive energy areas from each other. In fact, the rhombus area and its minimum energy value may effect on oxygen ionic conductivity. It can be clarified by two examples: 1. though the rhombus energy area is great, its minimum energy value may be far from the “zero energy”; 2. minimum configuration energy value may be close the “zero energy” while the rhombus energy area is small. The result of these two cases is difficulty in oxygen hopping from the surface. Greater rhombus energy area and minimum energy value close to zero are two factors that must be considered together. On the whole, minimum energy value divided by rhombus area can explain the ionic conductivity of a surface (ICS): ICSf

Ec;min Ar

(7)

where Ar is rhombus area, see Fig. 6g, h, and i. Lower value of ICS can show higher ionic conductor cube face. ICS values of right, left, and front plates were 0.548, 0.552, and, 0.551 eV/ A2, respectively. The right face had lower ICS confirming right surface is the most ionic conductor face. By the aid of our simple model, we could answer this fundamental question what the reason of the ionic conductivity variation with the concentration is. Now, with this clearness, it is followed to check temperature dependence of ionic conductivity and structural behavior in order to select the best suggested conductor. The effect of temperature (T ¼ 1273 Ke1873 K) on ionic conductivity was also studied. Fig. 7aed reveals MD simulation provides accurate results by appropriate least square method to the experiment [29]. Activation energy is obtained


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Fig. 6 e Ec for the modeled cube (Fig. 5): a) 3D surface of front face, b) counter plot of front plate outlines with color fills, c) 3D surface of left face, d) counter plot of left plate outlines with color fills, e) 3D surface of right side plate, f) counter plot of right plate outlines with color fills, g) counter plot of front face outlines with Ec interval label and minimum point, h) counter plot of left plate outlines with Ec interval label and minimum point, i) counter plot of right plate outlines with Ec interval label and minimum point, and j) Ec versus X. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Please cite this article in press as: Razmkhah M, et al., Nd2xGdxZr2O7 electrolytes: Thermal expansion and effect of temperature and dopant concentration on ionic conductivity of oxygen, International Journal of Hydrogen Energy (2014), http://dx.doi.org/ 10.1016/j.ijhydene.2014.03.177


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Fig. 6 e (continued).

from the slope of ln(sT) versus 1/T and represents facility of ionic movement. Low activation energy means easy ionic movements; this value is the lowest in the case of G12, Fig. 7d. It is worth to mention that finding a relationship between activation energy and ionic conductivity without considering the intercept is not possible. Intercept of Arrhenius plot represents number of DOIs [20]. Both activation energy and intercept of G12 are the lowest. Although the resistivity against ionic movement of G12 was low, number of DOIs is not high. Fig. 8 shows displacement of oxygen ions. Ions with displacement greater than 5 A were considered DOIs in

present study. This consideration is reasonable because 5 A is two times greater than mean oxygen displacement in the system. The figure shows DOI number of G12 is the lowest. Consequently, fewer numbers of DOIs dominates the facile ionic movement and the lowest ionic conductivity of G12 at studied temperature (1773 K) is observed. From the other side of view, DOIs have a main effect on ionic conductivity of solid electrolyte [20] that can be related to Ec of the cube faces surrounding oxygen ion. In other words, increasing number of plates with Ec closer to zero causes higher DOIs in complex studied electrolyte.


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Fig. 7 e Arrhenius plot of conductivity as a function of 1000/T: a) G8, b) G10, c) G12, d) comparison between G8, G10, and G12.

Effect of charge reduction As mentioned before, formal charges were considered for all ions, according to Lewis et al. [23]. However, as it is known at the experimental world, the charges of ions can be lower than formal ionic charges. In addition, Yamamura et al. [34] claimed the ionic charges of ions should be considered reduced. Accordingly, ionic conductivity of G10 electrolyte with 86% of formal ionic charge was simulated in order to investigate the charge effect in the range of studied temperature as shown in Fig. 7b. It is noticeable that reducing the charge to 86% of formal ionic charge value increases the difference between simulation results and experimental data. Since the Coulombic interaction restriction was lower than full charge condition, reducing the charge significantly improved movement of oxygen ions. As mentioned in the previous section, the pre-exponential factor in Arrhenius relation indicated number of DOIs. Number of DOIs in the system with 86% charge was progressed and a greater intercept was observed according to lower Coulombic interaction. In addition, as movement of oxygen ions improved, the activation energy became smaller as well. Because the results of

full ionic charge were closer to experimental data than 86% of formal charge, ionic charges of ions in all simulations were considered full charges.

RDF analysis Unusual behavior of solid oxide electrolytes makes them viable candidates for fuel cell application, discussed before. Although the structure is crystalline, oxygen ions move like liquid within crystal. RDF results substantiate the existence of such movement, shown in Fig. 9, since RDF represents distribution of ions around central ion. High and sharp peaks show well-ordered distribution due to lower movement while short and broad peaks mean disordered distribution due to higher movement of ions. RDF results of studied systems demonstrated oxygen ions are more distributed than the other ions. It means oxygen ions move like liquid in the solid structure. In addition, the figure represents ZreO distance was smaller than NdeO and GdeO because Zr ion has 4þ charges but Gd and Nd ions have 3þ charges; thus, Coulombic interaction between Zr and O is stronger than NdeO and GdeO interactions. Fig. 9 also compares RDFs of cations and anions.



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Fig. 8 e Displacement of ions versus atom index at 1773 K: a) G8, b) G10, c) G12.

RDF heights of NdeO and GdeO were lower than ZreO because of the fewer number of Nd and Gd than Zr ions. As mentioned before, adding dopant to zirconia structure improves the movements of oxygen ions. Comparing

oxygeneoxygen pair correlation function of doped and nondoped zirconia displayed the effect of dopant on ionic movement. Doped zirconia peaks, as observed in Fig. 10, indicated higher distribution of oxygen ions than non-doped zirconia.

Fig. 9 e Comparison between radial distribution function of ions versus distance at 1773 K.

Fig. 10 e RDF of oxygen ions for doped and non-doped zirconia at 1673 K.


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Fig. 13 e ZreO RDF for G10 at T [ 1373 K and 1873 K.

Fig. 11 e Trajectory of oxygen ions for doped (blue) and non-doped (red) zirconia at 1673 K. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Higher distribution refers to higher ionic movement. Trajectory of oxygen ions represents ionic movement as shown in Fig. 11. The figure compares trajectory of oxygen ions in the case of doped and non-doped zirconia system. Adding Nd and Gd dopants creates free space in solid structure and causes higher ionic movements. Besides, distribution of oxygen ions (moving ions) can explain the electrolyte with greater number of NdeZreZreNd plates having higher ionic distribution that may point to higher mobility. Distribution of oxygen ions is shown in Fig. 12 demonstrating peaks of G8 are short; in other words, movement of oxygen ions is high. Moreover, the figure confirmed that the structural ordering may not change with the concentration. By increasing system temperature, movement of ions increases as is obvious in Fig. 13, too. The figure shows

dispersion of anions increased by increasing temperature. If increasing continues, the solid tends toward liquid at melting point and the structure would be fully amorphous. Movement of ions at melting point was called liquid-like movement (LLM) [13]. According to Pramananda et al. [13], movement of oxygen ions was not LLM because Ea is greater than RT as listed in Table 2. Oxygen ions movements are due to hopping mechanism as well as referring to the unusual behavior of these electrolytes. In other words, because the electrolytes are crystalline and far from melting points the reason of oxygen ion hopping to the nearest vacancy is not LLM.

Thermal expansion It is known that SOFCs work at high operating temperatures. During heating process and going to high operating temperature, all parts of SOFC expand. Accordingly, matching thermal expansion of cathode, anode, and electrolyte materials is important and limits the selection of materials. Thermal expansion of NdGdSZ was studied as presented in Table 3. It seems that thermal expansion of the electrolytes has the same trend with ionic conductivity. Knowing that a solid

Table 2 e Activation energy versus RT. Electrolyte G8 G10 G12

Ea (kJ mol1)

RT (kJ mol1) (Tmax ¼ 1873 K)

92.22 91.57 83.67

15.57

Table 3 e Thermal expansion of G8, G10, and G12. Electrolyte

Fig. 12 e RDF of oxygen ions for G8 and G12 at 1773 K.

G8 G10 G12

a (K1) 2.602 105 2.429 105 2.400 105



expands by increasing the temperature because movements of particles enhance, G8 had the highest ionic movement and the highest particle movements. Consequently, the ionic conductivity may directly be related to the thermal expansion, i.e., highest ionic conductivity results in the highest particle movement and thermal expansion.

Conclusions Nd2xGdxZr2O7 electrolytes with x ¼ 0.8, 1.0, and 1.2 were investigated by molecular dynamics simulation in a spanning temperature of 1273 Ke1873 K. Ionic conductivity of oxygen ions, effect of ionic charge reduction, structural properties (MSD, Ec of cube faces, DOI, RDF, and trajectory of ions), and thermal expansion were also considered to compare target electrolytes. These groups of materials have unusual behavior that is liquid-like motion of oxygen ions in solid-state structure. The MSD, trajectory of oxygen ions, and RDF results of doped and non-doped zirconia structure proved the behavior. Stability of the electrolyte at high operating temperature was studied by MSD of the cations. The results showed that at high operating temperature (1773 K) electrolyte structure was stable and kept its crystalline structure. G8 had the highest ionic conductivity that was in good agreement with experimental data. A model that predicts the oxygen crossing plate was applied to explain the observed conductivity trend. The model indicated increasing Gd concentration decreases existence probability of easy crossing plate. RDF results also showed dispersion of oxygen ions in G8 electrolyte is the highest, in agreement with the easier hopping of oxygen ion from its lattice sites. In order to select an appropriate solid electrolyte for fuel cell application, its thermal expansion should be considered. At last, according to the highest ionic movement of G8, its thermal expansion was the highest.

Acknowledgments Ferdowsi University of Mashhad supported this research and the authors would like to appreciate all who provided the parallel computing environment, especially Mr. M. Foroughi, Mr. I. Darabi, and Mrs. F. Nakhaei. The authors are also grateful to Mr. M. Roudi for valuable comments.

List of symbols Activation energy Ea Atomic position r Boltzmann constant k BorneMayereBuckingham potential 4 Cell volume V Concentration of mobile ions n Configuration energy Ec Diffusion coefficient D Distance between the atoms i and j rij

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Einstein’s equation constant B Gas constant R Haven ratio HR Ionic charge q Ionic conductivity s Minimum configuration energy Ec,min Number of j atoms in a spherical shell Nj(r) Potential parameter Aij Potential parameter Cij Potential parameter rij Pre-exponential factor of Arrhenius equation s0 Pressure p Radial distribution function (RDF) gi,j(r) Rhombus area Ar Temperature T Thermal expansion coefficient a Time t Total number of j atoms Nj Total number of the atoms N

List of abbreviations Dynamic oxygen ion DOI Ionic conductivity of a surface ICS Liquid-like movement LLM Mean square displacement MSD Molecular dynamics MD Nd1.2Gd0.8Zr2O7 G8 NdGdZr2O7 G10 Nd0.8Gd1.2Zr2O7 G12 Nd2xGdxZr2O7 NdGdSZ Radial distribution function RDF Scandia-yttria-stabilized zirconia Sc-YSZ Solid oxide fuel cell SOFC Static oxygen ion SOI Yttrium stabilized zirconia YSZ

references

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