**4. Conclusion**

During recent decades, it has become feasible to simulate a complicated system on a computer due to rapid progress in parallel computing. Within the scale of atomistic and molecular simulation, the application of the classical molecular dynamics (MD) simulation method covers a vast variety of systems undergoing current scientific development. The method of MD solves the classical equations of motion for an ensemble of atoms. It results in time-dependent trajectories for all atoms in a system. From these atomistic trajectories, MD can provide detailed *in situ* atomistic information that is difficult to obtain experimentally. As one of the robust and well-developed simulation techniques, MD simulation is an ideal scientific tool to complement experimental observations to properly characterize a complicated system. Those that involve a vast time and spatial dimension, and heterogeneous materials interfaces can be modeled using a multi-scale framework. One of the best such examples that are becoming appropriate for MD is the study of the inner workings of a solid oxide fuel cell (SOFC), which is important as an electrochemical energy conversion and clean energy storage.

SOFC is a new alternative clean energy device that converts the energy of combustion and electrochemical interactions into electricity, which utilizes the superionic conductivity (> 10-1 Scm-1) of special materials at high temperature. Despite the advantages over conventional power generation technologies, there remain a number of challenges that delay the full commercialization of the SOFC and one of the challenges is to understand the basis of ionic transport in its solid electrolyte (e.g. YSZ, the Zr1−*<sup>x</sup>*Y*x*O2−*x/*2 system, with *x/*2 being the Y2O3 dopant concentration). For YSZ, the optimum ionic conductivity can vary with different synthesis routes and sintering conditions due to the resultant diverse local morphologies, grain boundaries, and microstructures.

Within the rigid ion model approximation, we have shown a systematic study of the static and dynamic properties of YSZ crystals and amorphous solids within the typical dilute Y2O3 concentration limit (i.e. 3.0 – 12.0 mol% Y2O3) in the temperature range 300 – 1400 K based on a simple semi-empirical Born–Meyer–Buckingham (BMB) interatomic potential through the standard techniques in classical MD. The results suggest that the vacancy assisted ion conductivity of YSZ as a function of mol% of Y2O3 at a given temperature seems to be a universal feature of YSZ electrolytes, regardless of varying local structures. Whether it is an amorphous or a crystal, the oxygen ionic conductivity shows a maximum at 8*.*0mol%Y2O3, close to the lower limit of the cubic YSZ phase stability that is confirmed by experiments. For YSZ amorphous solids, their lower absolute ionic conductivity relative to YSZ crystals is consistent with the trends observed in YSZ crystalline and stabilized amorphous thin films reported from experiments. For the YSZ amorphous solids, the mobile anions and the slowly migrating cations are strongly coupled in their motion. This mutual diffusion (cations and anions) found in the amorphous phases contributes considerably to the dynamics as seen through the timedependent van Hove correlation functions. This reduces the effective oxygen-ion conductivity. These moving ions carry charges, and thus produce an electrical response. It is expected that the intriguing features of mutual diffusion found in amorphous YSZ solids can therefore be detected by current experimental techniques at frequencies below the typical vibrational frequencies (>100 GHz). To gain further insight into the different correlated motions in various YSZ system and its interfaces, richness in morphologies, longer equilibration, better statistical methods and better atomic potentials are highly desirable.

### **5. Acknowledgements**

This work was supported and by the Office of Naval Research, both directly and through the Naval Research Laboratory.

#### **6. References**

366 Molecular Dynamics – Theoretical Developments and Applications in Nanotechnology and Energy

always influenced by interactions with the migrating cations, and therefore change with time. By involving the mutual diffusion (i.e. sites previously occupied by cations can be visited by anions and vice versa), the hopping processes of ions will therefore be influenced greatly by the changing intermediate surroundings, which makes fast diffusive ions with successive hopping jumps less probable. Therefore the MSD of the mobile O2− in the

During recent decades, it has become feasible to simulate a complicated system on a computer due to rapid progress in parallel computing. Within the scale of atomistic and molecular simulation, the application of the classical molecular dynamics (MD) simulation method covers a vast variety of systems undergoing current scientific development. The method of MD solves the classical equations of motion for an ensemble of atoms. It results in time-dependent trajectories for all atoms in a system. From these atomistic trajectories, MD can provide detailed *in situ* atomistic information that is difficult to obtain experimentally. As one of the robust and well-developed simulation techniques, MD simulation is an ideal scientific tool to complement experimental observations to properly characterize a complicated system. Those that involve a vast time and spatial dimension, and heterogeneous materials interfaces can be modeled using a multi-scale framework. One of the best such examples that are becoming appropriate for MD is the study of the inner workings of a solid oxide fuel cell (SOFC), which is important as an electrochemical energy conversion and clean energy

SOFC is a new alternative clean energy device that converts the energy of combustion and electrochemical interactions into electricity, which utilizes the superionic conductivity (> 10-1 Scm-1) of special materials at high temperature. Despite the advantages over conventional power generation technologies, there remain a number of challenges that delay the full commercialization of the SOFC and one of the challenges is to understand the basis of ionic transport in its solid electrolyte (e.g. YSZ, the Zr1−*<sup>x</sup>*Y*x*O2−*x/*2 system, with *x/*2 being the Y2O3 dopant concentration). For YSZ, the optimum ionic conductivity can vary with different synthesis routes and sintering conditions due to the resultant diverse local morphologies,

Within the rigid ion model approximation, we have shown a systematic study of the static and dynamic properties of YSZ crystals and amorphous solids within the typical dilute Y2O3 concentration limit (i.e. 3.0 – 12.0 mol% Y2O3) in the temperature range 300 – 1400 K based on a simple semi-empirical Born–Meyer–Buckingham (BMB) interatomic potential through the standard techniques in classical MD. The results suggest that the vacancy assisted ion conductivity of YSZ as a function of mol% of Y2O3 at a given temperature seems to be a universal feature of YSZ electrolytes, regardless of varying local structures. Whether it is an amorphous or a crystal, the oxygen ionic conductivity shows a maximum at 8*.*0mol%Y2O3, close to the lower limit of the cubic YSZ phase stability that is confirmed by experiments. For YSZ amorphous solids, their lower absolute ionic conductivity relative to YSZ crystals is consistent with the trends observed in YSZ crystalline and stabilized amorphous thin films reported from experiments. For the YSZ

amorphous solid will be less compared to the crystal (Fig. 9).

**4. Conclusion** 

storage.

grain boundaries, and microstructures.

Ackermann, R J; Rauh, E G. & Alexander, C A. (1975) High Temp. Sci. Vol. 7, pp. 305.


The Roles of Classical Molecular Dynamics Simulation in Solid Oxide Fuel Cells 369

Morinaga, M.; Cohen, J. B. & Faber, J. Jr. (1980) Acta Crystallogr. Vol. A36, pp. 520–

Ostanin, S; Salamatov E; Craven, A J; McComb, D W. & Vlachos D. (2002) Phys. Rev. B Vol.

Pornprasertsuk, R.; Cheng, J.; Huang, H. & Prinz, F. B. (2007) Solid State Ion. Vol. 178, pp.

Pietrucci, F; Bernasconi, M; Laio, A. & Parrinello, M. (2008) Phys. Rev. B Vol. 78, pp.

Predith, A; Ceder, G; Wolverton, C; Persson K. & Mueller T. (2008) Phys. Rev. B Vol. 77, pp.

Rapaport, D.C. 2004 The Art of Molecular Dynamics Simulation 2nd Edn (Cambridge:

Sayle, D C; Doig, J A; Parker, S C; Watson, G W. & Sayle, T X T. (2005) Phys. Chem. Chem.

Sayle, D C; Maicaneannu, S A. & Watson, G W. (2002) J. Am. Chem. Soc. Vol. 124, pp.

Turner, C.H.; W. An.; Dunlap. B.I.; Lau, K.C. & Wang, X. (2010) Annual Reports in

van Duin, A C T.; Merinov, B V; Jang, S S. & Goddard, W A III. (2008) J. Phys. Chem. A Vol.

Veal, B. W.; McKale, A. G.; Paulikas, A. P.; Rothman, S. J. & Nowicki, L. J. Physica B. Vol

Wang, X.; Lau, K. C.; Turner, C. H. & Dunlap, B.I. (2010) J. Electrochem. Soc. Vol. 157, pp.

Wang, X.; Lau, K. C.; Turner, C. H. & Dunlap, B.I. (2010) J. Electrochem. Soc. Vol. 195, pp.

Shimojo, F.; Okabe, T.; Tachibana, F.; Kobayashi, M. & Okazaki, H. (1992) J. Phys. Soc. Japan

Stapper, G; Bernasconi, M; Nicoloso, N. & Parrinello, M. (1999) Phys. Rev. B Vol. 59, pp.

Zacate, M.O.; Minervini, L.; Bradfield, D J.; Grimes, R W. & Sickafus, K E. (2000) Solid State

Zhang, C; Li, C J.; Zhang, G.; Ning, X J.; Li, C X.; Li, H. & Coddet, C. (2007) Mater. Sci. Eng. B

Schelling, P K; Phillpot, S.R. & Wolf, D. (2001) J. Am. Ceram. Soc. Vol. 84, pp. 1609.

Steele, D. & Fender, B. E. F. (1974) J. Phys. C: Solid State Phys. Vol. 7, pp. 1–11. Yamamura, Y; Kawasaki, S. & Sakai H. (1999) Solid State Ion. Vol. 126 pp. 181.

Ralph, M.; Schoeler, A. C. & Krumpelt, M. (2001) J. Mater. Sci. Vol. 36, pp. 1161.

Nakamura, A. & Wagner, J B Jr. (1986) J. Electrochem. Soc. Vol. 133 pp. 1542. Okazaki, H; Suzuki, H. & Ihata, K. (1994) Phys. Lett. A Vol. 188, pp. 291.

Ostanin, S. & Salamatov E. (2003) Phys. Rev. B Vol. 68, pp. 172106. Pascual, C. & Duran, P. (1983) J. Am. Ceram. Soc. Vol. 66 pp. 23.

530.

195.

094301.

144104.

11429.

B90–8.

4177.

797.

112, pp. 3133.

150, pp. 234–240.

Vol. 61, pp. 2848.

Ion. Vol. 128, pp. 243.

Vol. 137, pp. 24.

Cambridge University Press). Sayle, D C. (1999) J. Mater. Chem. Vol. 9, pp. 2961.

Sidebottom, D.L. (2009) Rev. Mod. Phys. Vol. 81, pp. 999.

Computational Chemistry, Vol. 6, pp. 201-234.

Sawaguchi, N. & Ogawa, H. (2000) Solid State Ion*.* Vol. 128 pp. 183.

Smith, D K. & Newkirk, H W. (1965) Acta Crystallogr. Vol. 18 pp. 983.

Phys. Vol. 7 pp. 16.

66, pp.132105.

Devanathan, R; Weber, W J; Singhal, S C. & Gale, J D. (2006) Solid State Ion. Vol. 177, pp. 1251.

Dwivedi, A. & Cormack, A N. (1990) Phil. Mag. A Vol. 61, pp. 1.


Devanathan, R; Weber, W J; Singhal, S C. & Gale, J D. (2006) Solid State Ion. Vol. 177, pp.

Dyre, J.C.; Maass, P.; Roling, B. & Sidebottom, D.L. (2009) Rep. Prog. Phys. Vol. 72, pp.

Frenkel, D. & Smit, B. (1996) Understanding Molecular Simulation: From Algorithms to

Fukui, T; Murata, K.; Ohara, S.; Abe, H.; Naito M. & Nogi, K. (2004) J. Power Sources, Vol.

Gatewood, D.S.; Turner, C.H. & Dunlap, B.I. (2011) ECS Transactions, Vol. 35, "Solid-Oxide

Hayashi, H; Saito, T; Maruyama, N; Inaba, H; Kawamura, K. & Mori, M. (2005) Solid State

Ishizawa, N.; Matsushima, Y.; Hayashi, M. & Ueki, M. (1999) Acta Crystallogr., Sect. B Vol.

Kilo, M; Argirusis, C; Borchardt, G. & Jackson, R A. (2003) Phys. Chem. Chem. Phys. Vol. 5,

Korte, C.; Peters, A.; Janek, J.; Hesse, D. & Zakharov, N. (2008) Phys. Chem. Chem. Phys.

Krishnamurthy, R.; Yoon, Y G.; Srolovitz, D J. & Car, R. (2004) J. Am. Ceram. Soc. Vol. 87 pp.

Minervini, L; Grimes, R W. & Sickafus, K E. (2000) J. Am.Ceram. Soc. Vol. 83, pp.

Morinaga, M.; Cohen, J. B. & Faber, J. Jr. (1979) Acta Crystallogr*.* Vol. A35, pp. 789–

Heiroth, S; Lippert Th; Wokaum, A. & Döbeli M. (2008) Appl.Phys. A Vol. 93 pp. 639. Howard, C J; Hill, R J. & Reichert B E. (1988) Acta Crystallogr. B Vol. 44, pp. 116.

Ioffe, A. J; Rutman, D. S. & Karpachov, S.V. (1978) Electrochim. Acta Vol. 23, pp. 141.

Khan, M S; Islam, M S. & Bates, D R. (1998) J. Mater. Chem. Vol. 8, pp. 2299.

Lammert, H. & Heuer, A. (2010) Phys. Rev. Lett. Vol. 104, pp. 125901.

Lashtabeg, A. & Skinner, S J. (2006) J. Mater. Chem. Vol. 16, pp. 3161.

Li, X. & Hafskjold, B. (1995) J. Phys.: Condens. Matter Vol. 7, pp. 1255. Lindan, P J D. & Gillan, M J (1993) J. Phys.: Condens. Matter Vol. 5, pp. 1019.

March, G E. (1982) Solid State Ion. Vol. 7 pp. 177.

Lau, K. C.; Turner, C.H. & Dunlap, B. I. (2008) Solid State Ion. Vol. 179, pp. 1912. Lau, K. C.; Turner, C.H. & Dunlap, B. I. (2009) Chem. Phys. Lett. Vol. 471, pp. 326. Lau, K. C. & Dunlap, B. I. (2009) J. Phys.: Condens. Matter Vol. 21, pp. 145402. Lau, K. C. & Dunlap, B. I. (2011) J. Phys.: Condens. Matter Vol. 23, pp. 035401.

Lewis, G V. & Catlow, C R A. (1985) J. Phys. C: Solid State Phys. Vol. 18, pp. 1149.

Dwivedi, A. & Cormack, A N. (1990) Phil. Mag. A Vol. 61, pp. 1.

Etsell, T H. & Flengas S N. (1970) Chem. Rev. Vol. 70, pp. 339.

Fisher, C A J. & Matsubara, H. (1998) Solid State Ion. Vol. 115, pp. 311. Fisher, C A J. & Matsubara, H. (1999) Comput. Mater. Sci. Vol. 14, pp. 177.

Applications (New York: Academic).

Gale, J. & Rohl, A.L. (2003) Mol. Simul. Vol. 29, pp. 291.

Hull, S. (2004) Rep. Prog. Phys. Vol. 67, pp. 1233-1314.

Ingel, R P. & Lewis D. (1986) J. Am. Ceram. Soc. Vol. 69, pp. 325.

Fuel Cells 12", pp. 1055–1063.

Ion. Vol. 176, pp. 613.

1251.

046501.

125, pp. 17.

*55*, pp. 726.

pp. 2219.

1821.

1873.

795.

Vol. 10, pp. 4623.


**Molecular Dynamics Simulation and** 

Kien Ling Khoo1,2 and Leonard A. Dissado2

*2Engineering Department, University of Leicester, Leicester* 

*1Invion Technologies Sdn Bhd* 

*1Malaysia 2UK* 

**Conductivity Mechanism in Fast Ionic** 

**Crystals Based on Hollandite NaxCrxTi8-xO16**

Fast ion conductors are keystone materials in the development of high performance solid oxide fuel cells and solid electrolytes. In spite the significant contributions in this area a fundamental understanding of the correlation between crystal structure and ionic conductivity is still lacking. In this chapter we report our recent computer simulation results on Hollandite ionic crystals. The objective of this work is to provide the structural parameters which will lead to the design and synthesis of high performance ionic

Hollandites are ionic crystals of a rather unusual kind, in which the ions of one type are in a disordered and highly mobile state (Dixon & Gillan, 1982). Such materials often have rather special crystal structures in that there are open tunnels or layers through which the mobile ions may move (West, 1988). Their crystal structure corresponds to a family of compounds of general formula AxM4-xNyO8. The basic formula of the Hollandite structure used in the research is Nax(Ti8-xCrx)O16, (Michiue & Watanabe, 1995a, 1996). The chromium and titanium ions are randomly placed in unit cells according to the relative proportions of titanium and chromium ions with a corresponding amount of sodium ions to compensate

for the smaller charge on the chromium ions (+3) compared to the titanium ions (+4).

The main interest of this Na-priderite is its structure as a promising (1-D) Na ion conductor (Michiue & Watanabe, 1995b). Priderites, titania-based hollandites, are typical onedimensional ion conductors in which the 1-D tunnels are available for transport of cations in the tunnel (hereafter the "tunnel ion") (Michiue & Watanabe, 1995a). Priderites are generally represented by AxMyTi8-yO16, where A is the alkali or alkaline earth ions and M, di- or trivalent cations (Michiue & Watanabe, 1995a; A. Byström & A.M. Byström, 1950). The host structure for the hollandite being used mainly consists of titanium ions and oxygen ions. These titanium ions are each octahedrally bonded to six oxygen ions. Two such octahedra are joined by sharing an edge, and these doubled groups share further edges above and below to form extended double strings parallel to the growth axis. Four such double strings are joined by corner sharing to form a unit tunnel. The sodium ions are situated in the

**1. Introduction** 

conductors.

Zhao, X. & Vanderbilt, D. (2002) Phys. Rev. B Vol. 65, pp. 075105. Zhu, Q. & Fan, B. (2005) Solid State Ion. Vol. 176, pp. 889. **18** 
