- Email: [email protected]
Structure and topological characteristics of amorphous silicon oxycarbide networks: Results from Reverse Monte Carlo simulations
LETTER TO THE EDITOR Journal of Non-Crystalline Solids 386 (2014) 29–33
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
Letter to the Editor
Structure and topological characteristics of amorphous silicon oxycarbide networks: Results from Reverse Monte Carlo simulations Wenruo Bai a, Scarlett Widgeon b,c, Sabyasachi Sen b,⁎ a b c
Department of Physics, Peking University, Beijing 100871, China Department of Chemical Engineering and Materials Science, University of California, Davis, CA 95616, USA Peter A Rock Thermochemistry Laboratory and NEAT ORU, University of California, Davis, CA 95616, USA
a r t i c l e
i n f o
Article history: Received 3 October 2013 Received in revised form 19 November 2013 Available online 8 December 2013 Keywords: Reverse Monte Carlo simulation; Polymer-derived ceramics; Mass-fractal spatial distribution; Silicon oxycarbide
a b s t r a c t The connectivity and length scale of spatial clustering of the structural units and the resultant topological aspects of amorphous SiOC networks, characteristic of polymer derived ceramics, are studied using Reverse Monte Carlo simulation, constrained by experimental density, composition and relative concentrations of SiCxO4 − x tetrahedra. Nanoscale clustering of SiCxO4 − x structural units results from mutual avoidance in connectivity between the constituent tetrahedra and the corresponding inefficiency in packing gives rise to a mass-fractal spatial distribution of the tetrahedra with a dimensionality of ~2.5. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Silicon-based polymer derived ceramics (PDCs) in the Si–C–O, Si–C– N and Si–B–C–N systems constitute an important class of technologically promising materials for use under extreme conditions due to their high chemical, thermal, and mechanical stability at high temperatures [1–9]. Synthesis of these PDCs involves low temperature polymerization and polycondensation reactions of a preceramic polymer, followed by pyrolysis at higher temperatures. Though x-ray amorphous, these materials are characterized by complex atomic structures consisting of structurally and compositionally distinct nanodomains. Fundamental understanding of the atomic structure at various length scales is therefore critical in deciphering the structure–property relationships in these materials and ultimately in controlling their properties for specific engineering applications. The atomic structures of silicon-based PDCs have therefore been extensively investigated over the last two decades using a wide variety of spectroscopic, scattering and electron microscopic techniques [1–15]. 29Si magic-angle-spinning (MAS) NMR is one of the most commonly employed techniques that has resulted in a wealth of information regarding the speciation of the SiCxO4 − x (0 ≤ x ≤ 4) tetrahedra in the SiOC network nanodomains [10,16–19]. Typically the experimental concentrations of the SiO4 and SiC4 units in SiCO PDCs are found to be significantly higher than those expected from a statistical mixing model of Si\O and Si\C bonds [14,17]. This result, when combined with the fact that there is no significant carbon– ⁎ Corresponding author. Tel.: +1 530 754 8397; fax: +1 530 752 1031. E-mail address: [email protected] (S. Sen). 0022-3093/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jnoncrysol.2013.11.030
oxygen bonding in the structure [20], directly implies partial segregation and clustering of the oxygen-rich and carbon-rich SiCxO4 − x tetrahedral units in the SiCO network [17]. However, the degree and length scale of the spatial clustering of these structural units remain poorly known, to date. Previous structural studies of SiCO PDCs have shown that besides bonding to silicon atoms, the majority of the carbon atoms are bonded to other carbon atoms to form nanodomains of sp2-bonded “free” carbon, presumably present as turbostratic carbon or as graphene-like sheets [20–25]. Therefore, the free carbon does not take part in the SiCO network. These carbon nanodomains can be isolated clusters or they can form a continuous network in SiCO PDCs with low or high carbon content, respectively [17,18]. A recent 29Si NMR spectroscopic study of SiCO PDCs with widely different carbon contents of 14 and 53 wt.% indicated that the constituent SiCxO4 − x tetrahedral units form a tenuous network that does not fill space homogeneously and thus can be described as a mass-fractal with fractal dimensions ranging between 2.2 and 2.5 [17]. However, the origin of such fractal character of the spatial distribution of these structural units has remained unclear, although it was tentatively argued that the presence of both C and O atoms with very different coordination numbers (4 and 2, respectively) as the nearest neighbors of Si atoms may lead to a steric hindrance and frustrated packing of the “mixed bonded” SiCxO4 − x units in the SiCO network. Such frustrated packing can result in an inefficient space filling and consequently a mass-fractal character of the spatial distribution of SiCxO4 − x units. Unfortunately, the spectroscopic and diffraction techniques that are typically employed for structural studies of amorphous materials are not
LETTER TO THE EDITOR 30
W. Bai et al. / Journal of Non-Crystalline Solids 386 (2014) 29–33
capable of addressing these topological issues at the length scale of several nanometers. The structures of the SiOC network and the free carbon phase in SiOC PDCs were simulated in a number of previous studies using ab initio molecular dynamics based on density functional theory (DFT) [26–29]. These studies indicate that at or below a carbon content of 12.5 at.%, the Si\C and Si\O bonds are homogenously distributed in the SiOC network [26]. Above this critical threshold, the Si\C bonds begin to percolate and the continuity of the homogeneous SiOC network is disrupted via defect formation. The SiC4 tetrahedra interconnect by corner sharing to form chains and rings and, simultaneously, voids in the SiOC network begin to interconnect to form pores in the structure. It was suggested that, with increasing carbon concentration, the free carbon may eventually reside in these pores [26]. Although these relatively small scale (up to ~200 atoms) simulations provide important information about the local structure and packing of the SiOC network, no attempts were made to test the consistency of the speciation of tetrahedral SiCxO4 − x units in these simulated networks with those observed in 29Si NMR experiments. Moreover, due to their small size, these simulations cannot provide insight into the structural and topological aspects of the SiOC network at nanometer length scales. Here we report the results of a relatively large scale (2756 atoms) Reverse Monte Carlo (RMC) simulation of a SiOC network constrained by experimentally determined density, composition and relative concentrations of SiCxO4 − x structural units. Such simulations are shown to provide important information regarding the degree and length scale of the spatial clustering of the SiCxO4 − x structural units and the resultant topological aspects of the amorphous SiOC network at nanometer length scale.
3. Results and discussion The average coordination numbers of the silicon, carbon, and oxygen atoms and the relative fractions of the various SiCxO4 − x structural units in the final optimized structure generated by the RMC simulation are compared in Fig. 1 with the corresponding values used as constraints. The results show that the coordination numbers of silicon, carbon, and oxygen atoms in the simulated structure are within ~0.1 of their nominal values and the agreement between experiment and simulation with regards to the relative fractions of the SiCxO4 − x structural units is within 1%. The radial distribution function (RDF) of the simulated SiCO network is shown in Fig. 2(a). The main peak positions in the RDF corresponding to the interatomic distances of the simulated structure compare well with those observed experimentally in previous studies [32]. The most intense peak at ~1.63 Å corresponds to the Si\O nearest neighbor distance, while a small peak near 1.95 Å is associated with the Si\C bond length. The peak centered at ~2.5 Å contains predominant contributions from intra-tetrahedral O–O correlations. The peak at ~ 3.0 Å corresponds to the distance between two Si atoms in the adjacent SiCxO4 − x tetrahedral units. The average Si\O\Si and Si\C\Si inter-tetrahedral
2. Simulation methodology The RMC simulations were performed on a cubic cell with a dimension of 3.35 nm, using periodic boundary conditions and the RMCA code [30,31]. A polysiloxane-derived SiOC PDC of composition SiO1.50C0.68 was chosen as the model system. Detailed structural studies of this PDC, based on 29Si and 13C NMR spectroscopy, were previously reported in the literature [17]. These studies indicated a chemical composition of SiO1.51C0.244 for the SiOC network in this PDC, implying that nearly 65% of the C atoms are in the free carbon phase [17]. Accordingly, the simulation cell in the present study contained 1000 Si, 1512 O and 244 C atoms to mimic the chemical composition of the SiOC network. The dimension of the simulation cell for the SiOC network of this PDC was chosen to correspond to a mass density of ~2.4 g cm−3, similar to the previously reported experimentally measured density of 2.4 ± 0.1 g cm−3 for a SiOC network of similar chemical composition (SiO1.49C0.30) [32]. It may be noted that the structural attributes that are of primary interest in the present study namely, the nature of intermediate range order, topology and clustering length scale of the SiOC network, are not expected to change in any significant way with small variations in density. The average nearest neighbor Si\O and Si\C distances were constrained to 1.63 and 1.93 Å, respectively, consistent with previously published diffraction and ab initio molecular dynamics simulation results for SiOC PDCs [27,32–34]. The coordination numbers of Si, C and O atoms were constrained to their experimental values of 4, 4 and 2, respectively, and no C\C or C\O bonding was allowed. Finally, the relative fractions of SiO4, SiO3C, SiO2C2, SiO3C and SiC4 species were constrained to their experimental values of 44.0, 30.4, 16.1, 3.0 and 6.5%, respectively, in the SiOC network of this PDC, as determined in a previous study using 29Si magic angle spinning (MAS) NMR spectroscopy [17]. The RMC structure was generated following two steps. First, the three dimensional configuration of the system was obtained on the basis of the nearest-neighbor bond lengths and coordination numbers as noted above and each coordination constraint was met by 95–99%. Then, using these initial atomic configurations RMC simulations were run for 107 steps in order to meet the constraint of the relative concentrations of various species by ≥98%.
Fig. 1. (a) Comparison between the relative fractions of the SiCxO4 − x tetrahedra in the SiOC network, determined experimentally by NMR (shown in red) and those in the structure generated by RMC simulation (shown in blue). (b) Average coordination numbers of silicon, carbon, and oxygen atoms in the RMC-simulated SiCO network and their nominal values of 4, 4 and 2, respectively.
LETTER TO THE EDITOR W. Bai et al. / Journal of Non-Crystalline Solids 386 (2014) 29–33
Fig. 2. (a) Radial distribution function of the simulated SiCO network (lower curve). Experimentally obtained radial distribution function of a SiOC network of similar composition, as reported in [32] is shown for comparison (upper curve). Curves are vertically offset for clarity. (b) Views of the simulated SiOC network along the normals to the six faces of the cubic simulation box. Si, O and C atoms are shown in red, green and blue, respectively.
31
bond angles are ~140° and 110°, respectively, consistent with previous reports of these bond angles in amorphous SiO2 and SiC [32,35]. The views of the RMC simulated SiOC network along the normals to the six faces of the cubic simulation box are shown in Fig. 2(b). These views of the network directly demonstrate that the carbon atoms in the network are not homogenously distributed throughout the structure and nanoscale percolating clusters of C-rich and O-rich SiCxO4 − x structural units exist in the network that span the entire simulation box. A semi-quantitative measure of the degree of such clustering can be obtained by comparing the relative fractions of the nearest neighbor SiO4 and SiC4 units for any central SiCxO4 − x unit (Fig. 3(a)). These results show that for SiO4 units, 63% of the nearest neighbors are other SiO4 units, while for SiC4 units, 27% of its nearest neighbors are other SiC4 units. In contrast, a purely random distribution of SiCxO4 − x units, in combination with the impossibility of any connection between SiO4 and SiC4 units, would imply relative fractions of 47.0 (12)% of nearest neighbors around central SiO4 (SiC4) units to be other SiO4 (SiC4) units. Therefore, the RMC-simulated SiOC network shows significant spatial clustering of SiO4 and SiC4 tetrahedra in the structure. This structural heterogeneity is also clear from an inspection of Fig. 3(b) where local regions of high concentrations of the SiO4 and SiC4 tetrahedra in the simulated SiOC network are shown. Typical length scales of these clusters are on the order of ~ 1 nm. This result is clearly indicative of the mutual avoidance in connectivity and frustrated packing of SiCx O4 − x tetrahedra. It may be noted here that the nature of the spatial clustering of SiO4 and SiC4 tetrahedra observed in the present simulations is quite different from a structural model of SiCO PDCs proposed in a previous study where a complete segregation of SiO4 units into SiO2 -like nano-domains was hypothesized [13]. The mixed-bonded SiCxO4 − x tetrahedra in this segregated model were assumed to form interfacial layers that connected the SiO 2 nanodomains to the free carbon phase. The avoidance in connectivity between certain SiCxO4 − x structural units, as observed in the present study, must stem from the bonding related steric constraints associated with the mixing of the tetrahedrally coordinated C atoms and 2-fold coordinated O atoms in the nearestneighbor shell of the tetrahedrally coordinated Si atoms and from the avoidance of carbon–oxygen bonding. Such spatial constraints may result into poor efficiency in the packing and consequently in the space filling ability of the SiCxO4 − x tetrahedral units that was recently hypothesized to be the reason behind mass fractal nature of SiOC networks. This hypothesis is tested in this study by calculating the scaling of the number of Si atoms (i.e. mass), enclosed within a sphere of observation, with the radius R of the sphere. Averages of ten sets of such measurements are shown in Fig. 4 where the centers of each set of spheres were randomly chosen points within the simulation cell. The double logarithmic plot of the number of Si atoms M vs. R displays a power law with exponent of ~ 2.5 (i.e. M ~ R2.5) up to R = 1 nm beyond which the dimensionality of mass distribution of Si atoms returns to 3 (i.e. M ~ R3). The fractal dimension of ~2.5 for distances below 1 nm is in excellent agreement with previous reports on experimental measurements of this quantity in SiOC networks in PDCs [17]. Such a fractal network is expected to give rise to unusual mechanical and transport properties as well as contain voids that may nest the free carbon phase in PDCs [26,27]. Finally, it should be noted that the RMC-simulated structural model proposed in this study is based simply on density, simple coordination and connectivity rules between SiCxO4 − x tetrahedral units whose relative fractions are directly obtained from 29Si NMR spectroscopy. The procedure results in a structural model that agrees reasonably well with diffraction results that serve as a check for internal selfconsistency. However, recent studies have indicated that the nature of intermediate range order in disordered structures may not be uniquely captured in pure RMC simulations [36]. Future studies using a combination of RMC with simultaneous energy minimization based on empirical potentials will be important in addressing this issue. Furthermore,
LETTER TO THE EDITOR 32
W. Bai et al. / Journal of Non-Crystalline Solids 386 (2014) 29–33
Fig. 3. (a) Relative fractions of the nearest neighbor SiO4 (blue) and SiC4 (red) tetrahedra for any central SiCxO4 − x unit in the SiOC network. (b) Spatial distribution of the Si atoms for the SiO4 (a) and SiC4 (b) tetrahedra in the simulation cell. Blue curved lines enclose areas where clustering is observed.
incorporation of the free carbon phase in future simulations will lead to a more complete picture of the intermediate-range structural and topological aspects of the structure of these PDCs. 4. Summary The structure of an RMC-simulated SiOC network clearly demonstrates the presence of clustering of SiCxO4 − x structural units at length scales on the order of ~1 nm resulting from mutual avoidance in connectivity and frustrated packing of SiCxO4 − x tetrahedral units. This lack in the space filling ability of the SiCxO4 − x tetrahedral units is due to the coexistence of C and O with very different coordination numbers (4 and 2, respectively) as nearest neighbors of the Si atoms. It is manifested in a fractal spatial distribution of Si atoms in the network with a mass-fractal dimension of ~2.5, over nanometer length scales. Acknowledgments Fig. 4. Double-logarithmic plot of the number (or mass) of Si atoms enclosed within a sphere of observation, as a function of the radius R of the sphere. Solid straight line represents a linear least squares fit through the data points for R ≤ 1 nm (Ln R ≤ 2.3). Note different scaling behavior of the data above and below ~1 nm.
This study was funded by a grant from the National Science Foundation (NSF MWN-0906070). WB acknowledges funding from the Global Research Experience in Advanced Technologies (GREAT) Program at UC Davis. We also gratefully acknowledge many stimulating discussions
LETTER TO THE EDITOR W. Bai et al. / Journal of Non-Crystalline Solids 386 (2014) 29–33
on this subject with Dr. Gabriela Mera and Profs. Alexandra Navrotsky, Ralf Riedel and Roland Faller. References [1] G.D. Soraru, G. D'Andrea, R. Campostrini, F. Babonneau, G. Mariotto, J. Am. Ceram. Soc. 78 (1995) 379. [2] H.J. Kleebe, C. Turquat, G.C. Soraru, J. Am. Ceram. Soc. 84 (2001) 73–80. [3] G. Gregori, C. Turquat, H.J. Kleebe, G.D. Soraru, Key Eng. Mater. 206–213 (2002) 2061. [4] H. Brequel, J. Parmentier, S. Walter, R. Badheka, G. Trimmel, S. Masse, J. Latournerie, P. Dempsey, C. Turquat, A. Desmartin-Chomel, L. Le Neindre-Prum, U.A. Jayasooriya, D. Hourlier, H.J. Kleebe, G.D. Soraru, S. Enzo, F. Babonneau, Chem. Mater. 16 (2004) 2585. [5] C. Turquat, H.J. Kleebe, G. Gregori, S. Walter, G.D. Soraru, J. Am. Ceram. Soc. 84 (2001) 2189. [6] H.J. Kleebe, Y.D. Blum, J. Eur. Ceram. Soc. 28 (2008) 1037. [7] G. Trimmel, B. Rita, F. Babonneau, J. Latournerie, P. Dempsey, D. Bahloul-Houlier, J. Parmentier, G.D. Soraru, J. Sol–Gel Sci. Technol. 26 (2003) 279. [8] Y. Iwamoto, W. Volger, E. Kroke, R. Riedel, T. Saitou, K. Matsunaga, J. Am. Ceram. Soc. 84 (2001) 2170. [9] G. Mera, R. Riedel, F. Poli, K. Muller, J. Eur. Ceram. Soc. 29 (2009) 2873. [10] L. Bois, J. Maquet, F. Babonneau, H. Mutin, D. Hahloul, Chem. Mater. 6 (1994) 796. [11] A. Saha, R. Raj, D.L. Williamson, H.J. Kleebe, J. Am. Ceram. Soc. 88 (2005) 232. [12] J. Schuhmacher, M. Weinmann, J. Bill, F. Aldinger, K. Müller, Chem. Mater. 10 (1998) 3913. [13] A. Saha, R. Raj, D.L. Williamson, J. Am. Ceram. Soc. 89 (2006) 2188. [14] R.J.P. Corriu, D. Leclerco, P.H. Mutin, A. Vioux, J. Mater. Sci. 30 (1995) 2313. [15] Y.L. Li, E. Kroke, R. Riedel, C. Fasel, C. Gervais, F. Babonneau, Appl. Organomet. Chem. 15 (2001) 820.
33
[16] H. Zhang, C.G. Pantano, J. Am. Ceram. Soc. 73 (1990) 958. [17] S. Widgeon, S. Sen, G. Mera, E. Ionescu, R. Riedel, A. Navrotsky, Chem. Mater. 22 (2010) 6221. [18] S. Widgeon, G. Mera, Y. Gao, E. Stanoyov, S. Sen, A. Navrotsky, R. Riedel, Chem. Mater. 24 (2012) 1181. [19] J. Schuhmacher, F. Berger, M. Weinmann, J. Bill, F. Aldinger, K. Müller, Appl. Organomet. Chem. 15 (2001) 809. [20] C.G. Pantano, A.T. Singh, H. Zhang, J. Sol–Gel Sci. Technol. 14 (1999) 7. [21] P. Colombo, G. Mera, R. Riedel, G.D. Sorarú, J. Am. Ceram. Soc. 93 (2010) 1805. [22] R. Riedel, G. Mera, R. Hauser, R. Klonczynski, J. Ceram. Soc. Jpn. 114 (2006) 425. [23] G. Mera, R. Riedel, Organosilicon-based polymers as precursors for ceramics, in: P. Colombo, R. Riedel, G.D. Sorarù, H.-J. Kleebe (Eds.), Polymer Derived Ceramics: From Nanostructure to Applications, DEStech Publications Inc., Lancaster, PA, USA, 2009, pp. 51–89. [24] L. Bois, J. Maquet, F. Babonneau, H. Mutin, D. Hahloul, Chem. Mater. 7 (1995) 975–981. [25] Y.D. Blum, D.B. MacQueen, H.J. Kleebe, J. Eur. Ceram. Soc. 25 (2005) 143. [26] P. Kroll, J. Mater. Chem. 20 (2010) 10528. [27] P. Kroll, J. Mater. Chem. 13 (2003) 1657. [28] P. Kroll, J. Non-Cryst. Solids 351 (2005) 1121. [29] N. Resta, C. Kohler, H.R. Trebin, J. Am. Ceram. Soc. 86 (2003) 1409. [30] R.L. Mc Greevy, L. Putszai, Mol. Simul. 1 (1988) 359. [31] R.L. McGreevy, J. Phys. Condens. Matter 13 (2001) R877. [32] H. Brequel, G.D. Soraru, L. Schiffini, S. Enzo, Mater. Sci. Forum 343–346 (2000) 677. [33] R. Atta-Fynn, P. Biswas, J. Phys. Condens. Matter 21 (2009) 265801. [34] G. Lucovsky, J.C. Phillips, Nanoscale Res. Lett. 5 (2010) 550. [35] J.P. Rino, I. Ebbsjö, P.S. Branicio, R.K. Kalia, A. Nakano, F. Shimojo, P. Vashishta, Phys. Rev. B 70 (2004) 045207. [36] C.R. Müller, V. Kathriarachchi, M. Schuch, P. Maass, V.G. Petkov, Phys. Chem. Chem. Phys. 12 (2010) 10444.
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
Letter to the Editor
Structure and topological characteristics of amorphous silicon oxycarbide networks: Results from Reverse Monte Carlo simulations Wenruo Bai a, Scarlett Widgeon b,c, Sabyasachi Sen b,⁎ a b c
Department of Physics, Peking University, Beijing 100871, China Department of Chemical Engineering and Materials Science, University of California, Davis, CA 95616, USA Peter A Rock Thermochemistry Laboratory and NEAT ORU, University of California, Davis, CA 95616, USA
a r t i c l e
i n f o
Article history: Received 3 October 2013 Received in revised form 19 November 2013 Available online 8 December 2013 Keywords: Reverse Monte Carlo simulation; Polymer-derived ceramics; Mass-fractal spatial distribution; Silicon oxycarbide
a b s t r a c t The connectivity and length scale of spatial clustering of the structural units and the resultant topological aspects of amorphous SiOC networks, characteristic of polymer derived ceramics, are studied using Reverse Monte Carlo simulation, constrained by experimental density, composition and relative concentrations of SiCxO4 − x tetrahedra. Nanoscale clustering of SiCxO4 − x structural units results from mutual avoidance in connectivity between the constituent tetrahedra and the corresponding inefficiency in packing gives rise to a mass-fractal spatial distribution of the tetrahedra with a dimensionality of ~2.5. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Silicon-based polymer derived ceramics (PDCs) in the Si–C–O, Si–C– N and Si–B–C–N systems constitute an important class of technologically promising materials for use under extreme conditions due to their high chemical, thermal, and mechanical stability at high temperatures [1–9]. Synthesis of these PDCs involves low temperature polymerization and polycondensation reactions of a preceramic polymer, followed by pyrolysis at higher temperatures. Though x-ray amorphous, these materials are characterized by complex atomic structures consisting of structurally and compositionally distinct nanodomains. Fundamental understanding of the atomic structure at various length scales is therefore critical in deciphering the structure–property relationships in these materials and ultimately in controlling their properties for specific engineering applications. The atomic structures of silicon-based PDCs have therefore been extensively investigated over the last two decades using a wide variety of spectroscopic, scattering and electron microscopic techniques [1–15]. 29Si magic-angle-spinning (MAS) NMR is one of the most commonly employed techniques that has resulted in a wealth of information regarding the speciation of the SiCxO4 − x (0 ≤ x ≤ 4) tetrahedra in the SiOC network nanodomains [10,16–19]. Typically the experimental concentrations of the SiO4 and SiC4 units in SiCO PDCs are found to be significantly higher than those expected from a statistical mixing model of Si\O and Si\C bonds [14,17]. This result, when combined with the fact that there is no significant carbon– ⁎ Corresponding author. Tel.: +1 530 754 8397; fax: +1 530 752 1031. E-mail address: [email protected] (S. Sen). 0022-3093/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jnoncrysol.2013.11.030
oxygen bonding in the structure [20], directly implies partial segregation and clustering of the oxygen-rich and carbon-rich SiCxO4 − x tetrahedral units in the SiCO network [17]. However, the degree and length scale of the spatial clustering of these structural units remain poorly known, to date. Previous structural studies of SiCO PDCs have shown that besides bonding to silicon atoms, the majority of the carbon atoms are bonded to other carbon atoms to form nanodomains of sp2-bonded “free” carbon, presumably present as turbostratic carbon or as graphene-like sheets [20–25]. Therefore, the free carbon does not take part in the SiCO network. These carbon nanodomains can be isolated clusters or they can form a continuous network in SiCO PDCs with low or high carbon content, respectively [17,18]. A recent 29Si NMR spectroscopic study of SiCO PDCs with widely different carbon contents of 14 and 53 wt.% indicated that the constituent SiCxO4 − x tetrahedral units form a tenuous network that does not fill space homogeneously and thus can be described as a mass-fractal with fractal dimensions ranging between 2.2 and 2.5 [17]. However, the origin of such fractal character of the spatial distribution of these structural units has remained unclear, although it was tentatively argued that the presence of both C and O atoms with very different coordination numbers (4 and 2, respectively) as the nearest neighbors of Si atoms may lead to a steric hindrance and frustrated packing of the “mixed bonded” SiCxO4 − x units in the SiCO network. Such frustrated packing can result in an inefficient space filling and consequently a mass-fractal character of the spatial distribution of SiCxO4 − x units. Unfortunately, the spectroscopic and diffraction techniques that are typically employed for structural studies of amorphous materials are not
LETTER TO THE EDITOR 30
W. Bai et al. / Journal of Non-Crystalline Solids 386 (2014) 29–33
capable of addressing these topological issues at the length scale of several nanometers. The structures of the SiOC network and the free carbon phase in SiOC PDCs were simulated in a number of previous studies using ab initio molecular dynamics based on density functional theory (DFT) [26–29]. These studies indicate that at or below a carbon content of 12.5 at.%, the Si\C and Si\O bonds are homogenously distributed in the SiOC network [26]. Above this critical threshold, the Si\C bonds begin to percolate and the continuity of the homogeneous SiOC network is disrupted via defect formation. The SiC4 tetrahedra interconnect by corner sharing to form chains and rings and, simultaneously, voids in the SiOC network begin to interconnect to form pores in the structure. It was suggested that, with increasing carbon concentration, the free carbon may eventually reside in these pores [26]. Although these relatively small scale (up to ~200 atoms) simulations provide important information about the local structure and packing of the SiOC network, no attempts were made to test the consistency of the speciation of tetrahedral SiCxO4 − x units in these simulated networks with those observed in 29Si NMR experiments. Moreover, due to their small size, these simulations cannot provide insight into the structural and topological aspects of the SiOC network at nanometer length scales. Here we report the results of a relatively large scale (2756 atoms) Reverse Monte Carlo (RMC) simulation of a SiOC network constrained by experimentally determined density, composition and relative concentrations of SiCxO4 − x structural units. Such simulations are shown to provide important information regarding the degree and length scale of the spatial clustering of the SiCxO4 − x structural units and the resultant topological aspects of the amorphous SiOC network at nanometer length scale.
3. Results and discussion The average coordination numbers of the silicon, carbon, and oxygen atoms and the relative fractions of the various SiCxO4 − x structural units in the final optimized structure generated by the RMC simulation are compared in Fig. 1 with the corresponding values used as constraints. The results show that the coordination numbers of silicon, carbon, and oxygen atoms in the simulated structure are within ~0.1 of their nominal values and the agreement between experiment and simulation with regards to the relative fractions of the SiCxO4 − x structural units is within 1%. The radial distribution function (RDF) of the simulated SiCO network is shown in Fig. 2(a). The main peak positions in the RDF corresponding to the interatomic distances of the simulated structure compare well with those observed experimentally in previous studies [32]. The most intense peak at ~1.63 Å corresponds to the Si\O nearest neighbor distance, while a small peak near 1.95 Å is associated with the Si\C bond length. The peak centered at ~2.5 Å contains predominant contributions from intra-tetrahedral O–O correlations. The peak at ~ 3.0 Å corresponds to the distance between two Si atoms in the adjacent SiCxO4 − x tetrahedral units. The average Si\O\Si and Si\C\Si inter-tetrahedral
2. Simulation methodology The RMC simulations were performed on a cubic cell with a dimension of 3.35 nm, using periodic boundary conditions and the RMCA code [30,31]. A polysiloxane-derived SiOC PDC of composition SiO1.50C0.68 was chosen as the model system. Detailed structural studies of this PDC, based on 29Si and 13C NMR spectroscopy, were previously reported in the literature [17]. These studies indicated a chemical composition of SiO1.51C0.244 for the SiOC network in this PDC, implying that nearly 65% of the C atoms are in the free carbon phase [17]. Accordingly, the simulation cell in the present study contained 1000 Si, 1512 O and 244 C atoms to mimic the chemical composition of the SiOC network. The dimension of the simulation cell for the SiOC network of this PDC was chosen to correspond to a mass density of ~2.4 g cm−3, similar to the previously reported experimentally measured density of 2.4 ± 0.1 g cm−3 for a SiOC network of similar chemical composition (SiO1.49C0.30) [32]. It may be noted that the structural attributes that are of primary interest in the present study namely, the nature of intermediate range order, topology and clustering length scale of the SiOC network, are not expected to change in any significant way with small variations in density. The average nearest neighbor Si\O and Si\C distances were constrained to 1.63 and 1.93 Å, respectively, consistent with previously published diffraction and ab initio molecular dynamics simulation results for SiOC PDCs [27,32–34]. The coordination numbers of Si, C and O atoms were constrained to their experimental values of 4, 4 and 2, respectively, and no C\C or C\O bonding was allowed. Finally, the relative fractions of SiO4, SiO3C, SiO2C2, SiO3C and SiC4 species were constrained to their experimental values of 44.0, 30.4, 16.1, 3.0 and 6.5%, respectively, in the SiOC network of this PDC, as determined in a previous study using 29Si magic angle spinning (MAS) NMR spectroscopy [17]. The RMC structure was generated following two steps. First, the three dimensional configuration of the system was obtained on the basis of the nearest-neighbor bond lengths and coordination numbers as noted above and each coordination constraint was met by 95–99%. Then, using these initial atomic configurations RMC simulations were run for 107 steps in order to meet the constraint of the relative concentrations of various species by ≥98%.
Fig. 1. (a) Comparison between the relative fractions of the SiCxO4 − x tetrahedra in the SiOC network, determined experimentally by NMR (shown in red) and those in the structure generated by RMC simulation (shown in blue). (b) Average coordination numbers of silicon, carbon, and oxygen atoms in the RMC-simulated SiCO network and their nominal values of 4, 4 and 2, respectively.
LETTER TO THE EDITOR W. Bai et al. / Journal of Non-Crystalline Solids 386 (2014) 29–33
Fig. 2. (a) Radial distribution function of the simulated SiCO network (lower curve). Experimentally obtained radial distribution function of a SiOC network of similar composition, as reported in [32] is shown for comparison (upper curve). Curves are vertically offset for clarity. (b) Views of the simulated SiOC network along the normals to the six faces of the cubic simulation box. Si, O and C atoms are shown in red, green and blue, respectively.
31
bond angles are ~140° and 110°, respectively, consistent with previous reports of these bond angles in amorphous SiO2 and SiC [32,35]. The views of the RMC simulated SiOC network along the normals to the six faces of the cubic simulation box are shown in Fig. 2(b). These views of the network directly demonstrate that the carbon atoms in the network are not homogenously distributed throughout the structure and nanoscale percolating clusters of C-rich and O-rich SiCxO4 − x structural units exist in the network that span the entire simulation box. A semi-quantitative measure of the degree of such clustering can be obtained by comparing the relative fractions of the nearest neighbor SiO4 and SiC4 units for any central SiCxO4 − x unit (Fig. 3(a)). These results show that for SiO4 units, 63% of the nearest neighbors are other SiO4 units, while for SiC4 units, 27% of its nearest neighbors are other SiC4 units. In contrast, a purely random distribution of SiCxO4 − x units, in combination with the impossibility of any connection between SiO4 and SiC4 units, would imply relative fractions of 47.0 (12)% of nearest neighbors around central SiO4 (SiC4) units to be other SiO4 (SiC4) units. Therefore, the RMC-simulated SiOC network shows significant spatial clustering of SiO4 and SiC4 tetrahedra in the structure. This structural heterogeneity is also clear from an inspection of Fig. 3(b) where local regions of high concentrations of the SiO4 and SiC4 tetrahedra in the simulated SiOC network are shown. Typical length scales of these clusters are on the order of ~ 1 nm. This result is clearly indicative of the mutual avoidance in connectivity and frustrated packing of SiCx O4 − x tetrahedra. It may be noted here that the nature of the spatial clustering of SiO4 and SiC4 tetrahedra observed in the present simulations is quite different from a structural model of SiCO PDCs proposed in a previous study where a complete segregation of SiO4 units into SiO2 -like nano-domains was hypothesized [13]. The mixed-bonded SiCxO4 − x tetrahedra in this segregated model were assumed to form interfacial layers that connected the SiO 2 nanodomains to the free carbon phase. The avoidance in connectivity between certain SiCxO4 − x structural units, as observed in the present study, must stem from the bonding related steric constraints associated with the mixing of the tetrahedrally coordinated C atoms and 2-fold coordinated O atoms in the nearestneighbor shell of the tetrahedrally coordinated Si atoms and from the avoidance of carbon–oxygen bonding. Such spatial constraints may result into poor efficiency in the packing and consequently in the space filling ability of the SiCxO4 − x tetrahedral units that was recently hypothesized to be the reason behind mass fractal nature of SiOC networks. This hypothesis is tested in this study by calculating the scaling of the number of Si atoms (i.e. mass), enclosed within a sphere of observation, with the radius R of the sphere. Averages of ten sets of such measurements are shown in Fig. 4 where the centers of each set of spheres were randomly chosen points within the simulation cell. The double logarithmic plot of the number of Si atoms M vs. R displays a power law with exponent of ~ 2.5 (i.e. M ~ R2.5) up to R = 1 nm beyond which the dimensionality of mass distribution of Si atoms returns to 3 (i.e. M ~ R3). The fractal dimension of ~2.5 for distances below 1 nm is in excellent agreement with previous reports on experimental measurements of this quantity in SiOC networks in PDCs [17]. Such a fractal network is expected to give rise to unusual mechanical and transport properties as well as contain voids that may nest the free carbon phase in PDCs [26,27]. Finally, it should be noted that the RMC-simulated structural model proposed in this study is based simply on density, simple coordination and connectivity rules between SiCxO4 − x tetrahedral units whose relative fractions are directly obtained from 29Si NMR spectroscopy. The procedure results in a structural model that agrees reasonably well with diffraction results that serve as a check for internal selfconsistency. However, recent studies have indicated that the nature of intermediate range order in disordered structures may not be uniquely captured in pure RMC simulations [36]. Future studies using a combination of RMC with simultaneous energy minimization based on empirical potentials will be important in addressing this issue. Furthermore,
LETTER TO THE EDITOR 32
W. Bai et al. / Journal of Non-Crystalline Solids 386 (2014) 29–33
Fig. 3. (a) Relative fractions of the nearest neighbor SiO4 (blue) and SiC4 (red) tetrahedra for any central SiCxO4 − x unit in the SiOC network. (b) Spatial distribution of the Si atoms for the SiO4 (a) and SiC4 (b) tetrahedra in the simulation cell. Blue curved lines enclose areas where clustering is observed.
incorporation of the free carbon phase in future simulations will lead to a more complete picture of the intermediate-range structural and topological aspects of the structure of these PDCs. 4. Summary The structure of an RMC-simulated SiOC network clearly demonstrates the presence of clustering of SiCxO4 − x structural units at length scales on the order of ~1 nm resulting from mutual avoidance in connectivity and frustrated packing of SiCxO4 − x tetrahedral units. This lack in the space filling ability of the SiCxO4 − x tetrahedral units is due to the coexistence of C and O with very different coordination numbers (4 and 2, respectively) as nearest neighbors of the Si atoms. It is manifested in a fractal spatial distribution of Si atoms in the network with a mass-fractal dimension of ~2.5, over nanometer length scales. Acknowledgments Fig. 4. Double-logarithmic plot of the number (or mass) of Si atoms enclosed within a sphere of observation, as a function of the radius R of the sphere. Solid straight line represents a linear least squares fit through the data points for R ≤ 1 nm (Ln R ≤ 2.3). Note different scaling behavior of the data above and below ~1 nm.
This study was funded by a grant from the National Science Foundation (NSF MWN-0906070). WB acknowledges funding from the Global Research Experience in Advanced Technologies (GREAT) Program at UC Davis. We also gratefully acknowledge many stimulating discussions
LETTER TO THE EDITOR W. Bai et al. / Journal of Non-Crystalline Solids 386 (2014) 29–33
on this subject with Dr. Gabriela Mera and Profs. Alexandra Navrotsky, Ralf Riedel and Roland Faller. References [1] G.D. Soraru, G. D'Andrea, R. Campostrini, F. Babonneau, G. Mariotto, J. Am. Ceram. Soc. 78 (1995) 379. [2] H.J. Kleebe, C. Turquat, G.C. Soraru, J. Am. Ceram. Soc. 84 (2001) 73–80. [3] G. Gregori, C. Turquat, H.J. Kleebe, G.D. Soraru, Key Eng. Mater. 206–213 (2002) 2061. [4] H. Brequel, J. Parmentier, S. Walter, R. Badheka, G. Trimmel, S. Masse, J. Latournerie, P. Dempsey, C. Turquat, A. Desmartin-Chomel, L. Le Neindre-Prum, U.A. Jayasooriya, D. Hourlier, H.J. Kleebe, G.D. Soraru, S. Enzo, F. Babonneau, Chem. Mater. 16 (2004) 2585. [5] C. Turquat, H.J. Kleebe, G. Gregori, S. Walter, G.D. Soraru, J. Am. Ceram. Soc. 84 (2001) 2189. [6] H.J. Kleebe, Y.D. Blum, J. Eur. Ceram. Soc. 28 (2008) 1037. [7] G. Trimmel, B. Rita, F. Babonneau, J. Latournerie, P. Dempsey, D. Bahloul-Houlier, J. Parmentier, G.D. Soraru, J. Sol–Gel Sci. Technol. 26 (2003) 279. [8] Y. Iwamoto, W. Volger, E. Kroke, R. Riedel, T. Saitou, K. Matsunaga, J. Am. Ceram. Soc. 84 (2001) 2170. [9] G. Mera, R. Riedel, F. Poli, K. Muller, J. Eur. Ceram. Soc. 29 (2009) 2873. [10] L. Bois, J. Maquet, F. Babonneau, H. Mutin, D. Hahloul, Chem. Mater. 6 (1994) 796. [11] A. Saha, R. Raj, D.L. Williamson, H.J. Kleebe, J. Am. Ceram. Soc. 88 (2005) 232. [12] J. Schuhmacher, M. Weinmann, J. Bill, F. Aldinger, K. Müller, Chem. Mater. 10 (1998) 3913. [13] A. Saha, R. Raj, D.L. Williamson, J. Am. Ceram. Soc. 89 (2006) 2188. [14] R.J.P. Corriu, D. Leclerco, P.H. Mutin, A. Vioux, J. Mater. Sci. 30 (1995) 2313. [15] Y.L. Li, E. Kroke, R. Riedel, C. Fasel, C. Gervais, F. Babonneau, Appl. Organomet. Chem. 15 (2001) 820.
33
[16] H. Zhang, C.G. Pantano, J. Am. Ceram. Soc. 73 (1990) 958. [17] S. Widgeon, S. Sen, G. Mera, E. Ionescu, R. Riedel, A. Navrotsky, Chem. Mater. 22 (2010) 6221. [18] S. Widgeon, G. Mera, Y. Gao, E. Stanoyov, S. Sen, A. Navrotsky, R. Riedel, Chem. Mater. 24 (2012) 1181. [19] J. Schuhmacher, F. Berger, M. Weinmann, J. Bill, F. Aldinger, K. Müller, Appl. Organomet. Chem. 15 (2001) 809. [20] C.G. Pantano, A.T. Singh, H. Zhang, J. Sol–Gel Sci. Technol. 14 (1999) 7. [21] P. Colombo, G. Mera, R. Riedel, G.D. Sorarú, J. Am. Ceram. Soc. 93 (2010) 1805. [22] R. Riedel, G. Mera, R. Hauser, R. Klonczynski, J. Ceram. Soc. Jpn. 114 (2006) 425. [23] G. Mera, R. Riedel, Organosilicon-based polymers as precursors for ceramics, in: P. Colombo, R. Riedel, G.D. Sorarù, H.-J. Kleebe (Eds.), Polymer Derived Ceramics: From Nanostructure to Applications, DEStech Publications Inc., Lancaster, PA, USA, 2009, pp. 51–89. [24] L. Bois, J. Maquet, F. Babonneau, H. Mutin, D. Hahloul, Chem. Mater. 7 (1995) 975–981. [25] Y.D. Blum, D.B. MacQueen, H.J. Kleebe, J. Eur. Ceram. Soc. 25 (2005) 143. [26] P. Kroll, J. Mater. Chem. 20 (2010) 10528. [27] P. Kroll, J. Mater. Chem. 13 (2003) 1657. [28] P. Kroll, J. Non-Cryst. Solids 351 (2005) 1121. [29] N. Resta, C. Kohler, H.R. Trebin, J. Am. Ceram. Soc. 86 (2003) 1409. [30] R.L. Mc Greevy, L. Putszai, Mol. Simul. 1 (1988) 359. [31] R.L. McGreevy, J. Phys. Condens. Matter 13 (2001) R877. [32] H. Brequel, G.D. Soraru, L. Schiffini, S. Enzo, Mater. Sci. Forum 343–346 (2000) 677. [33] R. Atta-Fynn, P. Biswas, J. Phys. Condens. Matter 21 (2009) 265801. [34] G. Lucovsky, J.C. Phillips, Nanoscale Res. Lett. 5 (2010) 550. [35] J.P. Rino, I. Ebbsjö, P.S. Branicio, R.K. Kalia, A. Nakano, F. Shimojo, P. Vashishta, Phys. Rev. B 70 (2004) 045207. [36] C.R. Müller, V. Kathriarachchi, M. Schuch, P. Maass, V.G. Petkov, Phys. Chem. Chem. Phys. 12 (2010) 10444.