- Email: [email protected]
Magic numbers and a growth pathway of high-nuclearity titanium carbide clusters
Solid State Communications 124 (2002) 253–256 www.elsevier.com/locate/ssc
Magic numbers and a growth pathway of high-nuclearity titanium carbide clusters Jijun Zhaoa,*, Bingchen Liub,c, Huajin Zhaib,c, Rufang Zhoub,c, Guoquan Nib,c, Zhizhan Xub a
Department of Physics and Astronomy, University of North Carolina at Chapel Hill, CB 3255, Chapel Hill, NC 27599, USA b Laboratory for High Intensity Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, People’s Republic of China c Laboratory for Quantum Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, People’s Republic of China Received 19 July 2002; accepted 13 September 2002 by H. Akai
Abstract Titanium carbide anionic clusters have been generated and analyzed by time-of-flight mass spectrometry. Our experiments 2 2 successfully reproduced all the reported magic numbers in the lower mass range (, 1200 amu), i.e. Ti3C2 8 , Ti6C13, Ti7C13, 2 2 2 Ti9C15, Ti13C22, and Ti14C24 [Phys. Rev. Lett. 78 (1997) 2983; J. Am. Chem. Soc. 120 (1998) 6556]. In the higher mass range 2 2 2 up to 1800 amu, new magic numbers at Ti15C2 26, Ti20C33/Ti20C34, and Ti25C42 are found, which cannot be understood by any of the previously proposed structural growth models. A staggered layer-by-layer growth pathway based on Ti5C8 subunits is introduced. Density functional calculations show high stabilities of the constructed structures. q 2002 Elsevier Science Ltd. All rights reserved. PACS: 36.40.Mr; 33.15.Ta; 61.46.þ w Keywords: A. Nanostructures; B. Laser processing; D. Crystal binding and equation of state
Following the discovery of carbon fullerenes, metallocarbohedrenes (met-cars) were reported and the related transition metal carbide clusters have received considerable attention [1 – 16]. In early laser vaporization experiments, cationic met-cars with stoichiometry M8C12 (M ¼ Ti, V, Zr, Hf, Nb, Cr, Fe, Mo, etc.) were found to be exceptionally abundant in the mass spectra [1– 4]. The identification of the structure of met-cars has stimulated considerable experimental and theoretical investigations [5,6]. A pentagonal dodecahedral cage structure with Th symmetry was initially proposed by Castleman’s group [1], while most subsequent ab initio calculations and experiments suggest a tetracapped tetrahedron (Td symmetry) as the lowest-energy structures of M8C12 [6 – 9]. In addition to the cage-like structures of * Corresponding author. Tel.: þ1-919-962-1386; fax: þ 1-919962-0480. E-mail address: [email protected] (J. Zhao).
M8C12, the cubic nanocrystal structure was also revealed for þ transition metal carbide clusters such as Ti14Cþ 13, V14C13 [11], NbmCþ [12], Nb C [4] and Ta C [14]. It was shown n m n m n that the formation of met-cars cages or crystal-like structures critically depend on the relative compositions of metal and carbon atoms [4,13]. Beyond M8C12, the growth pathway of high-nuclearity transition metal carbide clusters has only been studied by few experiments. A multicage structural pattern including double-, triple-, and quadruple-cage was proposed to interpret the mass spectrometric data of ZrmCn with m– n stoichiometry as 13 – 22/14– 23, 18– 29, 22 – 35 [10,14]. Further evidence for the quintuple-cage at M26C41 is still needed in the mass spectrum to verify this multicage growth mechanism. For titanium carbide anionic clusters, Wang et al. have observed new magic-numbered clusters and abundant Ti13C2 22 and put forward a novel layer-by-layer cubic growth pathway as an alternative to the multicage one
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Fig. 1. (a) A typical TixC2 y mass spectrum in the lower mass range (up to 1200 amu); (b) a typical TixC2 y mass spectrum in the higher mass range (900– 1800 amu). New magic numbers at 15–26, 20 – 33/20–34, and 25–42 are observed.
[15,16]. Based on a D4h cubic architecture with eight C2 dimers at the corners of a Ti13C14 cube, an ABA three-layer structure is constructed for Ti13C22. Wang et al. further stated that this novel cubic-layered growth mechanism can also account for all the magic numbers previously assigned to the multicages [10,14]. As a consequence, magic clusters 2 at Ti18C2 26 and Ti22C35 associated with ABAB and ABABA multi-layer structures would be expected. Unfortunately, these high-nuclearity clusters are out of the detectable range of Wang’s mass spectrum for TixC2 y [15,16]. To further explore the magic numbers and growth pathway of highnuclearity titanium carbide clusters, in this work we present carbon atom resolved mass spectra of TixC2 y cluster anions up to Ti25C2 42. A staggered layer-by-layer structural model based on Ti5C8 subunits is proposed. The detailed description of our experimental apparatus can be found elsewhere [17]. Briefly, a Smalley-type laser vaporization/molecular beam cluster source is used, similar to that in Wang’s study [15,16]. Instead of a pure titanium target rod and helium carrier gas containing 5% CH4 (10 atm stagnation pressure) in Refs. [15,16], we use a Ti –C mixture target rod (10:1 molar Ti to C ratio) produced under ultra-high pressure molding of Ti and C mixed powders and pure helium carrier gas (10 atm). The target is vaporized with a , 30 mJ laser pulse from a Nd:YAG laser (532 nm).
The cluster anions are analyzed by a Wiley – McLaren timeof-flight (TOF) mass spectrometer driven with a high voltage negative pulse generator (EG&G PARC Model 1211). The signal from a DMCP detector is directly fed to a LeCroy 9350AL digital oscilloscope (500 MHz bandwidth, 1 GHz sampling rate). A typical mass spectrum is obtained by averaging about 300 shots. The obtained TixC2 y cluster spectra are shown in Fig. 1. Different X-deflection voltages are used to examine the abundance distribution of the clusters anions in lower and higher mass ranges. Comparison with the TixC2 y spectra reported by Wang et al. [15,16] shows remarkably strong similarity. All the magic numbers reported in Refs. [15,16], 2 2 2 2 2 i.e. Ti3C2 8 , Ti6C13, Ti7C13, Ti9C15, Ti13C22, and Ti14C24, are well reproduced. Such a coincidence demonstrates an inherent origin of the formation of TixC2 y cluster anions, since the two studies have been conducted independently under quite different experimental conditions. Because of the consistence of the mass for one Ti atom and four carbon atoms, the assignment of the exact cluster compositions was ascertained using 13CH4 isotope substitution in Refs. [15,16]. The perfect resemblance of the mass spectra peaks in the present work and Refs. [15,16] strongly supports the assignment made in Fig. 1(a). The appearance 2 of C2 60 and C50 peaks in Fig. 1(a) indicates a carbon-rich environment in the cluster formation process. The prominent C2 60 peak provides a solid mass calibration that carbon atoms are resolved in the spectra in Fig. 1(a). The peak located at the position of 74 carbon atoms is certainly assigned to Ti13C2 22 not only by comparing with the peaked Ti13C2 22 in Refs. [15,16], but also with the data of Zr13C22 [10,14], and Nb13C22 [4]. Beyond Ti13C2 22 there are three peaks with uniform increment by a TiC2 unit [15,16], 2 implying that the assignment of the Ti14C2 24, Ti15C26, and 2 Ti16C28 in Fig. 1(b) is correct. Very importantly, it should be noted that in all the metal carbide clusters studied, it is common and unexceptional features that the series of bunches each composed of several peaks correspond to a progressional increment of metal atoms. For example, the numbers of metal atoms increase progressionally from 5 to 22 [10] and from 2 to 14 [14] in the ZrmCn series, from 11 to 50 in the TamCn [10], and from 3 to 21 in the NbmC2 n [4], respectively. Based on the above considerations, assignment of the mass spectrum beyond Ti13C2 22 can be completed as shown in Fig. 1(b). After the known magic peaks at Ti13C2 22 and Ti14C2 24, new magic numbers for high-nuclearity titanium carbide clusters are determined as Ti15C2 26 , 2 2 Ti20C2 33/Ti20C34, and Ti25C42. These magic numbers within the mass range of 1000– 1800 amu have never been reported by other investigators. The cubic-layered structures suggested by Wang et al. [15, 16] are obviously insufficient to explain the new magic numbers found for high-nuclearity clusters. The magic numbers at 18–26 and 22–35 predicted by Wang’s model for the high-nuclearity TixC2 y are not magic at all in the present experiments. The observed magic numbers at 20–33/20–34
J. Zhao et al. / Solid State Communications 124 (2002) 253–256
255
Fig. 2. Ti5C8 structural unit for constructing the high-nuclearity TixC2 y clusters. Larger balls: C; smaller balls: Ti.
and 25 – 42 are far away from the predictions by either the cubic-layered model (18 – 26 and 22 – 35) [15,16] or the multicage model (18 –29, 22 – 35, and 26 –41) [10,14]. It is worthy to be noted that the magic TixCy clusters with x – y stoichiometry as 15 –26, 20 –34, 25– 42 can be rewritten as (Ti5C10)(Ti5C8)m with m ¼ 2 – 4. Each magic clusters, 2 2 Ti15C2 26, Ti20C34, and Ti25C42 differ by the same Ti5C8 subunits. Based on the above observation, we propose a staggered layer-by-layer growth pattern on the basis of Ti5C8 subunit to interpret the magic-numbered clusters 2 2 2 Ti15C2 26, Ti20C33/Ti20C34, and Ti25C42. The essential Ti5C8 building block in our structural model is illustrated in Fig. 2. It can be viewed as one central Ti atom added on the top of a Ti4C8 quadrangular ring. In the Ti4C8 quadrangle, each Ti atom constitutes one side and links with two perpendicular C2 dimers on the corners. The growth of high-nuclearity magic TixCy (15 – 26, 20 – 34, 25 – 42) clusters can be realized by staggered layer-by-layer packing of the Ti5C8 subunits (see Fig. 3 for a fully relaxed Ti25C42). The Ti5C8 is added on the top of the original clusters in a staggered way that the four side Ti atoms can sit on the top of the C2 dimers in the neighboring layer. In these structures, the central Ti atoms are shared by two neighboring Ti4C8 quadrangles and serve as interlinks between them. On the bottom of the structural model, there is a Ti5C10 unit (or Ti5C9 in the case of Ti20C33), which can be obtained by adding an extra C2 dimer on the Ti5C8. Different from Wang’s model, the carbon atoms always exist in form of C2 and there is no carbon atom in the central strand of the clusters. Based on the staggered layer-by-layer packing of Ti5C8 building blocks, we construct the possible configurations for 2 all the magic-numbered clusters, Ti15C2 26, Ti20C34, and 2 Ti25C42. Full geometry optimizations are then performed by using a CASTEP package [18] based on density functional theory and plane-wave pseudopotential technique. The ion – electron interactions are modeled by ultrasoft non-local pseudopotential [19]. The density functional is treated by generalized gradient approximation (GGA) with exchangecorrelation potential parameterized by Perdew and Wang [20]. The energy cutoff of plane-wave basis is chosen as
Fig. 3. Equilibrium structures of Ti25C42. Larger balls: C; smaller balls: Ti.
250 eV. The clusters are placed in a tetragonal supercell with a sufficient large cell length on each direction. As an example, the optimized structure for the Ti25C42 clusters is shown in Fig. 3. We find that all these constructed structures are stable upon relaxation. At GGA level, the total binding energy obtained for Ti15C26, Ti20C34, and Ti25C42 clusters are 320.31, 426.49, and 528.52 eV, respectively. With one more Ti5C8 subunit, the total binding energy of clusters increase by 106.18 eV (from Ti15C26 to Ti20C34) or 102.03 eV (from Ti20C34 to Ti25C42), significantly larger than the binding energy 93.52 eV of an optimized individual Ti5C8 cluster. The energy difference indicates that extra binding energy of ,10 eV could be gained from each staggered layer-by-layer packing of Ti5C8 subunit. The average binding energies of these highnuclearity magic clusters (7.81–7.9 eV per atom) are close to those of Ti8C12 (Td symmetry, 7.87 eV/atom) and Ti13C22 (structure in Refs. [15,16], 7.95 eV/atom). Thus, these highnuclearity clusters should have high stabilities that are comparable to the known magic-numbered clusters (Ti8C12, Ti13C22). Similar to the layered growth model suggested by Wang et al. our model also implies possible one-dimensional nanowires based on layer-by-layer staggered packing of
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Ti5C8 subunits. Following this growth pathway, the successive magic-numbered clusters are predicted to be 2 2 Ti30C2 50, Ti35C58, and Ti40C66, etc. In summary, we have generated titanium carbide anionic clusters with a mass range up to 1800 amu in a Smalley-type cluster source and recorded their TOF mass spectra. For the lower mass range up to 1200 amu, our mass spectrum reproduces all the magic numbers reported by Wang et al. [15,16] in spite of differences in experimental conditions. For the higher mass range (1200– 1800 amu), we observe 2 2 new magic clusters as Ti15C2 26, Ti20C33/Ti20C34, and 2 Ti25C42, which cannot be accounted for by any previously proposed structural growth patterns (layered, multicage, and nanocrystal). A layer-by-layer growth pathway based on staggered packing of Ti5C8 subunits can successfully interpret these new magic numbers. Density functional calculations reproduce the high stabilities for the proposed configurations. The prediction of larger titanium carbide 2 2 magic-numbered clusters, i.e. Ti30C2 50, Ti35C58, and Ti40C66, etc. is still waiting future experimental validation.
Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 29890210) and the 973 National Science and Technology Major Development Program for Basic Research.
References [1] B.C. Guo, K.P. Kerns, A.W. Castleman Jr, Science 255 (1992) 1411–1413.
[2] B.C. Guo, S. Wei, J. Purnell, S.A. Buzza, A.W. Castleman Jr, Science 256 (1992) 515–516. [3] J.S. Pilgrim, M.A. Duncan, J. Am. Chem. Soc. 115 (1993) 6958–6961. [4] S. Wei, B.C. Guo, H.T. Deng, K. Kerns, J. Purnell, S.A. Buzza, A.W. Castleman Jr, J. Am. Chem. Soc. 116 (1994) 4475–4476. [5] A.W. Castleman Jr, K.H. Bowen Jr, J. Phys. Chem. 100 (1996) 12911–12944. and references therein. [6] M.M. Rohmer, M. Benard, J.M. Poblet, Chem. Rev. 100 (2000) 495 –542. and references therein. [7] I. Dance, J. Am. Chem. Soc. 118 (1996) 6309–6310. [8] M.M. Rohmer, M. Benard, C. Bo, J.M. Poblet, J. Am. Chem. Soc. 117 (1995) 508– 517. [9] H. Sakurai, A.W. Castleman Jr, J. Phys. Chem. 102 (1998) 10486–10492. [10] S. Wei, B.C. Guo, J. Purnell, S. Buzza, A.W. Castleman Jr, Science 256 (1992) 818–820. [11] J.S. Pilgrim, M.A. Ducan, J. Am. Chem. Soc. 115 (1993) 9724–9727. [12] J.S. Pilgrim, L.R. Brock, M.A. Ducan, J. Phys. Chem. 99 (1995) 544 –550. [13] B.V. Reddy, S.N. Khanna, Chem. Phys. Lett. 209 (1993) 104 –108. [14] S. Wei, A.W. Castleman Jr, Chem. Phys. Lett. 227 (1994) 305 –311. [15] L.S. Wang, H. Cheng, Phys. Rev. Lett. 78 (1997) 2983–2986. [16] L.S. Wang, X.B. Wang, J. Am. Chem. Soc. 120 (1998) 6556–6562. [17] H.J. Zhai, B.C. Liu, R.F. Zhou, G.Q. Ni, Z.Z. Xu, Chin. Phys. Lett. 17 (2000) 197–200. [18] CASTEP is a density functional theory package with planewave pseudopotential method distributed by Accelrys Inc.V. Milman, B. Winkler, J.A. White, C.J. Pickard, M.C. Payne, E.V. Akhmatskaya, R.H. Nobes, Int. J. Quant. Chem. 77 (2000) 895 –910. [19] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892–7895. [20] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244–13249.
Magic numbers and a growth pathway of high-nuclearity titanium carbide clusters Jijun Zhaoa,*, Bingchen Liub,c, Huajin Zhaib,c, Rufang Zhoub,c, Guoquan Nib,c, Zhizhan Xub a
Department of Physics and Astronomy, University of North Carolina at Chapel Hill, CB 3255, Chapel Hill, NC 27599, USA b Laboratory for High Intensity Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, People’s Republic of China c Laboratory for Quantum Optics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, People’s Republic of China Received 19 July 2002; accepted 13 September 2002 by H. Akai
Abstract Titanium carbide anionic clusters have been generated and analyzed by time-of-flight mass spectrometry. Our experiments 2 2 successfully reproduced all the reported magic numbers in the lower mass range (, 1200 amu), i.e. Ti3C2 8 , Ti6C13, Ti7C13, 2 2 2 Ti9C15, Ti13C22, and Ti14C24 [Phys. Rev. Lett. 78 (1997) 2983; J. Am. Chem. Soc. 120 (1998) 6556]. In the higher mass range 2 2 2 up to 1800 amu, new magic numbers at Ti15C2 26, Ti20C33/Ti20C34, and Ti25C42 are found, which cannot be understood by any of the previously proposed structural growth models. A staggered layer-by-layer growth pathway based on Ti5C8 subunits is introduced. Density functional calculations show high stabilities of the constructed structures. q 2002 Elsevier Science Ltd. All rights reserved. PACS: 36.40.Mr; 33.15.Ta; 61.46.þ w Keywords: A. Nanostructures; B. Laser processing; D. Crystal binding and equation of state
Following the discovery of carbon fullerenes, metallocarbohedrenes (met-cars) were reported and the related transition metal carbide clusters have received considerable attention [1 – 16]. In early laser vaporization experiments, cationic met-cars with stoichiometry M8C12 (M ¼ Ti, V, Zr, Hf, Nb, Cr, Fe, Mo, etc.) were found to be exceptionally abundant in the mass spectra [1– 4]. The identification of the structure of met-cars has stimulated considerable experimental and theoretical investigations [5,6]. A pentagonal dodecahedral cage structure with Th symmetry was initially proposed by Castleman’s group [1], while most subsequent ab initio calculations and experiments suggest a tetracapped tetrahedron (Td symmetry) as the lowest-energy structures of M8C12 [6 – 9]. In addition to the cage-like structures of * Corresponding author. Tel.: þ1-919-962-1386; fax: þ 1-919962-0480. E-mail address: [email protected] (J. Zhao).
M8C12, the cubic nanocrystal structure was also revealed for þ transition metal carbide clusters such as Ti14Cþ 13, V14C13 [11], NbmCþ [12], Nb C [4] and Ta C [14]. It was shown n m n m n that the formation of met-cars cages or crystal-like structures critically depend on the relative compositions of metal and carbon atoms [4,13]. Beyond M8C12, the growth pathway of high-nuclearity transition metal carbide clusters has only been studied by few experiments. A multicage structural pattern including double-, triple-, and quadruple-cage was proposed to interpret the mass spectrometric data of ZrmCn with m– n stoichiometry as 13 – 22/14– 23, 18– 29, 22 – 35 [10,14]. Further evidence for the quintuple-cage at M26C41 is still needed in the mass spectrum to verify this multicage growth mechanism. For titanium carbide anionic clusters, Wang et al. have observed new magic-numbered clusters and abundant Ti13C2 22 and put forward a novel layer-by-layer cubic growth pathway as an alternative to the multicage one
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Fig. 1. (a) A typical TixC2 y mass spectrum in the lower mass range (up to 1200 amu); (b) a typical TixC2 y mass spectrum in the higher mass range (900– 1800 amu). New magic numbers at 15–26, 20 – 33/20–34, and 25–42 are observed.
[15,16]. Based on a D4h cubic architecture with eight C2 dimers at the corners of a Ti13C14 cube, an ABA three-layer structure is constructed for Ti13C22. Wang et al. further stated that this novel cubic-layered growth mechanism can also account for all the magic numbers previously assigned to the multicages [10,14]. As a consequence, magic clusters 2 at Ti18C2 26 and Ti22C35 associated with ABAB and ABABA multi-layer structures would be expected. Unfortunately, these high-nuclearity clusters are out of the detectable range of Wang’s mass spectrum for TixC2 y [15,16]. To further explore the magic numbers and growth pathway of highnuclearity titanium carbide clusters, in this work we present carbon atom resolved mass spectra of TixC2 y cluster anions up to Ti25C2 42. A staggered layer-by-layer structural model based on Ti5C8 subunits is proposed. The detailed description of our experimental apparatus can be found elsewhere [17]. Briefly, a Smalley-type laser vaporization/molecular beam cluster source is used, similar to that in Wang’s study [15,16]. Instead of a pure titanium target rod and helium carrier gas containing 5% CH4 (10 atm stagnation pressure) in Refs. [15,16], we use a Ti –C mixture target rod (10:1 molar Ti to C ratio) produced under ultra-high pressure molding of Ti and C mixed powders and pure helium carrier gas (10 atm). The target is vaporized with a , 30 mJ laser pulse from a Nd:YAG laser (532 nm).
The cluster anions are analyzed by a Wiley – McLaren timeof-flight (TOF) mass spectrometer driven with a high voltage negative pulse generator (EG&G PARC Model 1211). The signal from a DMCP detector is directly fed to a LeCroy 9350AL digital oscilloscope (500 MHz bandwidth, 1 GHz sampling rate). A typical mass spectrum is obtained by averaging about 300 shots. The obtained TixC2 y cluster spectra are shown in Fig. 1. Different X-deflection voltages are used to examine the abundance distribution of the clusters anions in lower and higher mass ranges. Comparison with the TixC2 y spectra reported by Wang et al. [15,16] shows remarkably strong similarity. All the magic numbers reported in Refs. [15,16], 2 2 2 2 2 i.e. Ti3C2 8 , Ti6C13, Ti7C13, Ti9C15, Ti13C22, and Ti14C24, are well reproduced. Such a coincidence demonstrates an inherent origin of the formation of TixC2 y cluster anions, since the two studies have been conducted independently under quite different experimental conditions. Because of the consistence of the mass for one Ti atom and four carbon atoms, the assignment of the exact cluster compositions was ascertained using 13CH4 isotope substitution in Refs. [15,16]. The perfect resemblance of the mass spectra peaks in the present work and Refs. [15,16] strongly supports the assignment made in Fig. 1(a). The appearance 2 of C2 60 and C50 peaks in Fig. 1(a) indicates a carbon-rich environment in the cluster formation process. The prominent C2 60 peak provides a solid mass calibration that carbon atoms are resolved in the spectra in Fig. 1(a). The peak located at the position of 74 carbon atoms is certainly assigned to Ti13C2 22 not only by comparing with the peaked Ti13C2 22 in Refs. [15,16], but also with the data of Zr13C22 [10,14], and Nb13C22 [4]. Beyond Ti13C2 22 there are three peaks with uniform increment by a TiC2 unit [15,16], 2 implying that the assignment of the Ti14C2 24, Ti15C26, and 2 Ti16C28 in Fig. 1(b) is correct. Very importantly, it should be noted that in all the metal carbide clusters studied, it is common and unexceptional features that the series of bunches each composed of several peaks correspond to a progressional increment of metal atoms. For example, the numbers of metal atoms increase progressionally from 5 to 22 [10] and from 2 to 14 [14] in the ZrmCn series, from 11 to 50 in the TamCn [10], and from 3 to 21 in the NbmC2 n [4], respectively. Based on the above considerations, assignment of the mass spectrum beyond Ti13C2 22 can be completed as shown in Fig. 1(b). After the known magic peaks at Ti13C2 22 and Ti14C2 24, new magic numbers for high-nuclearity titanium carbide clusters are determined as Ti15C2 26 , 2 2 Ti20C2 33/Ti20C34, and Ti25C42. These magic numbers within the mass range of 1000– 1800 amu have never been reported by other investigators. The cubic-layered structures suggested by Wang et al. [15, 16] are obviously insufficient to explain the new magic numbers found for high-nuclearity clusters. The magic numbers at 18–26 and 22–35 predicted by Wang’s model for the high-nuclearity TixC2 y are not magic at all in the present experiments. The observed magic numbers at 20–33/20–34
J. Zhao et al. / Solid State Communications 124 (2002) 253–256
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Fig. 2. Ti5C8 structural unit for constructing the high-nuclearity TixC2 y clusters. Larger balls: C; smaller balls: Ti.
and 25 – 42 are far away from the predictions by either the cubic-layered model (18 – 26 and 22 – 35) [15,16] or the multicage model (18 –29, 22 – 35, and 26 –41) [10,14]. It is worthy to be noted that the magic TixCy clusters with x – y stoichiometry as 15 –26, 20 –34, 25– 42 can be rewritten as (Ti5C10)(Ti5C8)m with m ¼ 2 – 4. Each magic clusters, 2 2 Ti15C2 26, Ti20C34, and Ti25C42 differ by the same Ti5C8 subunits. Based on the above observation, we propose a staggered layer-by-layer growth pattern on the basis of Ti5C8 subunit to interpret the magic-numbered clusters 2 2 2 Ti15C2 26, Ti20C33/Ti20C34, and Ti25C42. The essential Ti5C8 building block in our structural model is illustrated in Fig. 2. It can be viewed as one central Ti atom added on the top of a Ti4C8 quadrangular ring. In the Ti4C8 quadrangle, each Ti atom constitutes one side and links with two perpendicular C2 dimers on the corners. The growth of high-nuclearity magic TixCy (15 – 26, 20 – 34, 25 – 42) clusters can be realized by staggered layer-by-layer packing of the Ti5C8 subunits (see Fig. 3 for a fully relaxed Ti25C42). The Ti5C8 is added on the top of the original clusters in a staggered way that the four side Ti atoms can sit on the top of the C2 dimers in the neighboring layer. In these structures, the central Ti atoms are shared by two neighboring Ti4C8 quadrangles and serve as interlinks between them. On the bottom of the structural model, there is a Ti5C10 unit (or Ti5C9 in the case of Ti20C33), which can be obtained by adding an extra C2 dimer on the Ti5C8. Different from Wang’s model, the carbon atoms always exist in form of C2 and there is no carbon atom in the central strand of the clusters. Based on the staggered layer-by-layer packing of Ti5C8 building blocks, we construct the possible configurations for 2 all the magic-numbered clusters, Ti15C2 26, Ti20C34, and 2 Ti25C42. Full geometry optimizations are then performed by using a CASTEP package [18] based on density functional theory and plane-wave pseudopotential technique. The ion – electron interactions are modeled by ultrasoft non-local pseudopotential [19]. The density functional is treated by generalized gradient approximation (GGA) with exchangecorrelation potential parameterized by Perdew and Wang [20]. The energy cutoff of plane-wave basis is chosen as
Fig. 3. Equilibrium structures of Ti25C42. Larger balls: C; smaller balls: Ti.
250 eV. The clusters are placed in a tetragonal supercell with a sufficient large cell length on each direction. As an example, the optimized structure for the Ti25C42 clusters is shown in Fig. 3. We find that all these constructed structures are stable upon relaxation. At GGA level, the total binding energy obtained for Ti15C26, Ti20C34, and Ti25C42 clusters are 320.31, 426.49, and 528.52 eV, respectively. With one more Ti5C8 subunit, the total binding energy of clusters increase by 106.18 eV (from Ti15C26 to Ti20C34) or 102.03 eV (from Ti20C34 to Ti25C42), significantly larger than the binding energy 93.52 eV of an optimized individual Ti5C8 cluster. The energy difference indicates that extra binding energy of ,10 eV could be gained from each staggered layer-by-layer packing of Ti5C8 subunit. The average binding energies of these highnuclearity magic clusters (7.81–7.9 eV per atom) are close to those of Ti8C12 (Td symmetry, 7.87 eV/atom) and Ti13C22 (structure in Refs. [15,16], 7.95 eV/atom). Thus, these highnuclearity clusters should have high stabilities that are comparable to the known magic-numbered clusters (Ti8C12, Ti13C22). Similar to the layered growth model suggested by Wang et al. our model also implies possible one-dimensional nanowires based on layer-by-layer staggered packing of
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Ti5C8 subunits. Following this growth pathway, the successive magic-numbered clusters are predicted to be 2 2 Ti30C2 50, Ti35C58, and Ti40C66, etc. In summary, we have generated titanium carbide anionic clusters with a mass range up to 1800 amu in a Smalley-type cluster source and recorded their TOF mass spectra. For the lower mass range up to 1200 amu, our mass spectrum reproduces all the magic numbers reported by Wang et al. [15,16] in spite of differences in experimental conditions. For the higher mass range (1200– 1800 amu), we observe 2 2 new magic clusters as Ti15C2 26, Ti20C33/Ti20C34, and 2 Ti25C42, which cannot be accounted for by any previously proposed structural growth patterns (layered, multicage, and nanocrystal). A layer-by-layer growth pathway based on staggered packing of Ti5C8 subunits can successfully interpret these new magic numbers. Density functional calculations reproduce the high stabilities for the proposed configurations. The prediction of larger titanium carbide 2 2 magic-numbered clusters, i.e. Ti30C2 50, Ti35C58, and Ti40C66, etc. is still waiting future experimental validation.
Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 29890210) and the 973 National Science and Technology Major Development Program for Basic Research.
References [1] B.C. Guo, K.P. Kerns, A.W. Castleman Jr, Science 255 (1992) 1411–1413.
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