- Email: [email protected]
First principles calculations of the agglomeration of Ti nanoparticles
Materials Letters 104 (2013) 91–93
Contents lists available at SciVerse ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
First principles calculations of the agglomeration of Ti nanoparticles A.N. Chibisov n Computational Center, Russian Academy of Sciences, 65 Kim Yu Chen Street, Khabarovsk 680000, Russia
art ic l e i nf o
a b s t r a c t
Article history: Received 9 February 2013 Accepted 24 March 2013 Available online 30 March 2013
We have used molecular dynamics and first-principles calculations to investigate the structure, electronic properties, and agglomeration of Ti nanoparticles. The results indicate that cluster agglomeration leads to a decrease in the band gap compared with the isolated Ti13 cluster. In addition, we found that titanium nanocluster growth occurred along the [0001] direction. The difference of the atomic structures of the icosahedral Ti13 cluster and the bulk phase of titanium was also studied. The results show that spin polarization disappears when nanoparticles agglomerate. & 2013 Elsevier B.V. All rights reserved.
Keywords: Simulation and modeling Titanium cluster Agglomeration
1. Introduction
2. Methods
The production of titanium nanowires [1,2] and nanocoatings requires an understanding of the regularity of the agglomeration of the isolated nanoparticles. Nanoparticles (nanoclusters) are structural units that have seldom a similar structure to the unit cell in the bulk crystal lattice. To create high-quality methods for the production of nanomaterials, it is necessary to study the energy, structure, and electronic properties of single (isolated) nanoparticles to understand what is happening to the properties [3] when particles join (agglomerate) to form continuous nanoscale films and nanowires. Theoretical [4,5] and experimental [6,7,8] studies have suggested that isolated titanium Ti13, Ti19, and Ti55 clusters prefer an icosahedral structure. In addition, it has been found that the bonding within the clusters is close to that in hexagonal bulk Ti [5,9]. X-ray diffraction analysis has shown that nanowires of titanium have the hexagonal structure [10], and that growth of the titanium nanowires occurs along the [0001] direction [11]. In the present work, we have studied the structural and electronic properties of titanium nanoparticles, and titanium nanoparticle agglomeration. Investigation of these properties is important because Ti has high corrosion and cavitation erosion resistance, a low coefficient of thermal expansion, and high mechanical strength, which is why titanium and its alloys are widely used in the manufacture of aerospace vehicles, defense technology, and metal-cutting tools [12]. In addition, Ti is also used for implants in medicine because of its corrosion resistance and biocompatibility with living tissue.
The total energies of the nanoclusters were calculated with the generalized gradient approximation (GGA) and spin polarization using the density functional theory (DFT) [13] in the ABINIT software package [14]. Pseudopotential for Ti atom was constructed using the program fhi98PP [15]. A special 1 1 1 G-point in the Monkhorst–Pack grid [16] with a cutoff energy of 816.34 eV was used to simulate the Ti clusters. The simulation clusters were placed in a very large cubic cell, which had a size of approximately 24 Å. The k-points were determined in the reciprocal lattice [16], and its volume was reduced by increasing the size of the direct lattice (the superlattice). Thus, to calculate the total energy of the cluster, one k-point (G-point) was enough. During the course of the calculation, the self-consistent structure was relaxed until the interatomic forces were less than 0.005 eV/Å, which is sufficient to obtain good results. In addition, the Ti2 dimer structure was calculated to validate the titanium pseudopotentials. The theoretical value of the Ti–Ti distance was 1.9055 Å, which is slightly less than the experimental value of 1.942270.0008 Å [17].
n
Tel./fax: +7 4212 22 72 67. E-mail address: [email protected]
0167-577X/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matlet.2013.03.107
3. Results and discussion Previously, we have studied the structural and electronic properties of the isolated icosahedral cluster Ti13 [18]. These results were in good agreement with the available results of other authors [4,9]. Fig. 1 shows the atomic structures of the Ti13 clusters. Fig. 1a shows the isolated icosahedral Ti13 cluster and Fig. 1b shows the hexagonal structure that has been cut from the bulk lattice of the titanium α-phase (space group: P63/mmc). Obviously, there is some structural similarity between the two clusters. Bulk titanium
92
A.N. Chibisov / Materials Letters 104 (2013) 91–93
Fig. 1. Atomic structures of (a) the icosahedral isolated Ti13 cluster, and (b) the Ti13 cluster with hexagonal structure, which is cut from the bulk titanium lattice.
has six Ti atoms that form the basal plane of a regular hexagon with sides of 2.957 Å. This hexagon has two parallel planes that are formed by three Ti atoms, which are labeled as planes 1 and 2 (Fig. 1b). The interplanar spacing between planes 1 and 2 is 4.676 Å, which corresponds to the c parameter of the bulk lattice. The hexagonal ring of Ti atoms is distorted by the free surface in the isolated Ti13 cluster, and the surface energy of the cluster is 0.31 eV/Å2 [18]. Planes 1 and 2 are parallel as they are in the bulk material. Interestingly, and what will be shown later to be very important, these planes are parallel to each other in the icosahedral structure with an interplanar spacing of about 3.7 Å (see Fig. 1a), which is considerably less than that in the bulk material. These structural distortions lead to a change in the electron distribution and the appearance of the energy gap, which is similar to the band gap Eg in semiconductors and spin polarization in the electronic states. The band gap Eg is 0.27 eV for the spin-up orientation, and 0.23 eV for the spin-down orientation. It is important to understand how the individual nanoparticles agglomerate, and what happens to their atomic and electronic structures after agglomeration. To model the process of nanoparticle agglomeration, we have used the molecular dynamics method with the isenthalpic ensemble. In this method, the equations of motion of the ions are solved using the algorithm proposed by Martyna et al. [19], and the system maintained at constant temperature and pressure. There are no published data for titanium nanoparticle agglomeration. However, there are data for the agglomeration (sintering) of titanium micropowders [20], where the initial stage of powder crystallite compaction was performed at 753 K and agglomeration was performed at a temperature of about 1155 K. Thus, for the molecular dynamics calculation, two isolated Ti13 nanoclusters were randomly placed in the simulation cell (24 Å) and the temperature was varied from 753 to 1155 K during the course of the calculation. After complete atom relaxation by molecular dynamics, i.e., reaching the global minimum of the total energy, additional calculations were performed to obtain the optimum local structure for the Ti13+Ti13 cluster using the density functional theory. These calculations were carried out to compare the Ti13+Ti13 cluster with an isolated cluster Ti13. Interestingly, when the two Ti13 clusters approached each other, planes 1 and 2 were parallel (see Fig. 1a), as in the isolated cluster Ti13 and the Ti13+Ti13 system (see Fig. 2), although the interplanar spacing between these planes was slightly larger (4.3 Å) than for the isolated Ti13 cluster (3.7 Å). Thus, it is more favorable for titanium nanoparticles to grow along the quasi-direct [0001] direction, because the local atomic structures of the isolated cluster Ti13 and bulk structure cluster are similar (see Fig. 1). Our theoretical results are in good agreement with those reported previously, where it was experimentally reported that titanium nanowire growth occurred along the [0001] direction [11]. The atomic cluster volumes increased by about 6% and their
Fig. 2. Atomic structure of the Ti13+Ti13 dimer cluster. The arrows indicate the interplanar spacing.
symmetry changed. The isolated Ti13 cluster has icosahedral Ih symmetry, whereas the symmetry of the nanoparticle is rhombohedral C3v(3m). Thus, Ti nanoclusters undergo a phase transition with a change of point group symmetry from icosahedral Ih to rhombohedral C3v (3m). Next, the electronic structure of Ti13+Ti13 dimer cluster will be discussed. The band gap value Eg for the Ti13+Ti13 dimer is 0.18 eV, i.e., the band gap is the same for both spin orientations. As a result, spin polarization disappeared during nanoparticle growth. Thus, nanocluster agglomeration leads to a decrease in Eg compared with the isolated Ti13 cluster.
4. Conclusions In summary, we have employed molecular dynamics and firstprinciples calculations to investigate the structures, electronic properties, and agglomeration of Ti nanoparticles. From the nanoparticle agglomeration, we found that titanium nanocluster growth occurred along the [0001] direction. Ti nanoclusters undergo a phase transition with a change of point group symmetry from icosahedral Ih to rhombohedral C3v(3m). These results are a significant advance in understanding the processes of growth of Ti nanoparticles and the physics of the electronic properties of titanium nanowires.
Acknowledgments This work was supported by a grant from the Presidium of Far East Branch of the Russian Academy of Sciences (No. 11-III-В-02018). Calculations were performed using a cluster at the Computational Center of the Russian Academy of Sciences in Khabarovsk (Russia). References [1] Hajiyani HR, Jafari M. J Magn Magn Mater 2012;324:418. [2] Chen Y-J, Hsu J-H, Lin H-N. Nanotechnology 2005;16:1112. [3] Lehtinen JS, Sajavaara T, Arutyunov KYu, Presnjakov MYu, Vasiliev AL. Phys Rev B 2012;85:094508. [4] Castro M, Liu S-R, Zhai H-J, Wang L-S. J Chem Phys 2003;118:2116.
A.N. Chibisov / Materials Letters 104 (2013) 91–93 [5] [6] [7] [8] [9] [10] [11] [12] [13]
Wang SY, Duan WH, Zhao DL, Wang CY. Phys Rev B 2002;65:165424. Wu HB, Desai SR, Wang LS. Phys Rev Lett 1996;76:212. Liu SR, Zhai HJ, Castro M, Wang LS. J Chem Phys 2003;118:2108. Lian L, Su C-X, Armentrout PB. J Chem Phys 1992;97:4084. Wang S-Y, Yu J-Z, Mizuseki H, Yan J-A, Kawazoe Y, Wang C-Y. J Chem Phys 2004;120:8463. Wu G, Adams B, Tian M, Chen A. Electrochem Commun 2009;11:736. Huang X, Chumlyakov YI, Ramirez AG. Nanotechnology 2012;23:125601. Nurul Amin AKM. Titanium alloys-towards achieving enhanced properties for diversified applications. Rijeka: InTech; 2012. Hohenberg P, Kohn W. Phys Rev 1964;136:B864.
93
[14] Gonze X, Amadon B, Anglade P-M, Beuken J-M, Bottin F, Boulanger P, et al. Comput Phys Commun 2009;180:2582. [15] Fuchs M, Scheffler M. Comput Phys Commun 1999;119:67. [16] Monkhorst HJ, Pack JD. Phys Rev B 1976;13:5188. [17] Doverstal M, Lindgren B, Sassenberg U, Arrington CA, Morse MD. J Chem Phys 1992;97:7087. [18] Chibisov AN, Zhitenev AN. Chem Phys Mesoscop (Original Russian Text published in Chimicheskaya Fizika i Mezoskopiya) 2012;14:467. [19] Martyna GJ, Tuckerman ME, Tobias DJ, Klein ML. Mol Phys 1996;87:1117. [20] Eriksson M. Licentiate thesis. Stockholm, Stockholm University; 2007.
Contents lists available at SciVerse ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
First principles calculations of the agglomeration of Ti nanoparticles A.N. Chibisov n Computational Center, Russian Academy of Sciences, 65 Kim Yu Chen Street, Khabarovsk 680000, Russia
art ic l e i nf o
a b s t r a c t
Article history: Received 9 February 2013 Accepted 24 March 2013 Available online 30 March 2013
We have used molecular dynamics and first-principles calculations to investigate the structure, electronic properties, and agglomeration of Ti nanoparticles. The results indicate that cluster agglomeration leads to a decrease in the band gap compared with the isolated Ti13 cluster. In addition, we found that titanium nanocluster growth occurred along the [0001] direction. The difference of the atomic structures of the icosahedral Ti13 cluster and the bulk phase of titanium was also studied. The results show that spin polarization disappears when nanoparticles agglomerate. & 2013 Elsevier B.V. All rights reserved.
Keywords: Simulation and modeling Titanium cluster Agglomeration
1. Introduction
2. Methods
The production of titanium nanowires [1,2] and nanocoatings requires an understanding of the regularity of the agglomeration of the isolated nanoparticles. Nanoparticles (nanoclusters) are structural units that have seldom a similar structure to the unit cell in the bulk crystal lattice. To create high-quality methods for the production of nanomaterials, it is necessary to study the energy, structure, and electronic properties of single (isolated) nanoparticles to understand what is happening to the properties [3] when particles join (agglomerate) to form continuous nanoscale films and nanowires. Theoretical [4,5] and experimental [6,7,8] studies have suggested that isolated titanium Ti13, Ti19, and Ti55 clusters prefer an icosahedral structure. In addition, it has been found that the bonding within the clusters is close to that in hexagonal bulk Ti [5,9]. X-ray diffraction analysis has shown that nanowires of titanium have the hexagonal structure [10], and that growth of the titanium nanowires occurs along the [0001] direction [11]. In the present work, we have studied the structural and electronic properties of titanium nanoparticles, and titanium nanoparticle agglomeration. Investigation of these properties is important because Ti has high corrosion and cavitation erosion resistance, a low coefficient of thermal expansion, and high mechanical strength, which is why titanium and its alloys are widely used in the manufacture of aerospace vehicles, defense technology, and metal-cutting tools [12]. In addition, Ti is also used for implants in medicine because of its corrosion resistance and biocompatibility with living tissue.
The total energies of the nanoclusters were calculated with the generalized gradient approximation (GGA) and spin polarization using the density functional theory (DFT) [13] in the ABINIT software package [14]. Pseudopotential for Ti atom was constructed using the program fhi98PP [15]. A special 1 1 1 G-point in the Monkhorst–Pack grid [16] with a cutoff energy of 816.34 eV was used to simulate the Ti clusters. The simulation clusters were placed in a very large cubic cell, which had a size of approximately 24 Å. The k-points were determined in the reciprocal lattice [16], and its volume was reduced by increasing the size of the direct lattice (the superlattice). Thus, to calculate the total energy of the cluster, one k-point (G-point) was enough. During the course of the calculation, the self-consistent structure was relaxed until the interatomic forces were less than 0.005 eV/Å, which is sufficient to obtain good results. In addition, the Ti2 dimer structure was calculated to validate the titanium pseudopotentials. The theoretical value of the Ti–Ti distance was 1.9055 Å, which is slightly less than the experimental value of 1.942270.0008 Å [17].
n
Tel./fax: +7 4212 22 72 67. E-mail address: [email protected]
0167-577X/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matlet.2013.03.107
3. Results and discussion Previously, we have studied the structural and electronic properties of the isolated icosahedral cluster Ti13 [18]. These results were in good agreement with the available results of other authors [4,9]. Fig. 1 shows the atomic structures of the Ti13 clusters. Fig. 1a shows the isolated icosahedral Ti13 cluster and Fig. 1b shows the hexagonal structure that has been cut from the bulk lattice of the titanium α-phase (space group: P63/mmc). Obviously, there is some structural similarity between the two clusters. Bulk titanium
92
A.N. Chibisov / Materials Letters 104 (2013) 91–93
Fig. 1. Atomic structures of (a) the icosahedral isolated Ti13 cluster, and (b) the Ti13 cluster with hexagonal structure, which is cut from the bulk titanium lattice.
has six Ti atoms that form the basal plane of a regular hexagon with sides of 2.957 Å. This hexagon has two parallel planes that are formed by three Ti atoms, which are labeled as planes 1 and 2 (Fig. 1b). The interplanar spacing between planes 1 and 2 is 4.676 Å, which corresponds to the c parameter of the bulk lattice. The hexagonal ring of Ti atoms is distorted by the free surface in the isolated Ti13 cluster, and the surface energy of the cluster is 0.31 eV/Å2 [18]. Planes 1 and 2 are parallel as they are in the bulk material. Interestingly, and what will be shown later to be very important, these planes are parallel to each other in the icosahedral structure with an interplanar spacing of about 3.7 Å (see Fig. 1a), which is considerably less than that in the bulk material. These structural distortions lead to a change in the electron distribution and the appearance of the energy gap, which is similar to the band gap Eg in semiconductors and spin polarization in the electronic states. The band gap Eg is 0.27 eV for the spin-up orientation, and 0.23 eV for the spin-down orientation. It is important to understand how the individual nanoparticles agglomerate, and what happens to their atomic and electronic structures after agglomeration. To model the process of nanoparticle agglomeration, we have used the molecular dynamics method with the isenthalpic ensemble. In this method, the equations of motion of the ions are solved using the algorithm proposed by Martyna et al. [19], and the system maintained at constant temperature and pressure. There are no published data for titanium nanoparticle agglomeration. However, there are data for the agglomeration (sintering) of titanium micropowders [20], where the initial stage of powder crystallite compaction was performed at 753 K and agglomeration was performed at a temperature of about 1155 K. Thus, for the molecular dynamics calculation, two isolated Ti13 nanoclusters were randomly placed in the simulation cell (24 Å) and the temperature was varied from 753 to 1155 K during the course of the calculation. After complete atom relaxation by molecular dynamics, i.e., reaching the global minimum of the total energy, additional calculations were performed to obtain the optimum local structure for the Ti13+Ti13 cluster using the density functional theory. These calculations were carried out to compare the Ti13+Ti13 cluster with an isolated cluster Ti13. Interestingly, when the two Ti13 clusters approached each other, planes 1 and 2 were parallel (see Fig. 1a), as in the isolated cluster Ti13 and the Ti13+Ti13 system (see Fig. 2), although the interplanar spacing between these planes was slightly larger (4.3 Å) than for the isolated Ti13 cluster (3.7 Å). Thus, it is more favorable for titanium nanoparticles to grow along the quasi-direct [0001] direction, because the local atomic structures of the isolated cluster Ti13 and bulk structure cluster are similar (see Fig. 1). Our theoretical results are in good agreement with those reported previously, where it was experimentally reported that titanium nanowire growth occurred along the [0001] direction [11]. The atomic cluster volumes increased by about 6% and their
Fig. 2. Atomic structure of the Ti13+Ti13 dimer cluster. The arrows indicate the interplanar spacing.
symmetry changed. The isolated Ti13 cluster has icosahedral Ih symmetry, whereas the symmetry of the nanoparticle is rhombohedral C3v(3m). Thus, Ti nanoclusters undergo a phase transition with a change of point group symmetry from icosahedral Ih to rhombohedral C3v (3m). Next, the electronic structure of Ti13+Ti13 dimer cluster will be discussed. The band gap value Eg for the Ti13+Ti13 dimer is 0.18 eV, i.e., the band gap is the same for both spin orientations. As a result, spin polarization disappeared during nanoparticle growth. Thus, nanocluster agglomeration leads to a decrease in Eg compared with the isolated Ti13 cluster.
4. Conclusions In summary, we have employed molecular dynamics and firstprinciples calculations to investigate the structures, electronic properties, and agglomeration of Ti nanoparticles. From the nanoparticle agglomeration, we found that titanium nanocluster growth occurred along the [0001] direction. Ti nanoclusters undergo a phase transition with a change of point group symmetry from icosahedral Ih to rhombohedral C3v(3m). These results are a significant advance in understanding the processes of growth of Ti nanoparticles and the physics of the electronic properties of titanium nanowires.
Acknowledgments This work was supported by a grant from the Presidium of Far East Branch of the Russian Academy of Sciences (No. 11-III-В-02018). Calculations were performed using a cluster at the Computational Center of the Russian Academy of Sciences in Khabarovsk (Russia). References [1] Hajiyani HR, Jafari M. J Magn Magn Mater 2012;324:418. [2] Chen Y-J, Hsu J-H, Lin H-N. Nanotechnology 2005;16:1112. [3] Lehtinen JS, Sajavaara T, Arutyunov KYu, Presnjakov MYu, Vasiliev AL. Phys Rev B 2012;85:094508. [4] Castro M, Liu S-R, Zhai H-J, Wang L-S. J Chem Phys 2003;118:2116.
A.N. Chibisov / Materials Letters 104 (2013) 91–93 [5] [6] [7] [8] [9] [10] [11] [12] [13]
Wang SY, Duan WH, Zhao DL, Wang CY. Phys Rev B 2002;65:165424. Wu HB, Desai SR, Wang LS. Phys Rev Lett 1996;76:212. Liu SR, Zhai HJ, Castro M, Wang LS. J Chem Phys 2003;118:2108. Lian L, Su C-X, Armentrout PB. J Chem Phys 1992;97:4084. Wang S-Y, Yu J-Z, Mizuseki H, Yan J-A, Kawazoe Y, Wang C-Y. J Chem Phys 2004;120:8463. Wu G, Adams B, Tian M, Chen A. Electrochem Commun 2009;11:736. Huang X, Chumlyakov YI, Ramirez AG. Nanotechnology 2012;23:125601. Nurul Amin AKM. Titanium alloys-towards achieving enhanced properties for diversified applications. Rijeka: InTech; 2012. Hohenberg P, Kohn W. Phys Rev 1964;136:B864.
93
[14] Gonze X, Amadon B, Anglade P-M, Beuken J-M, Bottin F, Boulanger P, et al. Comput Phys Commun 2009;180:2582. [15] Fuchs M, Scheffler M. Comput Phys Commun 1999;119:67. [16] Monkhorst HJ, Pack JD. Phys Rev B 1976;13:5188. [17] Doverstal M, Lindgren B, Sassenberg U, Arrington CA, Morse MD. J Chem Phys 1992;97:7087. [18] Chibisov AN, Zhitenev AN. Chem Phys Mesoscop (Original Russian Text published in Chimicheskaya Fizika i Mezoskopiya) 2012;14:467. [19] Martyna GJ, Tuckerman ME, Tobias DJ, Klein ML. Mol Phys 1996;87:1117. [20] Eriksson M. Licentiate thesis. Stockholm, Stockholm University; 2007.