The Behavior of a TiO 2 Nanoparticle under Extreme Conditions
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The Behavior of a TiO2 Nanoparticle under Extreme Conditions J. E. Lowther School of Physics and DST / NRF Centre of Excellence in Strong Materials, University of the Witwatersrand. Johannesburg, South Africa. ABSTRACT Compressibility of anatase nano particles of TiO2 changes from the bulk counterpart. This has been associated with amorphization and compaction. The behavior of such systems under extreme conditions is examined using a shell partial distribution function and some comparison made with rutile and baddeylite polytypes based nano structures. Particle energies of rutile and baddeylite nano particles appear to be rather size independent as compared to the anatase polytypes. The latter is associated with large relaxations and re-bonding in the relatively soft anatase phase of nano TiO2. INTRODUCTION Bulk TiO2 has several polytypes of which the most abundant ambient phases are rutile, anatase and brookite [1]. Under pressure the materials exhibits a large variety of structures. Anatase coverts to columbite at above 8GPa and rutile to columbite at about 10GPa. Thereafter columbite transforms to a baddeylite structure at about 18GPa a structure that is an ambient phase of ZrO2. An important high pressure cotunnite structure of TiO2 has been observed well above 50GPa [2] and is tentatively considered as being one of the hardest known oxides. The has also been much interest in the properties of nano structures of TiO2 and notably when such structures are subject to extreme conditions of temperature or pressure [1, 3-9]. There is particle size behavior under pressure as compared to the bulk counterpart and often changes in compressibility as measured by a bulk modulus[8, 9] are reported. There are also various indications of amorphization [9] [10]. This is especially significant for the anatase polytype. Based upon molecular dynamics calculations it was possible to study the behavior of an anatase structure and point out that the surface of the anatase nano-particle exhibits an amorphous type structure responsible for the apparent enhanced bulk modulus [9]. COMPUTATIONAL Both density functional theory and empirical molecular dynamics methods have been employed to examine the phases of TiO2. Density functional theory has shown that the several phases of TiO2 are very closely spaced in energy [2] [11]. Such calculations have also indicated that the anatase phase has lower elastic moduli than other phases. For example using plane wave calculations as implemented through the VASP algorithm [12] and within the generalised gradient approximation [13] the elastic constants are derived. From these an effective isotropic bulk (B) or shear (G) Voigt values can be obtained. These values are given in Table 1. b
Table 1: Voigt effective isotropic elastic constants (GPa). Equation of State values a[2]: [14]. Values c
from elastic constants [11].
B G
Anatase 190[202a][194b][217c] 51
Rutile Baddeylite 214[239a][243b][209c] 153[300a][249b][128c] 124[123c] 92[98c]
There are important implications from these values. The hardn
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