Study of Variation of R.M.S. Strain with Average Particle Size of Different Phases Evolved During High Energy Ball Milling Of Anatage Tio2 Suggesting Simultaneous Occurrence of Hall-Petch Effect and Inverse Hall-Petch Effect
Journal Title: International Journal of Engineering and Science Invention - Year 2018, Vol 7, Issue 3
Abstract
Average particle size (Grain size) plays an important role in controlling material strength. In polycrystalline materials with grain sizes in the micrometre range, strength increases with decreasing size obeying Hall–Petch relation. But in polycrystalline solids having average grain sizes of the order of a few nanometers (nm) an opposite behaviour was found, called an inverse Hall–Petch effect (IHPE). The reversal of behavior takes place at a certain critical size at which the strength becomes maximum and is termed as “strongest size”. In the present work simultaneous occurrence of Hall–Petch as well as inverse Hall–Petch effect (IHPE) has been reported. In the polymorphic mixture of different TiO2 phases, obtained by ball milling of spec. pure anatase TiO2, it is found that for anatase TiO2 phase and rutile TiO2 phase, variation of r.m.s. strain with particle size is in agreement with Hall-Petch relation whereas an inverse Hall-Petch effect is occurring in case of TiO2-II phase simultaneously, solely depending upon whether the saturation particle size of individual phase is above or below the critical particle size or strongest size for that phase. The phases (anatase and rutile) with saturation particle size above 10 nm shows Hall-Petch effect whereas the phase having saturation particle size below 10 nm show an inverse Hall-Petch effect.
Authors and Affiliations
Punarbasu Bose
Keywords
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