J. Phys. C: Solid State Phys. 21 (1988) 2229-2245. Printed in the UK Size-induced structural phase transitions and hyperfine properties of microcrystalline Fe,O, Pushan Ayyub, Manu Multani, Mustansir Barma, V R Palkar and R Vijayaraghavan Tata Institute of Fundamental Research, Homi Bhabha Road. Bombay 400 005. India Received 23 April 1987. in final form h October 1987 Abstract. Microcrystalline particles of Fe,O, having different sizes (varying between 70 and 5 nm) have been synthesised using a novel three-component micro-emulsion technique. A succession of crystal-size-induced structural transitions was observed. While n-FeZOi was found to nucleate for a particle size above 30 nm. y-Fe,O, was preferentially formed for a size below 30 nm. whereas amorphous Fe20, was formed at a particle size of 5 nm. These structui ai transformations have been related to the increase in the unit-cell volume that occurs as the particle size is decreased. The size dependence of the lattice parameter is shown to arise from a coupling of the surface energy to the dilatational lattice mode. A model Hamiltonian which incorporates this interaction and displays size-induced phase transitions is defined. The Mossbauer hyperfine field in the microcrystalline samples at 42 K was found to be substantially smaller than in the ‘bulk’. The hyperfine parameters of the amorphous sample were found to be similar to those pertaining to samples prepared by conventional techniques such as melt quenching. A large anisotropy in the ionic vibrational amplitudes was detected in samples with particles smaller than about 10 nm. 1. Introduction It is well known that the physical properties of materials exhibit substantial changes from their ’bulk’ values when the crystal dimension is reduced sufficiently. In particular, the electronic, optical and vibrational properties of microcrystals have been investigated extensively (Genzel 1974). For recent developments the reader is referred to the work of Bennemann and Koutecky (1985) and Davenas and Rabette (1986). Microcrystals of magnetically ordered materials may display paramagnetic behaviour much below Tc or TN (superparamagnetism), once the single-domain relaxation time becomes small compared with the observational time scale. A decrease in the particle size may also affect various types of phase transition involving spin reorientation (Schroeer and Nininger 1967). Again, the vacancy ordering in y-Fez03 has been found to disappear when the particle size is reduced below 20 nm (Haneda and Morrish 1977a). However, the precise interpretation of such phenomena is often complicated by the almost inevi- table distribution in particle sizes and shapes. It is therefore essential to employ a synthesis technique which would reproducibly yield fine particles with a narrow size distribution. Various aspects of the microcrystalline state in Fe,O, have been studied. Kiindig er a1 (1966) have performed a detailed Mossbauer analysis and established that the Morin 0022-3719/88/112229 + 17 $02.50 @ 1988 IOP Publishing Ltd 2229