Determination of particle size distribution in an Fe 2 O 3 -based catalyst using magnetometry and x-ray diffraction
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In this paper, the techniques of SQUID magnetometry and line broadening in x-ray diffraction are employed for determining an important parameter for catalysts, viz. the particle size distribution. Magnetization versus temperature (5 K-400 K) and magnetization versus field (up to 55 kOe) data are reported for an a - F e 2 O 3 based catalyst. After determining the region of superparamagnetism, the distribution function f{r) is determined assuming a log normal distribution and Langevin paramagnetism of superparamagnetic particles. The distribution is found to be fairly symmetric with center near 65 A and range of 35 to 115 A. From line-broadening of Bragg peaks in x-ray diffraction, particle radii varying between 75 A and 110 A are obtained. These results are compared with the reported Mossbauer measurements of Huffman et al. on the same sample.
I. INTRODUCTION Highly dispersed Fe-based compounds are known to be very effective catalysts in coal conversion processes.1'2 Generally, the efficiency of a catalyst increases as the particle size is reduced. Since it is quite difficult to prepare particles of uniform size, it becomes important to determine the particle size distribution of a given catalyst if its catalytic behavior is to be understood. Fe-based compounds usually order magnetically, and below a critical size and above blocking temperature TB, these particles exhibit superparamagnetic behavior.3"6 This superparamagnetic behavior has been used in a number of magnetic and Mossbauer studies to determine the average particle size although the determination of the particle size distribution poses a more serious problem.2"11 Assuming a log normal distribution, Richardson and Desai6 have outlined a procedure for determining the particle size distribution in a sample consisting of superparamagnetic particles, using the data of magnetic field dependence of the magnetization. In this work, we employ this technique to determine the particle size distribution of an a-Fe 2 O3-based catalyst. A modern SQUID (Superconducting Quantum Interference Device) magnetometer allows rapid acquisition of the data in a large temperature range and to fairly high magnetic fields. The results presented here cover the temperature range of 5 K to 400 K and magnetic field dependence to 55 kOe. Results obtained from the analysis of these data are compared with the particle size range determined from the line broadening of the Bragg peaks in x-ray diffraction (XRD). Finally, these findings are compared with the published analysis of Mossbauer a
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J. Mater. Res., Vol. 7, No. 7, Jul 1992 Downloaded: 13 Mar 2015
spectroscopy on the same sample.7 Details are presented in the following. II. THEORETICAL CONSIDERATIONS In order to provide a proper theoretical basis for discussion of the results, we outline the key features and equations of the theory used in the analysis. First, in the superparamagnetic region, the magnetization M must scale as H/T where H is the
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