Author: Chan, Man
Title: A study of effective relative permittivity/permeability of a composite containing dielectric/magnetic inclusions by using analytic methods and numerical simulations
Degree: M.Phil.
Year: 2009
Subject: Hong Kong Polytechnic University -- Dissertations.
Electromagnetic theory -- Mathematics.
Department: Department of Applied Physics
Pages: xv, 131 leaves : ill. (some col.) ; 30 cm.
Language: English
Abstract: We investigated the effective relative permittivity (Eeff) (or permeability (ueff) composites containing dielectric (or magnetic) inclusions with various analytic and finite element (FE) methods. A FE model was made to contain a 4x4x4 or 6x6x6 inclusion arrays; and the result is assumed to be closer to real value compared with the analytic approaches. In addition, a method combining FE simulations and vibrating sample magnetometer (VSM) measurements is developed to determine the permeability (u) of a soft magnet. For 2-phase composites, all analytic results match with the FE data at low inclusion volume fraction (Oi <= 0.1), indicating that all these theories give rather correct estimates of Eeff (or eff) at low Oi. However, at higher values of Oi, the analytic results are diversified. The data of the Maxwell-Garnett (M-G) and Landauer theories form the lower and upper bounds of the data. Results obtained from the Bruggeman, Rayleigh and Poon-Shin (P-S) theories rank in an ascending order. FE results are consistent with that of Rayleigh theory with deviation less than 0.2%, suggesting that the accuracy of FE simulations is high enough to determine the Eeff (or ueff) values of the models used in the study. For a model with a periodic inclusion array, the M-G theory underestimates the Eeff (or ueff) value, and other analytic theories overestimate the Eeff (or ueff) value. Further modifications of these analytic approaches may be needed. For 3-phase composites, a Maxwell-Garnett multiphase (MG-MP) theory and a Poon-Shin multiphase (PS-MP) theory were developed on the basis of 2-phase M-G and P-S theories. Three incremental-multiphase (I-MP) processes were proposed, in which inclusions are added in small incremental steps. The process in which the two types of inclusions are added in sequence is called as a sequential multiphase (SI-MP) process. The process in which the two types of inclusions are added randomly with fixed probabilities is called a randomly-accumulative multiphase (RA-MP) process. In the region of Oi <= 0.3, all the analytic results are close to the FE results, indicating that all the analytic theories are valid in this region. For 0.3 <= Oi <= 0.9, the analytic results deviate from FE data. The I-MP theory gives the highest Eeff (or ueff) value and MG-MP theory gives the lowest one. The SI-MP process proceeded by adding the inclusions of a lower relative permittivity (or permeability) first gives a higher Eeff (or ueff) among the three I-MP processes. The FE data lie between the SP-MP data and the MG-MP data. None of the analytic method is completely consistent with the FE method. We verified the validity of the proposed method for estimating the dynamic permeability of a soft magnet. The VSM and calculated values of u for samples having different aspect ratios are compared. The experimental data are fitted to a group of theoretically predicted curves corresponding to a certain range of u. The mean value gives the best estimate of the real D value. The method was successful in predicting the permeabilities of iron and nickel, with an advantage of having no need to prepare a ring-shaped sample as required in a standard Rowland's ring test.
Rights: All rights reserved
Access: open access

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