Composite soft magnetic materials consist of magnetic particles in a non-magnetic matrix. The properties of such materials can be modelled using effective medium theory. Measurements have been made of the complex permeability of composites produced using ferrite powder and polyester resin. The success of various effective medium expressions in predicting the variation of complex permeability with composition has been assessed

Devine, R

Paterson, J H

Phelps, A D R

English

Name not available

Complex permeability of soft magnetic ferrite polyester resin composites at frequencies above 1 MHz

University of Strathclyde Institutional Repository

Strathprints Institutional RepositoryPaterson, J H and Devine, R and Phelps, A D R (1999) Complex permeability of soft magneticferrite polyester resin composites at frequencies above 1 MHz. Journal of Magnetism and MagneticMaterials, 196-197. pp. 394-396. ISSN 0304-8853Strathprints is designed to allow users to access the research output of the University of Strathclyde.Copyright c© and Moral Rights for the papers on this site are retained by the individual authorsand/or other copyright owners. You may not engage in further distribution of the material for anyprofitmaking activities or any commercial gain. You may freely distribute both the url (http://strathprints.strath.ac.uk/) and the content of this paper for research or study, educational, ornot-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to Strathprints administrator:mailto:strathprints@strath.ac.ukhttp://strathprints.strath.ac.uk/,JR Journal of N magnetism ,~  and magnetic materials ELSEVIER Journal of Magnetism and Magnetic Materials 196-197 (1999) 394-396 Complex permeability of soft magnetic ferrite/polyester resin composites at frequencies above 1 MHz J.H. Paterson*, R. Devine, A.D.R. Phelps Department of Physicw and Applied Physics. University of Strathdyde, John Anderson BuiMing. Glasgow G40NG. UK Abstract Composite soft magnetic materials consist of magnetic particles in a non-magnetic matrix. The properties of such materials can be modelled using effective medium theory. Measurements have been made of the complex permeability ofcomposites produced using ferrite powder and polyester resin. The success of various effective medium expressions inpredicting the variation of complex permeability with composition has been assessed. ,,~ 1999 Elsevier Science B.V. All rights reserved. Keywords: Composites; Eerrites; Effective medium theory; Permeability Soft magnetic omposite materials, produced by em- bedding soft magnetic particles in a non-magnetic matrix, have a significant advantage over metallic or ceramic materials which can be produced using the es- tablished polymer processing techniques. They can bc readily moulded into complex shapes to produce mag- netic components for specific applications. The relation- ship between the properties of a composite material and those of its separate components can be modelled using effective medium theory. In this work, the high-frequency complex permeability of a series of ferrite/resin composites has been measured. The results have been compared with the predictions of various formalisms of effective medium theory in order to determine how suc- cessful this theory is in modelling the behaviour of these materials over the whole range of possible compositions. The general effective medium expression for permeab- ility for the case of two components i  based on the assumption that the components are embedded in a host medium. The resultant properties are those of the e~bc- *Corresponding author. Fax: + 44 141 552 2891; e-mail: j.h.paterson@strath.ac.uk. tit~e medium. The expression is,, + %,b + 2t,J il) where It is the permeability ofthe effective medium, #,, #b and Ph are the permeabilities of the two components a and b and of the host, respectively, and 11, andJb are the volume fractions of the components. Some assumptions must be made about the component distribution i  the composite, and about the host material. A number of different ways of doing this have been proposed [1,2]. If the assumption is made that the material consists of isolated particles of component a embedded in compon- ent b, which is therefore the host, Eq. (1) simplifies to It I~b r / p. Itb ~ II + 21tb " \ I t .  + 21tb/" (2) This is MaxwelI-Garnett (MGa) effective medium expres- sion. There is an equivalent expression, MGb, with b as the embedded component. The result for a given com- position will be different depending on which of these expression is used. The Bruggeman formalism assumes that both components are embedded in the effective 0304-8853/99/$ - see front matter !; 1999 Elsevier Science B.V. All rights reserved. Pll: S0304-8 853(98)00772-0 J.H. Paterson et al. / Journal of Magnetism and Magnetic Materials 196-197 (1999) 394-396 395 e~ t l  O E t= e~ 15 __ ! 10 10 100 frequeney(MHz) P-r I - -  g r "  1000 Fig. 1. Typical complex permeability spectrum of ferrite/resin composite. o 100 10 • experiment ::2; - -Brug  ~ .-"" .,'" .... M U / - j  ..." / / "  /," ~...--~  /" b 0.5 fferrite Fig. 2. Experimental nd modelled g' vs. ferrite volume fraction .ff~r~ito at 10 MHz. medium itself, and is expressed as 0 2"/] (3) Following the approach of Musal et. al. [2] the Max- well-Garnett expressions can be extended to work throughout the entire range of compositions 0 ~<f, ~< 1. MGa is useful when fa is small, since such a composite will appear to consist of isolated particles of a embedded in b. Similarly, MGb is appropriate when fa is large, and hencefb is small. Here, the medium is described as a com- bination of two phases. The isolated phase consists of particles of a embedded in b, while in the agglomerated phase, a is surrounded by isolated particles of b. The permeability of each phase can be calculated using the appropriate Maxwell-Garnett expression. Asfa increases, the relative concentration of the agglomerated phase will increase. The two phases are combined using a further Maxwell-Garnett expression, corresponding to the ag- glomerated phase embedded in the isolated phase, with the relative concentrations of the phases dependent on 4 3 o = 2 1 • experiment ,- / /  - . . . .  MGb , . /  - -  Brug / /  f "  I "  [ f1" f  0.5  fferrite Fig. 3. Experimental nd modelled g" vs. ferrite volume fraction fferrite at  10 MHz. f, andfb. The concentration of the agglomerated phase is defined as f l  ~, where x is a fitting parameter. The base magnetic material used in this work was an unsintered manganese-zinc ferrite powder, grade F9C, supplied by MMG-Neosid. The powder had an average particle size < 300 ~tm. In its sintered form this material has a nominal initial permeability "r of ~ 5000 and has a frequency response suitable for applications below 100 kHz. The matrix was a polyester laminating resin. A simple mixing and moulding process was used to produce toroidal composite samples with ferrite volume fractions up to ~ 50%. The complex permeability of each toroidal sample was measured over the range 1 MHz-1 GHz using a Hewlett-Packard HP4291B Ma- terial Analyser. A typical complex permeability spectrum is shown in Fig. 1. The frequency response is significantly different from that of the sintered material. Figs. 2 and 3 show the experimental measurements of ~t' and g", respectively, vs. ferrite volume fraction at 10 MHz, to- gether with the predictions of the effective medium ex- pressions detailed above. The trends in the data were similar at other frequencies in the measured range. The uncertainty in the permeability values was estimated from the manufacturer's specifications for the HP4291B. Since the permeability of the ferrite powder was not accurately known, the values of . t fe r r i t  e and .n fe r r i t  e used in the models were adjusted to give the best overall fit to the data. Since the resin is non-magnetic, ,'resin = 1 and ""resin = 0. MGa and MGb give very different results for g'. Neither gives a good fit over the whole range of compositions. The Bruggeman expression (denoted BRUG) is a significant improvement. The Musal ap- proach (denoted MU) was used for g' with the parameter x = 0.33, chosen empirically to give the best fit. This gives a reasonable fit to all the data. For t£', MGa and MU cannot be calculated since the MGa expression gives an undefined result if "b = 0. BRUG gives a reasonable fit to the data provided fa > ½, but gives zero below this value. These comparisons suggest that for these materials the Bruggeman expression works reasonably well, 396 J.H, Paterson et al. / Journal of Magnetism and Magnetic Materials 196-197 (1999) 394-396 particularly when the components are present in roughly equal fractions. The Musal approach works well over a wider range of composition, but it cannot be used for I-t". References [1] D.E. Aspnes, Am. J. Phys. 50 (1982) 704. E2] H.M. Musal Jr., H.T. Hahn, G.G. Bush, J. Appl. Phys. 63 (1988) 3768. Acknowledgements This work has been supported by DERA Malvern, UK. The ferrite powder was kindly supplied by Dr. lan Wilkinson of MMG Neosid. 

704. E2] H.M.

J.H. Paterson

R. Devine

A.D.R. Phelps

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Journal of Magnetism and Magnetic Materials

Complex permeability of soft magnetic ferrite/polyester resin composites at frequencies above 1 MHz

http://dx.doi.org/10.1016/S0304-8853(98)00772-0

Complex permeability of soft magnetic ferrite polyester resin composites at frequencies above 1 MHz

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