2 .sx General Properties of Ferrites .sx 2.1 FERRITE STRUCTURE .sx APART from ferromagnetic metals , a number of chemical compounds ( e.g. ferrites , garnets , plumbites and perovskites ) exhibit ferromagnetic properties .sx Of these compounds ferrites have to date proved to be the most important from the standpoint of microwave applications .sx As the majority of ferrites crystallise with a cubic structure , similar to the mineral spinel , ( magnesium aluminate Mg :sx ++:Al ;2; :sx +++:O;4;:--: ) , the term ferromagnetic spinel is sometimes used to describe those ferrites which exhibit magnetic properties .sx The general chemical formula of a ferrite is ( MFe;2;O;4;);n ; where M represents a metallic cation .sx It is found that a spinel crystal structure is only formed if the ionic radius of the cation M is less than about 1 A@15 .sx If it is greater than 1 A@15 then the electrostatic Coulomb forces are insufficient to ensure the stability of the crystal .sx For example Ca :sx ++: ( ionic radius 1.06 A@15 ) does not form spinel crystals , while Mn :sx ++: ( ionic radius 0.91 A@15 ) does .sx The cation M is generally divalent , but other valencies are possible if the number of anions is doubled , e.g. lithium ferrite Li :sx +:Fe;5;:+++:O;8;:--:. The ions forming ferrites of practical importance are Ni :sx ++: , Mn :sx ++: , Fe :sx ++: , Co :sx ++: , Cu :sx ++: , Zn :sx ++: , Cd :sx ++: , Li :sx +: , Mg :sx ++:. The spinel unit cell ( see Fig. 2.1 ) consists of a close packed cubic array of 32 oxygen anions , between which there are 96 spaces or interstices , 24 of which are filled with a cation , the remaining 72 being empty .sx The sites occupied by the cations are of two kinds known as tetrahedral or A sites and octahedral or B sites .sx The A sites of which eight are occupied , are surrounded by four oxygen anions and the B sites of which sixteen are occupied , are surrounded by six oxygen anions .sx When the chemical formula is written , the ions in the B sites are often enclosed in brackets to indicate their position , e.g. Fe(NiFe)O;4 ; for nickel ferrite .sx It might seem at first sight that the most likely arrangement of the cations would be with M :sx ++: ions on the A sites and Fe;2; :sx +++: ions on the B sites but in practice three types of spinel can be distinguished .sx ( 1 ) Normal spinels in which M :sx ++: ions occupy the A sites and Fe;2; :sx +++: the B sites .sx ( 2 ) Inverse spinels in which M :sx ++: ions occupy the B sites together with half the Fe :sx +++: ions , the other half being on the A sites .sx ( 3 ) Random spinels in which both M :sx ++: ions and Fe :sx +++: ions occur on the A and B sites .sx The preference of certain ions for A or B sites is of importance , as it is found that in general normal ferrite spinels are paramagnetic while inverse spinels are ferromagnetic .sx Many ions show no strong preference for a particular site , this being especially true for those ions with a noble gas configuration such as Li :sx +: , Mg :sx ++: , Al :sx +++: and also those with a half-filled 3d electron shell e.g. Fe :sx +++:Mn:++:. Where there is no strong site preference the most stable cation distribution can be calculated from a static model of charged spheres .sx Of the remaining ions in ferrites which are of microwave interest Zn :sx ++: , has a preference for A sites while only Ni :sx +++: and Cr :sx +++: have a strong preference for B sites .sx When two or more cations are present , the distribution of ions with weak site preference may be affected by the presence of an ion with a strong site preference .sx Most ferrite spinels can form solid solutions with each other in any proportion .sx This arises since there is a greater probability of a solid solution when two ferrite spinels are reacted together , than there is of the formation of separate crystals of the two spinels .sx A well-known example of a solid solution is nickel zinc ferrite , Ni;1-a;Zn;a;Fe;2;O;4 ; , where a can take any value between 0 and 1 .sx Unless great care is taken in the manufacture , the final ferrite formed is not exactly that corresponding to the proportions of raw materials used .sx This is because most ferrites can take up oxides into solution without forming a second phase and thus give rise to non-stoichiometric ferrite .sx In particular the ability of most ferrites to take up Fe;2;O;3 ; in solution is important .sx In the preparation of ferrites the component oxides are reacted at high temperatures .sx During this sintering process there is a tendency for most ferrites to give off oxygen , as the equilibrium pressure in this reaction is often greater than one atmosphere and increases rapidly with temperature .sx This gives rise to an oxygen deficiency in the final product and to the formation of ferrous ions .sx The presence of ferrous ions in microwave ferrites is undesirable however , since it causes increased dielectric and magnetic loss as is discussed in this chapter and Chapter 4 .sx For this reason , compounds are often made iron deficient , great care being taken to avoid loss of oxygen during sintering .sx 2.2. PREPARATION OF FERRITES .sx Ferrites are prepared by a ceramic technique which involves sintering the component oxides at temperatures between 1000@ and 1450@C .sx The stages in the preparation of ferrites are listed below :sx - Raw materials @16 Decomposition to oxide @16 Milling @16 Presintering ( partial reaction ) @16 Remilling @16 Pressing and Extruding to shape @16 Final sintering @16 Grinding to shape A number of raw materials can be used in the manufacture of ferrites ; these include oxides , carbonates , oxylates and nitrates .sx The last three compounds decompose to oxides on heat treatment , and are thus prepared 6in situ at a temperature near to that at which solid state reactions commence .sx This process should favour the formation of good quality homogeneous materials .sx For example in the case of MgMn ferrites it has been reported that the use of nitrates gives rise to better microwave properties .sx An explanation is that the high decomposition temperature of the nitrates and the presence of nitrogen oxides help to prevent the formation of ferrous ions during the sintering process .sx The raw materials are first milled , usually in a steel ball mill , to give a homogeneous mixture of very fine particles .sx The process is generally carried out with the raw materials in a slurry of methylated spirit or any other liquid which is easily removed after milling .sx The evaporation of the methylated spirit is carried out rapidly to avoid any heavier particles separating out .sx The mixture of raw materials is then pre-fired at a temperature some 200@C below its final firing temperature .sx This process causes partial reaction of the constituents and helps to reduce shrinkage during final sintering .sx The presintered powder is then remilled .sx Two methods of moulding the powder into shape prior to the final sintering are commonly employed ; die pressing and extrusion .sx For die pressing a small quantity of binder is added to the powder so that when the sample has been pressed to shape , it can be handled relatively easily .sx To avoid the possibility of contamination of the sintered ferrite , distilled water has been used as a binder , although for certain shapes ( e.g. rods ) organic wax emulsions have been found more satisfactory .sx Gentle heating to remove the binder is necessary as violent volatilisation could cause the sample to crack .sx A moulding pressure of between 2 and 10 tons/ sq .sx in .sx ensures a uniform end product without the risk of forming laminates in the pressed sample .sx For satisfactory extrusion a higher percentage of binder is required than for moulding .sx A solution of wax in petroleum has been used as a binder for extrusion and by careful choice of extrusion orifice very dense samples may be produced .sx As high a density as 99% has been achieved under special conditions .sx Extruded samples , in general , however are not as dense or uniform as those produced by die-pressing .sx The principal use of extrusion techniques has been for the manufacture of long thin rods , a shape often required in microwave applications .sx Rods as long as 12in .sx x 0.04 in .sx diameter have been produced by this method .sx The properties of the final product depend critically on the sintering process and the closest control of sintering time , temperature and atmosphere is required .sx Generally , the sintering process is carried out at a temperature between 1000@ and 1450@C for between 4 hours and 24 hours , depending on the ferrite .sx Ferrites containing lithium and cadmium are usually sintered at lower temperatures due to the volatility of LiO and CdO;2 ; while those containing nickel , cobalt and magnesium are sintered at the highest temperatures .sx By sintering for a long time at high temperatures , a uniform final product with a minimum of air pores can be obtained .sx The near absence of pores is a requirement for certain microwave ferrites .sx This is discussed in greater detail in Chapter 3 .sx As already mentioned , however , the oxygen equilibrium pressure increases rapidly with increasing temperatures and this sets a limit on the maximum sintering temperature that can be used without reduction of ferric iron to ferrous iron .sx The porosity of a particular polycrystalline ferrite sample is usually quoted with reference to its X-ray or single-crystal density .sx The X-ray density is determined from measurements of the spinel lattice constant and Table 2.1 gives values for a number of commonly used ferrites , for which the lattice constants are known .sx The density of typical polycrystalline pressed samples is between 80% and 95% of X-ray density , though figures as high as 99% have been achieved .sx During sintering , shrinkage of the ferrite sample occurs .sx This may be controlled by careful preparation and by ensuring a uniform temperature over the sample , although the final shape may not have the tolerances required in practice .sx Sintered ferrites , being ceramic in nature , require special methods of shaping .sx Cutting can be carried out by use of a thin diamond slitting wheel or by use of an ultrasonic machine with a knife edge cutting head .sx An accurate finish can then be obtained by surface grinding with a carborundum wheel .sx The growth of single crystals of ferrite was originally of interest mainly to the physicist , as the crystals produced were too small for use in microwave applications .sx However , the development of non-linear devices employing small single-crystal samples has modified this situation , although they are still extensively used for the study of the fundamental properties of ferrites .sx Two principal methods have been used for the formation of single crystals ; the borax melt and the flame fusion process .sx In the borax melt process , the constituent oxides of the ferrite are dissolved in a flux of molten borax by heating the mixture to between 1300@ and 1400@C and maintaining this temperature for several hours .sx The melt is then cooled at a few degrees per hour until crystals start to form , or alternatively the flux is evaporated at a constant rate .sx A disadvantage of the method is that the borax vapour evolved is very corrosive and destroys most refractory materials , which necessitates the use of special furnace equipment .sx Crystals of linear dimensions of about 1 cm can be obtained by this method .sx In the flame-fusion process constituent oxides are mixed in the correct proportions and sprinkled into an oxy-hydrogen flame .sx Crystals of reasonable length , e.g. 1-2 cm can then be grown on a refractory rod held in the flame .sx It is , however , very difficult to control the exact chemical composition of the crystal obtained by the flame-fusion process .sx 2.3 MAGNETIC PROPERTIES OF FERRITES .sx The purpose of the following section is to provide an elementary account of the magnetic properties of ferrites , together with enough background material to enable the reader to place the section in perspective .sx It is stressed that since the object is to equip the microwave user of ferrites with a knowledge of their magnetic properties , the finer details of the subject must be sought in the bibliography provided .sx Consideration will first be given to the origin of magnetism in electrons , atoms and ions , choosing as examples of the latter , elements which occur in ferrites .sx The mechanisms of para- , ferro- and ferri-magnetism will then be explained and reference made to the temperature behaviour of the saturation magnetisation of certain ferrites .sx In ferrites , one is principally concerned with the phenomenon of ferrimagnetism which will be treated in greater detail .sx