Crystal structure and properties of ferrites

Transcription

1 CHAPTER 2 Crystal structure and properties of ferrites 2.1 Crystal structure of ferrite Ferrite is a body-centered cubic (BCC) form of iron, in which a very small amount (a maximum of 0.02% at 1333 F / 723 C) of carbon is dissolved. This is far less carbon than can be dissolved in either austenite or marten site, because the BCC structure has much less interstitial space than the FCC structure. Ferrite is the component which gives steel and cast iron their magnetic properties, and is the classic example of a ferromagnetic material. This is also the reason that tool steel becomes non-magnetic above the hardening temperature - all of the ferrite has been converted to austenite. Most "mild" steels (plain carbon steels with up to about 0.2 wt% C) consist mostly of ferrite, with increasing amounts of cementite as the carbon content is increased, which together with ferrite, form the mechanical mixture pearlite. Any iron-carbon alloy will contain some amount of ferrite if it is allowed to reach equilibrium at room temperature [1]. 20

2 Spinel ferrites crystallize into the spinel structure, which is named after the mineral spinel, MgAl2O4. Primarily the oxygen ions lattice determines the spinel crystal structure. The radii of the oxygen ions are several times larger than the radii of the metallic ions in the compound. Consequently, the crystal structure can be thought of as being made up of the closest possible packing of layers of oxygen ions, with the metallic ions fit in at the interstices A and B. A metallic ion located at the A site has four nearest oxygen ion neighbors in tetrahedral coordination. The metallic ion, which is situated at site B, has six nearest oxygen ion neighbors in octahedral coordination. Magnetic oxides, which are commonly known as ferrites are ferrimagnetic in structure as originally proposed by Neel [2]. The ferrites by virtue of their structure can accommodate a variety of cations at different sites enabling a wide variation in properties. Further variation in synthetic methods can bring about large changes in extrinsic properties. A majority of them are high resistivity materials making them more suitable for high frequency and low loss applications. Spinel crystallizes in a close packed cubic structure and structure was determined first by Bragg [3] and Nishikawa [4]. The unit cell contains eight molecules and may thus be written as M 8 Fe 16 O 32. The crystal structure of spinel ferrite is shown in Fig The white circles in this figure represent the oxygen ions and the black and hatched circles 21

3 represents the metal ions. The radius of the oxygen ion is about 1.32 Å, which is much larger than that of metal ions ( Å) hence the oxygen ions in the lattice touch each other and form a close packed face-centered cubic lattice. In this oxygen lattice the metal ions take interstitial position which can be classified into two groups, one is a group of lattice sites called tetrahedral sites or 8A sites, each of which is surrounded by four oxygen ions as shown by the hatched circles in the Fig Fig. 2.1: AB 2 O 4 spinel (The red cubes are also contained in the back half of the unit cell) The other is a group of sites called octahedral or 16 B-sites, each of which is surrounded by six oxygen ions as shown by the black circles. These groups are called tetrahedral (A) sites and octahedral [B] sites. From the point of view of valence, it seems reasonable to have M 2+ ions on A-sites and Fe 3+ ions on B-sites, because of the number of oxygen ions 22

4 which surround A and B sites are in the ratio 2:3. There are ninety-six interstitial sites in the unit cell size, 64 tetrahedral, 32 octahedral; of these 8 and 16 respectively are occupied by cations. 2.2 Types of spinel ferrites The spinels are any of a class of minerals of general formulation A 2+ B 3+ 2 O 2-4 which crystallise in the cubic (isometric) crystal system, with the oxide anions arranged in a cubic close-packed lattice and the cations A and B occupying some or all of the octahedral and tetrahedral sites in the lattice. A and B can be divalent, trivalent, or quadrivalent cations, including magnesium, zinc, iron, manganese, aluminium, chromium, titanium, and silicon. Although the anion is normally oxide, structures are also known for the rest of the chalcogenides. A and B can also be the same metal under different charges, such as the case in Fe 3 O 4 (as Fe 2+ Fe 3+ 2 O 2-4 ). Members of the spinel group include [5]: Aluminium spinels: o Spinel MgAl 2 O 4, after which this class of minerals is named o Gahnite - ZnAl 2 O 4 o Hercynite - FeAl 2 O 4 23

5 Iron spinels: o Cuprospinel - CuFe 2 O 4 o Franklinite - (Fe,Mn,Zn)(Fe,Mn) 2 O 4 o Jacobsite - MnFe 2 O 4 o Magnetite - Fe 3 O 4 o Trevorite - NiFe 2 O 4 o Ulvöspinel - TiFe 2 O 4 o Zinc ferrite - (Zn, Fe) Fe 2 O 4 Chromium spinels: o Chromite - FeCr 2 O 4 o Magnesiochromite - MgCr 2 O 4 Others with the spinel structure: o Forsterite - Mg 2 SiO 4 o Ringwoodite - (Mg,Fe) 2 SiO 4, an abundant olivine polymorph within the Earth's mantle from about 520 to 660 km depth, and a rare mineral in meteorites Cation disorder in multi-site oxides is quantified in terms of an "inversion parameter" (δ). The spinel structure is cubic, with two distinct cation sites characterized by different oxygen coordination (octahedral and tetrahedral). There are twice as many octahedral sites as tetrahedral sites. 24

6 Normal spinel: The cation disorder is defined in terms of a "normal" spinel structure, such as that for ideal MgAl2O4, in which all the Mg resides on sites tetrahedrally coordinated with oxygen, and all the AI resides on sites octahedrally coordinated with oxygen. The inversion parameter is defined relative to this configuration, and is the ratio of the atomic fraction of AI on tetrahedral sites to the atomic fraction of AI on octahedral sites. For a perfect normal spinel, the inversion parameter is 0.0. Normal spinel structures are usually cubic closed-packed oxides with one octahedral and two tetrahedral sites per oxide. The tetrahedral points are smaller than the octahedral points. B 3+ ions occupy the octahedral holes because of a charge factor, but can only occupy half of the octahedral holes. A 2+ ions occupy 1/8th of the tetrahedral holes. This maximises the lattice energy if the ions are similar in size. A common example of a normal spinel is MgAl 2 O 4. Inverse spinel: For an ideal "inverse" spinel structure (such as for MgFe2O4), all of the Mg resides on octahedral sites, and the Fe is distributed equally over the remaining octahedral sites and all of the tetrahedral sites. In this case the inversion parameter would be 1.0. Inverse spinel structures however are slightly different in that one must take into account the crystal field stabilization energies (CFSE) of the transition metals present. Some ions may have a distinct preference on 25

7 the octahedral site which is dependent on the d-electron count. If the A 2+ ions have a strong preference for the octahedral site, they will force their way into it and displace half of the B 3+ ions from the octahedral sites to the tetrahedral sites. If the B 3+ ions have a low or zero octahedral site stabilization energy (OSSE), then they have no preference and will adopt the tetrahedral site. A common example of an inverse spinel is Fe 3 O 4, if the Fe 2+ (A 2+ ) ions are d 6 high-spin and the Fe 3+ (B 3+ ) ions are d 5 high-spin. Random spinel: For a "random" spinel structure, the cations are equally distributed over the two sites in ratios proportional to their stoichiometry and the site ratios. A random spinel structure has an inversion parameter of (2/3), or In spinel ferrites if the divalent metal ions and trivalent Fe 3+ ions are distributed randomly over the tetrahedral and octahedral B- sites, then the spinel ferrite is called random spinel. A whole range of possible distribution is observed. This can be represented in general terms by II δ III 1 δ A II 1 δ III 1+δ B 2 4 ( Me Fe ) [Me Fe ] O. where the ions inside the bracket are located in octahedral sites and the ions outside the brackets in tetrahedral sites. 26

8 2.3 Oxygen parameter (U) The interstices available in an ideal close packed structure of rigid oxygen anions can incorporate in the tetrahedral sites, only metal ion with a radius r tetra 0.30Å and in octahedral sites, only ions with a radius r oct 0.55Å. In order to accommodate cations like Co 2+, Cu 2+, Mg 2+, Ni 2+ and Zn 2+ the lattice has to be expanded. The difference in the expansion of octahedral and tetrahedral sites is characterized by a parameter called oxygen parameter (u). In an ideal spinel, the tetrahedral and octahedral sites are enlarged in the same ratio and accordingly the distance between the tetrahedral is (0 0 0) and the oxygen site is 3/8 and hence u ideal =3/8. However the incorporation of divalent metal ions in tetrahedral sites induces a larger expansion of the tetrahedral sites, leading to a large value for u than the ideal value. The tetrahedral sites are expanded by an equal displacement of the four oxygen ions onwards, along the body diagonals of the cube, still occupying the corners of an expanded regular tetrahedron. The four oxygen ions of the octahedral sites are shifted in such a way that this oxygen tetrahedron shrink by the same amount as the first expands. 2.4 Magnetic properties Magnetism is a property of materials that respond at an atomic or subatomic level to an applied magnetic field. For example, the most well 27

9 known form of magnetism is ferromagnetism such that some ferromagnetic materials produce their own persistent magnetic field. However, all materials are influenced to greater or lesser degree by the presence of a magnetic field. Some are attracted to a magnetic field (paramagnetism); others are repulsed by a magnetic field (diamagnetism); others have a much more complex relationship with an applied magnetic field. Substances that are negligibly affected by magnetic fields are known as non-magnetic substances. They include copper, aluminium, gases, and plastic. The magnetic state (or phase) of a material depends on temperature (and other variables such as pressure and applied magnetic field) so that a material may exhibit more than one form of magnetism depending on its temperature, etc. The origin of magnetism lies in the orbital and spin motions of electrons and how the electrons interact with one another. The best way to introduce the different types of magnetism is to describe how materials respond to magnetic fields. This may be surprising to some, but all matter is magnetic. It's just that some materials are much more magnetic than others. The main distinction is that in some materials there is no collective interaction of atomic magnetic moments, whereas in other materials there is a very strong interaction between atomic moments. The magnetic behavior of materials can be classified into the following five major groups: 28

10 Diamagnetism Paramagnetism Ferromagnetism Ferrimagnetism Antiferromagnetism Diamagnetism: Diamagnetism appears in all materials, and is the tendency of a material to oppose an applied magnetic field, and therefore, to be repelled by a magnetic field. However, in a material with paramagnetic properties (that is, with a tendency to enhance an external magnetic field), the paramagnetic behavior dominates [6]. Thus, despite its universal occurrence, diamagnetic behavior is observed only in a purely diamagnetic material. In a diamagnetic material, there are no unpaired electrons, so the intrinsic electron magnetic moments cannot produce any bulk effect. In these cases, the magnetization arises from the electrons' orbital motions, which can be understood classically as follows: When a material is put in a magnetic field, the electrons circling the nucleus will experience, in addition to their Coulomb attraction to the nucleus, a Lorentz force from the magnetic field. Depending on which direction the electron is orbiting, this force may increase the centripetal force on the electrons, pulling them in towards the nucleus, or it may decrease the force, pulling them away from the nucleus. This effect 29

11 systematically increases the orbital magnetic moments that were aligned opposite the field, and decreases the ones aligned parallel to the field (in accordance with Lenz's law). This results in a small bulk magnetic moment, with an opposite direction to the applied field. Fig. 2.2: Hierarchy of types of magnetism [7] Paramagnetism: In a paramagnetic material there are unpaired electrons, i.e. atomic or molecular orbitals with exactly one electron in them. While paired electrons are required by the Pauli exclusion principle to have their intrinsic ('spin') magnetic moments pointing in opposite directions, causing their magnetic fields to cancel out, an unpaired electron is free to align its magnetic moment in any direction. When an external magnetic field is applied, these magnetic moments will tend to align themselves in the same direction as the applied field, thus reinforcing it. 30

12 Ferromagnetism: A ferromagnet, like a paramagnetic substance, has unpaired electrons. However, in addition to the electrons' intrinsic magnetic moment's tendency to be parallel to an applied field, there is also in these materials a tendency for these magnetic moments to orient parallel to each other to maintain a lowered energy state. Thus, even when the applied field is removed, the electrons in the material maintain a parallel orientation. Every ferromagnetic substance has its own individual temperature, called the Curie temperature, or Curie point, above which it loses its ferromagnetic properties. This is because the thermal tendency to disorder overwhelms the energy-lowering due to ferromagnetic order. Some well-known ferromagnetic materials that exhibit easily detectable magnetic properties (to form magnets) are nickel, iron, cobalt, gadolinium and their alloys. Ferrimagnetism: Like ferromagnetism, ferrimagnets retain their magnetization in the absence of a field. However, like antiferromagnets, neighboring pairs of electron spins like to point in opposite directions. These two properties are not contradictory, because in the optimal geometrical arrangement, there is more magnetic moment from the sublattice of electrons that point in one direction, than from the sublattice that points in the opposite direction. 31

13 The first discovered magnetic substance, magnetite, was originally believed to be a ferromagnet; Louis Néel disproved this, however, with the discovery of ferrimagnetism. Fig. 2.3: Ferrimagnetic ordering Antiferromagnetism: In an antiferromagnet, unlike a ferromagnet, there is a tendency for the intrinsic magnetic moments of neighboring valencee electrons to point in opposite directions. When all atoms are arranged in a substance so that each neighbor is 'anti-aligned', the substance is antiferromagnetic. Antiferromagnets have magnetic moment, meaning no field is produced a zero net by them. Antiferromagnets are less common compared to the other types of behaviors, and are mostly observed at low temperatures. In varying temperatures, antiferromagnets can be seen to exhibit diamagnetic and ferrimagnetic properties. In some materials, neighboring electrons want to point in opposite directions, but theree is no geometrical arrangement in which each pair of 32

14 neighbors is anti-aligned. This is called a spin glass, and is an example of geometrical frustration Fig. 2.4: Antiferromagnetic ordering Magnetic domains: The magnetic moment of atoms in a ferromagnetic material cause them to behave something like tiny permanent magnets. They stick together and align themselves into small regions of more or less uniform alignment called magnetic domains or Weiss domains. Magnetic domains can be observed with a magnetic force microscope to reveal magnetic domain boundaries that resemble white lines in the sketch. There are many scientific experiments that can physically show magnetic fields. When a domain contains too many molecules, it becomes unstable and divides into two domains aligned in opposite directions so that they stick together more stably as shown at the right. When exposed to a magnetic field, the domain boundaries move so that the domains aligned with the magnetic field grow and dominate the structure as shown at the left. When the magnetizing field is removed, the domains may not return 33

15 to an unmagnetized state. This results in the ferromagnetic material's being magnetized, forming a permanent magnet. Fig. 2.5: Magnetic domains in ferromagnetic material. When magnetized strongly enough that the prevailing domain overruns all others to result in only one single domain, the material is magnetically saturated. When a magnetized ferromagnetic material is heated to the Curie point temperature, the molecules are agitated to the point that the magnetic domains lose the organization and the magnetic properties they cause cease. When the material is cooled, this domain alignment structure spontaneously returns, in a manner roughly analogous to how a liquid can freeze into a crystalline solid. 34

16 Fig. 2.6: Effect of a magnet on the domains Magnetic ordering and interactions In ferrites, the metallic ions occupy two crystallographically different sites, i.e. octahedral [B] and the tetrahedral (A) site. Three kind of magnetic interactions are possible, between the metallic ions, through the intermediate O 2- ions, by super-exchange mechanism, namely, A-A interaction, B-B interaction and A-B interaction. It has been established experimentally that these interaction energies are negative, and hence induce an anti-parallel orientation. In general, the magnitude of the interaction energy between the magnetic ion, Me I and Me II depends upon (i) the distances from these ions to the 35

17 oxygen which the interaction occurs and (ii) the angle Me I -O-Me II represented by the term φ as shown in Fig Fig. 2.7: Angle φ between Me I and Me II with oxygen ion. An angle of will give rise to the greatest exchange energy and the energy decreases very rapidly with increasing distances. The various possible configurations of the ions pairs in spinel ferrites with favourable distances and angle for an effective magnetic interaction as envisaged by Gorter are given in Fig Based on the values of the distance and the angle φ, it may be concluded that, of the three interactions the A-B interaction is of the greatest magnitude. The two configurations for A-B interaction have small distances (p,q and q,r) and the values of the angle φ are fairly high. Of the two configurations for the B-B interaction, only the first one will be effective since in the second configuration, the distance s is too large for effective interaction. The A-A interaction is the weakest, as the distance r is large and the angle φ 180 [8]. 36

18 A-B interaction B-B interaction A-A interaction φ = φ=154 0 φ=90 0 φ=125 0 φ=79 0 Fig. 2.8: Configuration of ion pairs in spinel ferrites with favourable distance and angles for effective magnetic interaction. Thus, with only A-B interaction predominating the spins of the A and B site ions in ferrites will be oppositely magnetized sublattice A and B with a resultant magnetic moment equal to the difference between those of A and B site ions. In general, the value of saturation magnetic moment for the B lattice (M B ) is greater than that of the A lattice (M A ), so that the resultant saturation magnetization (Ms) may be written as M s = M B -M A With this theory, Neel could satisfactorily explain the experimentally observed magnetic susceptibility and magnetic saturation data obtained for ferrites. Theoretically computed values of the saturation magnetic 37

19 moments per formula unit of the ferrites agree very well with the experimental values as seen from Table Magnetization The magnetization is a powerful tool to study the different parameters such as domain wall rotation, anisotropy, magnetic hardness or softness of material, magnetic ordering etc. Ferrites exhibit almost all the properties similar to that of ferromagnetic materials. When the magnetic field is applied to the ferromagnetic material, the magnetization may vary from zero to saturation value. This behaviour is expressed by Weiss [9] by introducing the idea of existence of domains. According to Weiss, though each domain is spontaneously magnetized in the direction of field, magnetization may vary from one domain to another domain. In general, specimen consists of many domains, in domain configuration i.e. a function of applied field. The magnetic moment of specimen is a vector sum of magnetic moment of each domain. As a result the magnetization or average magnetic moment per unit volume may have value between zero to saturation. Studies on magnetic hysteresis of ferrite provide useful information of the magnetic parameter like saturation magnetization (Ms) coercive force (H C ) and remanence ratio (Mr/Ms). According to the values of these parameters, the ferrites can be classified as soft and hard ferrites. The 38

20 ferrites with low coercive force are called soft ferrites and ferrites with high Hc are called hard ferrites. Soft ferrites are those material which do not retain permanent magnetism, which provide easy magnetic path. Hard ferrites retain permanent magnetism and are difficult to magnetize and demagnetize. According to Neel [2] the coercive force (H C ) is related to saturation magnetization, internal stress, porosity [10] and anisotropy [11]. The Hysteresis properties are highly sensitive to crystal structure, heat treatment, chemical composition, porosity and grain size. 2.5 Electrical properties The ferrospinel compounds are well known for their high electrical resistivity. Basically ferrites behave like semiconductors. For ferrites, the resistivity at room temperature can vary, depending upon chemical composition, between about 10 4 to 10 9 ohm-cm. It is known that low resistivity is caused in particular by the simultaneous presence of ferrous and ferric ions on equivalent lattice site (octahedral sites) [12]. For example Fe 3 O 4 at room temperature has resistivity approximately ohms-cm and NiFe 2 O 4 with some deficiency in iron and sintered in a sufficiently oxidizing atmosphere so that the product contains no ferrous ion, can have resistivity higher than 10 6 ohms-cm. Intermediate values of resistivity have been given by Koops [13]. 39

21 Ferrite behaves like semiconductors and their resistivity decreases with increase in temperature according to the relation ρ = ρ 0 exp( Eg / kt) 2.1 where, Eg represent activation energy, which according to Verwey and De Bore [14] is the energy needed to release an electron from the ion for a jump to the neighbouring ion. According to Verwey and De Bore the conductivity of high resistivity oxides can be increased by addition of small amount of impurities to the structure. The substitutions of cations of the low valance state give rise to p-type of conduction while the substitution for cation of high valance state to n-type of conduction [15]. The presence of Fe 2+ ions is sometimes desirable as it reduces magnetostriction and resistivity. In many ferrite systems it is observed that the slope of logρ vs 1000/T curve changes at the Curie point. The activation energy increases on changing from ferrimagnetic to paramagnetic region, this anomaly strongly supports the influence of magnetic ordering upon the conductivity process in the ferrites. 40

22 References [1] dated 16 Nov [2] L. Neel, Ann de Phys, 3 (1948) 137. [3] W.H. Bragg, Nature, London 95, 561, Phil. Mag. 30 (1915) 305. [4] S. Nishikawa, Proc. Tokyo Math. Phys. Soc. 8 (1915) 199. [5] dated 16 Nov [6] C. Westbrook, C. Kaut, Carolyn Kaut-Roth (1998). MRI (Magnetic Resonance Imaging) in practice (2 ed.). Wiley-Blackwell. p [7] HP Meyers (1997). Introductory solid state physics 2 ed. CRC Press. p [8] B. Vishwanathan and V.R.K. Murthy, Ferrite Material Science and Technology Narosa Publishing House, New Delhi (1990). [9] P. Weiss, J. Phys. 6 (1907) 667. [10] C.M. Srivastava, M.J. Patani, T.T. Srinivasan, J. Appl. Phys. 53 (1983) [11] A.M. Alpr, High temperature oxides Academic Press, New York, 25 (1971). [12] E.J.W. Verwey, P.W. Haaijman, F.R. Romeyn, G.W. Van. Oostehout. Philips. Res. Rep. 5 (1950) 173 [13] C.G. Koops, Phys. Rev. 83 (1951) 121. [14] E.J.W. Verwey and J.H. De Boer, Rec. Trav. Chim. Pay. Bas. 55 (1936) 531. [15] S.L. Snoek, New Development in ferromagnetic material Elsevier publishing co. New York, Amsterdam (1947). 41

23 Table 2.1 Theoretically computed values of the saturation magnetic moments per formula unit of the ferrites. Ferrite Magnetic moment per molecule (µ B ) Theoretical Experimental Fe 2 O CoFe 2 O CuFe 2 O MnFe 2 O NiFe 2 O