This chapter deals essentially with the reaction between two solids A and B to form one or more product phases (A m B n ). During the course of this heterogeneous solid-solid reaction A m B n separates the reactants spatially. Therefore the progress of the reaction has to be attributed to a transport of the reactants across phase boundaries and through the reaction product.

Solid state reactions

The influence of inhomogeneities on the saturation of the ferromagnetic resonance is investigated. In the region of moderate power levels, the susceptibility at resonance χ′′ varies linearly with the square of the rf field h. The magnitude of the slope ∂χ′′/∂h2 depends on the nature of the dominant scattering mechanism. If the uniform mode scatters primarily to spin waves of very large wavelength, the slope should be negative. Scattering to spin waves of short wavelength gives a positive contribution to the slope and can lead to a reversal of the sign. The theoretical predictions agree with measurements at X band on various polycrystalline garnets and ferrites.At very high power levels the opening angle of the precessing magnetization vector approaches a limiting value, which is related to the “line width” ΔHk of z directed spin waves having the same frequency as the uniform mode. Experiments on single crystals and polycrystals of rare earth substituted garnets show that ΔHk increases approximately linearly with the rare earth content. The materials investigated contain Gd, Yb, Er, Sm, Dy, Ho, or Tb and for a given ratio of substitution ΔHk increases in that order. The line width ΔHk of z directed spin waves is found to be approximately proportional to the line width ΔH of the uniform mode as measured in single crystals.Experimental results on cobalt and zinc substituted nickel ferrite are reported. ΔHk increases linearly with the cobalt content. For the nickel-zinc ferrites with a large magnetic moment the saturation curve (χ′′ vs h2) measured at X band shows a maximum well below the initial onset of nonlinearity. A theoretical explanation for this extraordinary behavior is given.A new nonlinear effect arising from spin wave instability in a microwave magnetic field applied parallel to the dc field has been observed. Spin waves which propagate in directions perpendicular to the dc field are most susceptible to this instability. The observed variation of the critical rf field strength agrees well with the theoretical predictions. It indicates that the spin-wave line width increases with increasing wave number and decreasing angle between propagation direction and dc magnetic field.

Recent Developments in Ferromagnetic Resonance at High Power Levels

Solid State Reactions

Grain growth in a high-purity ZnO and for the same ZnO with Bi2O3 additions from 0.5 to 4 wt% was studied for sintering from 900° to 1400°C in air. The results are discussed and compared with previous studies in terms of the phenomenological kinetic grain growth expression: Gn—Gn0=K0t exp(—Q/RT). For the pure ZnO, the grain growth exponent or n value was observed to be 3 while the apparent activation energy was 224 ± 16 kJ/mol. These parameters substantiate the Gupta and Coble conclusion of a Zn2+ lattice diffusion mechanism. Additions of Bi2O3 to promote liquidphase sintering increased the ZnO grain size and the grain growth exponent to about 5, but reduced the apparent activation energy to about 150 kJ/mol, independent of Bi2O3 content. The preexponential term K0 was also independent of Bi2O3 content. It is concluded that the grain growth of ZnO in liquid-phase-sintered ZnO-Bi2O3 ceramics is controlled by the phase boundary reaction of the solid ZnO grains and the Bi2O3-rich liquid phase.

Grain Growth in Sintered ZnO and ZnO-Bi2O3 Ceramics

Single crystalline nickel ferrite (NiFe2O4) which has an inverse spinel structure is reported to exhibit a mixed spinel structure when its grain size is reduced to nanometer range. It is known that structural transformations in the nanosize regime are not akin to those of bulk crystals. Additionally, magnetic properties like superparamagnetism and contribution to it by surface layers are critically influenced by the synthesis route of the samples. In this article, we present an investigation on the structural transformation of nanostructured NiFe2O4 using x-ray diffraction (XRD), Mossbauer and magnetization measurements, and Fourier transform infrared (FTIR) and micro-Raman spectroscopy. Nanostructured NiFe2O4 samples were synthesized by a coprecipitation technique followed by thermal processing. Four samples having average grain sizes 13, 20, 26, and 51 nm were synthesized. XRD results confirmed the samples to be nanostructured NiFe2O4 and gave evidence for the mixed spinel structure of the samples of lo...

Investigation of mixed spinel structure of nanostructured nickel ferrite

Pyrolytic graphite is a vapor-deposited form of carbon which is characterized by strong anisotropic properties. The anisotropy is caused by the tendency of the individual crystallites to align themselves in such a way that their c axes are perpendicular to the surface of deposition. The Individual crystallites are composed of parallel graphitic layers which are randomly oriented with respect to the c axis. The ultimate strength of pyrolytic graphite in tension, bending, and compression has been found to increase considerably with increasing test temperatures. Other properties such as thermal conductivity and electrical resistivity give extremely high and low conduction parallel and perpendicular to the basal planes, respectively, in addition to varying considerably with increasing test temperatures. Properties are also influenced by the as-deposited microstructure and by the amount of graphitization to which the material has been subjected. The properties and possible uses of this unique material are presented, discussed, and compared with the properties of other high-temperature materials.

Properties of Pyrolytic Graphite

The rate of nickel ferrite formation is influenced by the milling technique and in the case of wet milling by the type of liquid media used. The reactivity of different types of α-Fe2O3 of spherical shape decreases with an increase of the surface area ratio of α-Fe2O3 to NiO. The particle shape of the iron oxides also affects their reactivity; cubical α-Fe2O3 has the least reactivity in the formation of nickel ferrite. The validity of Jander's equation in ferrite formation is reviewed. Based on present findings the rate of ferrite formation is best represented by the equation dx/dt= (a-x)/t, in which x is the percentage of ferrite formed, t the time, and a the kinetic isothermal reaction rate coefficient which is related to the surface area ratio of the reacting oxides. The application of the foregoing equation to the formation of magnesium ferrites from data found in the literature is also satisfactory.

Kinetics of Nickel Ferrite Formation

Microstructure significantly affects the magnetic and electrical properties of ferrites. Domain behavior and its relation to microstructure of magnetic materials are reviewed, and the critical grain size necessary to maintain a single domain in nickel ferrite is calculated. Experimental data are given for BaO. 6Fe2 O3 and NiFe2O4 to show the relations among grain sue, coercive force, permeability, ferromagnetic resonance line width (ΔH), and dielectric losses. Predictions are made for the role of ferrites in the future of ceramic research.

Microstructure and Properties of Ferrites

A simple apparatus is described for measuring the magnetic loss as a function of magnetic field for ferrites at a frequency of 10,000 mc. The width of the ferromagnetic resonance curve is as important a factor in designing microwave devices as is the resistivity of these materials. The method of preparing ferrites and the physical properties of polycrystalline nickel ferrites as affected by preparation and firing techniques are discussed. It is shown that pores in the ferrite body substantially increase the width of the ferromagnetic resonance curve. The direct-current resistivity can be made to vary from 10 ohm-cm. to 109 ohm-cm. by changing the firing temperatures. The variation in the relative permeability with the bulk density of the body is discussed with reference to domain rotation and domain wall movement.

S. L. Blum

Papers

Properties of Pyrolytic Graphite

Kinetics of Nickel Ferrite Formation

Microstructure and Properties of Ferrites

Effects of Ceramic Parameters on Microwave Properties of Nickel Ferrite