Microwave Processing of Materials (1994) / Chapter Skim
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MICROWAVE FUNDAMENTALS
MICROWAVE FUNDAMENTALS
Pages 9-38
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From page 9... ...
Although there is a broad range of materials that can be processed using microwaves, there are fundamental characteristics and properties that make some materials particularly conducive to microwave processing and others difficult. While an empirical understanding of microwave processing is important in moving developmental processes into production, a more fundamental approach is required for development of optimized process cycles, equipment, and controls.
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From page 10... ...
The first involved space charge and the transit time of electron motion within a vacuum, which represented a fundamental limitation to the operating frequency and output power of conventional "ridded tubes. When the time of transit became an appreciable part of a microwave frequency cycle, performance degraded, forcing the designer to smaller and smaller sizes to achieve higher frequency.
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From page 11... ...
Large performance improvements have been achieved through the application of new materials and processes in microwave generators. For example, the application and ready availability of high thermal conductivity beryllium oxide or boron nitride has allowed significant improvements in maximum continuous wave power output of traveling wave tubes (from approximately 3 W to 3 kW)
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From page 12... ...
The magnetron is the major player in a class of tubes termed "crossed field," so named because the basic interaction clepends upon electron motion in electric and magnetic fields that are perpendicular to one another and thus "crossed." In its most familiar embodiment, shown schematically in Figure 2-4, a cylindrical electron emitter, or cathode, is surrounded by a cylindrical structure, or anode, at high potential and capable of supporting microwave fields. Magnets are arranged to supply a magnetic field parallel to the axis and hence perpendicular to the anode cathode electric field.
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From page 13... ...
near a parallel planar element receiving electrons (anode) and of an interspersed parallel grid controlling the electron flow.
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From page 14... ...
Magnetron "Cooker" 1 2.45 60 - 70 0.05 0.05 Industrial 5 to 15 2.45 60 - 70 3.50 0.35 Industrial 50 0.915 60 - 70 5.00 0.10 Power Grid (Transmitting)
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From page 18... ...
Since, as will become evident in this report, c' is not constant but can vary significantly with frequency and temperature, it will be referred to simply as the permittivity (Risman, 19911. The imaginary component of complex permittivity, e", is the dielectric loss factor.
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From page 19... ...
19 The wave equations for the electric and the magnetic fields derived from the Maxwell equations are -=_~28oRo8/l1 Ex -=_~28ollo8/F H' (1) where e0 and ,uO are, respectively, the free space permittivity (~.854 x low F/m)
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From page 20... ...
£ ///fs / Equation 5 indicates that the amplitu(le of the wave decreases exponentially as it propagates i.e., wave energy is dissipated during the propagation. For the isotropic medium consiclered here, one remarkable property of the wave is that it carries an equal amount of energy in the electric and magnetic fields.
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From page 21... ...
Stranding Waves The two remarkable properties of wave propagation stated earlier are that the wave carries an equal amount of the electric and magnetic energy and that the wave impedance stays constant in the propagation direction. These are intrinsic properties of transmission lines and are true as long as the forward and the backward traveling wave are separate.
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From page 22... ...
In this case, however, only a portion of the wave is reflected. Consider the case in which a boundary separates two media with at, Mu, and 62, p2 and wave impedances of Zen and Z2, respectively.
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From page 23... ...
Field distributions for various monies of propagation in rectangular and cylindrical waveguides are available in standard text books (Ramo and Whinnery, 1944; Iskander, 1992~. TO, and TM modes are considered in rectangular waveguides and TEn~ and TM modes are considered in cylindrical waveguicles, where the inrlices m, n, and ~ are the order of the modes.
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From page 24... ...
In general, at a conducting surface, electric field lines are normal to the surface, and magnetic field lines are Parallel to it. Awav from the surface all field lines follow continilitv Reform onrrvins' (`lit calculations of the field distributions, the wavelength and the wave impedance of a waveguide mode will be considered.
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From page 25... ...
Microwave Fundamentals O _ :~ .o · ~ · ,____._ t1..
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From page 26... ...
· c. ~ ., ~ ~ ~ ~ ~ ~ ~ ;f~=~3~ FIGURE 2-12 Field distributions and key expressions of calculation for modes in cylindrical waveguides.
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From page 27... ...
Also, heat transfer and related problems of uneven heating and thermal runaway are covered. In conductors, electrons move freely in the material in response to the electric field and an electric current results.
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From page 28... ...
Materials that are amenable to microwave heating are polarizable and have dipoles that reorient rapidly in response to changing electric field strength. However, if these materials possess low thermal conductivity and dielectric loss that increases dramatically as the temperature increases "hot spots" and thermal runaway may be experienced.
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From page 29... ...
Ion Hence, the loss tangent characterizes the ability of the material to convert absorbed microwave power into heat with absorption depending on electric-field intensity, frequency, loss factor, and permittivity. A "Iossy" material (high ten h and e")
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From page 30... ...
Met;a] Powders Al Co Cu Fe Mg Mo Sulfide Semiconductors FeS2 PbS CuFeS2 Mixed Valent Oxides Fe3O4 CuO CO2O3 NiO 10-x lo-6 Moderately Heated 577 ° C/6 min 697/3 228/7 768/7 120/7 660/4 iris _ i0-3 Easily Heated 1019/6.75 956/7 920/1 |0-4 _ ~Q-2 Easily Heated 1258/2.75 1012/6.25 1290/3 1305/6.25 Carbon and Graphite ~ 10 Easily Heated Alkali Halides KC1 KBr NaC1 NaBr LiCl i04 - 105 Very Little Heating 31/1 46/.25 83/7 40/4 35/0.5 Oxides i04 - i0~4 Very Little Heating SiO2 79/7 A1203 78/4.5 KAlSi3O ~67/7 CaCO3 74/4.25
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From page 31... ...
Those are the atomic and ionic polarizations induced by the electric field. Although atomic and ionic polarizations occur at microwave frequencies, they do not contribute to microwave heating.
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From page 32... ...
. ~ V P electronic I Ultra- | | Violet | Frequency Microwave Processing of Materials 4 FIGURE 2-13 Frequency dependence of the several contributions to the polarizability schematic (Kittel, 1959)
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From page 33... ...
is that the effect of the polarization in both c' and e" diminishes altogether above the microwave frequency. The broad range of possible material properties that can be effectively processed using microwaves is illustrated by Table 2-3, showing representative clielectric properties of a sampling of important materials.
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From page 34... ...
_ ~ -/ \ \ ~ ~^~ (Po/E] 1 Microwave Processing of Materials 2 3 FIGURE 2-14 Frequency dependence of real and imaginary parts of the dielectric constant in the Polanzation-Orientational Model (Kittel, 19591.
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From page 35... ...
The net field inside the sample is thus reduced, while the field outside the sample remains the same. The computation in this case involves a depolarization factor, N
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From page 36... ...
However, the thermophysical behavior of the sample must also be understood. Stable microwave heating depends on the rate of microwave power absorption and on the ability of the sample to dissipate the resulting heat, that is, if the temperature dependence of the power absorption is less than the temperature dependence of the heat dissipation at the surface of the specimen (plus insulation system)
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From page 37... ...
If the power is increased to exceed the upper critical power, the temperature will jump to the upper branch of the temperatur~power curve. These observations have been supported by modeling work performed to simulate microwave heating of alumina (Barmatz and Jackson, 1992; Johnson et al., 1993~.
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From page 38... ...
38 Microwave Processing of Materials Due to rapidly increasing dielectric loss factor, the area of the sample that first exceeds the critical temperature will continue to heat rapidly at the exclusion of the rest of the sample. Thus, process control schemes to control thermal runaway depend upon knowing the temperature at the interior of the specimen.
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