Dielectric Loss and Ferroelectric Hysteresis

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SEPTEMBER 2018 I SS U E #117 TECHNICALTIDBITS MATERION PERFORMANCE ALLOYS

DIELECTRIC LOSS AND FERROELECTRIC HYSTERESIS

Last month we made the observation that the per- The amount of energy converted to heat during a polar- mittivity of an ideal capacitor is equal to the relative ization cycle is known as the dissipation factor (Df), permittivity (dielectric constant, abbreviated loss tangent or tan ( ), with being the loss angle.

Dk or r) multiplied by the permittivity constant The derivation of the loss angle and the tangent thereof δ δ At a Loss! – A brief ( 0). This is true for direct current (DC) conditions, or can be a bit esoteric unless you are an electrical engi- ε discussion on energy lost for ideal, lossless dielectric materials. However, nature neer. Technical Tidbits always tries to strike a balance rarelyε presents us with ideal materials or conditions, between oversimplification (with a risk of inaccuracy) as waste heat in materials so we have to consider real-world cases. and getting too in depth for introductory material due to the presence of (getting lost in the weeds). However, if you are comfort- changing electric fields. As discussed last month, under the influence of an able with phasors as well as real and imaginary parts of externally applied electric field, the electric dipoles current and capacitance, then feel free to research on. in a polarizable material will align themselves with the field, if they are free to rotate or move, and if they Under AC conditions, all realistic dielectric materials will have enough time to do so. Of course, such movement have losses. Therefore, permittivity ( ) is represented as requires energy (readily available from the electric field) a complex number, with the real part relating to capaci- and internal friction results in the generation of a small tance and the imaginary part relatingε to dielectric losses Relative Permittivity/ amount of heat. The transfer of energy from the applied ( -j ). Per Eric Bogatin, when the complex permittivity Dielectric Constant electric field to unrecoverable heat loss is known as is plotted as a vector on the complex plane, the loss ( /D or ) dielectric loss or dissipation. As always, whenever angleε′ ε″ is the angle between the vector and the real axis. r K energy is used to do useful work, there is always some The tangent of the loss angle is thus precisely equal to Dielectric lost to waste heat. In other words, entropy increases. the imaginary part of the permittivity. So, as the angle ε κ increases, so does the loss tangent, and the amount Relaxation Time When an applied electric field is reversed, the dipoles of energy lost (dissipated) as heat. (See the right side will be facing the wrong direction. They will then rotate of Figure 1.) Dissipation Factor to align in the opposite direction. The time required for (Df) this to happen is called the relaxation time. If it is Alternatively, per Braithwaite and Weaver, if you imag- easy for the dipoles to align, then the relaxation time is ine a capacitor as a combination of an ideal capacitor Loss Tangent [tan ( )] low. This is a physical property that essentially measures and ideal resistor, you can plot a phasor diagram of the the rate of polarization. current in both elements, and the loss angle will be the Loss Angle δ angle between the resultant current and the capacitive Electric current. (Left side of Figure 1). Susceptibility/ Dielectric Susceptibility ( ) Loss Tangent as Derived by Loss Tangent as Derived by Bogatin e Braithwaite and Weaver (page 53) (pages 346 -359)

Ferroelectric Imaginary Part of Capacitive Current χ Dielectric (V/[1/ ωC] cos ωt) Constant (ε") Dielectric Resistive Current Real Part of Hysteresis (V/R sin ωt) Dielectric Resultant Current in Constant (ε') δ Capacitor Dielectric δ Constant (ε'-jε")

The next issue of Technical Tidbits will discuss the effect that dielectric properties have Figure 1. Loss Angle and Loss Tangent. on high frequency signals. The diagram on the left is a phasor plot of current, and that on the right is the dielectric constant plotted on the complex plane. In either case, the tangent of the loss angle describes the amount of energy dissipated as heat (dielectric loss).

©2018 Materion Brush Inc. MATERION PERFORMANCE ALLOYS DIELECTRIC LOSS AND FERROELECTRIC HYSTERESIS (CONTINUED) Ferroelectric materials are a class of dielectric Electric susceptibility ( e), also known as dielectric susceptibility, is the electrical equivalent of materials that can maintain a remnant polarization Written by Mike Gedeon of Materion magnetic susceptibility. It is relatedχ to the relative when the electric field is removed, and behave much Performance Alloys Marketing like ferromagnetic materials do in magnetic fields. permittivity by the following equation: r = 1+ e. Department. Mr. Gedeon’s primary (We will discuss magnetism and magnetic materials in focus is on electronic strip for the To fully describe the losses associated withε dielectricχ a few months.) These materials show ferroelectric automotive, telecom, and computer materials, we would need both the dielectric constant hysteresis as shown in Figure 2. The area within the markets with emphasis on and the loss tangent. Please note that both of these outer curve is a measure of the energy lost per cycle application development. are likely to be functions of frequency. To put all the as waste heat. This is another source of loss in some concepts together: dielectric materials. References:

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Health and Safety Handling copper beryllium in Figure 2. Schematic Drawing of a Ferroelectric Hysteresis Curve. solid form poses no special health In hysteresis curves, the area bounded by the curve is a measure of the energy lost per cycle as waste heat. risk. Like many industrial materials, beryllium-containing materials may pose a health risk if recommended safe handling practices are not followed. Inhalation of airborne beryllium may cause a serious lung disorder in susceptible individuals. The Occupational Safety and Health Administration (OSHA) has set mandatory limits on occupational respiratory exposures. Read and follow the guidance in the Safety Data Sheet (SDS) before working with this material. For additional information on safe handling practices or technical data on copper beryllium, contact TECHNICALTIDBITS Materion Performance Alloys or your local representative. Materion Performance Alloys Sales 6070 Parkland Blvd. +1.216.383.6800 Mayfield Heights, OH 44124 800.321.2076 [email protected] Technical Service +1.216.692.3108 800.375.4205 [email protected]