Grain boundary engineering of power inductor cores for MHz applications

Journal Pre-proof Grain boundary engineering of power inductor cores for MHz applications Parisa Andalib, Vincent G. Harris PII:

S0925-8388(19)34377-4

DOI:

https://doi.org/10.1016/j.jallcom.2019.153131

Reference:

JALCOM 153131

To appear in:

Journal of Alloys and Compounds

Received Date: 20 August 2019 Revised Date:

20 November 2019

Accepted Date: 20 November 2019

Please cite this article as: P. Andalib, V.G. Harris, Grain boundary engineering of power inductor cores for MHz applications, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/ j.jallcom.2019.153131. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Author Credit Statement Parisa Andalib: Conceptualization, Methodology, Data collection and analysis, Writing- original draft preparation, Visualization Vincent Harris: Conceptualization, Supervision, Writing- reviewing and editing

Grain boundary engineering of power inductor cores for MHz applications Parisa Andalib and Vincent G. Harris Center for Microwave Magnetic Materials and Integrated Circuits Department of Electrical and Computer Engineering Northeastern University, Boston, MA 021154-5000 USA Abstract: In this article we present the latest trends in processing, composition, theory, and utility of spinel ferrites for use as power inductor cores for a wide range of applications including power generation, conversion, and conditioning at MHz frequencies. Furthermore, it is a principle goal of this article to examine state of the art approaches and innovative methodologies to engineer grain boundary regions in composition, structure, and electrical and magnetic properties that allow spinel ferrites to operate at frequencies well above the state of technology (i.e., f>1 MHz) with low core power loss while concomitantly maintaining high efficiency, high permeability and saturation induction. Key terms: spinel, ferrite, inductor cores, grain boundaries, permeability, core loss I.

Introduction

Power generation, conversion, and conditioning functions are required by not only enormous systems, such as power grids, but also smaller systems, such as mobile communication platforms and components where microinductors are integrated with semiconductor circuitry. These seemingly desperate needs provide bookends for global interests in size, frequency, and technology maturity to address societal needs in energy conservation and performance. When one considers the need for game changing advances in power systems, from power grids to 5G communications, one must address the need for the evolution of these technologies towards ultrahigh frequencies [Wang 2014, Hu 2014 and Andalib 2009]. Recent

developments

in

modern

energy

generation, conditioning and conversion components and systems, including miniaturization and shifts to higher operational frequencies for applications of massive scales such as cloud computing centers, the retail high efficiency magnetic core market reached an alltime high in 2018. Based on the Micromarket Monitor Inc. [Micromarketmonitor.com] the major drivers for the global ferrite market (both permanent and soft ferrite magnets) is mainly the rapid growth of the consumer electronics and automotive industries that have high demands for ferrite cores. The global ferrite market value at 2013 was estimated at 3.9 B$ with a CAGR (compound annual growth rate) of 8.4%, which is expected to reach 5.96 B$ by 2019. Based on Markets Media Inc. [see: MarketsMedia.com], soft ferrites make up 1.7 B$ of this market (c. 2017) and is expected to hit 1.87 B$ by 2025 with a CAGR of 1%. Among end-users, the automotive market demand for ferrites has been experiencing the highest growth rate as this industry has been shifting toward electrical power generation. The growth in the automobile sector has led to an increase in the demand for ferrite magnets. In addition to the automotive sector, the consumer electronics sector has been experiencing a massive wave in market demand, with increases in various products keeping pace with the rise in the use of personal computers and its trend toward miniaturization and light weight laptops and cell phones. The major regional players in this market have been Asia-Pacific with a market of 2.93 B$, or about 75% of the market, while the rest of the

market belongs to America, Europe, Middle East and Africa. As these systems experience a reduced form factor and shifts to higher operational frequencies, thermal management becomes more challenging. The increase in the areal density of computational processors over the past few years places a massive strain on the thermal management of data centers and their associated hardware. Furthermore, the growth rate of the power density of these centers outpaces the existing cooling technologies placing limits on market growth. A high and mid-range data center contains thousands of rack-mounted computer servers, data storage and networking hardware systems. The collective heat dissipation in these centers is measured in 100s of GWh. Andrae and Edler [2015] estimated the 2015 global data center power usage at ~400 TWh and projected by 2030 the usage would exceed 3000 TWh (a conservative estimate), which would equate to ~ 8% of the 2030 world’s total power per annum [nature.com]. Less conservative estimates project the percentage of global use to be as high as 20% by 2025 [data-economy.com]. Currently, the estimated global 10 million data centers produce more than 200 million metric tons of carbon dioxide. Of this, 100 million metric tons are produced from US facilities at a cost of 13 billion USD per year. [datacenterknowledge.com and nrdc.org]. An estimated 40-50% of data center power is employed in sustaining their cooling systems depending upon the size and loads of the center’s electrical demand and infrastructure [fortune.com]. Preventing the massive dissipation of energy in a cost-effective manner is required to make data centers viable in our energy dependent society. One source of loss to server cabinets are power converters and conditioners that include several

inductor components per server. As such a principal challenge in the design and production of ferrite components is the management of escalating heat dissipation and its impact upon overall system efficiency. There are different strategies to mitigate excessive heat dissipation. These include the minimization of generated heat, the efficient removal of heat, or allowing the device to run hot (i.e., designing systems that do not degrade as operational temperature increases). Core power loss of inductor components is often the limiting factor that determines frequencydriven size reduction: operation beyond this boundary results in unacceptable inefficiencies. Hence, size reduction can be further improved by optimizing the magnetic core material toward attaining much reduced core power loss and higher performance efficiencies. Minimization of the core power loss has been of significant importance and a major pursuit of industry and academia in order to address the concerns associated with deployment of high efficiency and high power density equipment, and ultimately enable efficient thermal management of existing and future large-scale systems. Figure 1 illustrates many interactions between materials, devices and systems, technology pull, and frequencies and form factor trends. As one observes, at the lower frequencies (i.e., <100 KHz), the magnetic inductors are metallic or amorphous metallic (i.e., Metglases) and possess very high permeabilities and saturation inductions and typically large form factors. However, these same materials are metals or Ω-cm) and therefore semimetals ( ≤ 150 experience significant conduction losses that limit their applications to 10’s kHz. Improvements in the application of laminates in metals and metallic glass-based inductors to interrupt eddy currents continues to shift the useful bands to higher frequencies.

Technology Pull Power generation, conversion, conditioning

Next generation power Data centers, IoT, communication grid components technologies, power grid, power electronics, automotive, etc. Barriers to market insertion Industrial scale processing, cost & U.S. supply chain

Established technologies

mobile communication 5G 5G cellular communication, RADAR, satcom, microwave oven, etc. Underdeveloped technologies

Barriers to Market Insertion

10

102

103

104

105

106

107

108

109

1010

Frequency, Hz Fig. 1. Schematic diagram relating technology pull, barriers to market insertion and state of the technology material options [Goldman 2002]

In the same figure, we see that from 10’s – 100 KHz, is dominated by Metglases [metglas.com] and nanocrystalline alloys of the Nanoperm [mhw-intl.com] and Finemet [hitachimetals.com] varieties. These materials have high saturation induction, extremely high permeabilities, and electrical resistivities of ~100-150 µΩ-cm [Ouyang 2019]. However, from 100 KHz and above, these materials also suffer from excessive conduction losses and the only materials that can fulfill technology needs at these high frequencies are magnetoceramics. Magnetoceramics have moderate permeabilities but substantially lower saturation induction with much higher electrical resistivities allow for much higher operational frequencies. In this context, magnetoceramics include garnets, spinel, and hexaferrites with spinels being the crystal structure of choice most inductor applications below 1 GHz.

At operating frequencies below 1 MHz, MnZn-ferrites represent and attraction option. Although MnZn-ferrites are more semiconducting than insulating, Fig. 2 illustrates that these ferrites remain essential for a plethora of engineering products as materials in communication coils, transformers, flyback transformers, and deflection yokes among others applications, operating from 1 KHz – 1 MHz. Beyond this frequency, once again limited by conduction losses, NiZnferrites are choice materials.

For NiZn-ferrites, cation substitutions of Ni2+ for Mn2+ on the octahedral sublattice leads to much improved electrical resistivities from ~102-103 Ω-cm to ~106 -109 Ω-cm [Goldman 2006].

Fig. 2. Applications of soft ferrites [adapted from Nomura T. 2003]. This provides NiZn-ferrites with unique properties for higher frequency operations, including those at or above UHF.

However, transition from MnZn-ferrite to NiZnferrite comes at a cost to permeability, saturation induction and efficiency. Because the permeability of the NiZn-ferrite is substantially lower, as is the saturation induction, device form factors increase dramatically. Other substitutions, including Mg2+ and Cu2+ are both cations that strongly prefer occupation on octahedral sites and therefore play a similar role as Ni2+. Cu2+ cations are also added to provide improvements to density and therefore NiCuZnferrites have become very popular compositions for commercial products and new applications at higher frequencies, allowing for additional high frequency applications such as radio frequency

antenna, transformers, and isolators, circulators, and switches up to and beyond 1 GHz. Polycrystalline magnetoceramics, such as MnZn- and NiZn-ferrites, consist of close packed randomly oriented spinel grains separated by highly disordered grain boundaries. Electrical, mechanical and crystallographic properties of grain boundary (GB) regions have greatly influence over the performance of power ferrite inductor cores. At still higher operating frequencies, the FMR frequency must be shifted to higher frequencies by breaking crystal symmetry of the cubic spinels by introduction of period II cations (e.g., Ba, Sr). This allows for the formation of Magnetoplumbite and Ferroxplana hexaferrites. [Harris 2009 and Harris 2012].

II. Selection of the Principle Phase The principle phase in grain boundary engineered cores must be as carefully engineered as the grain boundary regions. Most rf design engineers will consider saturation induction, Curie temperature, permeability, magnetic anisotropy fields, coercivity, Snoek’s parameter, losses, electrical resistivity and temperature coefficients as key design parameters. However, in the effective application of grain boundary additives the rf engineer may relax some of these design constraints. For example, in the use of insulating incongruent magnetic grain boundary inclusions, studied by Andalib and Harris [2017], showed that an iron rich MnZn-ferrite composition (see Fig. 3) was not only acceptable but offered superior performance at operational frequencies above MHz.

the magnetostriction constant, Js is the saturation magnetic polarization at T=400 K, Bs is the saturation magnetic flux density, SPM is the second permeability maximum and Tc is the curie temperature.

The higher Fe content leads to enhanced saturation induction and Curie temperatures at the expense of higher core losses due to an increase in conductivity and long-range magnetic interactions. This trade-off has to be taken into account in the design of low loss MnZn power ferrites. As a rule of thumb, the initial Fe content for a MnZn power ferrite remains limited to ~54% of Fe2O3, which can be optimized case by case for specific applications [Ohta 1963]. In Fig. 3, adapted from Ohta [Konig 1975], the magnetocrystalline anisotropy constant, K1, magnetostriction constant, λs, saturation magnetization and Curie temperature, of the pure MnZn ferrite are mapped onto the MnZn-ferrite ternary phase diagram. It is necessary for low loss power MnZn-ferrites to be selected from the region corresponding to the highest magnetization and Curie temperature, while concomitantly maintaining near-zero anisotropy (K1) and magnetostriction (λs) constants. However, it is not possible to simultaneously realize all of these desirable properties in a single composition. Trade-offs in performance must be tolerated. One approach to rectifying this problem, is the selection of a composition from the region of high saturation magnetization and Curie temperature, while compensating for the anisotropy constant by the addition of suitable dopants that are soluble in the spinel lattice (e.g., Co2+, Ni2+). As a reminder to the reader, the focus of this review is to provide an in-depth examination of composition and process requirements that impact the grain boundary regions of low loss MnZn ferrite power inductor cores for MHz applications. As such, for further details on the selection of the principal phase, the reader is directed to the text provided by Goldman and references contained therein [Goldman 2006].

Fig. 3. Properties of MnZn ferrites superimposed on the MnZn-ferrite ternary phase diagrams. [Konig 1975 and Goldman 2006], where K1 is the anisotropy constant, λs is

III. Design of grain boundary regions

Grain boundaries are regions of chemical and microstructural discontinuity to the crystal lattice between neighboring grains. Crystal structure of the grain boundaries is defined by the crystallographic orientation of adjacent grains. This lattice perturbation in the grain boundary region results in the formation of 1D (interstitial and substitutional lattice defects), 2D (edge and screw dislocations, and stacking faults), and 3D (pores and voids) defects (See Fig. 4). The grain boundaries can be classified depending upon the nature of the interface between the principle grains as coincidental and general. Coincidental grain boundaries can be described as a planar interface of dense grains having crystal lattice planes of {111}, {110} and {311} Miller plane families. General boundaries have random interfaces with few corresponding to {111} and {110} planes and are shown to accommodate higher amounts of dopants [Berger 1990].

Fig. 4. Schematic of the lattice orientation transition, socalled grain boundary, at the interface of principle grains.

Grain boundaries can act as nucleation centers for the formation of domain walls [Fidler 1979]. As such, grain boundaries can affect magnetic domain wall widths and mobilities. Segregation of inclusions, impurities and vacancies to the GB region further enhanced by stress forces [Herring 1950]. Such phenomenon takes place during the dwell stage in sintering. The driving force for preferential collocation of impurities at the grain boundaries originates from the lower elastic strain field and the lower atomic densities characteristic of the grain boundary regions as opposed to the principle grains. In a similar manner, the secondary

phases segregate to the grain boundary in order to reduce the free energy of the crystal. Well delineated grain boundaries can be observed using scanning electron microscopy (SEM) after appropriate chemical etching treatments. This is a very effective tool to evaluate microstructure, density, and texture. A less popular, but still useful technique is the application of acoustic microscopy that allows for an evaluation of variations in elastic properties. In these applications, the grain boundary area can be readily distinguished from the principle grains. Analogously, thermal wave microscopy makes use of variation in thermal conductivity of the GB and principle grains. The ultimate tool is the application of transmission electron microscopy (TEM) that allows high resolution imaging of structures based on variations in electron density. Often, in SEM and TEM columns, energy dispersive X-ray spectroscopy (EDXS) is available by the generation of X-rays emanating from the surface of the crystal under bombardment by the electron beam. Here, a scanned beam allows for a high spatial resolution of the chemical constituents of the grains and grain boundaries. Using these techniques, the lattice disturbance at the grain boundaries of polycrystalline ferrites are shown to extend over 0.5 to 10 nm [Goldman 2006]. The perturbation in structure and chemistry are also exposed in the atomic structure and space charge distribution in the proximity of these regions. The space charge perturbation can extend up to a few 100 nm.

III. Electrical and Magnetic Properties of the Principle Grains and Grain Boundaries From an electrical point of view, polycrystalline ferrites can be modeled with an equivalent circuit. In this model, the principal grains are represented by a resistance, RG. Correspondingly, the GB region is represented by a parallel combination of resistance, RGB, and capacitance, CGB, that effectively describes the important contribution of the grain boundary insulating properties and polarization processes

to the electrical behavior of polycrystalline MnZn-ferrite cores [Cheng1984, Drofenik 1997]. The grain and grain boundary equivalent circuits are in series. Figure 5 depicts an interpretation of the polycrystalline ferrite with an expanded view of the GB region.

Fig. 5. Depiction of an interpretation of the polycrystalline ferrite as an equivalent circuit with an expanded view of the GB region.

The grain boundary region, being a discontinuity in structure and chemistry of the crystal lattice, is characterized as having a large electrical resistance, RGB, in comparison to the principal grains’, RG. The high RGB derives from a high intrinsic density of defects as well as reduced electron hopping between divalent and trivalent cations due to the preferential oxidation of divalent cations in this region [Goldman 2006]. The use of this model allows for the application of impedance spectroscopy to further analyze the impact of grain boundary modifications upon the electrical properties of polycrystalline ferrites. In particular, the eddy current loss suppression attributed to the grain boundary properties versus that of the bulk grains’ can be readily distinguished providing insight of the underlying mechanisms. Furthermore, the nature of the dissipation channels can be explored in terms of the morphological distribution of the additives and their solubility in the principle phase. According to the equivalent circuit model, the grain boundaries’ capacitive equivalent lumped element acts as an open circuit under DC condition, leaving the boundaries and grains to

act as electrically resistive elements. The second intercept corresponds to the DC response, representing the summation of the grains’ and grain boundaries’ resistances, i.e., Rg+Rgb. In contrast, the first intercept corresponds to the high frequency response, representing RG, only. This is due to the fact that at high frequencies the space charge (i.e., Maxwell-Wagner) polarization on the boundary surfaces and the subsequent displacement current act to shortcircuit the grain boundary layers. This model has great utility in distinguishing the electrical properties of secondary phase additives from the main phase, e.g., as was demonstrated by Andalib et al. [Andalib 2017], the addition of ferrimagnetic additives to MnZn-ferrite displaces the second intercept to higher values with increasing additive weight fraction, while the first intercept remains largely unchanged, indicating no solubility in the main phase thus proving the efficacy of the approach. As is well known, the two processes that give rise to magnetization of the MnZn-ferrite are: first, the spin rotation that responds to the direction and intensity of the applied magnetic field inside each magnetic domain until the sum of the magnetostatic energy and the anisotropy energy has reached its minimum value, and seconds, domain wall (DW) motion during the growth of magnetic domains toward the minimization of the total magnetostatic energy [Stopples 1996]. Therefore, the permeability spectrum of the MnZn-ferrite is defined by two distinct damping mechanisms at MHz frequencies, i.e., one associated with DW motion with resonance at lower frequencies and the other associated with spin rotation with nonresonant relaxation at higher frequencies. [Dionne 2003] Correspondingly, the overall magnetic response for a more general case can be described by the superposition of dispersive equations of these two mechanisms [Tsutaoka T. 1997 and 2003, Wohlfarth E. P. 1980]: 1

1

1

1

⁄

⁄

⁄

⁄

1

⁄

Where and are the initial susceptibilities associated with DW motion and spin rotation, respectively, where and are the frequencies of DW resonance frequencies and spin rotation. For the case of MnZn-ferrite, this equation can be simplified to: 1

1 1

1

⁄

⁄

⁄

boundary discontinuities. The thickness of this nonmagnetic region can vary depending on the thickness of the lattice orientation transition region and the segregation of insulating oxides in this region [Johnson and Visser 1987]. At the surface of the grains, where lattice mismatch gives rise to the boundary effect resulting in surface pinning of the spin system, an increase in exchange energy is experienced [Pankert 1994]. To probe further this phenomenon, the free energy about the equilibrium can be expanded as below and solved by imposing the pinned magnetization vector [Landau 1983 and Pankert 1994], where is the bulk susceptibility. !"



1 )%* '( + , $ %& '( 2 1 '( -'( . 2

Boundary condition: '( |

0 /

=0

The solution to this equation in the cylindrical coordinate system is a nonhomogeneous magnetization which is a Bessel function of the ratio of position and domain wall thickness as represented below. 2

3456

71

49 2

:; 2⁄29 : 2⁄29

<

This waveform captures the frustration of the magnetization vectors at the gain boundaries. Fig.6. Schematic diagram of the frequency dependent dispersive magnetization damping phenomena [Dionne 2003].

The schematic of the coexistence of these two magnetization processes as a function of frequency can be seen in figure 6 [Dionne 2003], where τ is the effective spin-lattice relaxation time. According to the nonmagnetic grain boundary (NMGB) model, the lattice disorder and magnetic discontinuity, characteristic to the grain boundary region, disturbs the magnetic flux over the boundary region contributing to the pinning of domain wall motion by the grain

Since the interfaces of two neighboring grains experience mismatched lattice orientation, these so-called grain boundaries, i.e., lattice orientation transition regions also experience copious anion vacancies that disrupt the indirect super-exchange coupling between ferrite grains that require an oxygen bridge for magnetic coupling of cation spins and long-range magnetism [Smit 1959]. Therefore, this area is the medium over which the spins of the neighboring grains interact via dipolar coupling [Pankert 1994]. Figure 7 represents the phenomenological energy surfaces for the case of cubic anisotropy. Such is the case for spinel ferrites and in

particular MnZn-ferrites. For K1<0 the magnetic anisotropy energy experiences maxima along the [100] family of crystal directions. For K1>0 the opposite trends occur with energy minima along these crystal directions.

Fig. 7. Phenomenological energy surfaces for the case of cubic anisotropy [Yang 2018].

In the grain boundary region, the spinel lattice experiences a breaking of crystal symmetry, thus resulting in a sharp local rise in the anisotropy field. This perturbation in magnetic anisotropy energy provides a barrier to spin rotation and domain wall motion increasing switching losses related to coercivity and residual effects. Such disruption to crystal lattice continuity are also observed in the surface termination of ferrite nanoparticles giving rise to anomalous ac and dc magnetic behaviors [Swaminathan 2005 and Swaminathan 2006]. The temperature dependence of permeability and hysteretic loss is strongly affected (inversely proportional) by the magnitude of magnetic anisotropy energy. Therefore, to attain the minimum loss the chemistry of the principle phase is required to be engineered to experience K1~0 at the anticipated operational temperature and frequency. The nonmagnetic grain boundary (NMGB) model presented by Johnson and Visser [1987]. assumes that the grain boundaries are regions of nonmagnetic, or low permeability, that surrounds the principal grains that cause internal demagnetization fields. As demonstrated by van der Zaag [1998], this theory sufficiently describes the initial permeability behavior for low anisotropy ferrites (e.g., MnZn-ferrite, specifically high permeability MnZn-ferrite) with an average grain size of D≤16 µm. According to this model, the effective

permeability of the polycrystalline ferrite can be expressed by µeff =µiD/(µiδ’+D), where D is the average grain size, µ i is the intrinsic permeability within the grain, µ GB is the permeability of grain boundary, and δ’=δ/µGB is the effective grain boundary thickness. Based on this model, the increase in the effective thickness of the grain boundaries due to the collocation of nonmagnetic impurities to this region results in a substantial sacrifice to the permeability. The demagnetizing field introduced to the system by the insertion of magnetic inclusions is smaller than the case of nonmagnetic inclusions. This depiction is consistent within the framework of the nonmagnetic grain boundary (NMGB) model presented by Johnson and Visser [1987]. One of the most important aspects of the design of magnetic cores is the minimization of core power loss. In order to optimally control all factors contributing to power dissipation, total core power loss (CPL) can be deconvolved into quasi-static and dynamic losses based on the frequency dependence of the underlying dissipation mechanisms. Hysteresis loss, being a quasi-static mechanism and sensitively related to microstructure, impurities, and defects including grain boundary microstructure, is the dominant dissipation channel associated with domain wall displacement in MnZn-ferrites. This loss is due to the so-called Barkhausen transitions of domain walls [Graham 1982] that derives from the pinning of magnetic domain walls as they are swept through the material in response to the applied ac magnetic fields. The fact that the energy dissipation by this loss is independent of frequency can be used to separate this component from other dissipation channels. =>*

?@ @

A2

B>*

?@ @

C

D> EF

Classical eddy current loss, being the dynamic loss that first appears in the dissipation frequency spectra of MnZn-ferrite, is an ohmic loss that becomes important at around 200 KHz and escalates rapidly to become a dominant contributing factor to the CPL at frequencies above 400 KHz. The minimization of this component mainly relies on the dispersion of the

grain boundary’s electrical properties. Eddy current induction simulations by Fiorillo [2014], shown in the figure 8, illustrates the induced current patterns at the two ends of the frequency spectra. At 10 KHz the induced currents in the low resistivity semiconducting grains, so called micro-eddy currents, remain trapped by the grain boundaries and circulate only within the individual grains due to the very high lowfrequency resistivity of the grain boundaries. Whereas at the higher frequencies, as the resistivity of the grain boundaries decline by the displacement currents due to the space charge (i.e., Maxwell-Wagner) polarization, the socalled long-range eddy currents strengthen until at ~10 MHz the grain boundaries are shortcircuited by the displacement currents, whereupon the long-range eddy current circulate throughout the entire cross section area of the polycrystal sample.

Fig. 8. Current pattern of a) micro-eddy currents and b) long-range eddy currents corresponding to 1 KHz and 10 MHz eddy current induction in the cross section of a commercial MnZn-ferrite sample, respectively [Fiorillo 2014].

The classical eddy current loss equation, derived from Maxwell equations, dates to Steinmetz [Graham 1982] and is provided by Fiorillo as: [Fiorillo 2014] MNOPPQM

I =@G5H * G A2 JKKL R

S T ⁄16 V

[J/m3]

R W R

,

Here, Jp is the peak amplitude of the magnetic polarization, and Mp/µ with Mp being the peak magnetization. The frequency dependance of this dissipation mechanism can be used in the extraction of its contribution to the total CPL. It is noteworthy that another magnetic loss is associated with the eddy current induction

mechanism. This so-called excess eddy current originates from the domain wall displacements including Barkhausen jumps of domain walls. This current is negligible for semiconductors such as the MnZn-ferrite due to their lower conductivity as opposed to metallic alloy where this loss becomes considerable. The model put forth by Bertotti for magnetic metallic alloys [Bertotti 1988, Fiorillo 2014] for excess eddy current power loss per unit volume is presented below. Here Bp is the peak magnetic flux, f is the frequency, S is the cross-sectional area of the core, and K is a constant found by fitting to the measured data. B@@&G@*

@&G@ @ *

X

Y E;.\ C ;.\ Z C

The residual loss is the next loss in the CPL spectrum that emerges as the operating frequency approaches the domain wall’s natural resonance frequency that falls in the MHz range. Domain wall motion can be described using the Landau-Lifshitz-Gilbert (LLG) equation of motion, where ] is the effective wall mass per unit area, is the damping coefficient per is the restoring coefficient per unit area, and unit area of the domain wall experiencing displacement x from its equilibrium position. [Dionne 2003]

]

]

;

abc

] k

^_

|ef |

d

alP o mnQ ablP ; m|ef |

g

^`

where h

where

r0

^

2' -

ij H

blP |ef |



;

p 0 or

Here, J is the spin exchange energy, a0 is the lattice constant, k is the wall damping time constant, and o is the wall surface area per unit volume. Solving this equation yields the natural undamped wall oscillation which by inspection is dependent on the spin exchange energy, A,

anisotropy and the wall surface area per unit volume. sKt

vc

uKt

m

wh|

; |o

.

The same calculations yield the domain wall associated susceptibility as presented below. x

]

2'

X)

o

+

$k

1

,

The frequency at which the domain wall associated permeability peaks (see figure 6), can be obtained by finding the minimum of the denominator. @H6 z yKt

X

1 2k

These equations indicate that the dispersion of the associated loss with this resonance, being residual loss, is also dependent on the wall damping time constant k . Therefore, this relaxation time is also another factor determining how the domain wall resonance will contribute to CPL at lower frequencies. Another source of loss at MHz frequencies is quantum tunneling of charge carriers through the intragranular boundaries. The significance of this nonlinear effect is due to very strong electric fields (e.g., at 100 mT this electric field is as strong as 1.5 KV/m at 500 KHz and ~3 KV/m at 1 MHz) induced across the narrow grain boundaries, leading to the tunneling of electric charge through these layers. Charge transport via quantum tunneling across grain boundaries can be categorized as a source of eddy current loss. This quantum tunneling effect only becomes a factor for high flux densities at high frequencies and is in part responsible for the measured nonlinear core loss enhancement that is not attributable to classical eddy current losses. [Roshen 2007]

Fig. 9. Schematic of the space charge polarization, the subsequent displacement current and quantum tunneling at the interfaces of the polycrystalline MnZn-ferrite.

Additionally, the dielectric loss from the relaxation of the electric dipoles gain significance at MHz frequencies. As can be seen in Fig. 10, for the case of Ferroxcube 3E27 MnZn-ferrite under the applied magnetic field of 50 mT, the dielectric loss becomes comparable to the ohmic eddy current loss at about 2 MHz and above [Loyau 2012]. Based on the equivalent circuit model, the dielectric loss of the polycrystalline ferrite is the power loss of the equivalent capacitors arising from the relaxation of electric dipoles. Therefore, this loss can be evaluated by measuring the imaginary part of the permittivity, ε″ of grains and grain boundaries. Analogously, this dissipated power can be calculated from the real part of the equivalent capacitance and the associated current density in the equivalent lumped element of each region. To the best of our knowledge, despite the significance of the dielectric loss experienced in MnZn ferrites at MHz frequencies, sufficient studies have not been conducted.

orders of magnitude higher than that of the principle grains. During the sintering, the grain boundaries serve as pathways for the transportation of constituent atoms and subsequent ripening by the Oswald mechanism [Ostwald 1896]. The presence of more grain boundaries during later stage sintering will result in faster phase transformation, recrystallization, and the convergence to pure phase. This has been shown by Yao et al. to require lower presintering temperatures and shorter soaking times. [Yao 1990] Fig. 10. Comparison of dissipation mechanisms of Ferroxcube 3E27 MnZn-ferrite under the applied magnetic field of 50 mT, studied by Loyau et. al. [2012].

IV. Modification of the Material Processing for the Control of Grain Boundary Properties Traditional ceramic processing protocols have been refined over the past several decades to enhance ferrite performance to meet technological advances and demands for reduced size and weight, together with enhanced efficiency and lower core loss. Although many subtle adjustments have been made over the years to improve the structure, chemistry and electromagnetic performance, the fundamental protocols remain largely the same. The ferrite processing can be viewed in three stages of presintering and attaining pure phase; obtaining a green compact of appropriate density, particle size and shape; and, the sintering of the final engineered product. When one considers that the Ostwald ripening of grains is both time and temperature dependent, it is obvious that sintering conditions are of great import to grain boundary properties. The presintering time and temperature determines to a large degree the grain boundary area. Higher presintering temperatures and longer presintering soak times result in the formation of larger grains and therefore fewer grain boundaries compared to fine-grained materials. Lattice disorder at the grain boundaries play an important role in the formation of pure phase crystals in that grain boundaries, possessing 10 to 30% lower density than the principle grains [Ruhle 1982], offer a pathway to high atomic diffusion - up to several

Attaining grain uniformity, in other words, the uniform distribution of grain boundaries, is essential in the manufacturing of low loss power ferrites for several reasons, including the prevention of local spikes in the induced eddy currents that result in localized overheating. Such effects lead to localized reduction in magnetization resulting in saturation of the core and catastrophic failure. This is an acute problem at spots with low densities of grain boudaries, commonly occuring with the formation of over-grown grains near to the surface. These nonuniform grains also give rise to anomalous strain fields that can manifest as magnetoelastic anisotropy losses. Such a uniform grain distribution must be controlled by determining the optimum ramp rates during the final sintering. In the fabrication of high frequency low loss ferrites in conjuction with lower sintering temperatures and the slower ramp rates result in the formation of thicker grain boundaries. In order to maintain a high grain boundary impedance at high frequency the grain boundary capacitance must decrease, thus creating less displacement current. The significance of grain boundary thickness is its impact on the capcitive behavior of these layers and the dispersion of displacement current and eddy current loss. Furthermore, maintaining a high density of grain boundaries (i.e. small grain size) is important in the design of high frequency low core loss MnZn-ferrites. Due to the crucial role that grain boundary electrical properties play in the suppression high frequency CPL, MnZn-ferrites for high frequency power applications require smaller grains. The grain size can be both

controlled by sintering conditions and grain growth inhibitors or promoters. At frequencies approaching and exceeding 1 MHz, the principle grains of MnZn-ferrite must remain small, on the order of ~ 5-10 µm, in order to both increase the resistivity from increased grain boundary density, and to shift the cut off frequency to upper MHz, far from the operational frequency. Tuning the grain size is feasible by controlling the sintering temperatures and times. The atmosphere used during sintering stages plays a pivotal role in the ferrite microstructure. The most crucial part of atmospheric control, including that used during the initial stages of cooling where rapid oxygen diffusion allows for control of the oxidation state of the ferrite cations in the grain boundary regions. The concentration of oxygen at the grain boundary regions reaches up to 10 times that of the principle grains with corresponding diffusion rates up to 106 to 108 times higher [Meiser 1980]. As a result, grain boundary oxidation during cooling is a crucial factor in the design of low loss and high permeability MnZn-ferrites. Oxidation of the grain boundary, being proportional to the electrical resistivity of the grain boundary, has a direct impact on the induced eddy current and therefore the core losses specifically at higher frequencies. During dwell, the partial pressure of oxygen (i.e., PO2) controls the Fe2+ concentration on the octahedral sites and therefore directly affects the electrical conductivity of the grains. As was discussed by Rikukawa [1985] an increase in PO2 results in a few wt% reduction in Fe2+ or the ratio of Fe2+ to the Fe3+ ions. Having stronger positive centers results in quenching the long range tunneling or hopping of electrons between the iron ions of different valence, which leads to a modest increase in principle grain resistivity. Additionally, the diffusion of cations into the principle grains, in the vicinity of the grain boundaries is determined in large by the concentration of the cation vacancies. Therefore, by controlling the concentration of vacancies one can control the diffusion rate. This may also be done by adjusting the PO2 during dwell to determine the appropriate cation mobility, which

controls the distribution of impurities along the boundaries. A high PO2 promotes the accumulation of impurities to the triple junctions by increasing the cation mobility, whereas low PO2 results in impurity cations remaining at the bicrystal junctions between two neighboring grains. For the optimization of PO2, other parameters impacted by atmospheric conditions, such as the likelihood of intragranlar Zn ablation at higher sintering temperatures and lower pressures, must be taken into account. Such ablation leaves behind signature intragranular pores and defects within the grains, driving the ferrite from its nominal composition and resulting in inferior performance. [Zaspalis 2003]. As temperature drops during the first stages of cooling, down to 900-1000 oC, there will be an enhancement observed in the strain energy of the system, resulting in further segregation of impurities to the grain boundary regions in order to release the stress by lowering the strain energy in this low-density region. The segregation can be directly controlled by the adjustment of cooling rates, as the slower cooling allows for the formation of enhanced segregation. V. Effectiveness of available approaches for the suppression of MHz eddy current loss At MHz frequencies considerable displacement currents across grain boundaries exacerbate eddy-current losses that worsen as the flux density in the grain boundary layers increase. In order to further extend the effectiveness of this approach to a broader range of frequencies, capacitance of the grain boundaries must be reduced to suppress displacement currents. For the case of polycrystalline ferrites, the space charge (i.e., Maxwell-Wagner) polarization (see Figs. 5 and 9 and the corresponding displacement currents, are affected by both electrical and structural properties, e.g., permittivity, microstructure and the thickness of the grain boundary layers. Although the grain boundaries’ insulating properties are essential in eddy current loss

suppression, the so-called “giant-dielectric phenomenon” of these layers can increase the overal dielectric constant up to 50,000 [Loyau 2012 and Sinclair 2002]. The giant dielectric constant (GDC) has been realized in inhomogeneous ceramics, where the polycrystalline ferrite material (henceforth referred to as bulk) effective permittivity is orders of magnitude larger than the intrinsic permittivity of the principle phase. This phenomenon is attributed to the internal barrier layers’ capacitive (IBLC) properties, i.e., grain boundaries’. As a result, the effective dielctric constant of the bulk is defined by the microstructure of the ceramic. In particular, the bulk effective permittivity is mainly defined by the properties of the very thin grain boundaries of only 10s of nm thickness due to their high capacitance, which dominates the capacitive properties of the polycrystalylline ferrite (in another words the effective dielectric permittivity). Therefore, the bulk permittivities are expected to be ~1000 times (the ratio of grain diameter, ~ few µm, to the grain boundary thickness, ~ few nm) higher than the intrinsic permittivity of each region. As an exmaple, for Ferroxcube 3E27 MnZn-ferrite the bulk effecitive permittivity is ~8.3×104, where the intrinsic permittivity of the grains and grain boundaries are ~350 and ~100, respectively. This high bulk effective permittivity is attributed to its intergranular layer thicknesses that is estimated to be ~10-20 nm. V.A. Collocation of Incongruent Insulating Nonmagnetic Additives to Grain Boundary Regions The collocation of insulating secondary phases to the grain boundaries, including oxides of CaO, SiO2, Nb2O5, Ta2O5, HfO2, ZrO2, V2O5 has been a standard approach for the suppression of induced eddy-currents. Using nonmagnetic oxides as grain boundary additives make MnZnferrites available for power applications to 100s KHz [Goldman 2006, Inaba 1996, Žnidaršič 1999, Otsuki 1991, Akashi 1961]. Modification of the grain boundaries using these nonmagnetic oxides may not provide appreciable improvement to core power loss suppression for

applications approaching MHz frequencies as the displacement currents emerge and increase. This approach has been extensively studied and shown to be greatly beneficial at 100s of KHz but offers <50% effectiveness in the suppression of eddy current losses at f>1 MHz. A new class of additives, consisting of high resistivity ferrimagnetic nanoparticles, was proposed by Chen and Harris in 2012 and commercialized by Metamagnetics Inc. This approach has been shown to significantly reduce core power losses in MnZn-ferrite inductors for operation at f>1 MHz. The extended utility is ascribed to modification of the dispersion of both permeability and dielectric properties of the grain boundaries towards retaining a high intergranular magnetic coupling and operational AC resistivity. [Chen and Harris US 9117565 B2, Andalib 2017, Andalib 2019, Hanson 2016] As was mentioned previously, the intergranular segregation of elements is dependent on the interfacial geometry that define the density of cation vacancies and thus the intrinsic grain boundary mobility. The more atomically disordered the grain boundaries, the more they can accommodate a high concentration of additive ions, where the diffusion of these ions can assist the crystallographic transition from one grain to the adjacent grain [Berger 1990]. We conjecture that the mobility of additives and the resulting elemental patterns and diffusion depth, detectable by energy dispersive x-ray spectroscopy (EDXS), are essential design metrics in determining the dispersive behavior of displacement currents at MHz frequencies. The diffusion rate is affected by different factors including the ionic radii of the additive ions, the nature of the cation vacancies at the grain boundaries, as well as the partial pressure of oxygen during the heat treatments. CaO has been the most commonly used grain boundary additive and has been studied most extensively for applications below MHz frequencies. Studies by Znidarsic et. al. [1995] showed that the addition of just 0.14 wt-% CaO leads to a 53% total core loss reduction at the expense of 31% reduction in permeability at an operating temperature of 80 oC at 0.7 MHz.

In contrast, additives with melting temperatures lower than the sintering temperature, such as SiO2 and V2O5, form an intergranular liquid phase during heat treatments that enhance mass transport along grain boundaries promoting grain growth and increasing the density of magnetic cores. When used in conjunction with CaO, the fluxes assist with the distribution of Ca2+ ions at grain boundaries and overcome grain growth inhibition related to the strain created by introduction of CaO. The Si4+ ion with a small ionic radius (i.e., 54 nm) is capable of filling cation vacancies in the surface regions of the principle grains. This is opposite the trend of Ca2+ ions of a very large ionic radius (i.e., 114 nm) that remain largely localized in the interfacial region, as demonstrated by EDXS measurements reproduced as Fig 11. As a result, codoping with Si4+ can be beneficial in reducing the capacitance of the GBs which leads to a lower displacement current at MHz frequencies.

Fig. 11. EDXS analysis of the segregation of CaO and SiO2 across the grain boundary regions [Tsunekawa 1979].

Typically, ~0.1 mol% of CaO and ~0.02 mol% of SiO2 are commonly employed. Addition of higher amounts of CaO have been reported to be detrimental to core magnetic properties, while higher amounts of SiO2 resulted in exaggerated grain growth and have been shown to have an adverse impact on the homogeneity of grain size and morphology. Additions of Niobium ions, typically up to 200 ppm into the MnZn-ferrite by the introduction of

Nb2O5, have been shown effective in the suppression of eddy current losses at MHz frequencies. EDXS analysis of Nb ion distribution in MnZn-ferrites indicates a sharp atomic concentration of Nb ions at the grain boundary regions. Nb-oxides, when used in conjunction with CaO and SiO2, was shown to reduce the diffusion depth of Ca2+ and Si4+ ions from 6 nm to less than 2 nm (see Fig. 12) [Inaba 1996, Tsunckawa1979], which was attributed by the authors to be associated with reduced lattice distortion of the main phase in the vicinity of the boundaries, from the paired Nb5+ and Ca2+ ions into the CaNb2O6 phase at the grain boundary, which results in the necessary charge balance. Formation of similar compounds of other divalent ions (i.e., Fe, Mn, Zn) with Nb2O6 was also suggested [Inaba 1996, Tsunekawa 1979]. Similarly, other additives with transition metal elements of high valence, i.e., 4+ and 5+, in oxides of V2O5, Nb2O5, Ta2O5 , TiO2 , ZrO2 , and HfO2, are also able to improve magnetic properties by forming ion pairs with Ca2+ and Fe2+ at the grain boundary region. Their efficacy is determined by the solubility of these additives in the spinel lattice, their melting point and sintering conditions. The narrowing of grain boundaries may not be desirable for the suppression of displacement currents since it leads to an increase in capacitance of the grain boundaries. Consequently, the effectiveness of cooping of 280 ppm of Nb2O5 with 350 ppm of CaO and 180 ppm SiO2, as presented by Inaba [1996], resulted in only 12% loss suppression at 1 MHz at a cost of 10% reduction in permeability.

be detrimental to magnetic performance. Studies by Topfer et al. [2015] shows ~20% reduction in loss at 1 MHz at the cost of a 34% drop in permeability (25 mT and 80 oC), by addition of 400 ppm of V2O5 to the host MnZn-ferrite containing 200 ppm of Nb2O5, 500 ppm of CaO, 100 ppm of SiO2 and 250 ppm ZrO2.

Fig. 13. Impact of optimization of the sintering temperature on the effectiveness of Nb2O5 and V2O5 grain boundary additives on the CPL of the host containing CaO and SiO2 additives. [Cheng 2001]

Fig. 12. EDXS analysis of chemical distribution reflecting the relative ion concentration of elements across the grain boundary of samples with Nb oxide (a) additive (b) and host [Inaba 1996].

Additionally, segregation of Nb cations has been associated with reduction of the Zn ion deficiency by preventing the Zn evaporation, where reduced lattice defects is beneficial in lowering internal stress [Pankert 1994]. V2O5 is another transition metal with high valence but a relatively low melting temperature of 670 °C, that results in the formation of liquid phase and partially evaporates during the sintering [Shokrollahi 2008]. Therefore, V2O5 is typically used as a co-additive, where it has been shown (see Fig. 13) to lead to 62% loss suppression at 3 MHz after optimizing the sintering temperature [Cheng 2001]. However, the impact of these additives was also shown to

Tables 2 and 3 summarize the impact of the addition of each grain boundary additive on the DC grain boundary resistivity, estimated AC grain boundary resistivity at the operational frequency and the percentage of the suppression of eddy current loss, based on the results presented by Otsuki et. al. [1991]. In this study, all modified samples have similar grain size in order to rule out grain size contribution to the trends and performance.

Table 2- DC and AC resistivity enhancement and eddy loss suppression at 1 MHz (100 mT, 60 °C) by CaO as the GB additives to the MnZn-ferrite containing 0.02 wt% of SiO2 [Otsuki 1991] >{ ? >{ ? CaO ρl{ | ρ ρl{ ΔB@ ⁄B@>{ ? G G HG |ρHG content 0.02

13.8

3.94

51.5%

0.04

30.8

5.04

80.1%

Note: ρl{ represents the resistivity of the host sample modified by additives collected under dc conditions.

Table 3- DC and AC resistivity enhancement and eddy loss suppression at 1 MHz (50 mT, RT) for different grain boundary additives (similar grain size) [Otsuki 1991]

Co-doping 0.02 wt% of SiO2 and 0.04 of wt% CaO GB additives

ρl{ |ρ>{G G

?

ρl{ |ρ>{ HG HG

?

ΔB@ ⁄B@>{

HfO2

8

1.85

45.8

Nb2O5

4.5

1.1

7

Ta2O5

5.5

1.56

36.1

V2O5

2.8

1.47

32

ZrO2

4.1

1.3

23.6

GB additives

HfO2 Nb2O5 Ta2O5 V2O5 ZrO2

ρl{ |ρ>{G G

Single doping ? ρl{ |ρ>{ HG HG

1 3.4 16.4 3.88 6.25

1.04 1.92 3.7 1.55 3.7

?

ΔB@ ⁄B@>{

?

?

4 48 73 35 73

By these evaluations, codoping of additives containing high valence (i.e. 4+ and 5+) cations with Ca2+ has been successful in increasing the DC resistivity by up to 2.8-8 times that of the host material. However, this effect is much smaller as the operational frequency approaches 1 MHz where they only provide 1.1-1.85 times higher AC resistivity values compared to the host compound, while, the addition of CaO and SiO2 oxide retains an AC resistivity 3.94-5 times higher than the host at 1 MHz. The significant reduction in the effectiveness of these GB modifiers, can be attributed to the narrowing of the grain boundary by the paring of Ca2+ with high valence ions as described previously, which results in increasing the capacitance of the grain boundaries and the displacement current.

ferrite as proposed by Chen and Harris in 2012 [US 9117565 B2]. Introduction of electrically insulating ferrimagnetic oxide nanoparticles of NiZn-ferrite and Yttrium Iron Garnet (Y3Fe5O12,YIG) ferrite was shown to effectively suppress the induced eddy current losses with minimal adverse effects to the magnetic properties and efficiencies of the cores (See Fig. 14). The high permeability and Curie temperature values associated with this approach was ascribed to the positive contribution of the magnetic secondary phase at the grain boundaries in strengthening the intergranular magnetic interactions between neighboring grains and reducing the local magnetic anisotropy field perturbations in contrast to their nonmagnetic counterparts. The required conditions for the nanoparticles of magnetic oxide additives include incongruency with respect to the host lattice, high melting point, low magnetic anisotropy, low coercivity, high permeability and magnetization, high AC resistivity, and uniformity in size, morphology and chemistry. In processing, the effective and homogenous distribution of well-dispersed nanoparticles to the intergranular regions is essential.

V.B. Collocation of Incongruent Insulating Magnetic Additives to Grain Boundary Regions

Fig 14. SEM image of a representative magnetic NP-doped sample illustrating the surface decoration of grain surfaces.

Another approach in suppression of the eddy current loss at MHz frequencies is the introduction of a second phase of high resistivity magnetic nanoparticles to the polycrystalline

The introduction of ferrimagnetic yttrium iron garnet (Y3Fe5O12; resistivity >1010 Ohm-cm) nanoparticles resulted in an 83% reduction in core power loss (see Fig. 15) mainly associated

with the reduction of eddy current losses (i.e., ~80%, see Fig. 16) at the cost of a 24% drop in permeability. In comparison, a control sample with a diamagnetic barium titanite oxide additive (BaTiO3; resistivity >1012 Ohm-cm) showed a comparable loss suppression at the cost of a 65% drop in permeability (see Fig. 17) [Andalib and Harris 2017 and 2019].

Fig. 17. Comparison of the effectiveness of ferrimagnetic vs. diamagnetic nanoparticles in retaining the amplitude permeability (at 0.5 MHz, 30 mT and RT) [Andalib and Harris 2017].

Impedance spectroscopy of the modified samples implied nearly unchanged resistivity of the main phase. Alternatively, the grain boundary resistivity increased nearly 10 times that of the host (Fig. 18). Fig. 15. Assessment of the effectiveness of ferromagnetic vs. diamagnetic nanoparticles in the suppression of core power loss density (at 0.5 MHz, 30 mT and RT) [Andalib and Harris 2017].

Fig. 18. Complex impedance dispersion curves and DC resistance of GBs (inset) of the parent compound and those modified with magnetic NPs. Fig. 16. Impact of the magnetic nanoparticle additions on the eddy current loss in comparison with the nonmagnetic counterpart (at 0.5 MHz, 30 mT and RT) [Andalib and Harris 2017].

Fig. 19. Capacitance of GBs for the parent compound and those modified with magnetic NPs [Andalib and Harris 2017].

As can be observed in figure 19, in addition to increasing the grain boundary resistivity, the introduction of the magnetic nanoparticles to the grain boundaries also reduced the undesirable charge polarization and displacement current by reducing the capacitance of the grain boundary layers. Based on this results, addition of these magnetic nanoparticles is able to reduce the induced electric field across the intergranular layers and suppress the quantum charge tunneling source to core loss. [Roshen 2007] Therefore, this technique has been demonstrated as a successful strategy to mitigate high frequency heat dissipation while maintaining a high permeability and efficiency. This approach requires only a small alteration to chemistry and processing and is therefore adaptable to industrial scale processing at low cost. The thermal image selected from the thermal movie (see Fig. 20) of the operating temperature (at 3 MHz, 10 mT) of the Metamagnetics HIEFF 13 material compared with a Ferroxcube 4F-1 over a 30 minutes time lapse showed that HI-EFF 13 core exhibits a peak temperature, half that of the 4F1 core [Metamagnetics 2014].

Fig. 20. Thermal image of comparison of the operating temperature (at 3 MHz, 10 mT) of the Metamagnetics HIEFF 13 material compared with a Ferroxcube 4F-1 over a 30 minute time lapse.

The performance factor is a valuable metric for the evaluation of commercial cores. Comparison of the standard performance factor (F = Bf) and permeability of the leading samples available for operation at MHz frequencies is presented for 2, 5 and 7 MHz in Fig. 21 based on the measurements performed by Hanson et al. [2016] in which the magnetic flux densities correspond to the CPL of 500 mW/cm3. The Metamagnetics HI-Eff 13 cores manufactured by Metamagnetics Inc. using ferrimagnetic NP additives demonstrates marked improvement in the standard performance factor while retaining a high permeability of ~400 and saturation induction Bs ~400-500 mT up to 7 MHz. The Snoek product, (µrxfr), was ~ 72008400 [Chen and Harris US 9117565 B2]

Andalib P, Scappuzzo F S and Harris V (2018), Device and method for deep transcranial magnetic stimulation, US Patent 9,925,388 Andalib P and Granpayeh N (2009), All-optical ultracompact photonic crystal AND gate based on nonlinear ring resonators, JOSA B 26 (1), 1016, Andalib P and Granpayeh N (2009), All-optical ultra-compact photonic crystal NOR gate based on nonlinear ring resonators, Journal of Optics A: Pure and Applied Optics 11 (8), 085203 Akashi T (1961), Effect of the addition of CaO and SiO2 on the magnetic characteristic and microstructures of Manganese-Zinc ferrites (Mn0.68Zn0.21Fe2.11O4+δ), Trans. J I M 2, 171-176 Alcf.anl.gov/intrepid Andrae A and Edler T (2015), Challenges 6, 117–157 Berger M, Laval J (1990), Local resistivity and crystallochemistry of grain boundaries in semiconducting ceramics, J de Physique Colloques 51(C1), C1965-C1970 Bertotti G (1988), General properties of power losses in soft Ferrimagnetic materials, IEEE Trans., Magn. 24, 612-630

Fig. 21. Comparison of the standard performance factor and permeability of the leading samples available for operation at MHz frequencies is presented for 2, 5 and 7 MHz (Ferroxcube 4F1, Fair-Rite 52, Fair-Rite 61, Fair-Rite 67, Metamagnetics HiEff13, National Magn. M5, National Magn. M, National Magn. M3, Ceramic Magn. N40, Ceramic Magn. CM5, Ceramic Magn. C2050, Ceramic Magn. C2025 and Ceramic Magn. XTH2).

VI. References Andalib P, Chen Y and Harris V G (2017), Concurrent core loss suppression and high permeability by introduction of highly insulating intergranular magnetic inclusions to MnZn ferrite, IEEE Magn. Lett. 9, 5100705, DOI: 10.1109/LMAG.2017.2771391

Chen Y and Harris V G, Magnetic grain boundary engineered ferrite core materials, US Patent 9,117,565 Chen Y, Andalib P, Harris V, Magnetic materials with ultrahigh resistivity intergrain nanoparticles, US Patent 16/181,298 Chen S H, Chang S C, Tsay C Y, Liu K S and Lin I N (2001), Improvement on magnetic power loss of MnZn-ferritematerials by V2O5 and Nb2O5 codoping, J European. Ceramic. Soc. 21, 1931-1935 Cheng H (1984), Modeling of electrical response for semiconducting ferrite, J. Appl. Phys. 58, 1831-1837Chung U C, Elissalde C, Morne S C, Maglione M, and Estournès C (2009), “Controlling internal barrier in low loss BaTiO3BaTiO3 supercapacitors,” Appl. Phys. Lett. 94, 072903

Dionne G F (2003), Magnetic Relaxation and Anisotropy Effects on High-Frequency Permeability, IEEE Trans. Magn. 39 (5), 31213126 Data-economy.com/data-centres-world-willconsume-1-5-earths-power-2025/ Datacenterknowledge.com/archives/2014/12/17/ undertaking-challenge-reduce-data-centercarbon-footprint Datacenterknowledge.com/asiapacific/greenpeace-china-s-data-centers-trackuse-more-energy-all-australia Drofenik M, Žnidaršič A, Zajc I (1997), High resistivity grain boundaries in doped MnZn ferrites for high frequency power supplies, J. Appl. Phys. 82, 333-340 Fiorillo F, Beatrice C, Bottauscio O, Carmi E (2014), Eddy-current losses in Mn-Zn ferrites, IEEE Trans. Magn. 50 (1), 6300109 Fortune.com/2019/09/18/internet-cloud-serverdata-center-energy-consumption-renewablecoal/ Graham Jr. C. D. (1982) Physical origin of losses in conducting ferromagnetic materials, J Appl. Phys. 53, 8276 Goldman A (2002), Magnetic Components for Power Electronics, Springer Science New York Goldman A (2006), Modern ferrite technology, 2nd ed., Springer US Harris V G, Geiler A, et al. (2009), Recent advances in processing and application of microwave ferrites, J. Magn. Magn. Mat. 321 (14), 2035-2047 Hanson A J, Belk J A, Lim S, Perreault J and Sullivan C R (2016) Measurements and performance factor comparison of magnetic materials at high frequency, IEEE Trans. On Power Electronics 31 (11), 7909-7924 Harris V G (2012), Modern Microwave Ferrites, IEEE Trans. on Mag. 48 (3), 1075-1104

Hitachimetals.com/materialsproducts/amorphous-nanocrystalline.php Hu B, Chen Z, Su Z, Wang X, Daigle A, Andalib P, Wolf J, McHenry M E, et al. (2014), Nanoscale-driven crystal growth of hexaferrite heterostructures for magnetoelectric tuning of microwave semiconductor integrated devices, ACS nano 8 (11), 11172-11180, DOI: 10.1021/nn504714f Herring C (1950), “Diffusional Viscosity of a Polycrystalline Solid,” J. Appl. Phys. 21, 437 Johnson M T and Visser E G (1990), A coherent model for the complex permeability in polycrystalline ferrites, IEEE Trans. Magn. 26(5), 1987-1989 Janghorban J and Shokrollahi H (2007), “Influence of V2O5 addition on the grain growth and magnetic properties of Mn–Zn high permeability ferrites, J Magn. Magn. Materials, 308 (2): 238-242 Inaba H, Abe T, Kitano Y, and Shimomura J (1996), Mechanism of Core Loss and the GrainBoundary Structure of Niobium-Doped Manganese–Zinc Ferrite, J. Solid State Chem. 121, 117-128 Konig U (1975), Improved manganese-zinc ferrites for power transformers, IEEE Transactions on Magnetics, Mag-11 (5), 13061308 Landau L D and Lifshitz E M (1983), Elektrodynamik der Kon- tinua (Berlin) Loyau V, Wang G Y, Lo Bue M and Mazaleyrat F (2012), An analysis of Mn-Zn ferrite microstructure by impedance spectroscopy scanning transmission electron microscopy and energy dispersion spectrometry characterizations, J. Appl. Phys. 111, 053928 Meiser H, Gleiter H, Mirwald R W (1980) Effect of hydrostatic pressure on the energy of grain boundaries em dash structural transformations. SCR Metal 14(1), 95–99

Micromarketmonitor.com/market-report/ferritemagnets-reports-1040172605.html

One-step internal barrier layer capacitor,” Appl. Phys. Lett. 80(12), 2153

Marketersmedia.com/global-soft-ferrite-coremarket-growth-rate-cagr-analysis-and-forecastto-2025-shared-in-a-latest-research/428875

Smith J. and H. P. J. Wijn (1959), Ferrites Wiley, New York

Metglas.com Metamagnetics, Inc. (2014), youtube.com/watch?v=dI-nF1OFS-g Mhwintl.com/products/magnetics/magnetec/nanoper m-low-cost-cores/ Nomura T (2003), Hand book of advanced ceramic, Magnetic Ceramics, CH 6.1 Nature.com/articles/d41586-018-06610-y

nrdc.org/resources/americas-data-centersconsuming-and-wasting-growing-amountsenergy Otsuki E, Yamada S, Otsuka T, Shoji K, Sato T (1991), Microstructure and physical properties of Mn-Zn ferrites for high-frequency power supplies, J Appl Phys 69, 5942-5944 Ouyang G, Chen Xi, Liang Y, Macziewski C and Cui J (2019), Review of Fe-6.5 wt%Si high silicon steel - A promising soft magnetic material for sub-kHz application, J Magn. And Magn. Mat. 481, 234-250 Ostwald W (1896), Lehrbuch der Allgemeinen Chemie 2(1), Leipzig (Germany) Ohta K (1963), J Phys. Soc. Japan 18, 685 Pankert J. (1994), Influence of grain boundaries on complex permeability in MnZn ferrites, J Magn. Magn. Mat. 138, 45-51 Roshen W A (2007), “High-frequency tunneling magnetic loss in soft ferrites,” IEEE Trans on Magn. Vol 43 (3), 968-973. Ruhle M (1982) In Symp on Grainoundary and Interface in Ceramics. Extended Abst 3 S II-82 Sinclair D C, Adams T B, Morisson F D and West A R (2002), “CaCu3Ti4O12:CaCu3Ti4O12:

Shokrollahi H, K Janghorbani (2007), Influence of additives on the magnetic properties, microstructure and densification of Mn–Zn soft ferrites, Mat. Sci. Eng. B 141, 91-107 Swaminathan R, McHenry M E, Poddar P and Srikanth H (2005), Magnetic Properties of Polydisperse and monodisperse NiZn ferrite nanoparticles interpreted in a surface structure model, J. Appl. Phys. 97, 10G104-10G104-3 Swaminathan R, Willard M A and McHenry M E (2006), Experimental Observations and Nucleation and Growth Theory of Polyhedral Magnetic Ferrite Nanoparticles Synthesized Using an RF plasma torch, Acta Mat. 54, 807816. Stoppels D (1996), Developments in soft magnetic power ferrites, J Magn. Magn. Mat. 160, 323-328 Tsunekawa H, Nakata A, Kamijo T, Okutani K, Mishra R K, and Thomas G (1979), IEEE Trans. Mag. MAG-15(6), 1855 Töpfer J and Angermann A (2015), “Complex additive systems for Mn-Zn ferrites with low power loss” J. Appl. Phys. 117, 17A504 Tsutaoka T (2003), Frequency dispersion of complex permeability in Mn–Zn and Ni–Zn spinel ferrites and their composite materials, J Appl. Phys. 93 (5), 2789-2796 Tsutaoka T, Nakamura T, and Hatakeyama K (1997), Magnetic field effect on the complex permeability spectra in a Ni-Zn ferrite, J. Appl. Phys. 82, 3068-3071 Van Der Zaag P J, Kolenbrander M, Rekveldt M Th (1998), The effect of intragranular domain walls in MgMnZn-ferrite, J. Appl. Phys. 83, 6870-6872 Wang X, Su Z, Sokolov A, Hu B, Andalib P, Chen Y, Harris V G (2014), Giant magnetoresistance due to magnetoelectric

currents in Sr3Co2Fe24O41hexaferrites, Applied Physics Letters 105 (11), 112408, DOI: 10.1063/1.4896326 Wohlfarth E P (1980), Ferromagnetic Materials North-Holland, Amsterdam 12, 243 Wu G, Yu Z, Tang Z, Sun K, Guo R, Zou X, Jiang X, and Lan Z (2018) “Effect of CaCO3 and V2O5 Composite Additives on the Microstructure and Magnetic Property of MnZn Ferrites”, IEEE Trans. on Magn, VOL. 54, NO. 11, Art. No. 6300707 Znidarsic A, Limpel M and Drofenik M (1995), “Effect of Dopants on the magnetic properties of MnZn ferrites for high frequency power supplies,” IEEE Tans. Magn. 31 (2), 950-953 Žnidaršič A and Drofenik M (1999), High resistivity grain boundaries in Cao-doped MnZn ferrties for high frequency power application, J. Am. Ceram. Soc. 82, 359-365

Highlights of the article In this article we present:

1. The latest trends in processing, composition, theory, and utility of spinel ferrites for use as power inductor cores. 2. We focus on inductor cores for a wide range of applications including power generation, conversion, and conditioning at MHz frequencies. 3. We put forth novel approaches to engineer grain boundary regions in composition, structure, and electrical and magnetic properties to allow spinel ferrites to operate at frequencies well above the state of technology (i.e., f>1 MHz) with low core power loss while concomitantly maintaining high efficiency, high permeability and saturation induction. 4. For the first time, the crucial role of dielectric properties of the grain boundaries and associated displacement current on the CPL of power ferrite at MHz is reviewed. 5. We address required material processing specifications for the fabrication of low loss MHz power applications 6. A survey of performance of the leading commercial low loss power ferrite products is presented. Parisa Andalib & Vincent Harris