Synthesis of various magnetic nanostructures and the microwave characterizations 1

1.1.3 Snoek’s law For soft magnetic bulk materials, the product of the intrinsic permeability μi and the resonance frequency ƒr is constrained by a constant related to the saturation...

Chapter 1

Introduction

This work is developed based on the synthesis of various magnetic nanostructures for the application in microwave absorption This chapter gives an overview on the fundamental knowledge on the microwave absorption, the development on magnetic materials for microwave application and large scale synthesis technologies for the magnetic materials After introducing the background information, the motivations of

my research work are listed

1.1 Fundamentals for microwave absorption

Microwave is the electromagnetic waves with wavelengths ranging from 1 cm to 1 m The corresponding frequency range is between 300MHz (0.3GHz) to 300GHz.[1] Microwave technology has been mainly the exclusive domain of the defense industry With the rapid development of communication systems for applications, such as cellular mobile telephony, broadband wireless access, wireless local area networks and satellite base cellular communications, microwave technology is closely bound up with our daily life because these communication systems are employed everywhere, including corporate offices, private homes and public recreation places Although we have benefited from these modern communication systems, the microwave radiation emitted by these systems have severe consequences on our body.[2] Another problem caused by the unprecedented growth of communication systems is the severe

electromagnetic interference among the electronic devices.[3] Therefore, microwave absorbing materials are required to alleviate these problems by absorbing the unwanted microwave

1.1.1 Description of microwave absorption ability

A schematic diagram for the measurement of microwave absorption ability is shown

in Fig 1.1 Ideally, the perpendicular incident microwave is converted into two parts:

the reflected and the absorbed microwaves If Pin is incident power density at a measuring point, and Pr is reflected power density at the same measuring point, Pab is absorbed power by the composite Their relation can be expressed as

respectively Thus, the microwave efficiency can be evaluated from R using Eq (1.3) Larger absolute value of R means more effective wave-absorbing ability of the absorbers.[4]

1.1.2 Calculation of microwave absorption ability

The specular method was commonly used as a theoretical approach in explaining the propagation characteristics of a transverse electromagnetic (TM) wave in a single-layer absorber backed by a perfect conductor For incident wave perpendicular

to the surface of a single-layer absorber backed by a perfect conductor, the input impedance (Zin) at the air-material interface is given by: [5,6]

Zin = Z0(μr∗/ϵr∗)12tanh(γ ∙ t) (1.4)

where Z0 = √(μ0/ϵ0) = 377Ω is intrinsic impedance of free space,

γ = [jω(μr∗εr∗)12] /c is propagation factor in the material, ω is angular frequency, c

is the speed of light and t is thickness of the sample The complex permittivity εr∗ and magnetic permeability μr∗ can be measured experimentally They could be given as

in decibels (dB) can be written as

RL= 20lg|Г| (1.8) When the reflection coefficient (Г) reaches its minimal value zero, which means

Zin = Z0, so called impedance match, the lowest reflection loss can be obtained

Usually, the microwave absorbing characteristics is evaluated by the resonance

frequency ƒr and the reflection loss RL as well as the thickness t of the absorber

Effective microwave absorption refers to a low RL value at a high ƒr position, and a

small t for the design of lightweight absorber

The initial expression of Zin is defined as

Zin = √μr

εr = √μr μ0

εrε0 = Z0 = √μ0

ε0 (1.9)Hence, materials with the property of μr= εr are ideal for microwave absorption

Unfortunately, for the existing materials, the relative permeability generally does not

approach the magnitude of the relative permittivity at microwave frequency band The

difference between these two parameters can be reduced when the permeability of the

magnetic materials is high

1.1.3 Snoek’s law

For soft magnetic bulk materials, the product of the intrinsic permeability μi and the

resonance frequency ƒr is constrained by a constant related to the saturation

magnetization 4πMs, as shown by the Snoek’s law[7]:

(μi− 1)ƒr = 2

3γ4πMs (1.10) where ƒr is resonance frequency and γ ≈ 3MHz/Oe gyromagnetic factor The expression in Eq (1.10) is valid for the polycrystalline bulk materials with uniaxial or cubic magnetocrystalline anisotropy field It shows that there exist trade-offs between high permeability levels and operation at high frequency band Hence an effective way to attain is using magnetic materials with high Ms can be used to obtain high permeability μi at microwave frequency band

There is another expression of Snoek’s law for planar materials, which is given as[8]

(μi− 1)fr = 1

2γ4πMs(Hha

H ea)1/2 (1.11) where 𝐻ℎ𝑎 and 𝐻𝑒𝑎 are the out-of-plane and in-plane anisotropy fields, respectively Other parameters in Eq (1.11) have the same meaning as those in Eq (1.10) When compared these two equations, the difference lies in the right side could be found A smaller 𝐻𝑒𝑎 with larger 𝐻ℎ𝑎is good combination for the materials with higher permeability and higher working frequency, which can be induced by an artificial or anintrinsic bianisotropy system.[9] Hence, the shape construction of magnetic particles is another effective way to attain high permeability μi at elevated frequency range

In a way, the Snoek’ law could be seen as a criterion for magnetic materials used as microwave absorber The calculated value from the right side of equations for the

Snoek’s law is used to evaluate whether a magnetic material could be an effective microwave absorber Researchers usually seek for a large calculated value when design an absorber For this part, we could know that both of the enhancement in the saturation magnetization and the induce shape anisotropic field into the particles can extend the Snoek’s limitation

1.1.4 Skin effect

In the view of the Snoek’s law, high saturation magnetization is required to obtain effective microwave absorption As such, metallic magnetic materials are commonly employed as microwave absorbing materials While for metallic materials, skin effect

is nontrivial due to their relative low resistivity When a microwave wave penetrates into a conductive material, mobile charges on the surface are made to oscillate back and forth in the same frequency as the impinging fields An alternating electric current will be brought by the movement of these charges The current density is greatest at

Fig 1.2 A schematic diagram of the skin effect

Field Strength

X

the conductor’s surface The decrease in current density with depth is so called skin effect,[10] as displayed by the scheme in Fig 1.2 When the depth is d, the corresponding electric field reduces from initial 0 to E, as below:

= 0 ⁄ (1.12)

The skin depth δ is the distance over which the current falls to 1/e of its original value, which is dependent on the electrical conductivity of the materials as well as the incident magnetic field The relationship is described as

Where ƒ is frequency of the wave in Hz, ρ is resistivity of the medium in Ω·m,

μ0 = 4π × 10 7 H/m, μr is relative permeability of the material

The skin effect can dissipate the incident microwave by inducing the eddy current on the surface of the material but hinder the microwave to penetrate into the inner part of the materials Thus, the particle size should not significantly exceed the skin depth for the sake of high microwave absorbing efficiency For example, the resistivity of iron

is ρ = 1 × 10 7Ω·m, when the frequency is ƒ = 5 GHz, its relative permeability is around 10.[11] As a result, the skin depth is around 1 μm Wu et al.[12] have proven that the 1μm carbonyl iron particles show better microwave absorbing performance than 10 μm carbonyl iron particles through experimental results and theoretical calculations The difference is well explained by size-dependent skin effect using the calculation model derived from Landau-Lifshitz-Gilbert (LLG) equation It is necessary to reduce the skin effect of metal-based materials to improve their microwave absorbing ability

1.2 Magnetic materials for microwave absorption

Based on the Snoek’s law and skin effect, the option of magnetic materials used for microwave absorbers should have high saturation magnetization, high anisotropy field and high resistivity

1.2.1 Metallic magnetic materials

Metallic materials (Fe, Co, Ni and their alloys) are commonly used for microwave absorbers due to their high saturation magnetizations.[13-15] The problem of the metallic materials is the skin effect due to the high conductivity, resulting in a very small skin depth Hence the metallic particles used for magnetic filler of microwave absorbers should be pulverized into small particles with a size comparable to the skin depth Non-metal elements, such as boron and silicone,[16-18] are doped into these

alloys to enhance the resistivity Besides, the skin effect could be reduced by structured metallic magnetic particles, such as the Fe nanowires, Co and Fe/Co nanoplatelets, FeSiB flakes and Ni fibers, as well as hollow structures.[19-23] For these structured particles, either the radius size or the thickness of magnetic particles

is less than or comparable with the skin depth Hence the skin effect could be effectively suppressed

1.2.2 Ferrites

Ferrites are usually non-conductive ferromagnetic ceramic compounds derived from iron oxides such as hematite (α-Fe2O3) or magnetite (Fe3O4) In the big family of ferrites, two groups of ferrites, hexagonal ferrites and spinel ferrites, are commonly used for microwave absorbers They are named according to their crystal structures

1.2.2.1 Hexagonal ferrites

There are several types of hexagonal ferrites named as M, W, Y and Z phases.[24-26] The hexagonal ferrites have attracted intensively attentions due to their very strong magnetic anisotropy At room temperature, Co2Z barium ferrite (Ba3Co2Fe24O41)

shows a c-plane anisotropy with a large out-of-plane anisotropy field of 12 kOe and a

small in-plane anisotropy field of about 0.120 kOe.[27] M-type barium ferrite (BaFe12O19) exhibits ferromagnetic resonance around 50 GHz due to its very high magnetocrystalline anisotropy induced by the anisotropic structure.[28] The disadvantage of hexagonal ferrites is the relative low saturation magnetization when

compared with metallic magnetic materials or spinel ferrites, resulting in an insufficient high permeability To overcome this problem, some divalent metal cations (Zn2+, Co2+, Ni2+ etc.) and trivalent cations (Al3+, Cr3+ etc.) are doped to substitute part of Ba2+ or Fe3+ cations.[29-31] The function of the doped element is to change the quantity of spin down or spin up moments, resulting in an enhancement of the saturation magnetization.[32] In some cases, a metallic magnetic layer is coated on the surface of hexagonal ferrites nanoparticles to increase the magnetization.[33]

1.2.2.2 Spinel ferrites

The crystal structure of spinel ferrite is much simpler than that of hexagonal ferrites Normal spinel structures are usually cubic closed-packed oxides with one octahedral and two tetrahedral sites per oxide The tetrahedral points are smaller than the

Fig 1.3 Schematic illustration of normal spinel structure, i.e A 2+ B 3+ 2 O 4 A 2+ is located at tetrahedral sites (bubbles in green tetrahedron); B 3+ is located at octahedral sites (yellow bubbles)

octahedral points B3+ ions occupy the octahedral holes because of a charge factor, but can only occupy half of the octahedral holes A2+ ions occupy 1/8th of the tetrahedral holes Fig 1.3 shows the schematic illustration of spinel structure with A2+ at tetrahedral sites (bubbles in the green tetrahedron) and B3+ at octahedral sites (yellow bubbles)

Inverse spinel structures however are slightly different in that one must take into account the crystal field stabilization energies (CFSE) of the transition metals present Some ions may have a distinct preference on the octahedral site which is dependent

on the d-electron count If the A2+ ions have a strong preference for the octahedral site, they will force their way into it and displace half of the B3+ ions from the octahedral sites If the B3+ ions have a low or zero octahedral site stability energy (OSSE), then they have no preference and will adopt the tetrahedral site A typical example of an inverse spine structure is Fe3O4 In which, Fe2+ ions and half of the Fe3+ ions occupy octahedral sites, while the other half of the Fe3+ ions occupy tetrahedral sites So the electron transfer between Fe3+ and Fe2+ gives rise to ion jumps and relaxation in the

Fe3O4 particles and contributes a particular dielectric loss

It is well known that, MnZn-ferrite (MnaZn1-aFe2O4) and NiZn-ferrite (NiaZn1-aFe2O4) are two typical spinel ferrites suitable for microwave application due to their high permeability Many researches have doped some magnetic or nonmagnetic elements,[34-37] such as Cr, Cu, Co and rare earth elements into the MnZn- and

NiZn-ferrites to enhance the resistivity and further improve the microwave absorbing property As seen from the overviews, no obvious improvement has been made on increasing the saturation magnetization The Snoek’s law limitation still exists even for the doped spinel ferrites, resulting in the resonance frequency positioning at megahertz Inspired by hexagonal ferrites, we have known that the Snoek’s law could

be extended by magnetically anisotropic materials For spinel ferrites, the magnetic anisotropy can be induced by shaping the materials into anisotropic structures Fe3O4

is selected for our works due to its relatively high saturation magnetization (~ 90 emu/g), as well as the well-developed synthesis technologies for Fe3O4

1.3 Brief review of size-controlled synthesis technology

In the design of microwave absorber, magnetic materials have to be used as fine particles dispersed in an insulating matrix Besides the intrinsic properties of magnetic materials, the microstructure and morphology are also important to the microwave absorption performance of the composite The uniformity of magnetic particles in size and shape is very necessary to form homogeneous composite For materials with morphological features on the nanoscale, size-dependent properties become more important For magnetic materials, the particle size is of great importance to the physical properties, such as magnetization, coercivity, domain structure and some critical temperature points (the Curie temperature, the Néel temperature and the blocking temperature) The magnetic recording density is remarkably enhanced while