Magnetic Susceptibility

10 Key excerpts on "Magnetic Susceptibility"

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  Magnetic Cell Separation

  • (Author)
  • 2011(Publication Date)
  • Elsevier Science

    (Publisher)

  CHAPTER 1 Magnetic Susceptibility Maciej Zborowski Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, Cleveland, OH 44195, USA zMagnetic Susceptibility is a material property that describes re-sponse to an applied magnetic field [1–7]. Experimentally it is measured by the amount of force exerted on a defined amount of the substance by a well ‐ defined magnetic field. Every substance is responsive to the magnetic field, but in the majority of cases the response is too weak to be of practical importance. Such substances are considered ‘‘nonmagnetic’’ for all intents and purposes. The Magnetic Susceptibility of the ‘‘nonmagnetic’’ materials becomes ap-parent in the presence of high magnetic fields and gradients that become increasingly accessible for biological and clinical applications [8]. Here we restrict the discussion to the static and quasistatic magnetic field e V ects, and therefore the static Magnetic Susceptibility. The simplest experimental configuration to measure Magnetic Susceptibility is that of the magnetic balance, Fig. 1.1, the design of which goes back to Faraday. The most sensitive methods of Magnetic Susceptibility measurement apply alternating current (AC) fields and sample vibration, and are reviewed elsewhere [9, 10]. The magnetic force exerted on a volume V of substance characterized by the volume Magnetic Susceptibility w is expressed by Eq. (1.1): F ¼ w VH d B 0 d x ð 1 : 1 Þ # 2008 Elsevier B.V. All rights reserved DOI: 10.1016/S0075-7535(06)32001-3 Laboratory Techniques in Biochemistry and Molecular Biology, Volume 32 Magnetic Cell Separation M. Zborowski and J. J. Chalmers (Editors) where H and B 0 are magnitudes of the applied magnetic field vectors (for definitions see Chapter 2 and Appendices A, B, and C). The volume Magnetic Susceptibility is dimensionless.

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  Crude Oil Exploration in the World

  • Mohamed Abdel-Aziz Younes(Author)
  • 2012(Publication Date)
  • IntechOpen

    (Publisher)

  2. Magnetic Susceptibility All substances, solids and fluids, are affected by the application of a magnetic field. The direction of magnetic force lines changes in the presence of different types of magnetic substances. Diamagnetic substances cause a reduction in the density of magnetic force lines making the applied field weaker. In contrast paramagnetic and ferrimagnetic substances cause an increase in the density of magnetic force lines making the applied field stronger. The analogue of such a change of magnetic field inside a substance, named magnetic induction B, is described as follows in the SI system: B =  0 (H+M) (1), where H is the magnetic field strength,  0 is the permeability of free space, and M is the intensity of magnetisation of a substance, related to the unit of volume. The  0 is equal to 4  10 -7 Henry/m. It is convenient to have the parameters in equation (1) independent of magnetic field strength. Thus dividing equation (1) by H we have:  = B/H =  0 +  0 M/H =  0 +  0  v (2) In this equation  is the relative permeability, which is proportional to the dimensionless coefficient the volume Magnetic Susceptibility (  v ). The volume Magnetic Susceptibility is a measure of how magnetisable a substance can become in the presence of a magnetic field (Equation 3).  v= M/H [dimensionless] (3) Magnetic Susceptibility is one of the most informative fundamental magnetic parameters (Ivakhnenko, 1999). Besides the volume susceptibility, there exists specific or mass Magnetic Susceptibility,  m , Magnetic Susceptibility of Petroleum Reservoir Crude Oils in Petroleum Engineering 73  m =Mm/H=  v /  [10 -8 m 3 kg -1 ] (4) measured in m 3 kg -1 . Mass Magnetic Susceptibility is defined as the ratio of the mass magnetisation (M m ) to the magnetic field (H) or as the volume Magnetic Susceptibility (  v ) divided by the density (  ) of the substance (Equation 4).

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  Environmental Magnetism

  Principles and Applications of Enviromagnetics

  • Mark Evans, Friedrich Heller(Authors)
  • 2003(Publication Date)
  • Academic Press

    (Publisher)

  The outcome, in terms of our mental picture, is that two types of arrow are required, one longer than the other. As in antiferromagnetism, the two sets are opposed, but a strong magnetization can obviously arise if the two types are sufficiently unequal. This point will be discussed further in Chapter 3 in the context of specific minerals of interest. 2.2 Magnetic Susceptibility Suppose a suitable piece of a material in which we are interested is placed in a uniform magnetic field (H) and thereby acquires a magnetization per unit volume of M (Fig. 2.1). Its Magnetic Susceptibility (K) is defined as the magnetization acquired per unit field, K- M/H (2.1) In SI units, both M and H are measured in A/m, so K is dimensionless. Strictly speaking, K is called the volume susceptibility: to obtain what is called the mass susceptibility, we divide by the density (p), • = K/p (2.2) Because K is dimensionless, X has units of reciprocal density, m 3/kg. In some situations, it is more convenient to introduce the magnetic moment of the entire body. This is simply given by the product Mv, where v is the total volume, the resulting units being Am 2. In diamagnetic materials, the precessing electrons give rise to values of X on the order of 10 -8 m3/kg. Water is one of the strongest, with • -0.90 • 10 -8 m3/kg, many common rock-forming silicates, such as quartz and calcite, having values about half as large. Paramagnetic materials have strongly temperature-dependent susceptibilities de- scribed by Curie's law (Pierre Curie, 1859-1906), K = C/T (2.3) 10 2 Basic Magnetism Magnetic Susceptibility H v H = magnetic field [A/m] M = magnetization/volume [A/m] v = volume [m31 p = density [kg/m 3] Volume susceptibility Mass susceptibility K: = M/H [dimensionless] X = rJp [m3/kg] Magnetic moment = Mv [Am 2] Figure 2.1 Definition of Magnetic Susceptibilityand related parameters. where T is absolute temperature and C is Curie's constant (see Box 2.2).

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  Electrons, Neutrons and Protons in Engineering

  A Study of Engineering Materials and Processes Whose Characteristics May Be Explained by Considering the Behavior of Small Particles When Grouped Into Systems Such as Nuclei, Atoms, Gases, and Crystals

  • J. R. Eaton(Author)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  (20.3) 388 MAGNETIC PROPERTIES OF MATERIALS 389 The term (μ — μ 0 )Η, known as the intensity of magnetization, may be attribu-ted to the response of the material to the applied magnetic intensity. The factor (μ — 0 ), known as the Magnetic Susceptibility κ, is a property of the material. The susceptibility κ is explained on the basis of the microscopic behavior of matter, which differs from one class of materials to another. If κ is negative, the material is said to be diamagnetic. In diamagnetic ma-terials, a magnetic field of given intensity is established less readily than in free space. If κ is positive but of value small compared to μ θ9 the material is said to be paramagnetic; if κ is positive and large compared to μ θ9 the material is said to be ferromagnetic. Both paramagnetic and ferromagnetic materials are mag-netized more readily than free space. The magnetic properties of materials arise from three different sources, all of which find common expression in Ampere's law which states that the flow of current produces a magnetomotive force: (1) Each nucleus, consisting of an assembly of charged particles of finite volume, spins on its axis. As the movement of each proton in a circular path constitutes current flow, it follows that the spinning nucleus gives rise to a magnetic effect. However, it is found that this effect is too small to account for the bulk magnetic properties of matter. (2) The orbital motion of electrons about the nucleus of an atom results in magnetic effects similar to those of current flow in a closed circuit. Although the motion of the electrons is far more complicated than that described by the Bohr model, the net angular motion of each electron gives rise to magnetic ef-fects. In atoms with closed-shell structures, the combined magnetic effects of the several electrons is zero, but in other structures the combined effect is detec-table.

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  The Organic Chemistry of Iron Pt 1

  • Ernst A. Koerner Von Gustorf(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  [1] and M is the (induced) magnetic moment per unit volume (often called intensity of magnetization and denoted then by I ). Here B , H, and M are vector quantities. If we consider an isotropic substance, M depends only on H and is independent of direction M = KH [3] where K is a scalar, the volume susceptibility, which is a measure of the ease of magnetic polarization of the substance. Eq. [2] may now be rewritten B = (1 + 4πκ)Η [4] Often, the quantity that is actually measured is the gram sus-ceptibility (also specific susceptibility) χ defined by X g = K/p [5] and therefrom the molar susceptibility χ is derived where χ^ = x x M = K x V [6] A M A g Here, p is the density, M the molecular weight and V the mo-lecular volume. Paramagnetic substances have χ > 0, whereas diamagnetic substances have χ < 0. Table 1 shows the most 216 Edgar König common types of magnetic behaviour and their properties. The units commonly employed are in case of χ , 10 cgs/g (cgs/g = emu/g = cm /g) and in case of χ , Table 1: Types of magnetic behaviour. g 10 6 cgs/mole. Type Diamagnetism Paramagnetism Ferromagnetism Antiferromagnetism Sign of Susceptibility negative positive positive positive Magnitude of Y at 20°C 1 x 10 6 0 - 100 x 10~ 6 io 2 - io-0 - lOOO x 10~ 6 Dependence on H no no yes yes, no Origin electron charge electron spin /electron (spin exchange In anisotropic substances, e.g. a noncubic single crys-tal, M depends on the direction and on the magnitude of H , and eq. [3] has to be replaced by M = ( K ) H where ( κ) is a symmetric tensor according to Mi M 2 M 3 Kll Ki2 Ki3 K2 1 K22 K23 K31 K 3 2 K33 Hi H2 H 3 [7] [8] In eq. [8], the vector components of IVI and H refer to an or-thogonal coordinate system fixed in the crystal. B. DIAMAGNETISM The effect of a magnetic field on the motion of electrons is to cause a precession of each electronic orbit about the direction of H .

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  Seeing Beneath the Soil

  Prospecting Methods in Archaeology

  • Oliver Anthony Clark, Anthony Clark(Authors)
  • 2003(Publication Date)
  • Taylor & Francis

    (Publisher)

  in situ, but has been eroded and re-deposited in locations such as lake basins and estuaries. The displaced soil can be identified in cores and sections even if the ancient landscape to which it belonged has been swept from the face of the Earth. This is particularly valuable in areas where archaeology is elusive, and where it is uncertain whether human occupation has existed at all in the past. The stratigraphy of such deposits also provides a sequential picture of landscape evolution in which Magnetic Susceptibility peaks can reveal phases of clearance and exploitation.

  Definitions

  Because of the magnetic fields generated by their orbiting electrons, all atoms react to magnetic fields, and have a Magnetic Susceptibility, which is denoted by the Greek letter kappa (). This is commonly slightly negative, when it is known as diamagnetism. Materials with positive susceptibility become magnetized by a magnetic field, an effect especially strong in iron and its compounds. Unlike permanent magnetism, it is only measurable in the presence of the magnetizing field, and is defined as the ratio of the intensity of the induced field to that of the magnetizing field, or K=M/H. Because M and H are measured in the same units in the SI system, these cancel out and the ratio is basically ‘dimensionless’. Therefore, it does not need any unit to define it, although ‘SI’ needs to be added to distinguish readings from those in the old cgs system, which are numerically different.

  In practice a large sample will give a stronger signal in a measuring instrument than a small one. Readings can be related to a standard size of sample, ‘volume-specific’. Although commonly used, this can be imprecise because one often does not know how closely packed the material is—how much of the volume is the material being measured, and how much is air, water or pebbles. The best results are obtained by drying and sieving to remove these biasing effects, and then weighing the sample to produce ‘mass-specific’ readings which give better standardization. All this applies to laboratory measurement on prepared samples: field measurements are more rough and ready, and can only be calibrated in terms of volume susceptibility.

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  Classical Electromagnetism in a Nutshell

  • Anupam Garg(Author)
  • 2012(Publication Date)
  • Princeton University Press

    (Publisher)

  16 Magnetostatics in matter

  Our purpose in this chapter is to obtain a theory for the spatially averaged or macroscopic magnetic field in matter and to develop models for the response of certain types of materials to applied magnetic fields. While the mathematical development parallels that of electrostatics in dielectrics, the physics is quite different. The biggest difference is that, unlike the electric case, the Magnetic Susceptibility may be either positive or negative, i.e., the magnetic response can either oppose or reinforce the applied field. The two cases are known as diamagnetic and paramagnetic , respectively. This difference can be traced to the lack of any work done by the magnetic field on a moving charge. Second, except for ferromagnets and superconductors, the response is much weaker than in the electric case. Thus, there is often little penalty for confusing the magnetic field B with the magnetizing field H , and many authors even use the symbols interchangeably. This leads to much confusion, which we shall avoid with only partial success.

  100 Magnetic permeability and susceptibility

  In magnetostatics, where we study only steady-state situations, the macroscopic equations to be solved are Ampere’s law,

  and the law that B is solenoidal,

  As in the electrostatic case, one needs a constitutive relation between B and H to solve eqs. (100.1) and (100.2). For many materials a linear relationship holds to very good approximation over a large range. If the material is isotropic, we write1

  The dimensionless number μ (in the Gaussian system), or μ/μ 0 (in SI), is known as the permeability of the medium. It has the same value in the two systems. In solid or liquid crystals, it must be replaced by a tensor.

  We also define the Magnetic Susceptibility in parallel with the electric susceptibility:

  This is related to the permeability via It is also a dimensionless number, but

  For the majority of materials for which eq. (100.3) is a good approximation,

  χm

  is very small, of order 10−5 . As mentioned above, unlike

  χe

  ,

  χm

  can be either positive (paramagnets ) or negative (diamagnets ). Because of the smallness of

  χm

  , if either a para- or diamagnetic body is placed in an external B

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  Electronic, Magnetic, and Optical Materials

  • Pradeep Fulay, Jung-Kun Lee(Authors)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  The relative value and sign of Magnetic Susceptibility ( χ m ) or magnetic permeability ( μ ) are often used to classify magnetic materials. The relationships between magnetic field and magnetization for different materials are shown in Figure 11.9. Note that this diagram is not to scale. Also, it does not show the nonlinear nature of ferromagnetic and ferrimagnetic materials. In principle, if you apply a very high magnetic field, the inductance of the paramagnetic materials can be comparable to that of the ferromagnetic and ferromagnetic materials, since the inductance of the ferromagnetic and ferromagnetic materials is saturated at high magnetic field (Figure 11.13). The Magnetic Susceptibility values for some diamagnetic and paramagnetic elements are pre-sented in Table 11.5. H H H H Diamagnetic (μ < μ 0 ) Paramagnetic (μ > μ 0 ) Ferrimagnetic (μ > > μ 0 ) Ferromagnetic (μ > > μ 0 ) Flux density or inductance Vacuum μ 0 H FIGURE 11.9 Magnetic permeability for different types of magnetic materials. Values are not to scale. (From Askeland, D. and Fulay P., The Science and Engineering of Materials , Thomson, Washington, DC, 2006. With permission.) 488 Electronic, Magnetic, and Optical Materials 11.4.3 S UPERPARAMAGNETIC M ATERIALS Another technologically important class of materials is superparamagnetic materials. The superparamagnetism is seen in ferromagnetic and ferrimagnetic materials fabricated in the form of nanoparticles or nanoscale structures, that is, the grain size of a polycrystalline mate-rial becomes of the order of a few nanometers. For example, in the bulk form, BCC (Chapter 2) iron (Fe) is ferromagnetic. As we decrease the size of iron particles or grains from the bulk to a few micrometers and then down to a few nanometers, the thermal energy at room temperature (~ k B T ) becomes comparable with the magnetic energy. Such nanoparticles or nanoscale grains eventually become single domain.

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  Superconductivity

  • Charles P. Poole, Horacio A. Farach, Richard J. Creswick, Ruslan Prozorov(Authors)
  • 2014(Publication Date)
  • Elsevier

    (Publisher)

  5

  Magnetic properties

  The chapter begins with a discussion of susceptibility and magnetic moment. It continues with a treatment of magnetization hysteresis and magnetization anisotropies. Demagnetization factors are explained in detail and then summarized using figures and a table of formulae. The shielding currents and internal magnetic fields characteristic of several ellipsoidal type geometric shapes are explained. Susceptibility and resistivity results are compared with each other. Paramagnetism, Pauli-paramagnetism, and antiferromagnetism are characterized. The properties of an ideal Type II superconductor are delineated.

  Keywords

  Magnetization; superconducting matrix; vector fields; hysteresis loops; expelled flux; magnetic moment; Meissner effect; flux shielding; uniaxial compression; mass susceptibility; internal fields

  I Introduction

  Superconductivity can be defined as the state of perfect diamagnetism, and consequently researchers have always been interested in the magnetic properties of superconductors. In the second chapter, we explained how magnetic fields are excluded from and expelled from superconductors. In Chapter 4 , we examined the thermodynamics of the interactions of a superconductor with a magnetic field. This chapter extends the discourse to a number of additional magnetic properties.

  We begin with a discussion of magnetization, zero-field-cooling (ZFC), and field-cooling (FC), with comments on the granularity and porosity of high-temperature superconductors. Next, we will explain how magnetization depends on the shape of the material and how this shape dependence affects the measured susceptibility. Both ac and dc susceptibilities will be treated. Finally, we will show how samples can be categorized in terms of traditional magnetic behavior, such as diamagnetism, paramagnetism, and antiferromagnetism. The chapter will conclude with remarks on ideal Type II superconductors and on magnets.

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  Molecular Magnetochemistry

  • Sergey Vulfson PhD(Author)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  CHAPTER 1

  DETERMINATION OF AVERAGE MAGNETIC SUSCEPTIBILITIES

  The experimental methods for determination of the average, i.e. scalar, magnetic susceptibilities can be divided into three groups.

  In the first group there are methods based on measuring the force with which the sample interacts with a magnetic field. For example, the Magnetic Susceptibility of a substance placed in a homogeneous magnetic field, can be found with the help of the Gouy balance,

  1 ,2 ,3 ,4 and 5

  the capillary Quincke method,

  2 ,4

  or the viscosimeter method.

  6 ,7

  The Faraday method and its modifications, such as Fereday-Domenicali

  5 ,8

  or Gordon methods,9 are based on measuring the Magnetic Susceptibility in non-homogeneous field

  The second group is composed of induction methods.1 These are based on measurements of the electromotive force produced by vibrating sample or of the inductance of a coil after the sample is inserted into it

  Methods based on the analysis of 1 H chemical shifts in NMR form the third group.

  10 ,11 ,12 ,13 ,14 and 15

  The original method of the determination of magnetic susceptibilities of paramagnetic solid compounds by high field Mossbauer spectroscopy is also included into this group.16

  The author does not consider the specifics of each group. The details of each method can be found in the literature (for example

  1 ,2 ,3 ,4 and 5

  ). Instead, we will focus only on principles of the most widespread and the most promising experimental approaches with the identification of their special features, advantages, and disadvantages.

  1.1.

  Force Methods

  1.1.1.

  The Gouy Method

  The Gouy method is the simplest to implement and, therefore, the most widely used. Gouy set up includes an electromagnet which generates a homogeneous field of 5-25 kG (depending on the magnetic properties of samples); an analytical balance, with the precision of 10−5

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