5 Key excerpts on "Diamagnetism"

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  eBook - ePub

  Nanoparticles - Nanocomposites – Nanomaterials

  An Introduction for Beginners

  • Dieter Vollath(Author)
  • 2013(Publication Date)
  • Wiley-VCH

    (Publisher)

  8 Magnetic Nanomaterials, Superparamagnetism

  8.1 Magnetic Materials

  On putting any material into a magnetic field, one observes two, more or less distinct, reactions: the material is pulled into the magnetic field – paramagnetic behavior – or it is repelled from the magnetic field – diamagnetic behavior. Both reactions are connected to the electronic structure of the atoms, molecules, or solids. Any material is diamagnetic; however, in many cases, this Diamagnetism is superimposed by paramagnetism, which is stronger; therefore, these materials belong to the group of the paramagnetic materials.

  Diamagnetism is caused by the movement of the electrons around the atomic nucleus. According to Faraday's law of magnetism (more specifically known as Lenz's rule) the magnetic field caused by the circular motion of the electrons is oriented opposite to the external field. The electrons move not only around the nucleus, they also rotate around their axis. This spin of the electrons also causes a magnetic moment. In cases, where the electrons are paired, the spins are directed opposite. Therefore, in an atom with an even number of electrons, the magnetic moments of the spins compensate each other; these atoms are diamagnetic. All the other atoms are paramagnetic. The same rules are valid in the case of compounds. For the further discussion in connection to nanoparticles and nanomaterials, only paramagnetic materials in their different varieties are of importance.

  Figure 8.1 displays the situation for a crystallized solid without an external magnetic field. This figure shows the cases where the orientation of the elemen­tary dipoles are disordered, paramagnetism, and the one, with ordered mag­netic dipoles, ferromagnetism. In ferromagnetic materials, the dipoles interact; a process leading to a long-range ordering, lining up the dipoles parallel, or in the case of antiferromagnetic materials, antiparallel. A ferromagnetic body, as depicted in Figure 8.1

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  Fundamentals of Electric Machines: A Primer with MATLAB

  A Primer with MATLAB

  • Warsame Hassan Ali, Matthew N. O. Sadiku, Samir Abood(Authors)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  Curie temperature. In this process, magnetic fields are automatically directed in one direction at the Curie temperature to generate a magnetic field. At the Curie temperature, these magnetic fields are directed back to their random direction of high temperature. The intensity of one field is equal in size and is the direction of one field parallel to some in the same direction. Also, a total torque of each field does not have to be in the direction of the other field’s intensity itself. Thus, the piece of the electromagnetic material may not have a total magnetic torque, but when placed within an external magnetic field, the inhibition of the individual fields will go together in the same direction forming a total determination. So, the notable magnetic property of the ferromagnetic material is to turn into another kind of magnetic material at Curie temperature. The elements Fe, Ni, and Co are typical ferromagnetic materials which are characterized by the ability to attract and repulse with other magnetic objects.

  FIGURE 1.2Magnet applications in the loudspeakers.

  Paramagnets: This substance that shows a positive response to the magnetic field, but it’s a weak response. The amount of response is determined by a standard called magnetic susceptibility, which represents the ratio of the magnetic force of the material to the magnetic field strength, which is a quantity without units. The paramagnetic phenomenon is observed in substances whose atoms contain single electrons (while these electrons are usually conjugal and opposite), so its magnetic torque can’t be zero. Paramagnetic materials include transient and rare substances in nature or generally substances whose atoms contain non-conjugate electrons. The magnetic properties of these substances depend on the temperature. Examples of these substances are sodium, potassium, and liquefied oxygen.

  Diamagnetism

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  Gateway to Condensed Matter Physics and Molecular Biophysics

  Concepts and Theoretical Perspectives

  • Ranjan Chaudhury(Author)
  • 2021(Publication Date)
  • Apple Academic Press

    (Publisher)

  Z. Therefore, in the classical theory, the free energy of a system remains invariant when an external electromagnetic field is applied. Again, magnetization induced is proportional to the derivative of the free energy with respect to the external magnetic field. Thus, our simple calculation presented above shows that no magnetization is induced in a classical system even in the presence of an external magnetic field, in thermodynamic equilibrium.

  The above analysis clearly implies that magnetism of materials, as observed, will have to be essentially a quantum phenomenon. Therefore, we will have to deal explicitly with the quantum mechanical Hamiltonians for describing all types of magnetism. To clarify this point, for example, even though the phenomenon of Diamagnetism is a universal one and is based on the property of classical electromagnetic induction, the finite diamagnetic response is only obtainable in a fully quantum mechanical treatment of the material system which is coupled to the electromagnetic field. For the other forms of magnetism, however, the microscopic origin itself is quantum mechanical besides the necessity of using quantum variables in the Hamiltonian.

  The phenomenon of Diamagnetism or more precisely, orbital Diamagnetism is a universal one, as stated before. Every system in this universe exhibits diamagnetic response, i.e., negative magnetic susceptibility. Its magnitude, i.e., the absolute magnitude of the diamagnetic susceptibility, however, is generally quite small and is very often masked by the higher magnitude of the spin response (positive magnetic susceptibility) from the other forms of magnetism like paramagnetism. The only exceptions are superconductors and some of the band insulators. These above-mentioned systems behave as “super-diamagnets,” where the diamagnetic susceptibility attains the highest value possible

  v i z .

  − 1

  4 π

  .

  . Moreover, these systems have vanishingly small spin susceptibilities. As a result, the overall magnetic response of these systems is very prominently diamagnetic.

  The origin of orbital Diamagnetism is electromagnetic induction, as has been pointed out before. The applied magnetic field is opposed by the induced orbital screening current, governed by Faraday’s Law or Lenz’s Law. The simplest quantum mechanical model incorporating this effect was suggested by Landau among many others. The model essentially describes a collection of non-interacting electrons in the presence of an external electromagnetic field. It should be emphasized that the system of electrons is treated quantum mechanically but the electromagnetic (e.m.) field is regarded as classical. The Hamiltonian of such a system is given by, as used earlier in Eqn. (2.1)

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  Magnetic Resonance Imaging

  Physical Principles and Sequence Design

  • Robert W. Brown, Y.-C. Norman Cheng, E. Mark Haacke, Michael R. Thompson, Ramesh Venkatesan(Authors)
  • 2014(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  losses in gradient-echo imaging. On the other hand, susceptibility is also another intrinsic tissue property and local variations in susceptibility can be useful in identifying special properties or states of the body; this is the focus of the present chapter. These differences will manifest themselves as signal changes in both magnitude and phase images, and can be used to diagnose or extract important information about body function.

  We begin by laying out brief descriptions of different magnetic behavior of various material, the ‘isms’ of para-, dia-, ferro-, antiferro-, ferri-, and superparamagnetism. The magnetic susceptibility and permeability parameters in the field equations are considered next. These parameters can be strong functions of positions, especially at tissue interfaces and in the vicinity of contrast agent particles; thus, objects embedded in the background material are studied in the third section. The full expressions for the local field for both a sphere and an arbitrarily oriented cylinder are presented. The remainder of the chapter is devoted to the blood oxygenation dependent susceptibility in functional MRI.

  25.1 Paramagnetism, Diamagnetism, and Ferromagnetism

  Inside of a body, a spin is subject to an internal field due to its neighbors, in addition to any external field. The internal field is dominated by the nearby atomic electrons, and individually their contributions can be well approximated by magnetic dipole fields corresponding to the magnetic dipole moments associated with their orbital and spin degrees of freedom. Neighboring nuclear magnetic moments are reduced in importance owing to the inverse-mass dependence first noted in Ch. 2 , but the existence and size of the atomic moment is also based on the question of whether there are unpaired constituents, in this case the atomic electrons. The electron magnetic moments are intrinsic or can be induced and, in this section, the classification of materials according to the different kinds of magnetic dipole moments is laid out.

  25.1.1 Paramagnetism

  The quantum stacking of electrons in an atom or molecule involves a systematic cancelation of spin moments for each pair. An atom with an unpaired electron has a nonvanishing permanent magnetic moment with an associated nonzero dipole magnetic field, and is referred to as ‘paramagnetic.’ While these moments would be randomly distributed in the absence of outside interactions, they would tend to align with an external magnetic field, producing a bulk magnetic moment and a corresponding macroscopic magnetic field augmenting the external field.

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  Rad Tech's Guide to MRI

  Basic Physics, Instrumentation, and Quality Control

  • William H. Faulkner, Euclid Seeram(Authors)
  • 2020(Publication Date)
  • Wiley-Blackwell

    (Publisher)
• Some substances have both diamagnetic and paramagnetic properties. In this event, since the paramagnetic effects are stronger, the substance exhibits paramagnetic characteristics.
• Ferromagnetic substances are similar to paramagnetic substances in that they become magnetized when placed in an externally applied magnetic field.
• Ferromagnetic substances, however, will remain magnetized when the externally applied field is removed.
• Iron is an example of a ferromagnetic substance.
• A dipole is a magnet with two poles: north and south.
• By convention, the magnetic field of a dipole runs from the north pole around to the south pole.
• When two identical poles are brought together, the resultant fields oppose each other and thus they repel.
• When two opposite poles are brought together, the resultant fields combine and the two magnets are pulled toward each other.
• The strength of a magnetic field is expressed in terms of Gauss or Tesla.
• Gauss is the CGS (Centimeter‐Gram‐Second ) unit of magnetic flux density.
• Tesla is the International Standard (SI ) unit of magnetic flux density.
• The earth's magnetic field strength is approximately 0.5 G.
• One Tesla equals 10 000 G.

Nuclear Magnetism

In the early days of MRI, the term

nuclear magnetic resonance

(NMR ) was used. The word nuclear, however, elicited visions of radioactivity, thus the name was changed to MRI. In reality, the term nuclear