MAGNETIC+MATERIALS - Types of Materials • ...

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Unformatted text preview: Types of Materials •  Metals: –  Strong, duc4le –  High thermal & electrical conduc4vity –  Opaque, reflec4ve. •  Polymers/plas4cs: covalent bonding –  SoD, duc4le, low strength, low density –  Thermal & electrical insulators –  Op4cally translucent or transparent. •  Ceramics: ionic bonding (refractory) – compounds of metallic & non- metallic elements (oxides, nitrides, carbides) –  BriNle, glassy –  Non- conduc4ng (insulators) •  Composites: –  Composed of two or more individual materials (metals, ceramic, and polymers) –  Proper4es are varied Material Proper4es [1] Mechanical (Force > Deformation) [2] Electrical (Electrical Field > Conductivity) [3] Thermal (Heating > Heat Capacity/Thermal Conductivity) [4] Magnetic (Magnetic Field > Attraction/repulsion & magnitude of response) [5] Optical (Light > Reflection/Refraction) [6] Deteriorative (e.g. Chemical Exposure > Breakdown) MAGNETIC MATERIALS Magne&c Response to an applied magne&c field Magne4c Materials Electricity and magne4sm are two aspects of the same force. Moving charges create a magnetic field, and changing magnetic fields induce electric currents (by induction). Michael Faraday The English chemist and physicist Michael Faraday (b. Sept. 22, 1791, d. Aug. 25, 1867) is known for his pioneering experiments in electricity and magne1sm . Many consider him the greatest experimentalist who ever lived. Several concepts that he derived directly from experiments, such as lines of magne1c force, have become common ideas in modern physics. James Clerk Maxwell James Clerk Maxwell (1831 – 1879): In 1865 he published A Dynamical Theory of the Electromagne4c Field, deriving an electrodynamic formula4on of wave propaga4on using Lagrangian and Hamiltonian techniques, obtaining the theore4cal possibility of genera4ng electromagne4c radia4on. (The deriva4on is independent of the microscopic structures which may underlie such phenomena.) The flux of E through any closed surface = electrical charge density/εo Circula4on of E around a curve C = Δ(flux of B through S)/dt Flux of B through any closed surface = 0 c2(circula4on of B around C) = Δ(flux of E through S)/dt + flux of electric current through S/εo The origin of magne4sm in materials • Magne4c Fields are created by moving electric charge! • Where is the moving charge? Magne4sm in MaNer •  Magnetic moments originate, on an atomic scale, from the orbit and spin of sub-atomic particles - but these effects are also influenced by the electronic configuration of different elements and the way that they combine chemically. •  Electrons in matter have two "classical" motions - spin and orbit. •  In matter, the greatest magnetic effects are due to the spins of electrons rather than their orbital moments. •  The orbital moments play a part as well, but when there are uncompensated spins present in a molecule, the orbital contribution is overwhelmed. The Pauli Exclusion Principle According to the Schrödinger wave equa&on, the wave func&on that describes allowable energy states for electrons to occupy in an atom is characterized by its quantum numbers: n, l, m, and s. n = The principal quantum number. It describes the energy of a given state. l = The angular momentum quantum number. The higher the angular momentum quantum number, the lower the probability of the electron being near the nucleus, and vice versa. It determines the geometric characteris4cs (or shape) of the electron probability distribu4on. m = The magne1c quantum number. Describes the orienta4on of the electron orbital magne4c field with respect to an applied field. This number determines the orienta4on in space of the electron probability distribu4on. Since m affects the energy of the electrons only when they are in an applied field, in the absence of a field, electrons having different m values may s4ll have the same energy. s = The spin quantum number. This is the quantum number that iden4fies the electrons in a state as being either "spin up" or "spin down”. This quantum number is very important for determining magne4c effects in maNer. Electron Spin States Electron spins can exist in two states - spin up (or spin 1/2 and spin down (or spin - 1/2). These two quantum mechanical states produce an4parallel spin magne4c vectors. The Pauli Exclusion Principle The Pauli Exclusion Principle states that no two electrons may occupy the same energy state in an atom. This means that no two electrons may have the same set of values for the quantum numbers n, l, m, s because they would then be indis4nguishable. As electrons are added, they fill up each possible state in a given shell before filling the shell associated with the next higher energy state. The filling of the shells is governed by Schrödinger's wave equa4on and the quantum numbers. Hund’s Rule Electrons are added to subshells in parallel spin configura4ons first (HUND'S RULE). If all electrons are paired, there is no "spin" magne4c moment. These materials are s4ll magne4c though, due to the electron's orbital mo4on. “Uncompenstated” Spins The spin structure of the transi4on series elements (iron in par4cular) is most important for magne4c biomaterials. This is due to the uncompensated spins in the 3d orbital. This gives rise to a "spin" magne4c moment. The spin moment is much stronger than the orbital moment and is aligned parallel to an applied field. Magne4c Materials Magne4c effects in materials can be divided into three categories which are based on electronic configura4on: 1) DIAMAGNETS - Materials in which all electron spins are paired (i.e. there are no uncompensated spins). 2) PARAMAGNETS - Materials in which there are uncompensated spins (i.e. there is not a spin - 1/2 for every spin +1/2). 3) FERROMAGNETS - Materials in which there are uncompensated spins which are coupled/linked either directly or via an intermediate anion. Diamagne4sm • According to Faraday’s Law, when a magne4c field is applied/changed, there is an electric field induced/changed due to effects on the orbi4ng (i.e. moving) electron. • This produces a torque on the electron which gives the electron extra angular momentum. • This extra angular momentum produces a magne4c moment, the sign of which is nega4ve [i.e. opposes the inducing field]. • Therefore, diamagne4c materials are repelled in magne4c fields [they have weak, nega4ve magne4c suscep4bility]. • Diamagne4c materials are materials in which the electron spin moments are compensated. Paramagne4sm Paramagne4c materials are those in which individual atoms, ions or molecules have some number of uncompensated spins and thus a permanent net spin magne4c moment. As the spin moment is much larger than the orbital moment, we would therefore expect that the behaviour of paramagne4c materials when placed in a magne4c field will be governed by the behaviour of the spin magne4c moments. This is indeed the case. Paramagne4sm When paramagne4c substances are placed in an external magne4c field, the uncompensated spin moments tend to align, to some degree, parallel to the applied field direc4on. The magne4c energies involved in this alignment are rela4vely small and the energy associated with thermal agita4on tends to work against the alignment, having a randomizing effect. The degree of alignment of the uncompensated spins with the applied magne4c field depends therefore on the strength of the field (the stronger the field, the greater the degree of alignment up to very high fields) and the temperature (the hoNer the material, the lower the degree of alignment in the same applied field). Since the spin moments in paramagne4c materials align with the applied field, they add to it, so that the net effect is that these materials are aNracted to a magne4c field (and they have a posi4ve magne4c suscep4bility). Paramagne4sm The linear temperature dependence of the magne4c suscep4bility in paramagne4c materials was worked out by Pierre Curie and is known as Curie's Law: M = C (B/T) so the magne4c suscep4bility of paramagne4c materials is also temperature dependent. When B=0, the magne4za4on is also 0. This means that when a paramagnet is not in a magne4c field, it has zero net magne4za4on. Remember, Curie's Law applies only to paramagnets. Ferromagne4sm •  Ferromagne4sm may be thought of as a special case of paramagne4sm in which the individual spin magne4c moments are interac4ng (ie. the moments are coupled). •  The uncompensated spins in individual atoms of a ferromagne4c material may couple either directly (direct exchange) or through an intermediate anion - usually oxygen (super exchange). •  In crystals of a ferromagne4c material, this gives rise to a net magne4c moment due to the coupling of spins in a preferred orienta4on (keep in mind that this coupling is quantum mechanical in nature and not purely due to the magne4c forces ac4ng between neighbouring atoms). •  As with paramagnets, ferromagnets have strong, posi4ve magne4c suscep4bility. •  Unlike paramagnets, when the applied field is removed, they retain a component of magne4za4on in the direc4on of the applied field - they are "permanently" magne4zed (they have hysteresis). •  Also, their suscep4bility is not dependent upon temperature in a way that follows the Curie Law. Temperature Dependence of Ferromagne4sm Since ferromagne4sm results from the interac4on of atomic moments in materials, there is an exchange energy associated with coupling the spin moments. At room temperature, if a material is magne4cally blocked, this exchange energy is much greater than the energy due to randomizing thermal effects (kT). If thermal energy exceeds the spin coupling (exchange) energy, the coupling breaks down and the material behaves as a paramagnet. This temperature is dependent on the material and is called the Curie temperature (or, in the case of an4ferromagne4c materials [which will be explained in a moment], the Néel temperature). Temperature Dependence of Ferromagne4sm At the Curie (or Néel) Temperature, quantum mechanical coupling of spin moments breaks down. Temperature Dependence of Ferromagne4sm So a paramagnet follows the Curie Law dependence on temperature while a ferromagnet does not. Ferromagne4sm: Domain Forma4on In crystals of materials containing transi4on series elements, the exchange coupling between the ions (either direct or super) gives rise to a net magne4za4on. However, if too many spins are oriented in the same direc4on in a material, the macroscopic magne4c energy of the par4cle is too high. Charges distributed at the surface of the par4cle act to form an internal demagne4zing field which opposes the field due to the spins. In order to reduce this magnetosta4c energy, the par4cle segments into magne4c domains of differing orienta4on. Ferromagne4sm: Domain Forma4on Domain walls are regions of spin transi4on. If energy, from an external magne4c field is applied to the par4cle, domains with components parallel to the field will grow at the expense of those with an4parallel components. This process will con4nue un4l there is only one domain aligned parallel to the applied field. When the field is removed, the domains return. Special Cases of Ferromagne4sm The exchange coupling of spins in ferromagnets does not always lead to all spins being aligned in the same direc4on. Aside from the normal ferromagnet (which is rarely encountered in biological material), three special cases should be considered: 1) An4ferromagnets 2) Ferrimagnets 3) Superparamagnets An4ferromagne4sm No net magne4za4on In an4ferromagne4c materials, uncompensated spins are coupled an4parallel to one another. Ferrihydrite (ferri4n) is a biological example of an an4ferromagnet. An4ferromagne4sm In an4ferromagnets, a net magne4za4on may arise due to spin can4ng or lauce defects. Ferrimagne4sm In Ferrimagne4c materials, neighboring spin lauces are an4parallel but of unequal magnitude. This gives rise to a rela4vely strong net magne4za4on (par4cularly when compared to an4ferromagnets. Magne4te is an example of a ferrimagnet. Superparamagne4sm Superparamagne4c materials are an unusual case. They contain uncompensated spins and may be ferro- , ferri- , or an4ferromagne4c. The difference between superparamagne4c materials and these other cases is that, although the spins are coupled, thermal energy causes the spins to flip between energy minima. This leads to these materials behaving as paramagnets (i.e. upon removal of the applied field, they retain no magne4za4on). Superparamagne4sm Superparamagne4sm is a phenomenon of very fine par4cles and is governed by the Néel- Arrhenius equa4on. # vM sH c & τ = f o exp% ( $ 2 kT ' € v τ∝ T As you can see, the relaxa4on 4me (the amount of 4me the magne4za4on of the material remains in one stable direc4on aDer removal of an external field) is exponen4ally dependent on temperature and volume for a given material. Superparamagne4sm does not normally occur in larger par4cles as the temperature required to significantly reduce the relaxa4on 4me is higher than the Curie/Neel temperature (the temperature at which coupling breaks down) for the material. Superparamagne4sm The above diagram shows the two easy axes of magne4za4on (in this case at 0 and 180) with TB being the blocking temperature. In the case of ferromagnets, TB is generally high compared to body or room temperature and may be above the Curie/Néel temperature. Applica4ons HARD DRIVES MAGNETIC CELL SEPARATION MRI CONTRAST NANOMAGNETIC CELLULAR REMOTE CONTROL NANO- AND MICROMAGNETIC TARGETING OF GENES, DRUGS AND CELLS. ...
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This note was uploaded on 02/28/2012 for the course EMA 3010 taught by Professor Unknown during the Fall '08 term at University of Florida.

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