(word processor parameters LM=8, RM=75, TM=2, BM=2) Taken from KeelyNet BBS (214) 324-3501 Sponsored by Vangard Sciences PO BOX 1031 Mesquite, TX 75150 There are ABSOLUTELY NO RESTRICTIONS on duplicating, publishing or distributing the files on KeelyNet except where noted! October 30, 1993 DIAMAG1.ASC -------------------------------------------------------------------- This is a brief piece on Diamagnetism, as there have been some questions about it by several people on the net in relation to the Sweet and other devices. Three groups of magnetic substances Substances may be classified into three groups in accordance with their magnetic properties: diamagnetic, paramagnetic and ferromagnetic. The values of diamagnetic susceptibility lie in the range of -13 x 10(-6th) (BISMUTH) TO -0.8 X 10(-6TH) for copper. Paramagnetic bodies are characterized by positive susceptibility - for example. 0.4 x 10 (-6th) for potassium and 320 x 10(-6th) for iron chloride. Ferromagnetic bodies are characterized by large values of permeability. These are hundreds and even thousands of times greater than those of other bodies. Let us examine the structural features which explain these differences in magnetic properties for substances which otherwise do not show great differences in properties. Diamagnetism, it will soon be seen, is a universal property of all bodies inasmuch as they consist of electrons. The above values show that diamagnetic properties are weaker than paramagnetic ones and, 'a fortori', weaker than ferromagnetic properties. Diamagnetic properties may be detected only in the absence of properties resulting in positive magnetism. Paramagnetic and ferromagnetic bodies have diamagnetic properties, but they are obscured by the stronger positive paramagnetism. Thus, diamagnetism exists for any system containing electrons. On the other hand, positive magnetism arises only in bodies the atoms of which possess a magnetic moment. The phenomenon of paramagnetism is very similar to the process of electrisation of a dielectric, which consists of rigid dipoles possessing a constant dipole movement. The presence of a magnetic moment in atoms is also a necessary condition for the existence of ferromagnetic properties. However, the peculiarities of ferromagnetic substances are due to a very specific property, viz., the formation within a body of vast regions - domains - within which the magnetic moments of thousands of Page 1 millions of atoms are arranged parallel to one another. Diamagnetism Diamagnetism is a direct consequence of the tendency for an electron to move in a circle in a magnetic field. In a magnetic field with an induction 'B', an unbound charged particle moves in a circle with an angular frequency (w=eB/mc). It can be rigorously proven that the action of a magnetic field on an electron moving in a central field - in particular, in the field of an atomic nucleus - produces an analogous effect: the electron will move in a circle about a line of force, but at one-half the frequency, viz., (eB/2mc). This motion is superimposed on other motions which may be performed by the electron, the chaotic motion of particles of the electron gas or the motion of the electron about an atomic nucleus. Fundamental considerations show that such motion may be equated to a circular electric current. When the magnetic field is switched on, the electrons begin to rotate about the magnetic field and each produces an elementary current. I=(ve/2(Pi)R) = (eW/2(pi)). Multiplying this value by the area of the circle described by an electron in its motion about a line of force, we obtain the value of the diamagnetic moment created by one electron: M = 1 eW e(2) - - ----- S = - ----- mc(2) SB c 2(pi) 4(pi) The reason for the minus sign is clear from figure 1, (not included) the direction of the moment is opposite to that of the field. When a system consists of a large number of electrons, we must take the summation of the above expression with respect to all the electrons: e(2) ---- M = - ---- \ 4(pi)mc(2) > S B / i ---- Since by definition magnetic susceptibility is equal to the ratio of magnetic moment per unit volume (or unit mass or mole) to induction, ---- Ne(2) \ X = - ----- > S 4(pi)mc(2) / i ---- If 'N' is Avogadro's number, 'X' represents molar diamagnetic susceptibility. (x = x/u). Thus, 'X' is given by the areas circumscribed by electrons in their secondary motion in the magnetic field. Page 2 In principal, this computation can be made if we know the wave function of the system. i.e., in the final analysis, the electron density. Actually, since the computation is very cumbersome, the diamagnetic susceptibility is determined experimentally. It should be emphasized that diamagnetic susceptibility is determined by the electron structure of the system and does not depend (at least for atoms and molecules) on the external conditions, including temperature. Diamagnetic susceptibility, like molecular refraction, possesses additivity. If the diamagnetic susceptibility is taken for a mole of substance, the susceptibility 'X' of a molecule may be expressed with considerable accuracy as ---- \ X = > n X / A A ---- where n is the number of atoms of type A in the molecule a and X is the increment for the given atom. For purposes A of illustration, we can use the same example as for refraction. C,H and Cl atoms have the increments 7.4,2.0 and 18.5 (X x 10(6) ), respectively. Thus, we obtain 15.4 for A methane, 64.9 for chloroform, and 81.4 for carbon tetrachloride. These values are in close agreement with experimental results. The significance of this additivity consists probably in the following: outer electrons weakly affect diamagnetic susceptibility. In so far as additivity is realized, diamagnetic susceptibility is an atomic rather than molecular property. Diamagnetic susceptibility, as indicated in the preceding article, is a property associated with substances, the atoms and molecules of which do not have a constant magnetic moment. Such particles include in the first place atoms and ions with completed shells - the ions F-, Cl- and Na+ and atoms of the noble gasses. Atoms and ions which in addition to a completed shell contain two more s- electrons with anti-parallel spins, e.g., Zn, Be, Ca and Pb++, are also diamagnetic. The group of diamagnetic molecules is incomparably larger than the group of paramagnetic molecules. The later exists more in the nature of exceptions. This is due to the fact that practically all molecules have valent bonds formed by a pair of electrons with anti- parallel spins. Usually, the total moment about a nucleus, as well as the spin moment, equals zero in such molecules. Thus, bodies consisting of atoms and ions such as those cited above and practically all bodies the building blocks of which are molecules - therefore, practically all organic substances are diamagnetic. Diamagnetic susceptibility describes the electron cloud of a Page 3 molecule. If the distribution of electrons in a molecule is strongly anisotropic, it's magnetic susceptibility is also anisotropic. The anisotropy of diamagnetic susceptibility is manifested particularly in molecules of the aromatic compounds. For example, in benzene, X||, the molar diamagnetic susceptibility in a direction lying in the plane of a benzene ring, equals -37 x 10(-6) cm(3)/mole and X1, the molar diamagnetic susceptibility in a direction perpendicular to the plane of a ring, equals -91 x 10(-6) cm(3)/mole; in naphthalene x|| = -40 x 10(-6) cm(3)/mole and X1 = 190 x 10(-6) cm(3)/mole. Anisotropy may be detected by measuring crystals oriented in different directions in the field. Measurements of powders, liquids and gasses yield a value of magnetic susceptibility for an averaged orientation. -------------------------------------------------------------------- If you have comments or other information relating to such topics as this paper covers, please upload to KeelyNet or send to the Vangard Sciences address as listed on the first page. Thank you for your consideration, interest and support. Jerry W. 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