265 lines
11 KiB
Plaintext
265 lines
11 KiB
Plaintext
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(word processor parameters LM=8, RM=75, TM=2, BM=2)
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Taken from KeelyNet BBS (214) 324-3501
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Sponsored by Vangard Sciences
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PO BOX 1031
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Mesquite, TX 75150
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There are ABSOLUTELY NO RESTRICTIONS
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on duplicating, publishing or distributing the
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files on KeelyNet except where noted!
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October 30, 1993
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DIAMAG1.ASC
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This is a brief piece on Diamagnetism, as there have been some
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questions about it by several people on the net in relation to the
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Sweet and other devices.
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Three groups of magnetic substances
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Substances may be classified into three groups in accordance with
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their magnetic properties: diamagnetic, paramagnetic and
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ferromagnetic. The values of diamagnetic susceptibility lie in the
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range of -13 x 10(-6th) (BISMUTH) TO -0.8 X 10(-6TH) for copper.
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Paramagnetic bodies are characterized by positive susceptibility -
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for example. 0.4 x 10 (-6th) for potassium and 320 x 10(-6th) for
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iron chloride.
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Ferromagnetic bodies are characterized by large values of
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permeability. These are hundreds and even thousands of times
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greater than those of other bodies.
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Let us examine the structural features which explain these
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differences in magnetic properties for substances which otherwise do
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not show great differences in properties.
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Diamagnetism, it will soon be seen, is a universal property of all
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bodies inasmuch as they consist of electrons. The above values show
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that diamagnetic properties are weaker than paramagnetic ones and,
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'a fortori', weaker than ferromagnetic properties.
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Diamagnetic properties may be detected only in the absence of
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properties resulting in positive magnetism.
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Paramagnetic and ferromagnetic bodies have diamagnetic properties,
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but they are obscured by the stronger positive paramagnetism. Thus,
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diamagnetism exists for any system containing electrons. On the
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other hand, positive magnetism arises only in bodies the atoms of
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which possess a magnetic moment. The phenomenon of paramagnetism is
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very similar to the process of electrisation of a dielectric, which
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consists of rigid dipoles possessing a constant dipole movement.
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The presence of a magnetic moment in atoms is also a necessary
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condition for the existence of ferromagnetic properties. However,
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the peculiarities of ferromagnetic substances are due to a very
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specific property, viz., the formation within a body of vast regions
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- domains - within which the magnetic moments of thousands of
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Page 1
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millions of atoms are arranged parallel to one another.
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Diamagnetism
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Diamagnetism is a direct consequence of the tendency for an electron
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to move in a circle in a magnetic field. In a magnetic field with
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an induction 'B', an unbound charged particle moves in a circle with
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an angular frequency (w=eB/mc).
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It can be rigorously proven that the action of a magnetic field on
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an electron moving in a central field - in particular, in the field
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of an atomic nucleus - produces an analogous effect: the electron
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will move in a circle about a line of force, but at one-half the
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frequency, viz., (eB/2mc).
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This motion is superimposed on other motions which may be performed
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by the electron, the chaotic motion of particles of the electron gas
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or the motion of the electron about an atomic nucleus.
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Fundamental considerations show that such motion may be equated to a
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circular electric current. When the magnetic field is switched on,
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the electrons begin to rotate about the magnetic field and each
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produces an elementary current. I=(ve/2(Pi)R) = (eW/2(pi)).
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Multiplying this value by the area of the circle described by an
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electron in its motion about a line of force, we obtain the value of
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the diamagnetic moment created by one electron:
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M = 1 eW e(2)
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- - ----- S = - ----- mc(2) SB
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c 2(pi) 4(pi)
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The reason for the minus sign is clear from figure 1, (not included)
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the direction of the moment is opposite to that of the field.
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When a system consists of a large number of electrons, we must take
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the summation of the above expression with respect to all the
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electrons:
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e(2) ----
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M = - ---- \
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4(pi)mc(2) > S B
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/ i
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----
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Since by definition magnetic susceptibility is equal to the ratio of
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magnetic moment per unit volume (or unit mass or mole) to induction,
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----
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Ne(2) \
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X = - ----- > S
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4(pi)mc(2) / i
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----
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If 'N' is Avogadro's number, 'X' represents molar diamagnetic
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susceptibility. (x = x/u).
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Thus, 'X' is given by the areas circumscribed by electrons in their
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secondary motion in the magnetic field.
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Page 2
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In principal, this computation can be made if we know the wave
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function of the system. i.e., in the final analysis, the electron
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density. Actually, since the computation is very cumbersome, the
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diamagnetic susceptibility is determined experimentally.
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It should be emphasized that diamagnetic susceptibility is
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determined by the electron structure of the system and does not
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depend (at least for atoms and molecules) on the external
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conditions, including temperature.
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Diamagnetic susceptibility, like molecular refraction, possesses
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additivity. If the diamagnetic susceptibility is taken for a mole
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of substance, the susceptibility 'X' of a molecule may be expressed
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with considerable accuracy as
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----
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\
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X = > n X
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/ A A
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----
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where n is the number of atoms of type A in the molecule
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a
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and X is the increment for the given atom. For purposes
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A
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of illustration, we can use the same example as for refraction.
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C,H and Cl atoms have the increments 7.4,2.0 and 18.5 (X x 10(6) ),
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respectively. Thus, we obtain 15.4 for A methane, 64.9 for
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chloroform, and 81.4 for carbon tetrachloride. These values are in
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close agreement with experimental results.
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The significance of this additivity consists probably in the
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following: outer electrons weakly affect diamagnetic susceptibility.
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In so far as additivity is realized, diamagnetic susceptibility is
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an atomic rather than molecular property.
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Diamagnetic susceptibility, as indicated in the preceding article,
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is a property associated with substances, the atoms and molecules of
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which do not have a constant magnetic moment. Such particles
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include in the first place atoms and ions with completed shells -
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the ions F-, Cl- and Na+ and atoms of the noble gasses. Atoms and
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ions which in addition to a completed shell contain two more s-
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electrons with anti-parallel spins, e.g., Zn, Be, Ca and Pb++, are
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also diamagnetic.
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The group of diamagnetic molecules is incomparably larger than the
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group of paramagnetic molecules. The later exists more in the
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nature of exceptions. This is due to the fact that practically all
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molecules have valent bonds formed by a pair of electrons with anti-
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parallel spins. Usually, the total moment about a nucleus, as well
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as the spin moment, equals zero in such molecules. Thus, bodies
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consisting of atoms and ions such as those cited above and
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practically all bodies the building blocks of which are molecules -
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therefore, practically all organic substances are diamagnetic.
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Diamagnetic susceptibility describes the electron cloud of a
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Page 3
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molecule. If the distribution of electrons in a molecule is
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strongly anisotropic, it's magnetic susceptibility is also
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anisotropic. The anisotropy of diamagnetic susceptibility is
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manifested particularly in molecules of the aromatic compounds.
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For example, in benzene, X||, the molar diamagnetic susceptibility
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in a direction lying in the plane of a benzene ring, equals
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-37 x 10(-6) cm(3)/mole
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and X1, the molar diamagnetic susceptibility in a direction
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perpendicular to the plane of a ring, equals
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-91 x 10(-6) cm(3)/mole;
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in naphthalene
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x|| = -40 x 10(-6) cm(3)/mole and X1 = 190 x 10(-6) cm(3)/mole.
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Anisotropy may be detected by measuring crystals oriented in
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different directions in the field. Measurements of powders, liquids
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and gasses yield a value of magnetic susceptibility for an averaged
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orientation.
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--------------------------------------------------------------------
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If you have comments or other information relating to such topics
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as this paper covers, please upload to KeelyNet or send to the
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Vangard Sciences address as listed on the first page.
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Thank you for your consideration, interest and support.
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Jerry W. Decker.........Ron Barker...........Chuck Henderson
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Vangard Sciences/KeelyNet
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--------------------------------------------------------------------
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If we can be of service, you may contact
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Jerry at (214) 324-8741 or Ron at (214) 242-9346
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Page 4
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