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Three groups of magnetic substances

By KeelyNet    3/26/05

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                   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

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       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.

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