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3. Rule 3--sharing of polyhedra-1
-this explains how geometric units (polyhedra) fit
together in an atomic array of a mineral
-polyhedral are most stable if they are connected at points--the sharing of
edges and part-
icularly faces decreases stability--this does not exclude
the presence of polyhedral units
sharing edges in some minerals--the explanation of this preferred occurrence
is based on
the
proximity of cations and + sign replusion
in adjacent polyhedra--simply stated,
cations are situated at a greater distance if polyhedra share points, (less repulsion) and closer
if
they share faces (more repulsion)
4. Rule 4--sharing of polyhedra-2
-in
minerals containing different cations, those of
high valence numbers and small CN tend
not to
share polyhedra with each other--if they do, shared
edges shrink and cations are
displaced
away from shared edges
5. Rule
5--the principle of parsimony
-the
number of different cations, anions or anionic
groups tends to be small--although
elements
can substitute for each other during mineral formation, this tends to be
limited
To determine
the atomic structure of a mineral:
1.
define each individual bond in the mineral--C1-A,....C2-A.... where C1 and C2....is
(are)
the cation bond(s) with the anion, A.
2.
use Pauling's rule #1 and r.r. to determine the
CN--the # of anions around each cation
which defines the shape of each polyhedron--do this r.r
calculation only if the bond type is
isodesmic----if mesodesmic
or anisodesmic, refer to the notes under these bond
types to
explain how to obtain or determine the number of anions around each cation giving the
corresponding polyhedron shape or configuration
3.
use Pauling's rule #2 and establish the e.v. for
each C-A bond--surround the anions with
the corresponding cation(s) so as the sum of all
the e.v. numbers equals the valence number
of the anion--the configuration of the # of cations
around each anion also defines the
polyhedron
in the table under Pauling's rule #1
4. join polyhedra via a common
anion. (See rule #3--join at points by default)
As a summary,
1. all isodesmic
bonds reaching an O have ev values less than
1---all mesodesmic
bonds reaching an O, equal to 1---all anisodesmic
bonds reaching an O, greater than 1.
2. in a mineral structure there can be only 1 anisodesmic
bond to an O, all other bonds to that O
must be comprised of 1 or more isodesmic bond(s).
3. in a mineral structure there can be 1 or 2 mesodesmic
bonds reaching an O---if only 1,
there is in addition, 1 or more isodesmic bonds
reaching the O----if 2, then no additional
isodesmic bonds can reach that O.
IONIC
SUBSTITUTION)
Ionic Substitution
-is the ability of ions of different elements to take or occupy sites (proxy)
in the atomic structure
of a mineral during the formation of the mineral--cation
proxy on a large scale is most important
since this is the basis for solid solution (discussed
later)-
-ionic
substitution can exist with an abundant ion substituting (proxying)
for the preferred ion in a
large number of atomic sites. The substituting ion is shown in the
mineral formula.
-if trace concentrations of cations proxy in
the atomic structure, the cations cannot be shown
in the
mineral formula--however, the study of trace concentrations of cations in minerals which proxy
for a major cation can be paramount in certain
geologic studies
factors influencing ionic substitution:
1. C.N.
-cations which can proxy must form the
same (predetermined) C.N. with the
anion--as discussed in Pauling's rules the cations
must have the appropriate
ionic radius (cations of different elements must
have similar ionic radii) and
the temperature and pressure of mineral formation must be appropriate
if rr is
borderline
consider the Al-O and Si-O bond
Al+3 can proxy for Si+4 in silicates only at high
temperatures as in a
magma but cannot do so during the formation of clay minerals--explain
in detail why this is fact
2. Ionic Charge and electroneutrality
-any cation which may proxy for a preferred cation must have the same or
similar valence number--if the number is too different, the energy for
sub-
stitution is too great and will not occur--if
there is a proxy and a difference
in valence number, to adhere to the electroneutrality
rule, another proxy
for a second element in the formula must occur--an example is the ionic
substitution of Ca+2 and Na+1 in plagioclase
feldspar--for every Ca+2
that substitutes for a Na+1 in the mineral, NaAlSi3O8 there must be a
simultaneous substitution of an Al+3 for a Si+4 to keep
electroneutrality
and the mineral, CaAl2Si2O8 will form--this is very important to
know
3. Electronegativity
-if the electronegativity (numbers) between the
preferred element and the
substituting element is too great and would result in a much less ionic
character with the anion, the substitution will not occur. An example is
Cu+1 substituting for Na+1 in a Na mineral as NaAlSi3O8--even
though both ions
have the same ionic size and therefore should form the same CN with the
anion, O (condition # 1 above) and both have the same valence,
+1(condition # 2 above), the electronegativities
are quite different (Cu = 1.9
and Na = 0.9) resulting in a much weaker ionic bond with the anion, O if
Cu were to substitute--a slight difference in electronegativities
would allow
substitution to occur as a .1 or .2 difference
--hence, the substitution of Cu+1 for Na+1 will not
occur.
CLICK
HERE TO SEE MORE ON ATOMIC PACKING AND PAULING'S RULES
CLICK
HERE FOR EVEN MORE ON PAULING'S RULES
-the next section deals with
important concepts in Mineralogy, some of which are more fully
understood with a knowledge of Pauling's rules and ionic
substitution--some of these concepts are
isomorphism, solid solution, and polymorphism, all of which are
important in classifying minerals
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