Dear Liang,
I'm not sure if we are talking about the same "Z", but I'll
give it a try.
To the best of my knowledge, "Z" simply denotes the number
of formula units per unit cell.
In order to "determine" Z, we have to distinguish two
cases:
1) The crystal structure is known.
In this case, you simply count the atoms in the unit cell
and divide by the "contents" of one formula unit.
Note that often the definition of a formula unit may be
arbitrary (i.e. a matter of choice), which means that
defining formula unit and Z always need to go together.
2) The crystal structure is unknown and you are trying to
determine it. In order to do so successfully, you need
to have a good idea about how many atoms of which type
are in the unit cell. Thus, you will need additional
information like elemental analysis etc.
Once you have an idea about what the formula unit
would be, you should "guess" Z in order to know the
total contents of the unit cell. Based on the formula
unit, Z is usually an integer (or, depending on the
symmetry of the cell, at least something like 3/2 or so).
To estimate Z, you need the unit cell volume (i.e. the
cell dimensions need to be determined first).
If you know the measured density, than you may deduce
Z from that, because it should be similar to the theoretical
density of the crystal structure. However, the real (measured)
density is often somewhat lower than the calculated density.
If you do not know the real density, there are other ways
to estimate Z. For example, for organic or organometallic
compounds you may guess Z by assuming that every non-hydrogen
atom in the formula contributes about 17 cubic Angstroms
to the unit cell volume. This may be a crude estimate (especially
if the structure contains several heavy atoms), but as Z
is typically integer, there won't be too many choices.
Alternatively, you may try to calculate Z by using the
density of a very similar compound instead.
If Z turn out to be ambiguous and you do not succeed in solving
the structure, you should give another choice of Z a try.
Example: your estimate calculations lead to a "Z" of
3.7. In this case, assuming Z=4 would be the first choice.
If the structure determination fails, Try Z=3 next.
Of course, considering the space group symmetry ususually
limits the number of choices further, so it would be a
good idea to have a look into the International Tables
of Crystallography and see which Wyckoff multiplicities
may actually occur in the space group of your choice.
Hope I could help.
Cheers,
Frank
Liang wrote:
Dear all,
could anyone give me some knowledge about how to determine the "Z" of
the unite cell. I understand it can be determined from the density
measured from the sample. In some papers, I find it was deduced from the
electron diffraction patterns and I have not completely understanding
about how to calculate the "Z" just from the electron diffraction
patterns. Which is better In this two method, calculated from the
measured density or deduced from the electron diffraction patterns? And
are there any other way to determine the "Z" ?
Thanx for your comments!
