Hi, If you have an organic or organometalic compound you may also use the fact that the average atomic volume is between 18 and 20 Å^3 almost independently of the atomic species (except for H atoms) so you may get your experimental atomic volume and divide it by 18 or 20 and extract the number of non-hydrogen atoms and then divide by the expected formula unit (without H) to get Z. In general that ratio should be equal to the number of asymmetric units of your space group, except if your molecule got internal symmetry compatible with the space group symmetry and Z will be a fraction of the number of asymmetric units and the fraction will tell you the order of the symmetry element where your molecule is located. If Z is larger than the number of asymmetric units of your space group you may have more than one independent molecule not related by space group symmetry in the asymmetric unit. In the case of aducts or molecular units having solvent or other co-crystals things get a bit complicated because the calculated Z may differ a lot from an integer number so in that case you may need to guess a value and try to solve the structure by itself.
Now, if you are talking about Z for a high symmetry inorganic compound forget about having a number close to the number of asymmetric units of your space group because in those cases most of the atoms lie on special positions (symmetry elements) and Z may be any (small) number. Typically, NaCl got Z=4 in a space group Fm3m with 192 A.U. while a cubic perovskite ABO3 got Z=1 in Pm3m with 48 A.U. per cell. In any case, there are probably a nice number of odd observations (Z values very different from expected in the CCD, the ICSD, the COD and other databases) that are clearly justified after the structure is analyzed, so all these and other suggestions may work most of the time but you may just have the exceptional structure in your hands, so keep your mind open. Hope this helps too! Leo Dr. Leopoldo Suescun Prof. Agr (Assoc. Prof.) de Física Tel: (+598 2) 9290648/9249859 Cryssmat-Lab./DETEMA Fax: (+598 2) 9241906 Facultad de Quimica, Universidad de la Republica ,_. | \ | v- ,' \ | ( \__Montevideo, Uruguay -----Original Message----- From: Frank Girgsdies [mailto:girgs...@fhi-berlin.mpg.de] Sent: Wednesday, June 17, 2009 3:47 AM To: Rietveld_l@ill.fr Subject: Re: Source and comparison of X-ray scintillator screens 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! > > No virus found in this incoming message. Checked by AVG - www.avg.com Version: 8.5.364 / Virus Database: 270.12.76/2183 - Release Date: 06/17/09 05:53:00 No virus found in this outgoing message. Checked by AVG - www.avg.com Version: 8.5.364 / Virus Database: 270.12.76/2183 - Release Date: 06/17/09 05:53:00
