Hi. This is a case of radians - we have to change degrees into radians. And we get good results, but only for some substances (and always for cubic, orthorhombic and tetragonal ones).
Regards, Luke K. > Hi > > Just a general warning about using Excel with trigonometric functions: > =sin(0) gives 0 > =sin(90) gives 0.893997 > =sin(180) gives -0.80115 > > In other words, I haven't gotten sine and cosine to work reliably with > Excel. It might be a good idea to check the calculations using some > other software, maybe just a good old hand calculator. > > That was my five cents. :) > > /Arto > > > > On 2014-02-11 10:13, "Łukasz Kruszewski" wrote: >> Ok - sorry, changed degrees into radians. But there is still a >> difference >> for sulphur in aluminite. >> >> Best regards, >> >> Luke K. >> >> >>> OK, here it goes: >>> >>> Uiso = 1/3 * [U22 + 1/sin^2(beta)*(U11 + U33 + 2U13cos(beta)] = >>> 1/3 * [0.01562 + (1/sin^2(110.18))*(0.01937 + 0.01277 + 2* >>> (-0.00027)*cos(110.18)] = >>> 1/3 * [0.01562 + (1/(0.9386)^2) * (0.03214 + (-0.00054)*(-0.345)] = >>> 1/3 * [0.01562 + (1/0.88097) * 0.0323263] = >>> 1/3 * [0.01562 + 1.135 * 0.0323263] = >>> 1/3 * (0.01562 + 0.03669) = 1/3 * 0.05231 = 0.01726 >>> >>> The given Uiso for sulphur is, meanwhile, 0.01621. >>> >>> I have also been trying to calculate Uiso for melanophlogite, which is >>> cubic, co the formula goes: >>> >>> Uiso = 1/3* (U11 + U22 + U33). >>> >>> Using this formula, I have obtained the value of 0.0339, which is >>> exactly >>> the same as the one given in the corresponding CIF file. >>> However, calculating the Uiso using the GENERAL formula gives the value >>> of >>> 0.0287. Both values (0.0339 and 0.0287) were calculated using an EXCEL >>> spread sheet. So how is such a difference possible? >>> >>> Best regards! >>> >>> Luke Kruszewski >>> >>> >>>> Dear Łukasz, >>>> >>>> There must be something wrong with your calculation. A quick >>>> examination >>>> shows that S must have a higher displacement parameter than Al and >>>> that >>>> Ueq must be approximately 0.016. >>>> >>>> I hope this helps. >>>> >>>> Bob Gould >>>> >>>> >>>> On 10/02/2014 21:50, "Łukasz Kruszewski" wrote: >>>>> Dear Rietveld friends, >>>>> >>>>> I'm having some problems with calculating Uiso from the anisotropic >>>>> parameters. Here is an example - I copy first two sites of aluminite >>>>> (monoclinic): >>>>> >>>>> _atom_site_aniso_label >>>>> _atom_site_aniso_U_11 >>>>> _atom_site_aniso_U_22 >>>>> _atom_site_aniso_U_33 >>>>> _atom_site_aniso_U_12 >>>>> _atom_site_aniso_U_13 >>>>> _atom_site_aniso_U_23 >>>>> S 0.01937 0.01562 0.01277 -0.00248 -0.00027 0.00954 >>>>> Al1 0.01117 0.01169 0.01295 0.00006 -0.00012 0.00789 >>>>> >>>>> Using the formula for Uiso for the monoclinic system, which is: >>>>> >>>>> >>>>> 1/3 * [U22 + 1/sin^2(beta)*(U11 + U33 + 2U13cos(beta)] >>>>> >>>>> for the "S" site we obtain the value of 0,0054 >>>>> >>>>> for "Al": 0.01225 >>>>> >>>>> Meanwhile, the listed Uiso are: >>>>> >>>>> _atom_site_label >>>>> _atom_site_fract_x >>>>> _atom_site_fract_y >>>>> _atom_site_fract_z >>>>> _atom_site_U_iso_or_equiv >>>>> S 0.70076 0.37376 0.93018 0.01621 >>>>> Al1 0.65581 0.45332 0.47633 0.01229 >>>>> >>>>> While the author-given value for Al is close to the one calculated >>>>> myself, >>>>> the one for S is much different. By the way, 0.01621 * 1/3 = 0.0054. >>>>> >>>>> I could find it a simple mistake, I've found such a problem in case >>>>> of >>>>> many other structures. And here's my kind question: am I missing >>>>> something? >>>>> >>>>> Best regards! >>>>> >>>> >>>> -- >>>> Robert Gould >>>> Tel.UK: +44 (0)131 667 7230 or +44 (0)796 040 3872 >>>> Canada: +1 519 387 8223 >>>> >>>> >>>> --- >>>> This email is free from viruses and malware because avast! Antivirus >>>> protection is active. >>>> http://www.avast.com >>>> >>>> >>> >>> >> > > -- Łukasz Kruszewski, Ph.D., adjunct Polish Academy of Sciences Institute of Geological Sciences X-Ray Diffraction Laboratory (coordinator) Twarda 51/55 str. 00-818 Warsaw Poland
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