One should handle each part of the pattern in it's natural scale: -Pattern representation (purely, without instrumental broadening) in Q -Geometric part of the instrumental function in an angular scale (e.g. radian) -Wavelength part of the instrumental function in the nm or k-scale (1/nm) for simple handling as done in BGMN plus related programs.
Am Mittwoch, den 21.02.2007, 07:38 -0600 schrieb Von Dreele, Robert B.: > However, the profile shape functions are not simple functions of Q but are > simple (Gaussian & Lorentzian) functions of 2-theta. Case closed. > > ________________________________ > > From: Klaus-Dieter Liss [mailto:[EMAIL PROTECTED] > Sent: Wed 2/21/2007 4:03 AM > To: rietveld_l@ill.fr > Subject: Powder Diffraction In Q-Space > > > > Dear Powder-Diffraction User, > > with the advancement of modern research infrastructure such as > instruments, computing, complementary techniques, I like to raise again > the necessity to present powder diffraction data in Q-space rather than > in instrumental units. Other communities are already well ahead > (single-xtal, SANS, SAXS, reflectometry etc) and to my view, only the > powder diffractionist stick to their out-dated units (2-theta, TOF, > d-spacing...). > > there is a poll I started a while ago under > http://elpopo.ing.unitn.it:8064/maudFor/viewtopic.php?t=205 > which, so far, is not very representative and I would encourage you to > give your opinions. > > I suppose, all of us have learned the basics of crystallography > somewhere during the career and the laws of Bragg diffraction. So, all > of us are familiar with reciprocal space, where, for example, a > reciprocal lattice can be constructed in order to represent the crystal > symmetry in the natural space of diffraction. The Ewald construction and > the Laue equation are examples which make most use of this. > > Further, reciprocal space is LINEAR, i.e. A second order reflection has > double the distance from the origin than the fundamental reflection and > a 110 reflection sqrt(2) times the distance than a 100 of a cubic > system, etc. > > This alone would be a very good reason to plot all diffraction patterns > as a function of reciprocal space coordinates Q. For Powder Diffraction, > this means, patterns should NOT be plotted as a function of 2-theta, d, > tof etc but Q which is the only natural unit! > > The relations are: > > Q = 4 * Pi * sin(theta) / lambda; > > or > > Q = 2 * Pi / d; > > The benefits of plotting and publishing data in this representation are > obvious: > * reciprocal space is the NATURAL space diffraction takes place; > * reciprocal space is LINEAR and symmetries can be identified by eye; > * the representation directly reflects crystal SYMMETRY; > * the representation is INDEPENDENT of the instrument, type of radiation > (electrons, neutrons, X-rays, light, atoms...) > * the representation is INDEPENDENT of the wavelength used; > * presentations and publications are directly COMPARABLE; > * reciprocal space is WIDELY USED outside the powder diffraction > community, such as single crystal diffraction SA(NX)S or reflectometry; > > Therefore I propose, that publishing data in other units should be avoided. > _________________ > > Klaus-Dieter Liss > > -- > > Dr. Klaus-Dieter Liss > Research Scientist, Bragg Institute > Australian Nuclear Science and Technology Organisation > PMB 1, Menai NSW 2234, Australia > > T: +61-2-9717+9479 > F: +61-2-9717+3606 > M: 0419 166 978 > E: [EMAIL PROTECTED] > http://www.ansto.gov.au/ansto/bragg/staff/s_liss.html > see also: http://liss.freeshell.org <http://liss.freeshell.org/> > > > > -- Joerg Bergmann <[EMAIL PROTECTED]>
