Job vacancies at ISIS
Hello, There are two positions available in the ISIS Crystallography group: FBU127 Instrument Scientist - Magnetic Diffraction Department ISIS Department Summary: We are looking for a highly motivated and independent scientist, who will take the lead in commissioning WISH, develop appropriate data analysis tools and build its science programme. The jobholder will also be required to provide an appropriate level of support for the ISIS User Programme, particularly but not exclusively on WISH, and will be strongly encouraged to build collaborations with UK and foreign visiting scientists. Salary Between £31100 and £35543 per annum Benefits 25 days holiday per year Date posted 10 Sep 2007 Closing date 26 Oct 2007 Requirements PhD in Physics FBU128 Postdoctoral Research Fellow - Crystallography Department ISIS Department Summary: The ISIS neutron and muon facility invites applications for a Post-Doctoral Research Fellow in the area of physical and materials crystallography. The project is to develop the scientific portfolio for a high-resolution neutron time-of-flight magnetic diffractometer (WISH). The Research fellow will also be part of the team developing analysis technique and commissioning the WISH instrument. In addition, the Research Fellow will join the existing ISIS research programmes in the field of transition-metal magnetism, the ordering of charges and orbitals and coupled degrees of freedom, and magnetism of geometrically frustrated lattices. Salary Between £24638 and £27998 per annum Benefits 25 days holiday per year Date posted 10 Sep 2007 Closing date 26 Oct 2007 Requirements PhD in Physics For additional information and application, please refer to the following link: http://www.stfc.ac.uk/About/Vacs/Contents.aspx Paolo G. Radaelli
XPRESS access mechanism
Dear Colleague, Starting from cycle 2004/03 (April-May 2005), ISIS has started to offer a Measure-by-Courier powder diffraction access mechanism to the GEM diffractometer (XPRESS). This mechanism is aimed at new and infrequent users, research programmes requiring only limited and/or occasional neutron beamtime and chemistry programmes operating a tight loop between synthesis and structural characterisation. A total of 1 beam day per cycle on the GEM powder diffractometer will be devoted to this programme. Initially, samples will only be measured at room temperature and in standard containers, but access to sample environment is currently being planned.Fully reduced and corrected high-quality data, ready for Rietveld refinement, will be provided to the user, together with example files and guidelines for refinement. The user is expected to carry out the structural analysis with minimal assistance. The next XPRESS run is scheduled for TUESDAY, JULY 19 2005 To access XPRESS and read the full instructions, please follow the link on the ISIS proposal page http://www.isis.rl.ac.uk/applying/. The system is designed to be self explanatory. Your Login ID (email address) and password is the same as for the normal proposal submission. If you are not currently an ISIS user, you will be asked to register on line prior to submission of an XPRESS request. I very much looking forward to receiving your first XPRESS requests. Paolo Radaelli *** Prof. Paolo G. Radaelli Crystallography Group Leader ISIS Facility, Rutherford Appleton Laboratory Chilton, Didcot, Oxfordshire OX11 0QX, United Kingdom Phone: +44-1235-445685 FAX: +44-1235-445642 ***
bursaries available: Neutron Scattering from Biological Systems
The Institute of Physics and the Faraday Division of the Royal Society of Chemistry Neutron Scattering Group Student and Young researcher bursaries available for Neutron Scattering from Biological Systems Cosener's House, Abingdon, OXON, 13-14 December 2004 The Neutron Scattering Group is pleased to offer a number of student and young postdoctoral researcher bursaries to assist with the costs of attending the British Crystallographic Association Physical Crystallography Group autumn 2004 meeting on Neutron Scattering from Biological Systems. Applicants are expected to be contributing at the meeting through either a poster or oral presentation. Applications should be submitted to the group chairman (Prof Don McKenzie Paul) as soon as possible. The number and value of bursaries awarded will be limited by available funds, something of the order of ten awards being available. Successful applicants will be required to claim their travel and subsistence awards against receipts. Applications should take the form of a letter of introduction from the student, outlining their background and the contribution they expect to make. Each application should also be supported by a letter of reference from the student's supervisor. Informal applications by email or telephone would also be welcomed. Successful applicants are expected to acknowledge the support of the Neutron Scattering Group in their presentation, and on their return, provide the Neutron Scattering Group committee with a short written report on their contribution and the meeting of 200 words or half a page of A4. Eligibility: Applicants are expected to be student members of the Institute of Physics or the Royal Society of Chemistry, and also to be a member of the Neutron Scattering Group (or be in the process of joining). A maximum of two bursaries can be awarded to a given student in the course of their PhD studies, and, in general, no applicant is eligible to receive more than one bursary in any academic year. Prof Don McKenzie Paul Chairman of the Neutron Scattering Group Department of Physics University of Warwick Coventry CV4 7AL Tel : 024 76 523603 Fax : 024 76 692016 Email : [EMAIL PROTECTED]
Meeting Announcement: Neutron Scattering from Biological Systems
Autumn Meeting 2004 BCA Physical Crystallography Group and the IoP Structural Condensed Matter Physics Group Neutron Scattering from Biological Systems Cosener's House, Abingdon, OXON, 13-14 December 2004 Hosted at Cosener's House, Abingdon, OXON and supported by the PCG and Rutherford Appleton Laboratory. Organising Committee: John R. Helliwell (Dept. of Chemistry, University of Manchester), Jeff Penford (ISIS Facility, CCLRC), John S.O. Evans (Dept. of Chemistry, University of Durham) and P.A. Thomas (dept. of Physics, University of Warwick) Local Organiser Paolo G. Radaelli http://www.isis.rl.ac.uk/disordered/gem/PGR.htm ISIS Facility, RAL, CCLRC In this meeting we aim to give a broad overview of the contribution of neutrons to biology, with particular emphasis on neutron protein crystallography, neutron fibre diffraction, small-angle scattering and reflectometry from systems such as enzymes, amyloids, membranes, proteins absorbed on surfaces, drug delivery vehicles, biosensors and many more. These topics will be introduced by a series of invited and contributing speakers and by a poster session, but there will also be ample time for an open discussion about the present and future of neutron techniques and facilities. In particular, we will explore the opportunities for neutron scattering experiments in biology at existing and future neutron sources, such as the ISIS Second Target Station. We expect a stimulating discussion on these topics to continue over our traditional Christmas Dinner. The level of the presentations will be suitable for beginners and expert alike. The meeting will start at 1:30 PM on December 13, 2004 and end at 12:30 PM on December 14, 2004. We encourage graduate students to attend, and to bring posters for display at the meeting. Confirmed speakers: Mathew Blackley (EMBL - Grenoble) Giovanna Fragneto (Institut Laue-Langevin), Hermann Heumann (Max Planck Institute of Biochemistry), Jayne Lawrence (King's College London) Bob Thomas (University of Oxford), Peter Timmins (Institut Laue-Langevin), Tim Wess (University of Cardiff) A registration form is available as an HTML document by clicking the link below Registration Form http://bca.cryst.bbk.ac.uk/bca/pcg/reg2004.htm.
RE: Rietveld refinement and PDF refinement ?
do you really have the resolution even on HRPD to see the diffuse scattering between Bragg peaks at high Q ? No we don't, but this is not the main point (by the way, we don't use HRPD for PDF, it doesn't go to sufficiently short wavelengths). The main reason to go to high Q is to avoid truncation errors. If you truncate S(Q), all your G(r) peaks will be convoluted with the Fourier transform of a step function, which is a sinx/x function. The width of the central peak is roughly 1/Qmax. If you use a wavelength of 0.5 A, this corresponds to about 0.08 A, or an equivalent B of 0.5. This in itself can be a problem when you want to look at sharp correlation features. Even worse, the ripples will propagate to adjacent PDF peaks, generating unphysical features. There are ways to suppress the ripples by convoluting the data with an appropriate smooth function rather than truncating them (these are extensively used in disordered materials work), but they all tend to broaden the features. You can also fit a model including the ripples (as in PDFfit) but it is clearly better not to have them if you are trying to exploit the model independence of PDF. Going to high Q does not solve all the problems. If the high-Q data are noisy, your truncation function will have higher frequency but also higher (and random) amplitude in the ripples, so there is always a compromise Qmax, depending on statistics. Finally, very high-Q data are quite difficult to normalise, because of the epithermal background. You may get better temperature factors with high-Q PDF refinement, but you will also do that with high-Q Rietveld. Generally, all crystallographic parameters come out worse from PDF refinements than from Rietveld on the same data sets. I think this is because you are trying to fit an average structure to something that contains correlations, so the fit is bound to be worse. You could fit a correlated model, but then you would not get temperature factors in the usual sense. I also doubt that just because PDF uses data between the Bragg peaks, then it must be superior for seeing details not centered on atoms in real space in a crystal, eg the split atom sites in (In/Ga)As). You might do just as well with Bragg scattering if you use the result of Rietveld refinement to construct a Fourier map of the structure. Happily, a sampling of reciprocal space (Bragg peaks) is sufficient to re-construct the entire density of a periodic structure in real space, not just point atoms, to a resolution limited only by Q. You are right. PDF is not always superior. It is the interpretation of the Fourier density in terms of correlated displacements that emerges uniquely from PDF, although you can often guess it right from the Fourier map in the first place. The case of Jahn-Teller polarons in manganites (La,Ca)MnO3 is quite illuminating. Several groups noticed that the high-temperature phase (above the CMR transition) has large DW factors for O. We showed that this affects primarily the longitudinal component along the Mn-O bonds, and guessed that this was caused by an alternation of short and long Mn-O distances. Simon Billinge showed the same thing quite convincingly from PDF data. Only the latter can be considered direct evidence (with some caveats). But you do agree that in a PDF experiment you integrate over energy, so you only see an instantaneous snapshot of the structure... Yes, I agree with this and the fact that inelasticity corrections are an issue. Sometimes they are exploited to obtain additional information, and there is a claim that one can measure phonon dispersions with this method, but the issue is quite controversial. So while I am convinced of the interest of PDF for non-crystalline materials, with short or intermediate range order, I am not yet convinced that you gain much from PDF refinement of crystalline materials, where you can also apply Rietveld refinement. I agree completely. The directional information gained from phasing and the fact of locking in to specific Fourier components is a major asset of Rietveld analysis. PDF is useful when correlated disorder is important (and large), even if superimposed on an ordered structure. Paolo Radaelli
RE: Rietveld refinement and PDF refinement ?
I would argue that the Bragg diffuse scattering both reflect the average instantaneous atomic structure. Yes. If you integrate over energy, the scattering function factors to a delta function in time, corresponding to an instantaneous snapshot of the spatial correlations. It is not a question of Bragg or or diffuse scattering. Your statement about integrating over energy is correct regardless of Bragg or diffuse scattering, but Brian's statement is not, at least in the context of the PDF/Bragg discussion, so it is and it isn't would have been a more appropriate statement on my part. It is true that in diffraction you measure the intermediate scattering function S(Q,t=0), but this is not the same thing as saying that you can then Fourier-transform any part of it you like to a G(x, t=0). To get a real-space function G(x) you have to integrate over the *whole* Q domain, and in doing so for Bragg scattering you set to zero everything that is outside the nodes of the RL. However, it is easy to see that this can be equivalent to setting an energy cut-off. This is because fluctuations in time and space are usually correlated, so by selecting an integration range in Q for you Bragg peaks, you also effectively select an integration range in energy. Your superstructure example shows it clearly: if you are far from the phase transition and the correlation length of your tilt fluctuation is 10 A, you would not see a Bragg peak there and you would get the time-average structure (without the superstructure). Clearly there is the limiting case of critical scattering very near the phase transition, where the fluctuating regions are so large that you effectively take a snapshot of each of them. There could even be a deeper point here to do with ergodicity, whereby you could show that coherent space average and coherent time average are effectively the same (I am not positive about this, though). The point I was trying to make is a different one. We are discussing about the difference between Bragg and PDF. If all the scattering is near the Bragg peaks, so that you integrate it all in crystallography, there is and there cannot be any difference between the two techniques. I am sure we are not discussing this case. The interesting case is when there is additional diffuse scattering. What I am saying is that if this diffuse scattering is inelastic, then PDF will reflect istantaneous correlations in a way that is missed by Bragg scattering. Let's look at the case of two bonded atoms again, with a bond length L, and lets this time assume that they vibrate harmonically in the transverse direction, and that the semi-axis of the thermal ellipsoid is a. The possible istantaneous bond lengths range from L to sqrt(L^2+4a^2) for an uncorrelated or anti-correlated motion, but is always L for a correlated motion. Bragg scattering will give you a distance of L between the two centres, which is only correct for correlated motion. It also provides information about the two ellipsoids, which is the same you would get by averaging the scattering density over time, regardless of correlations. Istantaneous correlations are only contained in the diffuse scattering, and are in principle accessible by PDF. Paolo Radaelli
RE: Rietveld refinement and PDF refinement ?
Two very good points by Armel: all the very good PDF studies ...are made by using synchrotron data or neutron data from spallation sources This is because they are the only means to get to high Q (i.e., high resolution in real space) and sufficiently high resolution (in reciprocal space) simultaneously. The RMC method is somewhat similar and does not require such high Q, but it has the drawback of requiring a starting model (arguably, there is also a uniqueness issue with RMC). One nice feature of the latest generation of TOF instruments is that one does not have to choose in advance between PDF and crystallography, as long as one has appropriate references (empty can, empty instrument etc.), which are collected as a matter of course anyway. PDF analysis requires better statistics, but, in the context of a large phase diagram study, it is always possible to collect a few data point to PDF accuracy. So, this PDF advantage does not impress me a lot True, in most cases PDF=Rietveld + Common Sense. However, there are some exceptions. For some nice cases see the work of Simon Hibble et al. (e.g., Hibble SJ, Hannon AC, Cheyne SM Structure of AuCN determined from total neutron diffraction INORG CHEM 42 (15): 4724-4730 JUL 28 2003 and references cited therein) and that by Simon Billinge (e.g. Petkov V, Billinge SJL, Larson P, et al. Structure of nanocrystalline materials using atomic pair distribution function analysis: Study of LiMoS2 PHYS REV B 65 (9): art. no. 092105 MAR 1 2002 ). Particularly, Simon Billinge makes the point that the future of PDF is in the study of materials with short and intermediate-range order but no long-range order (nano-crystallography). It is an interesting point of view, although, at the moment, there are not very many examples of this in the literature. Paolo Radaelli
RE: Rietveld refinement and PDF refinement ?
The only truly unique PDF information is about *correlations*. Let's say you have two bonded sites, both with anisotropic thermal ellipsoids along the bond, and let's assume that the motion is purely harmonic. A sharp PDF peak will indicate that the atoms move predominanly in-phase, a broad PDF peak that the atoms move predominantly out-of-phase. The two scenarios will give identical Fourier maps as reconstructed from the Bragg peaks, whatever the Qmax, so the additional width (or additional narrowness) of the peak with respect to an uncorrelated model arises purely from the non-Bragg scattering. You can make the same argument for static correlations. Ga(1-x)In(x)As is a typical case. It is not a split-site problem, in that both Ga/In and As will be slightly displaced locally depending on their surrounding, but the displacements are correlated in such a way as to give a shorter bond length for Ga-As and a longer one for In-As. Of course, PDF is also used to look at more general issues of static/dynamic disorder that could also be examined using Bragg scattering, and in many case it does quite well. PDF is not (yet) very good for structural refinements (so it is to be used only in desperate cases of highly disordered systems) and is pretty hopeless for weak ordered displacement patters, since the extra Bragg peaks in crystallography lock-in on the new modulation even in the presence of large unrelated displacements. For this very reason, PDF tends to miss phase transitions, particularly at higher temperatures, which led to some very wierd claims in the past literature. There is a lot of controversy about PDF being able to say something about weak disordered displacement patters (e.g., dynamic stripes), but I am personally very skeptical. PDF requires exquisite data and a true passion for data analysis. If you have a good problem, you can get (probably) the best PDF data worldwide almost routinely on my instrument GEM at the ISIS facility (see also the cited paper by Billinge). Paolo Radaelli
RE: Debye Temperature Lattice Thermal Expansion
This is to answer the question from Alexandros: The simplest approximation to the thermal expansion coefficient uses the Debye or Einstein specific heat through the so-called Gruneisen formula alpha=gamma*cv/(3*B*Vm) where alpha is the linear expansion coefficient (1/3 of the volume TEC), B is the Bulk modulus, cv is the lattice specific heat, Vm is the molar volume and gamma is the Gruneisen coefficient. Note that the high-temperature limit for both the Debye and Einstein formulas (cfr. Ashcroft Mermin, chapter 23) is cv-3*n*Kb, where n is the number of atoms in a molecule and Kb is the Boltzmann constant (8.31 J/mol/K). For oxides with the perovskite structure, B~150-180 GPa, Vm~3x10^-5 m^3/mol and n=5, so alpha-gamma*7x10^-6 at high temperatures. Typical values of gamma are of the order of 2. The problem with using this formula to extract the Debye temperature (thetad) from thermal expansion data is that it invariably yields irrealistically low values of Thetad. The reason of this is that gamma is an anharmonicity coefficient, which is not the same for different phonons. So, strictly speaking, one gets an anharmonicity-weighted Debye temperature. This problem has been addressed for alkali halides and perovskites in a useful paper by H. Inaba (J. Cer. Soc. Japan, 106, 1988, p 272), which also contains references to other materials. Inaba proposes a semi-empirical model which works well for non-pathological systems, and (in principle) should allow one to extract the true Debye temperature. In practice, I think this is more useful when Thetad is known and one wants to fit the TE data. By the way, getting Debye tempeatures from Debye-Waller factors is also risky, because one gets a complicated average over the phonons that project on that particulat site and direction. Paolo
Job Opening
ARGONNE NATIONAL LABORATORY/ISIS NEUTRON FACILITY POSTDOCTORAL POSITION The Materials Science Division at Argonne National Laboratory is seeking candidates for a postdoctoral research associate position in neutron diffraction. The successful candidate will be located predominantly at the ISIS pulsed neutron facility at the Rutherford Appleton Laboratory in the UK. The research involves using the new high-intensity powder diffractometer GEM and other state-of-the-art facilities at ISIS to study the structural and magnetic phase diagrams of materials displaying subtle transitions driven by parameters such as composition, temperature, magnetic field and pressure. With the advent of GEM, it has become possible for the first time to obtain high-precision structural parameters, often comparable to those from single crystals, with a few minutes' data acquisitions. Therefore, multi-dimensional phase diagrams can be constructed using internal structural parameters, such as anisotropic Debye-Waller factors. Because of the absolute accuracy of these parameters, close comparisons with lattice dynamics models are also possible. Areas of science that will be the focus of this work include existing and new research programs at both ISIS and Argonne, namely: magnetoresistive materials, including both perovskite and layered compounds, magnetoelastic materials, ferroelectric materials, ionic conductors including battery and fuel-cell materials and ceramic membranes. Candidates must have a Ph.D. in Physics, Chemistry, Materials Science or related subject. Experience in neutron scattering or diffraction and computer analysis/programming is preferred. Postdoctoral appointees at Argonne much have received their Ph.D. within the last three years. The deadline for applications is July 10, 2001 or until the position is filled. Please send applications, including a resume and publication list to Dr. James D. Jorgensen, Materials Science Division, Argonne National Laboratory, Argonne, IL 60439 ([EMAIL PROTECTED]). Further information can also be obtained from Dr. Jorgensen or Dr. Paolo Radaelli ([EMAIL PROTECTED]). Information on GEM can be found on the following web site: http://www.isis.rl.ac.uk/disordered/gem/gem_home.htm Argonne National Laboratory is an affirmative action/equal opportunity institution. Women and minorities are especially encouraged to apply.
RE: Most cited powder diffraction papers
Armil: What criterion was adopted in the search? The following famous paper, clearly of structural subject, is not on your list, but has 768 citations: STRUCTURAL-PROPERTIES OF OXYGEN-DEFICIENT YBA2CU3O7-DELTA JORGENSEN JD, VEAL BW, PAULIKAS AP, NOWICKI LJ, CRABTREE GW, CLAUS H, KWOK WK PHYSICAL REVIEW B-CONDENSED MATTER 41: (4) 1863-1877 FEB 1 1990 Paolo
post-doc position at MSU-ISIS
MICHIGAN STATE UNIVERSITY/ISIS NEUTRON FACILITY POSTDOCTORAL POSITION The Department of Physics and Astronomy at Michigan State University is looking to fill a postdoctoral research associate position in the local-structure-property relationship of complex oxides. The successful candidate will be located predominantly at the ISIS pulsed neutron facility at the Rutherford Appleton Laboratory in the UK. The research involves using neutron diffraction, including Pair Distribution Function analysis, and scattering to study the relationsip of structure and local structure to the properties of such materials as colossal magnetoresistant manganites and high-temperature superconductors. Candidates must have a Ph.D. in Physics, Chemistry, Materials Science or related subject. Experience in neutron scattering or diffraction and computer analysis/programming is preferred. Deadline for applications is April 16th, 2001 or until the position is filled. Please send applications, including a vita, statement of research, and at least two letters of recommendation, to Prof. Simon J.L. Billinge, Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824-1116 USA (www.pa.msu.edu/cmp/billinge-group). Further information can also be obtained from Dr. Paolo Radaelli ([EMAIL PROTECTED]). Michigan State University is an affirmative action/equal opportunity institution. Women and minorities are especially encouraged to apply.
RE: Thermal Parameters and Occupancies
One important consideration on the issue of thermal parameters vs occupancies is the Q-range (Q=4pisin(theta)/lambda) where useful information exists. This is a function of the wavelength used, the resolution, the complexity of the structure and the radiation (x-rays vs neutrons). The best results are obtained for simple structures using good-resolution TOF neutron diffraction. I include a comparison between single-crystal synchrotron x-ray and TOF neutron powder data on Y2O3 (3g sample, Q up to 25 A-1). Clearly, one obtains very good *anisotropic* D-W factors within one or a few error bars of the SX values. Also, notice the error bars on oxygen coordinates, which are 1/10 of the x-ray ones. Short data acquisition times also yield sensible results. The oxygen occupancy was also refined at the same time, yielding 1.013(1) for the long run, so there is a little problem at the 1% level. Another issue is that of the absolute value of the D-W factors, which is critical to distinguish between static and dynamic disorder. In order to get accurate values, one has to perform a careful attenuation correction. Paolo SXXD* GEM-8 hours GEM-1 min GEM-10 sec Y1 U11*100 0.32(1) 0.357(6) 0.36(2) 0.34(2) U12*100 0.056(7) 0.063(9) 0.04(2) -0.08(5) Y2 X 0.96764(3) 0.96745(2) 0.96750(4) 0.9676(8) U11*100 0.27(1) 0.285(7) 0.33(2) 0.34(4) U22*100 0.27(1) 0.282(9) 0.29(2) 0.28(4) U33*100 0.27(1) 0 .28(1) 0.40(3) 0.22(5) U23*100 -0.026(6) -0.035(8) -0.02(2) -0.01(4) O X 0.3907(2) 0.39065(2) 0.39065(6) 0.3908(1) Y 0.1518(2) 0.15187(2) 0.15188(6) 0.1520(1) Z 0.3801(2) 0.38009(2) 0.38017(6) 0.3802(1) U11*1000.51(5)0.49(1)0.44(2) 0.32(5) U22*1000.53(5)0.457(9)0.41(2) 0.45(5) U33*1000.41(5)0.348(9)0.25(2) 0.25(4) U12*100 -0.03(4) -0.034(7) -0.01(2) -0.04(3) U13*100 -0.06(4) -0.060(6) -0.07(2) -0.09(3) U23*100 -0.05(4) -0.050(8) -0.08(2) -0.03(4) *E.N. Maslen et al. Acta Cryst. B52,(1996) P. 414-422 Photon Factory data
RE: Riet_L: Scale factor in Rietveld (with a question for Bob and Juan)
Hi everybody: Here is a useful couple of formulas for you neutron lot. They can be used to predict in advance the Rietveld scale factor S for a TOF powder pattern. I remind you that the profile intensity Y is defined as Y=S|F|^2*H(T-Thkl)*L*A*E*O/Vo (see old GSAS manual, page 122). The profile H(T-Thkl) is normalised so that its TOF integral (in mmsec) is 1. The following formula defines the scale factor S of a TOF powder pattern normalised to an equivalent amount of vanadium (corrected for attenuation): [1] S=K*Ltot*f/Vo [mmsec/Angstrom/barns], where K= 1365 [Angstrom^2*mmsec/barns/m] Vo = Unit cell volume [Angstrom^3] Ltot = Total flightpath [m] f= Fractional density [dimensionless] = mass/volume/theoretical density For the more curious, K=252.8*(2Vv/sigmaV/Zv), where Vv = Vanadium unit cell volume=27.54 A^3 SigmaV = Vanadium total neutron cross section = 5.1 barns Zv = Number of vanadium atoms in a unit cell = 2 252.8 = wavelength-velocity conversion constant for neutrons. From this, it is easy to deduce the second formula: [2] S=505.56*Ltot*Sinf/sigmas, where Sinf = Q-infinity limit of the scattered intensity S(Q) sigmas = Total neutron cross section for a unit cell of the sample (Just the sum of the individual sigmas of the atoms). For the novices, I remind you that the scattered intensity flatens out at high Q (or it should if all the corrections are done propertly). I verified both formulas using my diffractometer GEM, which has detectors from 15 degrees to 170 degrees 2th. Needless to say that the refined scale factors for the different banks are equal with an uncertaintly of about 3%. [2] is extremely accurate, better than 1% at high angle. [1] is slightly less accurate at the moment (~10%), but I plan to improve my corrections to reach a 1-2% level. If these levels of accuracy can be reached, these formulas could be valuable to obtain absolute |F|^2 for problems with multi-site substitutions/vacancies. I'll leave to the reactor people as an exercise to derive the equivalent of this formulas. Note that, for CW data, you rearly if ever to S(Q) saturation. Finally, here is a question for Bob and Juan. To me, it would be much more natural to remove Vo from the scale factor, that is to redefine a new S' so that Y=S'*L*A*E*|F|^2/Vo^2 and S'=K*Ltot*f This way, the scale factor will only depend on the sample effective density and not its crystal structure. This is very useful in phase transitions involving a change in the size of the unit cell, as you can imagine. Is there any rationale in doing it the way it's currently done? Best Paolo
RE: Lorentz Factor in TOF neutron diffraction
To answer Nail's question: The Lorentz factor can be deduced from the expression of the integrated intensity of a single reflection of a TOF powder pattern (in the absence of attenuation): I=[e(lam)*Omega]*[Vs/(32*pi*Vu^2)]*[lam^4*i(lam)]*[1/sin^3(theta)]*[Mhkl*|Fh kl|^2]= =[e(lam)*Omega]*[Vs/(2*pi*Vu^2)]*[i(lam)]*[Mhkl*|Fhkl|^2]*[d^4*sin(theta)] in this formula,Omega is the detector solid angle, e(lam) its efficiency, Vs is the sample volume, Vu is the unit cell volume, lam is the wavelength, i(lam) the incident spectrum (neutrons/cm^2/Angstrom), theta is the Bragg angle, Mhkl is the reflection multiplicity and Fhkl is the structure factor. The second formula is deduced from the first, keeping in mind that lam^4/sin^3(theta)=16d^4*sin(theta). The reference to this formula is given in B. Buras and L. Gerward, Acta Cryst A31 (1975) p372, and also reported in the book by R. A. Young, "The Rietveld method" IUCr-Oxford University Press (1995) p. 214. In there, the expression for the integrated intensity over the full Debye-Scherrer cone is given. The expression I quote is easily deduced by noting that for such a cone Omega=8*pi*sin(theta)*cos(theta)*Dtheta I hope this answers your question. Paolo
