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Rietveld Plot of Deuterated Ammonium Cyanate (NH₄NCO)

Rietveld Method

The Rietveld method (invented by Hugo Rietveld in the late 1960's) revolutionised the ability of powder diffraction to routinely provide quality crystallographic structure data. This method was described in 2 papers in the International Union of Crystallography journals, Acta Crystallographica and Journal of Applied Crystallography. (1968 paper, 1969 paper).

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Hugo Rietveld

For this work he received in 1995 the Aminoff Prize of the Swedish Academy of Sciences and in 2003 The Barrett Award of the Denver X-ray Conference.

The original Rietveld software was written in Algol ("Rietveld Method Report",RCN-104, April 1969 (Reactor Centrum Nederland, Petten, The Netherlands)). It was later rewritten in Fortran by Hugo Rietveld and used in Petten and Institutt for Atomenergi, Kjeller, Norway around 1970. Alan Hewat, visiting Petten in 1971, obtained a version of the Fortran code which was then modified at Harwell, England. Alan added (amongst other things) the ability to refine anisotropic temperature factors. This version was widely distributed within the crystallographic powder diffraction community. Due to the wide neutron diffraction user community at Harwell during the 1970's, use of the Rietveld method then started to take off. It looks like all Rietveld code in common use until at least the 1980's was derived from the Harwell code. The only known exception being a Rietveld program written by John Taylor (Australian Atomic Energy Commission (AAEC)/ANSTO, Lucas Heights, Australia), an early 1970's adaption of a single crystal programme (ORFLS) for profile analysis. (J. C. Taylor and P. W. Wilson, A Neutron-Diffraction Study of Anhydrous Uranium Tetrachloride" Acta Cryst. (1973). B29, 1942-1944), (J. C. Taylor, P. W. Wilson and J. W. Kelly, The structures of fluorides. I. Deviations from ideal symmetry in the structure of crystalline UF6: a neutron diffraction analysis" Acta Cryst. (1973). B29, 7-12).

Alan Hewat

The invention of constrained molecule Rietveld refinement was the work of G. Stuart Pawley at the University of Edinburgh; as implemented in the EDINP Rietveld software and published in 1975. In 1981, Stuart Pawley also created what is now called the Pawley method (or Pawley fitting) for structureless whole profile fitting and the extraction of HKL intensities from powder diffraction data. In Pawley fitting, each HKL intensity is a parameter in the least-squares matrix. At the time, the Pawley method was not well matched to the limited computational power of existing crystallographic computers. It is only relatively recently that Pawley fitting of data has regained the interest of of software developers due to the availability of powerful desktop personal computers.

The first to report on the use of X-ray powder data for the refinement of a structure with the Rietveld Method were:

• Malmros and Thomas, "Least squares structure refinement based on profile analysis of powder film intensity data measured on an automatic microdensitometer", Journal of Applied Crystallography, 10, 7-11, 1977.
• Young, Mackie and Von Dreele, "Application of the pattern-fitting structure-refinement method of X-ray powder diffractometer patterns", Journal of Applied Crystallography, 10, 262-269, 1977.
• C.P. Khattak and D. E. Cox, "Profile analysis of X-ray powder diffractometer data: structural refinement of La0.75Sr0.25CrO3", Journal of Applied Crystallography, 10, 262-269, 1977.

The Rietveld method was later shown by Rod Hill and Chris Howard ("Quantitative phase analysis from neutron powder diffraction data using the Rietveld method" J. Appl. Cryst. (1987). 20, 467-474) and Dave Bish and Scott Howard ("Quantitative phase analysis using the Rietveld method", J. Appl. Cryst. (1988). 21, 86-91) to give effective quantitative phase analysis of simple to complex materials where the crystal structures are known. Before this advance, accurate, standardless quantitative phase analysis of complex materials using powder diffraction was near impossible; the Rietveld method made is possible. Microstructural information such as crystallite size, shape and strain can also be obtained by using Rietveld analysis.

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Rod Hill, Chris Howard and Dave Bish

The ability to use Rietveld for quantitative phase analysis opened the method up for routine commercial use on industrial process development and process control. The first commercial quantitative analysis Rietveld software package for industry came soon after in 1989. This was the SIROQUANT package, written by John Taylor, who at that point was now at the Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Lucas Heights, Australia. Other commercial quantitative phase analysis Rietveld software also came on the scene. These include Quasar by Philips Scientific (now called PANalytical) and Riqas by MDI (Materials Data Inc).

John Taylor (1935-2002)

Armel Le Bail, at Le Mans, France, further developed the Rietveld Method in 1988 to enable quick, stable, structureless whole profile fitting and extraction of HKL intensities for ab-initio structure solution. This method was very easy to implement in existing Rietveld software. It was not unreasonable that less than a day of programming time was required to add this functionality into existing Rietveld software. This further development is called Le Bail fitting, or the Le Bail method, and revolutionised the ability of crystallographers to solve (and not just refine) crystal structures from powder diffraction data. (Link 1)

Armel Le Bail

The Rietveld method is now being used under some circumstances for the refinement of protein crystal structures. A group led by Robert Von Dreele (then at Los Alamos National Laboratory in New Mexico, USA) was the first to publish on such a result. (R. B. Von Dreele, Combined Rietveld and stereochemical restraint refinement of a protein crystal structure" J. Appl. Cryst. (1999). 32, 1084-1089.), (R. B. Von Dreele, P. W. Stephens, G. D. Smith and R. H. Blessing, The first protein crystal structure determined from high-resolution X-ray powder diffraction data: a variant of T3R3 human insulin-zinc complex produced by grinding" Acta Cryst. (2000). D56, 1549-1553) (R. B. Von Dreele, Binding of N-acetylglucosamine to chicken egg lysozyme: a powder diffraction study" Acta Cryst. (2001). D57, 1836-1842). An example of the fitting of protein data using the GSAS Rietveld software (written by Robert Von Dreele and Allen Larson) is included below.

Robert Von Dreele

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GSAS whole profile fit to a powder diffraction pattern of a protein sample (images from CCP14 website)

Following are a small selection of papers that are representative of the early history of Rietveld analysis as published in the open literature.

• Rietveld, H. M. (1967). Line profiles of neutron powder diffraction peaks for structure refinement (WO3). Acta Cryst. 22, 151-152.
• Rietveld, H. M. (1969). "A profile refinement method for nuclear and magnetic structures." J. Appl. Cryst. 2, 65-71.
• Taylor, J. C. and H. J. Hurst (1971). Decomposition of overlapping peaks in neutron powder diffraction patterns. Acta Cryst. B27, 2018-2022.
• Hewat, A. W. (1973). Location of hydrogen atoms in ammonium dihydrogen phosphate by neutron powder profile refinement. Nature (London) 246, 90-1. .
• Hewat, A. W. (1973). The Rietveld computer program for the profile analysis of neutron diffraction powder patterns, modified for anisotropic thermal vibration. . UKAEA Research Group Report R7350 (unpublished). .
• Taylor, J. C. and P. W. Wilson (1974). Crystal structure of uranium tetrabromide by X-ray and neutron diffraction. . Acta Cryst. B 30, 2664-2667
• Mackenzie, G. A., G. S. Pawley, et al. (1975). Neutron powder diffraction analysis and constrained refinement of perfluorodiphenyl. . Acta Cryst. A31, 851-852. .
• Von Dreele, R. B., L. Eyring, et al. (1975). Refinement of crystal structure of Pr7O12 by powder neutron diffraction. Acta Cryst. B 31, 971-974.
• Hewat, A. W. (1975). Design for a conventional high resolution neutron powder diffractometer. . Nucl. Inst. Methods 127, 361-70. .
• Hewat, A. W. and I. Bailey (1976). "D1A, a high resolution neutron powder diffractometer with a bank of mylar collimators ." Nucl. Instrum. Methods 137: 463-71.
• Pawley, G. S., G. A. MacKenzie, et al. (1977). Neutron powder diffraction and constrained refinement. The structures of p-dibromo- and p-diiodotetrafluorobenzene . . Acta Crystallogr., Sect. A A33, 142-5. .
• Young, R. A., P. E. Mackie, et al. (1977). Application of the pattern-fitting structure-refinement method to X-ray powder diffractometer patterns . . J. Appl. Crystallogr. 10, 262-9. .
• Malmros, G. and J. O. Thomas (1977). Least squares structure refinement based on profile analysis of powder film intensity data measured on an automatic microdensitometer. . J. Appl. Cryst. 10, 7-11. .
• Windsor, C. G., L. J. Bunce, et al. (1977). Neutron TOF powder diffraction on an electron LINAC. . Nuc. Inst. Methods 140, 241-250. .
• Young, R. A., P. E. Mackie, et al. (1977). Application of the pattern-fitting structure-refinement method to X-ray powder diffractometer patterns . . J. Appl. Crystallogr. 10, 262-9. .
• David, W. I. F., A. M. Glazer, A. W. Hewat (1979). The structure and ferroelastic phase transition of bismuth vanadate (BiVO4) . . Phase Transitions 1, 155-69. .

Ammonium Cyanate (NH₄NCO)

Ammonium Cyanate (NH₄NCO) has had a central part in the history of chemistry. It was Frankfurt born Friedrich Wöhler (1800-82), who in the late 1820's converted the "inorganic" Ammonium Cyanate into "organic" urea. ("On the Artificial Production of Urea" by F. Wöhler Annalen der Physik und Chemie, 88, Leipzig, 1828; link 1, link 2). This experiment slowly shattered the then dominant vitalism theory, where is was thought that organic compounds contained a "vital force" or vital life force, in comparison to inorganic compounds that did not. The actual history of this synthesis is not as described in many high school text books. The direct synthesis of Urea from Ammonium Cyanate occurred two years later by Wöhler and Liebig.

Friedrich Wöhler (1800-82)

On 22nd February 1828, Wöhler wrote a letter which included the following text to Jöns Jacob Berzelius (1779-1848) ("Berzelius' accurate determination of atomic and molecular weights helped to establish the laws of combination and the atomic theory. He also invented the system of chemical symbols now used universally.") :

"While I certainly hope that my letter of 12 January and the postscript of 2 February have arrived, and I live daily, or better hourly, in the eager hope of receiving your reply, still I will not wait for it but rather write already again, because I cannot, so to say, hold my chemical water and must tell you that I can make urea without the help of a kidney or even an animal, neither man nor dog."

Isomerism is an area where crystallography using X-ray and neutron diffraction plays an important analytical role in understanding the properties of compounds and materials. In the field of isomerism, Wöhler was in on the ground floor:

Wöhler made the disconcerting discovery that cyanic acid appeared to be identical in composition to fulminic acid which had been discovered by Liebig. Fulminates and cyanates have very different chemical properties and it was assumed that either Liebig or Wöhler had made a mistake. Liebig accused Wöhler of being an incompetent analyst. Unsurprisingly, this unprofessional conduct failed to resolve the paradox. However, in 1826, Wöhler and Liebig agreed to meet in order to examine carefully, their respective analyses. The outcome of this meeting was satisfying for both parties, if somewhat paradoxical: it was concluded that neither chemist had made a mistake in their respective analyses and that, therefore, they must both be correct. It had been shown that apparently different compounds could have the same chemical composition and yet have very different chemical properties. The resolution of this disagreement resulted in the two chemists becoming good friends and to fruitful collaboration in future years. This included a series of experiments that demonstrated how benzaldehyde could be converted into several different compounds, each containing the C₁₄H₁₀O₂ group, which they subsequently named the ‘benzoyl’ group.

These collaborative experiments, together with Berzelius’ own work, in which he had failed to detect any difference in chemical composition between racemic and tartaric acids, helped to pave the way for his theory of isomerism, published in 1831. The theory of isomerism postulated that substances could have the same chemical composition and yet have different chemical properties, due to their differing three-dimensional arrangement of atoms. Wöhler had already shown a striking example of isomerism three years earlier, in that urea, extracted from canine urine, had the same chemical composition as did ammonium cyanate.

Crystal Structure of Ammonium Cyanate (NH₄NCO)

Until recently the crystal structure of Ammonium Cyanate was unknown; surprising for a simple compound with such a prestigous place in the history of science and chemistry. Initially it was solved in 1998 from powder diffraction data collected on the X-ray synchrotron at Daresbury, Cheshire, England. As X-rays are not very sensitive to light atoms such as hydrogen. "Nitrogen-Hydrogen - Oxygen" hydrogen bonds were reported based on both fitting to the X-ray diffraction data and Hartree-Fock calculations. ("New light on an old story: The solid-state transformation of ammonium cyanate into urea"; Dunitz JD, Harris KDM, Johnston RL, Kariuki BM, MacLean EJ, Psallidas K, Schweizer WB, Tykwinski RR Journal of the American Chemical Society, 120 (50): 13274-13275 December 23 1998)

However further studies using neutron powder diffraction showed that the hydrogen bonding scheme was not correct. A new 2003 paper showing that "Nitrogen-Hydrogen - Nitrogen" hydrogren bonding was occurring. The data from deuterated ammonium cyanate (collected at the NRC Neutron scattering facility at Chalk River, Ontario) and refinement from this paper was used to generate the Rietveld plot shown in the CPDW logo. ("Ammonium cyanate shows N-H center dot center dot center dot N hydrogen bonding, not N-H center dot center dot center dot O" MacLean EJ, Harris KDM, Kariuki BM, Kitchin SJ, Tykwinski RR, Swainson IP, Dunitz JD, Journal of the American Chemical Society, 125 (47): 14449-14451 November 26 2003)

Following are images showing some of the hydrogen bonds (in dark blue). The left images is the Ammonium Cyanate structure as solved by X-ray data but with incorrect hydrogen bonding from the Ammonium hydrogens to Oxygen. The right image is the Ammonium Cyanate structure as corrected using neutron data, and with correct hydrogen bonding from the Ammonium hydrogens to Nitrogen.

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Ammonium Cyanate structure: a) as solved by X-ray data but with incorrect hydrogen bonding and b) as corrected using neutron data and with correct hydrogen bonding.

Crystal Structure Co-ordinates of Ammonium Cyanate (NH4NCO) (powder X-ray diffraction derived and as corrected by powder neutron diffraction)

          First obtained from X-ray data   As corrected by neutrons (14°K)
Cell        Tetragonal                      Tetragonal
Spacegroup: P4/n ; origin at -1             P4/ nmm ; origin at -1 
a=b=        5.1431(1) Å                     5.0822(1) Å 
c=          5.5552(2) Å                     5.5513(1) Å

N1          0.25     0.75     0.0           0.25   0.75       0.0 
H1/D1       0.245(1) 0.908(1) 0.100(1)      0.25   0.9163(5) -0.1069(6)
O1          0.25     0.25     0.296(1)      0.25   0.25       0.2818(9)
C1          0.25     0.25     0.526(1)      0.25   0.25       0.5007(10)
N2          0.25     0.25     0.737(1)      0.25   0.25       0.7153(5)

Neutrons are far more sensitive to light atoms such as hydrogen, and thus more suitable for accurately locating light atoms in the unit cell by refinement of powder diffraction.

The Beaver

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The hard working beaver is but one of many mammals associated as a symbol of Canada. It was probably defined as a Canadian national symbol by its inclusion on the first Canadian postage stamp in 1851 ("Three Penny Beaver") and is currently depicted on the Canadian 5 cent coin (a "nickel"). (There was intent to put a photo of a beaver on this page; but typing "free beaver images" into http://www.google.com/ only gave links to hard core porn sites.)

"The beaver attained official status as an emblem of Canada when an "act to provide for the recognition of the beaver (castor canadensis) as a symbol of the sovereignty of Canada" received royal assent on March 24, 1975."

The Canadian Beaver (Castor Canadensis) is a large, herbivore (vegetarian) rodent that prefers to live in water, being able to stay under water for up to ten to fifteen minutes. An adult can grow up to four feet long (including tail) and weigh more than 60 pounds. It's paddle like tail serves as a prop when the beaver sits upright and as a rudder when it swims. Their favourite food is tree bark. Beavers have special muscles that seal their ears while they are diving; and their eyes are protected with a pair of see-through eyelids.

Most famous for construction of dams, this instinct for dam construction is prompted by the sound of running water. Beaver Defeaters and beaver deceivers use this fact to try by engineering culverts in such as way as to not generate the sound of running water. Before the start of the fur trade, there were an estimated 6 million beaver in Canada. In the mid 19th century the beaver were close to extinction. Legislation was enacted to to protect the beaver from going extinct, and now their numbers in North America are such that in some areas they are approaching nuisance levels.

Here, the CPDW beaver (drawn by Lorne Whitlock of PorkCoffee Illustration and Design) is following his instinct (as, no doubt activated by the sound of flowing water) by gnawing through through a nuclear fuel bundle for a CANDU power reactor. People concerned with nuclear safety will no doubt conclude that beavers, nuclear fuel bundles and the sound of running water are a potentially dangerous combination.

The CPDW Beaver as drawn by Lorne Whitlock of Pork Coffee

Why sit a beaver on a nuclear fuel bundle as a symbol of a powder diffraction workshop? Well?! . . . . Neutrons from nuclear reactors can also provide a useful radiation source for performing powder diffraction; and this will be one of the topics in the workshop. It is also hoped that this logo and name can also be used for the current C2 workhorse neutron powder diffractometer at the NRC Neutron group in Chalk River Laboratories, Ontario.

Convergent Evolution?

Questions have been asked and concerns raised if we just ripped off the idea for this logo from the Canadian Nuclear FAQ maintained by Jeremy Whitlock; which also has a Beaver with a Canadian Flag on a CANDU nuclear fuel bundle. An initial logo design below shows the CPDW beaver on a wooden log, before it has acquired a taste for nuclear materials. Other NRC Neutron staff suggested it would be better to have a beaver interested in neutron powder diffraction sitting on a fuel bundle; and it was made so.

Original CPDW Beaver as drawn by Lorne Whitlock of Pork Coffee of Tuesday 30th December 2003

Why not use the Canadian Silver Beaver (Castor Canadensis Argentum) for the CPDW Beaver Logo?

It was originally hoped that the CPDW beaver would be of a Canadian Silver Beaver (Castor Canadensis Argentum). However the artist could not find an example image of Castor Canadensis Argentum to base a logo on; thus the logo was based on the Canadian Beaver (Castor Canadensis). Citizens of the Upper Ottawa Valley familiar with Fred's Steak house in Chapeau, Quebec (over the river from Pembroke, Ontario) may have seen with their own eyes, the rare breeding pair of silver beavers they had on display for visitors. Alas, recent sad news is a report that they both froze to death in the grueling winter of 2002/2003. It should be noted that the Canadian Silver Beaver (Castor Canadensis Argentum) is not an official symbol of Canada, where (as noted before) the Canadian Beaver (Castor Canadensis) has received royal assent as a symbol of the sovereignty of Canada.