A Rietveld-Approach for the Analysis of Neutron Time-of-Flight Transmission Data

A novel technique to obtain crystallographic information on a sample with a temporal resolution in the order of ten seconds is presented. The crystallographic information is derived from neutron time-of-flight (TOF) transmission patterns utilising neutrons traveling through a sample without interaction. The application of a pulsed neutron source provides Bragg-edge transmission patterns over a large wavelength range with sufficient statistics within seconds. This allows to study kinetics of structural phase transitions and chemical reactions that last for much less than one hour. Since no beam path is required for diffracted intensity, equipment for special sample environments, e.g. temperature, atmosphere or pressure, can be designed much easier than for a diffraction experiment. The acquired patterns are naturally based on different laws than conventional diffraction patterns. Thus, the available Rietveld software for powder diffraction data analysis can not be used or even easily adapted for the analysis of transmission data. The large number of spectra acquired during the course of a phase transition, typically in the order of 1000, requires automated analysis. Consequently, a software 'BETMAn' (Bragg-Edge Transmission Analysis) was developed. BETMAn allows for the first time to apply the Rietveld method to neutrons transmission patterns. BETMAn and its application for studying the mechanisms and kinetics of structural phase transitions and chemical reactions are presented in this work.

[1]  R. Dreele.  Quantitative texture analysis by Rietveld refinement , 1997 .

[2]  G. Placzek.  INCOHERENT NEUTRON SCATTERING BY POLYCRYSTALS , 1954 .

[3]  E. Fermi,et al.  The Transmission of Slow Neutrons through Microcrystalline Materials , 1947 .

[4]  D. Q. Wang,et al.  Strain measurement using neutron diffraction , 1996 .

[5]  Kurt Binder,et al.  Total Coherent Cross Sections for the Scattering of Neutrons from Crystals , 1970 .

[6]  H. Fuess,,et al.  Powder diffraction in the range of milliseconds , 1992 .

[7]  J. R. Granada,et al.  Total Scattering Cross Section of Solids for Cold and Epithermal Neutrons , 1984 .

[8]  W. A. Johnson.  Reaction Kinetics in Processes of Nucleation and Growth , 1939 .

[9]  M. Weinberg.  Transformation kinetics of particles with surface and bulk nucleation , 1992 .

[10]  P. Withers,et al.  In Situ Monitoring of Thermally Cycled Metal Matrix Composites by Neutron Diffraction and Laser Extensometry , 1997 .

[12]  D. Balzar,et al.  Elastic-strain tensor by Rietveld refinement of diffraction measurements , 1998 .

[13]  M. Starink.  Kinetic equations for diffusion-controlled precipitation reactions , 1997 .

[14]  H. Rietveld.  Line profiles of neutron powder-diffraction peaks for structure refinement , 1967 .

[15]  R. J. Hill,et al.  Quantitative phase analysis from neutron powder diffraction data using the Rietveld method , 1987 .

[16]  G. D. Smith,et al.  The distribution of substitutional alloying elements during the bainite transformation , 1990 .

[17]  EFFECT OF EXCITONS ON THE SCATTERING OF NEUTRONS BY CRYSTALS , 1966 .

[18]  C. D. Bowman,et al.  The Los Alamos National Laboratory Spallation Neutron Sources , 1990 .

[19]  J. Nye.  Physical Properties of Crystals: Their Representation by Tensors and Matrices , 1957 .

[20]  V. F. Sears,et al.  Debye–Waller factor for elemental crystals , 1991 .

[21]  H. Bhadeshia,et al.  Bainite: An atom-probe study of the incomplete reaction phenomenon , 1982 .

[22]  G. S. Pawley,et al.  Unit-cell refinement from powder diffraction scans , 1981 .

[23]  J. Hanan,et al.  In-situ investigation of the reduction of NiO by a neutron transmission method , 2002 .

[24]  M. Avrami,et al.  Kinetics of Phase Change 2 , 1940 .

[25]  J. E. Lynn,et al.  Vibrational properties of Pu and Ga in a Pu-Ga alloy from neutron-resonance Doppler spectroscopy , 1998 .

[26]  H. K. D. H. Bhadeshia,et al.  Partitioning of carbon from supersaturated ferrite plates , 1992 .

[27]  C. Shull,et al.  EXPERIMENTAL LIMIT FOR THE NEUTRON CHARGE. , 1967 .

[28]  M. Sakata,et al.  An analysis of the Rietveld refinement method , 1979 .

[29]  Grosse-Kunstleve.  Algorithms for deriving crystallographic space-group information. , 1999, Acta crystallographica. Section A, Foundations of crystallography.

[30]  J. Szymanski,et al.  Current-mode detector for neutron time-of-flight studies☆ , 1990 .

[31]  M. Iizumi.  Real-time neutron diffraction studies of phase transition kinetics , 1986 .

[32]  L. Hove,et al.  Effect of short wavelength interference on neuteron scattering by dense systems of heavy nuclei , 1951 .

[33]  B. Derby,et al.  Analysis Of Neutron-Diffraction Peak Broadening Caused By Internal-Stresses In Composite-Materials , 1995 .

[34]  J. Christian,et al.  The theory of transformations in metals and alloys , 2003 .

[35]  D. Bish,et al.  Quantitative phase analysis using the Rietveld method , 1988 .

[36]  F. Natterer.  The Mathematics of Computerized Tomography , 1986 .

[37]  C. Bowman,et al.  Real time neutron transmission investigation of the austenite-bainite transformation in grey iron , 1994 .

[38]  M. Avrami.  Granulation, Phase Change, and Microstructure Kinetics of Phase Change. III , 1941 .

[39]  J. M. Hastings,et al.  Neutron Diffraction Studies of Cold‐Worked Brass , 1952 .

[40]  N. Popa.  Texture in Rietveld refinement , 1992 .

[41]  F. Allen,et al.  The crystallographic information file (CIF) : a new standard archive file for crystallography , 1991 .

[42]  M. Dahms.  The iterative series‐expansion method for quantitative texture analysis. II. Applications , 1992 .

[43]  C. Kittel.  Introduction to solid state physics , 1954 .

[44]  Peter van der Linden.  Expert C programming - deep C secrets , 1994 .

[45]  Robert Weinstock,et al.  The Inelastic Scattering of Slow Neutrons. , 1943 .

[46]  J. Mayers,et al.  Temperature measurement by neutron resonance radiography , 1989 .

[47]  J. G. Maldonado,et al.  Retransformation (α′→γ) kinetics of strain induced martensite in 304 stainless steel , 2000 .

[48]  Clarence Zener,et al.  Interference of Growing Spherical Precipitate Particles , 1950 .

[49]  Mark R. Daymond,et al.  Use of Rietveld refinement for elastic macrostrain determination and for evaluation of plastic strain history from diffraction spectra , 1997 .

[50]  Andrew Putnis,et al.  An Introduction to Mineral Sciences , 1992 .

[51]  G. Placzek.  The Scattering of Neutrons by Systems of Heavy Nuclei , 1952 .

[52]  P. Withers,et al.  A new stroboscopic neutron diffraction method for monitoring materials subjected to cyclic loads: Thermal cycling of metal matrix composites , 1996 .

[53]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[54]  R. Young,et al.  The Rietveld method , 2006 .

[55]  Hans-Rudolf Wenk,et al.  Some basic concepts of texture analysis and comparison of three methods to calculate orientation distributions from pole figures , 1988 .

[56]  M. Avrami.  Kinetics of Phase Change. I General Theory , 1939 .

[57]  R. Young,et al.  Suggested guidelines for the publication of Rietveld analyses and pattern decomposition studies , 1982 .

[58]  B. Willis,et al.  Neutron diffraction studies of anharmonic temperature factors in BaF2 , 1968 .

[59]  Edward Prince,et al.  Mathematical techniques in crystallography and materials science , 1982 .

[60]  H. Scott.  The Estimation of Standard Deviations in Powder Diffraction Rietveld Refinements , 1983 .

[61]  T. G. Worlton,et al.  Multicomponent profile refinement of time-of-flight neutron diffraction data , 1976 .

[62]  J. King.  Search for a Small Charge Carried by Molecules , 1960 .

[63]  J. Cohen,et al.  Residual Stress: Measurement by Diffraction and Interpretation , 1987 .

[64]  R. Dreele,et al.  Neutron Powder Diffraction , 2002 .

[65]  H. Rietveld.  A profile refinement method for nuclear and magnetic structures , 1969 .

[66]  K. Raymond.  Application of constraints to derivatives in least‐squares refinement , 1972 .

[67]  John W. Cahn,et al.  The kinetics of grain boundary nucleated reactions , 1956 .

[68]  C. S. Roberts.  Effect of Carbon on the Volume Fractions and Lattice Parameters Of Retained Austenite and Martensite , 1953 .

[69]  A. Albinati,et al.  The Rietveld method in neutron and X-ray powder diffraction , 1982 .

[70]  M. Hagen,et al.  Time resolved studies on a millisecond time scale by elastic neutron scattering: transient properties of the ferroelectric phase transition in Rb2ZnCl4 , 1994 .

[71]  Baumann,et al.  Experimental limit for the charge of the free neutron. , 1982, Physical review. D, Particles and fields.