DOCSLIB.ORG

Emergence of Long-Range Order in Sheets of Magnetic Dimers

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Emergence of Long-Range Order in Sheets of Magnetic Dimers Emergence of long-range order in sheets of magnetic dimers S. Haravifarda,b, A. Banerjeea,c, J. van Wezeld, D. M. Silevitcha, A. M. dos Santosc, J. C. Langb, E. Kermarrece, G. Srajerb, B. D. Gauline, J. J. Molaisonc, H. A. Dabkowskae, and T. F. Rosenbauma,1,2 aThe James Franck Institute and Department of Physics, The University of Chicago, Chicago, IL 60637; bAdvanced Photon Source, Argonne National Laboratory, Argonne, IL 60439; cNeutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, TN 37831; dSchool of Physics, The University of Bristol, Bristol BS8 1TL, United Kingdom; and eDepartment of Physics and Astronomy and Brockhouse Institute for Material Research, McMaster University, Hamilton, ON, Canada L8S 4M1 Edited by David D. Awschalom, The University of Chicago, Chicago, IL, and approved August 28, 2014 (received for review July 14, 2014) Quantum spins placed on the corners of a square lattice can dimerize whose nearest-neighbor interactions are mediated by in-plane and form singlets, which then can be transformed into a magnetic oxygen bonds; layered Cu–O compounds of this kind are of state as the interactions between dimers increase beyond thresh- broad interest due to their role in driving phenomena such old. This is a strictly 2D transition in theory, but real-world materials as high-temperature superconductivity. At ambient conditions, often need the third dimension to stabilize long-range order. We use SCBO forms a crystal in the tetragonal space group I-42m with + + high pressures to convert sheets of Cu2 spin 1/2 dimers from local a = b = 8.995 Å and c = 6.659 Å. The Cu2 ions form orthogonal singlets to global antiferromagnet in the model system SrCu2(BO3)2. structural and magnetic dimers in the a–b plane (4). As each Single-crystal neutron diffraction measurements at pressures above dimer sits on a mirror plane that passes through the center of its 5 GPa provide a direct signature of the antiferromagnetic ordered orthogonal neighbor, the unit cell contains four dimers on two state, whereas high-resolution neutron powder and X-ray diffrac- layers with alternating orientations (3) (Fig. 1). SCBO has a non- tion at commensurate pressures reveal a tilting of the Cu spins out of magnetic, singlet ground state (5), with 0.6 < x < 0.69 (6). Hy- the plane with a critical exponent characteristic of 3D transitions. drostatic pressure can be used to tune x, with a transition into an The addition of anisotropic, interplane, spin–orbit terms in the ven- intermediate phase observed at P ∼2 GPa (7, 8). The magnetic erable Shastry–Sutherland Hamiltonian accounts for the influence characteristics of the singlet–triplettransitionemergeeveninX-ray of the third dimension. scattering experiments due to a remarkably robust spin–lattice coupling (7, 9, 10). At P ∼4.5 GPa a second phase transition has condensed matter physics | quantum magnetism | phase transition | been observed, marked by a structural transition from tetragonal dimensional cross-over | neutron and X-ray scattering to monoclinic ordering (7, 11). In this article, we use both X-ray and neutron scattering measurements to illuminate the structural wo-dimensional systems lie at the boundary between the and magnetic configurations that permit long-range order to Torder-destroying effects of fluctuations in lower dimension emerge for P > 5 GPa, directly identifying for the first time, to our and the emergence of true long-range order in higher dimension. knowledge, the predicted antiferromagnetic state. How ordered states form and remain stable at finite temperature Results and Discussion is a fundamental question that cuts across the sciences. In physics, surfaces, quantum wells, and layered compounds all We begin with fundamental symmetry considerations. In SCBO’s have provided insights into the peculiar nature of 2D phases, low-pressure tetragonal phase, structural Bragg reflections phase transitions, and dimensional cross-over effects. Of partic- ular interest for quantum phase transitions is the theoretically Significance tractable case of interacting magnetic spins placed on a 2D square lattice, the Shastry–Sutherland model (1). The geometry Magnetic materials are composed of individual spins that interact prevents simultaneous satisfaction of all spin–spin coupling with each other and under suitable conditions can arrange them- terms, leading to a frustrated state that in turn enhances the selves in an ordered array. When spins are confined to two- effects of quantum fluctuations. As the coupling terms are tuned, dimensional sheets, small perturbations can disrupt their order magnetic order can emerge, but its nature and the potential in- and destroy the magnetic state. We show how a set of interact- fluence of other sheets of spins in a real physical system have not ing, quantum-mechanical spins placed on the corners of a square been probed directly. array evolves from a set of locally bonded entities to a globally The Shastry–Sutherland model can be described by the Ham- ordered structure. The system stabilizes itself against fluctuations iltonian: through subtle local contractions, elongations, and tilts. The com- X X bination of neutron and X-ray scattering at pressures up to 60,000 atmospheres reveals the complex interplay of structural H = J Si · Sj + J′ Si · Sj; [1] nn nnn distortions and spin alignments that permit long-range order to emerge in this model quantum magnet. where a set of S = 1/2 spins sits on a square lattice and interacts via a regular array of diagonal bonds. This creates a network of Author contributions: S.H. and T.F.R. designed research; S.H., A.B., A.M.d.S., J.C.L., E.K., J G.S., B.D.G., and J.J.M. performed research; S.H., B.D.G., and H.A.D. contributed new dimers with antiferromagnetic intradimer coupling and inter- reagents/analytic tools; S.H., J.v.W., D.M.S., and T.F.R. analyzed data; and S.H., J.v.W., dimer coupling J′. The ground state depends on the ratio of D.M.S., and T.F.R. wrote the paper. J′=J = x. For x < 0.7, the ground state consists of S = 0 singlets, The authors declare no conflict of interest. x > whereas for 0.9 a global antiferromagnetic phase is expected. This article is a PNAS Direct Submission. x For intermediate values of , a variety of locally ordered states 1Present address: Division of Physics, Mathematics and Astronomy, California Institute of has been predicted (2). Technology, Pasadena, CA 91125. – The first known experimental realization of the Shastry 2To whom correspondence should be addressed. Email: [email protected]. Sutherland lattice is SrCu2(BO3)2 (SCBO) (3). The magnetism in This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 2+ SCBO consists of S = 1/2 Cu ions in well-separated planes 1073/pnas.1413318111/-/DCSupplemental. 14372–14377 | PNAS | October 7, 2014 | vol. 111 | no. 40 www.pnas.org/cgi/doi/10.1073/pnas.1413318111 Downloaded by guest on September 30, 2021 refinement indicates a space group of P121 (#3). We test this identification using a simulation of the expected neutron diffrac- tion intensity at T = 90 K, including the cross-sections for both SCBO’s structural and antiferromagnetic components, and com- pare experiment and computer simulation in Fig. 3B.Thespace group identifications also permit us to track the lattice parameters as a function of temperature. We see in Fig. 3C that the evolution can be described as an increase in c associated with a simultaneous decrease in a, and a slight decrease in b as temperature is cooled below T ∼ 120 K. The change in lattice constants is accompanied by a decrease in the monoclinic angle β; the overall volume of the unit cell changes by less than 1%. We plot in Fig. 4 a comparison between single-crystal X-ray diffraction in a diamond anvil cell and powder neutron diffraction in a Paris–Edinburgh cell for P = 5.5 GPa at the position and temperature where a forbidden (0 3 0) peak develops. The intensity scaling by 100 is consistent with the relative cross-sections for X-ray and neutron scattering. The simulation of the neutron intensity (dashed line) incorporates the antiferromagnetic structure de- scribed below; different spin configurations contribute from 0 to 30% of the total neutron signal at (0 3 0) (Fig. S1) and provide a quantitative test of the enhancement measured at that Q in Fig. Fig. 1. Crystallographic structure of SrCu2(BO3)2 (SCBO). (Upper) Low-tem- A perature structure of SCBO projected into the a–b plane. (Lower) a–c plane. 3 . The high-resolution single-crystal synchrotron X-ray data per- Solid, dashed, and dotted blue lines show the interactions between the mit us to focus in on the critical behavior of the symmetry change + dimerized Cu2 ions, representing the intradimer (J = 84 K), in-plane inter- from C121 to P121 with decreasing T (Fig. 4, Inset). A power-law dimer (J’ = 54 K), and out-of-plane interdimer (J′′ = 8 K) (6) interactions, fit to the data gives Tc = 122 ± 0.2 K and a critical exponent β = respectively. This hierarchy of direct exchange interactions underlies the 0.36 ± 0.04, consistent with the value of β = 0.37 expected for a 3D effectively 2D nature of the system in the absence of global magnetic order. Heisenberg transition (15) rather than the nominally expected 2D behavior. That this transition is associated with magnetic order is further corroborated by the rapid decrease in the neutron diffrac- satisfying h + k + l = 2n+1 are forbidden due to the symmetry of tion intensity at the forbidden odd-index peaks as expected for the the I-42m space group. Above the monoclinic transition at P ∼ 4.5 Q dependence of Cu’s magnetic form factor.
Load more

Recommended publications
  • Powder Methods Handout
    Powder Methods Beyond Simple Phase ID Possibilities, Sample Preparation and Data Collection Cora Lind-Kovacs Department of Chemistry & Biochemistry The University of Toledo History of Powder Diffraction Discovery of X-rays: Roentgen, 1895 (Nobel Prize 1901) Diffraction of X-rays: von Laue, 1912 (Nobel Prize 1914) Diffraction laws: Bragg & Bragg, 1912-1913 (Nobel Prize 1915) Powder diffraction: Developed independently in two countries: – Debye and Scherrer in Germany, 1916 – Hull in the United States, 1917 Original methods: Film based First commercial diffractometer: Philips, 1947 (PW1050) 2 http://www.msm.cam.ac.uk/xray/images/pdiff3.jpg Original Powder Setups Oldest method: Debye-Scherrer camera - Capillary sample surrounded by cylindrical film - Simple, cheap setup 3 Cullity; “Elements of X-ray Diffraction” Modern Powder Setups Powder diffractometers - theta-theta or theta-2theta - point or area detectors Scintag theta-theta diffractometer with Peltier cooled solid-state detector Inel diffractometer with 120° PSD (position sensitive detector) 4 Physical Basis of Powder Diffraction Powder diffraction obeys the same laws of physics as single crystal diffraction Location of diffraction peaks is given by Bragg’s law - 2d sin = n Intensity of diffraction peaks is proportional to square of structure factor amplitude N 2 2 2 2 - .F(hkl) f j exp(2i(hx j ky j lz j ))·exp[-8 u (sin ()/ ] j1 5 Goal of crystallography: Get structure Single crystal experiments - Grow crystals (often hardest step) - Collect data (usually easy, both
    [Show full text]
  • Structure Determination from Powder Diffraction Data. Most of Us Are Familiar with the More Common Process of Structure Refinement by the Rietveld Method
    COMMISSION ON POWDER DIFFRACTION INTERNATIONAL UNION OF CRYSTALLOGRAPHY http://www.iucr.org/iucr-top/comm/cpd/ NEWSLETTER No. 25, July 2001 http://www.iucr.org/iucr-top/comm/cpd/Newsletters/ . IN THIS ISSUE Structure Determination from Powder Diffraction Data (Bill David, Editor) CPD chairman’s message, Paolo Scardi 2 Ab-initio structure determination of oligopeptides from powder diffraction data 20 Editor’s message, Bill David 2 K D M Harris, R L Johnston, E Tedesco and G W Turner CPD projects: 3 Correlating crystal structure with the physical Quantitative Phase Analysis RR, Ian Madsen properties of pharmaceutical compounds 22 Size-Strain RR, Davor Balzar N Shankland, W I F David, K Shankland, A Kennedy, C S Frampton and A Florence WWW sites related to Powder Diffraction 3 EXPO: New developments 23 A Altomare, C Giacovazzo, A G G Moliterni and R Rizzi IUCr Commission on Powder Diffraction 4 Structure determination from powder diffraction data News from ICDD and IXAS 26 Revisiting the 1998 SDPD Round Robin 7 Computer Corner, L M D Cranswick 28 A Le Bail and L M D Cranswick What’s On 35 A 117-atom structure from powder diffraction data 9 L B McCusker, Ch Baerlocher and T Wessels Companies 36 Drug polymorphism and powder diffraction 12 How to receive the CPD Newsletter 36 P Sieger, R Dinnebier, K Shankland and W I F David Calls for contributions to CPD newsletter 26 36 Malaria, synchrotron radiation and Monte Carlo 14 P W Stephens, S Pagola, D S Bohle and A D Kosar A case of mistaken identity: metastable Me2SBr2 16 A N Fitch, G B M Vaughan and A J Mora Combined Rietveld and stereochemical- restraint refinement with high resolution powder diffraction offers a new approach for obtaining protein-drug structures 17 R B Von Dreele On the reliablility of Rwp in structure prediction 19 L Smrcok and M Durík ISSN 1591-9552 CPD Chairman’s Message The CPD Newsletter is a very popular publication – more than 2000 people have now asked to receive a copy.
    [Show full text]
  • Chapter 7: Basics of X-Ray Diffraction
    Chapter 7: Basics of X-ray Diffraction Providing Solutions To Your Diffraction Needs. Chapter 7: Basics of X-ray Diffraction Scintag has prepared this section for use by customers and authorized personnel. The information contained herein is the property of Scintag and shall not be reproduced in whole or in part without Scintag prior written approval. Scintag reserves the right to make changes without notice in the specifications and materials contained herein and shall not be responsible for any damage (including consequential) caused by reliance on the material presented, including but not limited to typographical, arithmetic, or listing error. 10040 Bubb Road Cupertino, CA 95014 U.S.A. www.scintag.com Phone: 408-253-6100 © 1999 Scintag Inc. All Rights Reserved. Page 7.1 Fax: 408-253-6300 Email: [email protected] © Scintag, Inc. AIII - C Chapter 7: Basics of X-ray Diffraction TABLE OF CONTENTS Chapter cover page 7.1 Table of Contents 7.2 Introduction to Powder/Polycrystalline Diffraction 7.3 Theoretical Considerations 7.4 Samples 7.6 Goniometer 7.7 Diffractometer Slit System 7.9 Diffraction Spectra 7.10 ICDD Data base 7.11 Preferred Orientation 7.12 Applications 7.13 Texture Analysis 7.20 End of Chapter 7.25 © 1999 Scintag Inc. All Rights Reserved. Page 7.2 Chapter 7: Basics of X-ray Diffraction INTRODUCTION TO POWDER/POLYCRYSTALLINE DIFFRACTION About 95% of all solid materials can be described as crystalline. When X-rays interact with a crystalline substance (Phase), one gets a diffraction pattern. In 1919 A.W.Hull gave a paper titled, “A New Method of Chemical Analysis”.
    [Show full text]
  • The Fundamentals of Neutron Powder Diffraction
    U John R.D. Copley CD QC Nisr National Institute of Special 100 Standards and Technology Publication .U57 Technology Administration U.S. Department of Commerce 960-2 #960-2 2001 c.% NIST Recommended Practice Gui Special Publication 960-2 The Fundamentals of Neutron Powder Diffraction John R.D. Copley Materials Science and Engineering Laboratory November 2001 U.S. Department of Commerce Donald L. Evans, Secretary Technology Administration Phillip J. Bond, Under Secretary for Technology National Institute of Standards and Technology Karen H. Brown, Acting Director Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best avail- able for the purpose. National Institute of Standards and Technology Special Publication 960-2 Natl. Inst. Stand. Technol. Spec. Publ. 960-2 40 pages (November 2001) CODEN: NSPUE2 U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 2001 For sale by the Superintendent of Documents U.S. Government Printing Office Internet: bookstore.gpo.gov Phone: (202) 512-1800 Fax: (202) 512-2250 Mail: Stop SSOP, Washington, DC 20402-0001 Table of Contents /. INTRODUCTION 1 1. 1 Structure and Properties .7 1.2 Diffraction 1 1. 3 The Meaning of "Structure" 7 1.4 Crystals and Powders 2 1.5 Scattering, Diffraction and Absorption 2 //. METHODS 3 11.1 Definitions 3 11.2 Basic Theory 3 11.3 Instrumentation 6 11.4 The BT1 Spectrometer at the NIST Research Reactor .
    [Show full text]
  • X-Ray Powder Diffraction
    X-RAY POWDER DIFFRACTION XRD for the analyst Getting acquainted with the principles Martin Ermrich nλ = 2d sin θ Detlef Opper The Analytical X-ray Company X-RAY POWDER DIFFRACTION XRD for the analyst Getting acquainted with the principles Martin Ermrich Detlef Opper XRD for the analyst Published in 2011 by: PANalytical GmbH Nürnberger Str. 113 34123 Kassel +49 (0) 561 5742 0 [email protected] All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form by any means electronic, mechanical, photocopying or otherwise without first obtaining written permission of the copyright owner. www.panalytical.de 2nd revised edition published in 2013 by: PANalytical B.V. Lelyweg 1, 7602 EA Almelo P.O. Box 13, 7600 AA Almelo, The Netherlands Tel: +31 (0)546 534 444 Fax: +31 (0)546 534 598 [email protected] www.panalytical.com ISBN: 978-90-809086-0-4 We encourage any feedback about the content of this booklet. Please send to the address above, referring to XRD_for_the_analyst. 2 XRD for the analyst Contents 1. Introduction..................................................7 2. What is XRD?.................................................8 3. Basics of XRD................................................10 3.1 What are X-rays?.............................................10 3.2 Interaction of X-rays with matter ...............................11 3.3 Generation of X-rays..........................................12 3.3.1 Introduction.................................................12 3.3.2 The
    [Show full text]
  • Crystallography and Databases
    I Bruno, I et al 2017 Crystallography and Databases. CODATA '$7$6&,(1&( S Data Science Journal, 16: 38, pp. 1–17, DOI: U -2851$/ https://doi.org/10.5334/dsj-2017-038 REVIEW Crystallography and Databases Ian Bruno1, Saulius Gražulis2, John R Helliwell3, Soorya N Kabekkodu4, Brian McMahon5 and John Westbrook6 1 Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK 2 Vilnius University Institute of Biotechnology, Sauletekio al. 7, LT-10257 Vilnius, LT 3 School of Chemistry, University of Manchester, M13 9PL, UK 4 International Centre for Diffraction Data, 12 Campus Boulevard, Newtown Square, PA 19073, US 5 International Union of Crystallography, 5 Abbey Square, Chester CH1 2HU, UK 6 Department of Chemistry and Chemical Biology, Research Collaboratory for Structural Bioinformatics Protein Data Bank, Center for Integrative Proteomics Research, Institute for Quantitative Biomedicine, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, US Corresponding author: Brian McMahon ([email protected]) Crystallographic databases have existed as electronic resources for over 50 years, and have provided comprehensive archives of crystal structures of inorganic, organic, metal–organic and biological macromolecular compounds of immense value to a wide range of structural sciences. They thus serve a variety of scientific disciplines, but are all driven by considerations of accuracy, precise characterization, and potential for search, analysis and reuse. They also serve a variety of end-users in academia and industry, and have evolved through different funding and licensing models. The diversity of their operational mechanisms combined with their undisputed value as scientific research tools gives rise to a rich ecosystem.
    [Show full text]
  • How to Analyze Minerals
    How to Analyze Minerals Fundamentals Acknowledgement This tutorial was made possible by the many contributions of ICDD members working in the fields of mineralogy and geology. The data shown in this presentation were contributed by ICDD members and/or clinic instructors Overview • The vast majority of minerals are crystalline solids made of periodic arrays of atoms • Crystalline solids, when exposed to monochromatic X‐rays will diffract according to the principles of Bragg’s law. This is the principle behind single crystal crystallographic analysis and powder diffraction analysis • In powder diffraction analyses a randomly oriented, finely ground powder is required for multi‐phase identification and quantitation. Diffraction ‐ Bragg’s Law Incident coherent X‐ray beam X‐rays scattered from the second plane travel the extra distance depicted by the yellow lines. Simple geometry shows this distance = d 2d∙sinθ d = interplanar spacing of parallel planes of atoms When this extra distance is equal to one wavelength, the x‐rays scattered from the 2nd plane are in phase with x‐rays scattered from the 1st plane (as are those from any successive plane). This “constructive interference” produces a diffraction peak maximum at this angle. This is the basis of Bragg’s Law: λ = 2d∙sinθ XRPD Pattern for NaCl λ = 1.5406 Å (Cu Kα1) a = 5.6404 Å Bragg’s law prescribes the 2θ angular position for each peak based on the interplanar distance for the planes from which it arises. 2θ = 2 asin(λ/2d) (1 1 1) (2 0 0) (2 2 0) (3 1 1) (2 2 2) d = 3.256 Å d = 2.820 Å d = 1.994 Å d = 1.701 Å d = 1.628 Å 2θ = 27.37° 2θ = 31.70° 2θ = 45.45° 2θ = 53.87° 2θ = 56.47° Why It Works • Each crystalline component phase of an unknown specimen produces its own powder diffraction pattern.
    [Show full text]
  • An Introduction to X-Ray Diffraction by Single Crystals and Powders
    An Introduction to X-Ray Diffraction by Single Crystals and Powders Patrick McArdle NUI, Galway, Ireland 1 pma 2019 The Nature of Crystalline Materials • Crystalline materials differ from amorphous materials in that they have long range order. They also exhibit X-ray powder diffraction patterns. • Amorphous materials may have very short range order (e.g. molecular dimers) but do not have long range order and do not exhibit X-ray powder diffraction patterns. • The packing of atoms, molecules or ions within a crystal occurs in a symmetrical manner and furthermore this symmetrical arrangement is repetitive throughout a piece of crystalline material. • This repetitive arrangement forms a crystal lattice. A crystal lattice can be constructed as follows: 2 pma 2019 A 2-dimensional Lattice Pick any position within the 2 dimensional lattice in Fig. 1(a) and note the arrangement about this point. Place a dot at this position and then place dots at all other identical positions as in Fig. 1(b). Join these lattice points using lines to give a lattice grid. The basic building block of this lattice (unit cell) is indicated in Fig. 1(c). 3 pma 2019 Unit Cell Types and The Seven Crystal Systems Cubic a = b = c. = = = 90º. c Tetragonal a = b c. = = = 90º. b Orthorhombic a b c. = = = 90 º. a Monoclinic a b c. = = 90º, 90º. Orthorhombic Triclinic a b c.. 90º. Rhombohedral a = b = c. = = 90 º. (or Trigonal) Hexagonal a = b c. = = 90º, = 120º. In general, six parameters are required to define the shape and size of a unit cell, these being three cell edge lengths (conventionally, defined as a, b, and c), and three angles (conventionally, defined as , , and ).
    [Show full text]
  • Applications of Neutron Powder Diffraction in Materials Research
    ACXRI 96 APPLICATIONS OF NEUTRON POWDER DIFFRACTION •!••---• IN MATERIALS RESEARCH 111111111111:1111 MY9700777 S. J. Kennedy Neutron Scattering Group Australian Nuclear Science and Technology Organisation Private Mail Bag 1, Menai NSW 2234, Australia Abstract The aim of this article is to provide an overview of the applications of neutron powder diffraction in materials science. The technique is introduced with particular attention to comparison with the X-ray powder diffraction technique to which it is complementary. The diffractometers and special environment ancillaries operating around the HIFAR research reactor at the Australian Nuclear Science and Technology Organisation (ANSTO) are described. Applications of the technique which take advantage of the unique properties of thermal neutrons have been selected from recent materials studies undertaken at ANSTO. Introduction Although the ability of neutron diffraction to determine atomic and magnetic structures has been recognised for many years, the technique has traditionally been considered cumbersome to compete with x-ray powder diffraction for routine structural investigations. With improvements in diffractometer technology and increased primary neutron fluxes it is now possible to obtain high quality neutron powder diffraction data in relatively short times. Thus a wide range of problems in materials research that take advantage of the unique properties of the neutron can now be solved at many neutron scattering centres around the world. It is outside the scope of this article to discuss the development of the technique in any detail. My intention is simply to provide an introduction to the technique and to indicate that neutron powder diffraction is a powerful tool and is readily available to many of those interested in materials research.
    [Show full text]
  • X-Ray Powder Diffraction This Handout Provides Background on Theory and Methodology the Use and Theory of X-Ray Powder Diffraction
    X-Ray Powder Diffraction This handout provides background on Theory and Methodology the use and theory of X-ray powder diffraction. Examples of applications of The three-dimensional structure of this method to geologic studies are nonamorphous materials, such as provided. minerals, is defined by regular, repeating planes of atoms that form a crystal Introduction lattice. When a focused X-ray beam interacts with these planes of atoms, part Rocks, sediments, and precipitates are of the beam is transmitted, part is examples of geologic materials that are absorbed by the sample, part is refracted composed of minerals. Numerous and scattered, and part is diffracted. analytical techniques are used to Diffraction of an X-ray beam by a characterize these materials. One of crystalline solid is analogous to Figure 1. Simplified sketch of one these methods, X-ray powder diffraction diffraction of light by droplets of water, possible configuration of the X-ray source (X-ray tube), the X-ray detector, (XRD), is an instrumental technique that producing the familiar rainbow. X-rays is used to identify minerals, as well as and the sample during an X-ray scan. In are diffracted by each mineral this configuration, the X-ray tube and the other crystalline materials. In many differently, depending on what atoms detector both move through the angle geologic investigations, XRD make up the crystal lattice and how these theta (q), and the sample remains complements other mineralogical atoms are arranged. stationary. methods, including optical light In X-ray powder diffractometry, X-rays microscopy, electron microprobe are generated within a sealed tube that is microscopy, and scanning electron under vacuum.
    [Show full text]
  • X-Ray and Neutron CRYSTALLOGRAPHY a Powerful Combination by Robert B
    x-ray and neutron CRYSTALLOGRAPHY a powerful combination by Robert B. Von Dreele Determining the structure of a crystalline material remains the most powerful way to understand that material’s properties–which may explain why so many Nobel Prizes have been awarded in the field of crystal- , lography. The standard tools of the crystallographer are single-crystal and powder diffraction. introduced earlier in "Neutron Scattering-A Primer.” What was not mentioned was that until twenty years ago powder diffraction could not be used for solving a new crystal structure, but only for determining the presence of known crystalline had to be grown into large single crystals before crystallographers could unravel the positions of each atom within the repeating motif of a crystal lattice. This severe limitation disappeared after H. M. Rietveld developed a workable approach for resolving the known as Rietveld refinement. has opened up essentially all crystalline materials to relatively rapid structure analysis. This Escher painting shows a square lattice with a complicated unit cell, illustrating in two di- 10- “ mensions several kinds of symmetries found in real crystals. (We have darkened lines of the original grid to emphasize the unit cell.) If the colors are ignored, this pattern has both four- fold and twofold rotational symmetry as well as a number of mirror symmetry operations. When the color is included, the fourfold rotation becomes a color-transformation operator. Similar changes occur in the nature of the other symmetry operators as well. Reproduced with permis- sion: © 1990 M. C. Escher Heirs/Cordon Art, Baarn, Holland. 133 X-Ray and Neutron Crystallography This article presents a further improvement in powder-pattern analysis–that of combining x-ray and neutron diffraction data.
    [Show full text]
  • Modern X-Ray Diffraction Methods in Mineralogy and Geosciences
    Reviews in Mineralogy & Geochemistry Vol. 78 pp. 1-31, 2014 1 Copyright © Mineralogical Society of America Modern X-ray Diffraction Methods in Mineralogy and Geosciences Barbara Lavina High Pressure Science and Engineering Center and Department of Physics and Astronomy University of Nevada Las Vegas, Nevada 89154, U.S.A. [email protected] Przemyslaw Dera Hawaii Institute of Geophysics and Planetology School of Ocean and Earth Science and Technology University of Hawaii at Manoa 1680 East West Road, POST Bldg, Office 819E Honolulu, Hawaii 96822, U.S.A. Robert T. Downs Department of Geosciences University of Arizona Tucson, Arizona 85721-0077, U.S.A. INTRODUCTION A century has passed since the first X-ray diffraction experiment (Friedrich et al. 1912). During this time, X-ray diffraction has become a commonly used technique for the identification and characterization of materials and the field has seen continuous development. Advances in the theory of diffraction, in the generation of X-rays, in techniques and data analysis tools changed the ways X-ray diffraction is performed, the quality of the data analysis, and expanded the range of samples and problems that can be addressed. X-ray diffraction was first applied exclusively to crystalline structures idealized as perfect, rigid, space and time averaged arrangements of atoms, but now has been extended to virtually any material scattering X-rays. Materials of interest in geoscience vary greatly in size from giant crystals (meters in size) to nanoparticles (Hochella et al. 2008; Waychunas 2009), from nearly pure and perfect to heavily substituted and poorly ordered. As a consequence, a diverse range of modern diffraction capabilities is required to properly address the problems posed.
    [Show full text]