What is Crystallography: Definition and 42 Discussions

Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure). The word "crystallography" is derived from the Greek words crystallon "cold drop, frozen drop", with its meaning extending to all solids with some degree of transparency, and graphein "to write". In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming that 2014 would be the International Year of Crystallography.Before the development of X-ray diffraction crystallography (see below), the study of crystals was based on physical measurements of their geometry using a goniometer. This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing the symmetry of the crystal in question. The position in 3D space of each crystal face is plotted on a stereographic net such as a Wulff net or Lambert net. The pole to each face is plotted on the net. Each point is labelled with its Miller index. The final plot allows the symmetry of the crystal to be established.
Crystallographic methods now depend on analysis of the diffraction patterns of a sample targeted by a beam of some type. X-rays are most commonly used; other beams used include electrons or neutrons. Crystallographers often explicitly state the type of beam used, as in the terms X-ray crystallography, neutron diffraction and electron diffraction. These three types of radiation interact with the specimen in different ways.

X-rays interact with the spatial distribution of electrons in the sample.
Electrons are charged particles and therefore interact with the total charge distribution of both the atomic nuclei and the electrons of the sample.
Neutrons are scattered by the atomic nuclei through the strong nuclear forces, but in addition, the magnetic moment of neutrons is non-zero. They are therefore also scattered by magnetic fields. When neutrons are scattered from hydrogen-containing materials, they produce diffraction patterns with high noise levels. However, the material can sometimes be treated to substitute deuterium for hydrogen.Because of these different forms of interaction, the three types of radiation are suitable for different crystallographic studies.

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  1. G

    Engineering Bravais lattice from lattice points

    I am confused on how to use these translations to tell what type of unit cell I have. I know that this is not a face centered unit cell because you need 4 total atoms and I only have two. From what I understand, to apply a body centering translation you add or subtract it from the lattice point...
  2. S

    I Miller indices and periodic boundary conditions

    I work in the field of quantum chemistry, in particular computations with periodic boundary conditions (PBC) needed for crystallographers. The crystallography data is usually presented as a set of fractional coordinates which are recounted to Cartesian ones. In the fractional coordinates, each...
  3. S

    XRD Result Analysis on Polymer

    So i just have my XRD result (Polymer Specimen) which i use to determine crystallinity of my material, and it turns out that my material has no obvious peak, and have a broad peak which usually associated with amorphous material. I added some filler to my material and it became more and more...
  4. Dario56

    I Questions About Bragg's Law of X-Ray Diffraction

    Bragg's law is schematically shown on the picture: Two parallel and plane waves are shown which propagate towards the crystal. For plane waves, wave fronts are flat planes perpendicular to the wave propagation with infinite size. In reality, there are no plane waves. Nevertheless, they are...
  5. S

    A What is the Structure of Gallium Oxide?

    I have three questions regarding the material Gallium Oxide. I was reading in several articles and they introduced its structure as it has monoclinic structure and it consists tetrahedral and octahedral structures in it. What I can't understand I can connect this structure to the chemical...
  6. P

    Problem on Diffraction Grating and Laser Crystallography

    First question: When shining a laser (##\lambda = 630nm##) through a 2D crystal, diffraction patterns are observed. Why? Possible reasons: 1. Atoms and the space between them act as diffraction gratings. 2. Bragg Diffraction, although in this case the pattern would be observed on the same...
  7. Jezza

    I Standard crystallographic notation confusion

    I'm revising for my condensed matter exam, and I've never understood the point group notation, in particular of the 32 crystallographic point groups, so let me try and explain what I understand of it and point out where my confusion lies. Please point out any other misunderstandings I have. We...
  8. Cryo

    A Nonlinear susceptibility and group reps

    Dear All short explanation: I am trying to leverage my limited understanding of representation theory to explain (to myself) how many non-vanshing components of, for example, nonlinear optical susceptibility tensor ##\chi^{(2)}_{\alpha\beta\gamma}## can one have in a crystal with known point...
  9. codcodo

    Mathematics of Macromolecular Crystallography

    I would really appreciate it if I could get book recommendations on the rigorous mathematical theory of x ray crystallography. Which areas of mathematics (pure and applied) would be most useful and applicable?
  10. H

    A Help with determination of crystal orientation

    Dear all, Hi, I am looking for a non-destructive method of determining the crystal orientation of a smaller-than-50x50x50 μm single crystal, mounted on a quartz substrate. I've considered several x-ray methods like Laue method, or microfocused XRD, but there are some experimental difficulty...
  11. John Lutz

    Regarding Home Lab made to study crystallography

    1) Is it possible to create crystals at home beyond child crystal kits one can buy? I'm very serious about putting work into studying and growing crystals. If so, what do I need? 2) Also how would it be possible to introduce vacancies in crystal growth ? I have heard of things like ionic...
  12. hzx

    A crystallography problem using 3D geometry

    Homework Statement Three close-packed planes of atoms are stacked to form fcc lattice. The stacking sequence of the three planes can be altered to form the hexagonal close packed structure by sliding the third plane by the vector r over the second. If the planes in the fcc structure are all...
  13. hzx

    Crystallography; from hcp to fcc

    Homework Statement Three close-packed planes of atoms are stacked to form fcc lattice. The stacking sequence of the three planes can be altered to form the hexagonal close packed structure by sliding the third plane by the vector r over the second. If the planes in the fcc structure are all...
  14. Poliona

    Understanding the Hard Sphere Model of Crystallography

    I am currently studying C Hammond's "Basics of Crystallography and Diffraction" (third ed.). In the first chapter ,concerning hard sphere model, I have found the following statement: There are, in fact, no examples of elements with this structure because, as the model building shows,the atoms...
  15. C_Pu

    I Peak profile fitting in X-ray Crystallography, why Voigt?

    Hi,I've been doing a lab cycle on X-ray crystallography. We are using Cu X-ray source on chloride salt crystals. It seems that the Bragg peak profile are commonly acknowledged to be a Voigt function, which is a convolution of Gaussian and Lorentzian. I am wondering what's the physical reason for...
  16. N

    X-ray crystallography; intensity peaks vary with voltage

    Homework Statement I have done a simple lab experiment to find the lattice constant for NaCl. Using a diffractometer, radioactive counts were measured as a function of crystal orientation angle for electron voltages of 20 and 30 kV. The average lattice constant found wasclose to the accepted...
  17. adamaero

    Crystallography, diffraction, identifying the pure element

    Homework Statement The only things you know about the sample are: (i) it has some kind of cubic lattice, and (ii) it is a pure element. Identify the element in the crystalline sample. SC: R = 0.5a FCC: R = 0.25a√2 BCC: R = 0.25a√3 Distances from Bragg peaks: d1 = 0.2037 nm d2 = 0.1746 nm d3...
  18. O

    X ray crystallography - interpreting my graph

    Homework Statement I am currently part way through a laboratory experiment that utilises basic crystallography to ultimately calculate lattice constants and structure factors for NaCl (we receive formal training in the next academic year via full treatment of von Laue, Bragg diffraction etc). I...
  19. Alvis

    Solid State Physics, FCC or BCC and why?

    Homework Statement Based on sizes for Na(.97 Angstroms), Cs(1.67 Angstroms), and Cl(1.81 Angstroms), which lattice type would you expect for NaCl and CsCl and why? Homework Equations My equation for the hole size for a bcc is (4/sqrt(3))(radius)-2(radius), I assume you put in the radius of Cl...
  20. H

    I Solid State NMR and X-ray Crystallography resources

    Hello, I need to learn how Solid State NMR and X-ray Crystallography work (theory and practical application). I'm primary interested in how those experimental techniques are used to determine molecular structures. I'm an undergrad physics student and I need this to pass my final exam. So if some...
  21. I

    The limiting sphere in crystallography

    Hello there ! I am writing here, because I could not find any good explanation in the literature and on the web Going straightaway to the point, my question is connected to Ewald's sphere and so called the limiting sphere. I red that limiting sphere is such a construction that appoints the...
  22. G

    Distance between points in crystal

    I am wondering how can I solve following problem. I would like to see how can it be solved.
  23. A

    Have you read any other books about crystallography?

    Hi! I don't know if this question has been asked before, but I searched the forum but didn't get answer.Do you know another good book about crystallography?Thanks!
  24. A

    Strange Miller Index Notation [00.1]

    Do someone knows what this dot "." means? I just know this notation [001]. Thank u Abigale
  25. A

    Hexagonal System 194 - crystallography

    Hello everyone ! I am currently reading a paper about crystal properties of R2CuIn3 where R=Tb,H0, Er. It states : 1.that based on bibliography they are crystallized in the hexagonal system P6/mmc. With the use of POWLS software , it was found that there was a second phase Cu2In , so its...
  26. T

    X-ray crystallography - Electron-density map

    Homework Statement Hello, i have the following task in my homework: When doing an X-ray crystallography experiment to determine the structure of biomolecules (protein/DNA), why do consider interpreting an electron-density map (EDM) instead of directly using the diffraction data? 2. The...
  27. S

    Question about crystallography

    Hi, I am now studying crystall structure and stucked in a question. Any kind of help will be highly appreciated. In crystall structure talking about translational symmetry they said that for any crystall a translational vector of the kind , T = m*a + n*b + p*c where a,b,c are...
  28. I

    A Simple Crystallography Question

    Hi could anyone help with a simple crystallography question. I am studying domain growth in crystals via Monte-Carlo simulations of atomistic models. I am writing a program to simulate the (neutron ) scattering pattern from a data-file of atomic positions via the rather brute force method...
  29. Z

    X-ray crystallography, protons or electrons?

    X-ray crystallography is now 100 years old so this question is probably pretty simple. Is the diffraction coming from the nucleons or the electrons in the sample? Ie. The electrons occupy a more diverse location within the sample (depending on what level/shell they occupy, in fact some may be...
  30. 7

    Complex problem from crystallography - rotating the crystal

    The problem statement: What I have managed to do: This problem seems a bit tricky at first because it is talking about rotating a crystal while also changing the voltage - changing two variables at the same time makes no sense to me. This is why I assumed that while we change the voltage...
  31. R

    Bragg's Law in Crystallography

    I took a course on protein crystallography last year and there's one thing I couldn't figure out then, and still can't figure out now. My understanding of Bragg's law hinges on the fact that in-phase scattered waves constructively interfere, and the requirement to be in-phase is met only when...
  32. M

    Braggs law and x-ray crystallography

    I'm trying to figure out how Braggs law is useful for analysing crystal structures. So here's the equation: nλ = 2dsinθ where λ is the wavelength of incident radiation, d is the distance between each layer of atoms in the crystal and θ is the angle of incidence. So to keep things simple let's...
  33. V

    A problem from crystallography

    Homework Statement In a tetragonal lattice a=b=0.25 nm and c= 0.18nm, deduce the spacing between (1,1,1) planes. Homework Equations the basic equation in this case is...
  34. A

    Crystallography Primer/Reading ?

    Hello, I'm going to be doing some work with crystallography and diffraction studies and I need a quick crash course in crystallography. I haven't done much of either outside of labs as an undergrad. Anyone have any suggested reading for quickly getting up to speed (or at least becoming...
  35. R

    Polarization and crystallography

    Can anyone explain what is principal section and optic axis of a crystal? Any help wud be highly appreciated. Thank You
  36. D

    Which lattice plane shows no diffraction peak in fcc crystal?

    Consider x ray diffraction from a crystal with an fcc(face centered cubic) lattice. The lattice plane for which there is NO diffraction peak is - 1. (2,1,2) 2. (1,1,1) 3. (2,0,0) 4. (3,1,1) I think Bragg's law must be used. nλ=2d sinλθ.
  37. N

    Diamond Structre Crystallography Questions

    Hi, these are a couple of questions from a lab at uni, i wasn't entirely sure where to begin so if anybody has any idea help would be much appreciated (i)A large model of the diamond structure can be described as two interpenetrating FCC lattices (i haven't found any diagrams that display...
  38. kelvin490

    Important definition in crystallography

    Can anyone tell me what's the definition of close packed plane in lattice structure? How can I be sure the close packed plane in FCC structure is (111) ?
  39. B

    Can Math Help Predict Binding Energies in Enzymology and Crystallography?

    This is a concept that has always eluded me. I'm a Biologist who works in the Pharmaceutical Industry and I need to get a better understanding of Biophysics with respect to enzymology, specifically with regards to crystallography, electron microscopy, and catalytic site binding physics. I...
  40. F

    Crystallography, Ashcroft&Mermin

    Homework Statement I'm having nightmares with this problem, apparently simple (A&M Chapter 7 Prob 2). I have to show that a trigonal primitive lattice, depending on its angle, can represent fcc or bcc. This I kind of figured it out intuitively. But the serious problem is number b), where I...
  41. E

    Modelling missing hydrogens from X-ray crystallography

    I had recently stumbled upon a computer program that can automatically add missing hydrogen atoms to protein structures from files from the protein data bank. (due to the hydrogen atom having only 1 electron, hence making its electron density too low to be detected by X-ray crystallography...