Understanding Crystal Structure Determination with X-Ray Diffraction
Discover how crystal structures are determined using X-ray diffraction, a powerful technique that reveals the atomic arrangement within materials. Explore Bragg's Law, reflective properties of crystal lattice planes, and the Nobel prize-winning method of calling diffraction a reflection.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Q1: How do we determine the crystal structure?
X-Ray Diffraction Sample Incident Beam Transmitted Beam Diffracted Beam
X-Ray Diffraction Bragg Reflection Sample Incident Beam Transmitted Beam Braggs Law (Part 1): For every diffracted beam there exists a set of crystal lattice planes such that the diffracted beam appears to be specularly reflected from this set of planes.
X-Ray Diffraction Braggs recipe for Nobel prize? Call the diffraction a reflection!!!
X-Ray Diffraction Braggs Law (Part 1): the diffracted beam appears to be specularly reflected from a set of crystal lattice planes. Specular reflection: Angle of incidence =Angle of reflection (both measured from the plane and not from the normal) r i plane The incident beam, the reflected beam and the plane normal lie in one plane
X-Ray Diffraction r i dhkl Bragg s law (Part 2): n = 2 sin d hkl
r i dhkl P R Q = 2 sin d Path Difference =PQ+QR hkl
i r P R Q = 2 sin d Path Difference =PQ+QR hkl Constructive inteference n = 2 sin d hkl Bragg s law
Two equivalent ways of stating Braggs Law n = 2 sin d 1st Form hkl dhkl = 2 sin n d a = = hkl d , , nh nk nl n + + 2 2 2 ( ) ( ) ( ) nh nk nl = 2 sin d 2nd Form nh nk nl
Two equivalent ways of stating Braggs Law = n = 2 sin d 2 sin d nh nk nl hkl nthorder reflection from (hkl) plane 1st order reflection from (nh nk nl) plane e.g. a 2nd order reflection from (111) plane can be described as 1st order reflection from (222) plane
BRAGG VIEW OF DIFFRACTION X-rays that hit the crystal are elastically scattered by the sets of (hkl) planes The path difference for rays 1 and 2 equals to the length of two blue lines: - 1 ( = ) 2 2 sin d hkl 1 1 2 2 dhkl 11
BRAGG LAW The diffraction maxima will be created by reflection from a set of planes at angle that results in the integer wavelength difference in the path of the rays: = 2 hklsin n d Consequence 1: Each set of planes (hkl) is characterized by its own value hkl at which the diffraction maximum is observed Consequence 2: Each crystalline compound is characterized by a set of reflections at characteristic dhkl , or hkl (diffraction fingerprint of the compound) 12
BRAGG VIEW OF DIFFRACTION 1 1 2 dhkl The deviation of the ray from its initial path equals 2 13
7.3.1 The source and property of X-ray X-ray tube the wavelengths of X-ray are in the range of 100-0.01 1-0.01 : hard x-ray 100 1 soft x-ray 2.5-0.5 : used in crystal structure analysis 1-0.05 : used in detection of materials wound medical perspective,
X-rays produced by electronic transition between atomic energy levels High energy electron beam A part of the electrons are blocked; their kinetic energies giving rise to white x-ray. M L L radiation K As for Cu: K 1=1.540594 K 2=1.544422 e 1.54056 e IK 1 2IK 2
K1 K 2 Notice: K 2 can not be striped by the monochromator.
