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Symmetries in Superconductors By: Hugh Heldenbrand Yoon-Mi Kim January 15, 2001 Computational Chemistry Seminar
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Problem Statement How can the different symmetries of a crystal be used to describe it?
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Introduction Superconductors. State University of New York at Binghamton: Preparation, Structure and Properties of a High- temperature Superconductor (YBa 2 Cu 3 O 7 ). “Model the system using CAChe software...” (Observations and Questions). MacSpartan vs. CAChe (demo version)
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Computational Method Our program was CAChe, “the happy union on computational chemistry and highly sophisticated graphics.” (CAChe 4.1 A Chemist’s Guide) When we went to enter the space group and fractional coordinates for YBa 2 Cu 3 O 7 we got an error message that we thought was related to the fact that we were using demo version software.
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Computational Method This is the point where the computer would say “path not found for space groups.”
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Point Group Symmetries There are four main types of symmetry operations: Rotation (C n )--the object appears identical if rotated about an axis by = 360/n = 2 /n degrees. Improper Rotation (S n )—a combination of a rotation and a mirror plane reflection perpendicular to the axis of rotation.
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Point Group Symmetries Inversion (center of symmetry, i)--each point in the object is converted to an identical point by projecting through a common center and extending an equal distance beyond this center. Reflection (mirror plane, )--each point in the object is converted to an identical point by projecting through a mirror plane and extending an equal distance beyond this plane.
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Space-Group Symmetries 230 space groups The International Union of Crystallography publishes them in Volume A of International Tables for Crystallography.
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The Herman-Mauguin System The space group of YBa 2 Cu 3 O 7 is: P mmm, a= 3.820, b=3.886, c=11.683
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Herman-Mauguin System The first letter identifies the centering of the lattice P = Primitive I = Body centered F = Face centered C = C-centered B = B-centered A = A-centered Our crystal is P, so it has a primitive Bravais lattice (there are no atoms outside the eight that make up the corners).
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Herman-Mauguin System The “mmm” in the space group for YBa 2 Cu 3 O 7 means that it has three “mirror plane” transitions. A mirror plane is simply a plane through which the crystal can be reflected identically on both sides.
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Herman-Mauguin System The a= 3.820, b=3.886, c=11.683 in the space group gives the dimensions of the crystal. Since a, b, and c are all different numbers, the crystal is orthorhombic.
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Database of Superconductors Here is a website with 3-D models of superconductors, which could be produced with a program like CAChe. http://barns.ill.fr/dif/xtal-3d.super.html
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Conclusion Why does a crystal’s symmetry matter?
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Bibliography http://www.chem.ox.ac.uk/icl/heyes/structure_of_ solids/Lecture4/Lec4.html http://imr.chem.binghamton.edu/labs/super/superc. html http://barns.ill.fr/dif/xtal-3d.super.html Huheey, James et al. Inorganic Chemistry: Principle of Structure and Reactivity. New York: Harper Collins, 1993.
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