Symmetries in Superconductors

1
Symmetries in Superconductors

• By Hugh Heldenbrand
• Yoon-Mi Kim
• January 15, 2001
• Computational Chemistry Seminar

2
Problem Statement

• How can the different symmetries of a crystal be
  used to describe it?

3
Introduction

• Superconductors.
• State University of New York at Binghamton
  Preparation, Structure and Properties of a
  High-temperature Superconductor (YBa2Cu3O7).
• Model the system using CAChe software . . .
  (Observations and Questions).
• MacSpartan vs. CAChe (demo version)

4
Computational Method

• Our program was CAChe, the happy union on
  computational chemistry and highly sophisticated
  graphics. (CAChe 4.1 A Chemists Guide)
• When we went to enter the space group and
  fractional coordinates for YBa2Cu3O7 we got an
  error message that we thought was related to the
  fact that we were using demo version software.

5
(No Transcript)
6
(No Transcript)
7
Computational Method

• This is the point where the computer would say
  path not found for space groups.

8
(No Transcript)
9
Point Group Symmetries

• There are four main types of symmetry operations
• Rotation (Cn)--the object appears identical if
  rotated about an axis by a 360/n 2p/n
  degrees.
• Improper Rotation (Sn)a combination of a
  rotation and a mirror plane reflection
  perpendicular to the axis of rotation.

10
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.

11
(No Transcript)
12
(No Transcript)
13
Space-Group Symmetries

• 230 space groups
• The International Union of Crystallography
  publishes them in Volume A of International
  Tables for Crystallography.

14
The Herman-Mauguin System

• The space group of YBa2Cu3O7 is
• P mmm, a 3.820, b3.886, c11.683

15
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).

16
Herman-Mauguin System

• The mmm in the space group for YBa2Cu3O7 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.

17
Herman-Mauguin System

• The a 3.820, b3.886, c11.683 in the space
  group gives the dimensions of the crystal.
• Since a, b, and c are all different numbers, the
  crystal is orthorhombic.

18
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

19
Conclusion

• Why does a crystals symmetry matter?

20
Bibliography

• http//www.chem.ox.ac.uk/icl/heyes/structure_of_so
  lids/Lecture4/Lec4.html
• http//imr.chem.binghamton.edu/labs/super/superc.h
  tml
• 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.