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MATERIALS SCIENCE & ENGINEERING

MATERIALS SCIENCE & ENGINEERING . Part of . A Learner’s Guide. AN INTRODUCTORY E-BOOK. Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email: anandh@iitk.ac.in, URL: home.iitk.ac.in/~anandh.

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MATERIALS SCIENCE & ENGINEERING

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  1. MATERIALS SCIENCE & ENGINEERING Part of A Learner’s Guide AN INTRODUCTORY E-BOOK Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email:anandh@iitk.ac.in, URL:home.iitk.ac.in/~anandh http://home.iitk.ac.in/~anandh/E-book.htm

  2. Mystery of the missing entries in the Bravais List!  Few illustrations • Another point of view:There are 7 crystal systemsEach of them “can have” P, I, F, C type lattice (4 types)Hence the “potential” number is (7  4) = 28But 14 of these are only distinct Points to note: • Every lattice that you can construct is present somewhere in the list  the issue is where to put them • Concept of choice of unit cell is also invoked along with the classification of Bravais lattices • The factors which are taken to into account are (like for the unit cell): Symmetry Size

  3. What we choose Mystery of the missing entries in the Bravais List! But then Cubic crystals need not have any 4-fold axes!!(cubic lattices do need to have!) Hence Cannot be called Cubic Hence even though this lattice remains as it is  it is called Simple Tetragonal(which is smaller in size)

  4. What we choose Mystery of the missing entries in the Bravais List! Smaller sized Body Centred Cell is chosen FCT = BCT Face Centred Tetragonal = Body Centred Tetragonal

  5. What we choose Mystery of the missing entries in the Bravais List! Smaller sized Simple Cell is chosen CCT = ST C Centred Tetragonal = Simple Tetragonal

  6. Mystery of the missing entries in the Bravais List! Putting a lattice point at body centre destroys the 6-fold axis Hence body centred hexagonal lattice NOT possible

  7. Mystery of the missing entries in the Bravais List! Putting a lattice point at body centre destroys the 6-fold axis

  8. Mystery of the missing entries in the Bravais List! Putting a lattice point at body centre destroys the 6-fold axis

  9. & what we don’t Mystery of the missing entries in the Bravais List! Cubic F  Tetragonal I(not chosen) As the FCC lattice has higher symmetry than the BCT cell(the one with higher symmetry is chosen)

  10. Some example of the allowed and disallowed transfers • Crystal system Bravais lattices • Cubic P I F C • Tetragonal P I F • Orthorhombic P I F C • Hexagonal P • Trigonal P • Monoclinic P C • Triclinic P x Slide Courtesy Dr. Rajesh Prasad

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