Download presentation

Presentation is loading. Please wait.

Published byCrystal Morgan Modified over 2 years ago

1
Common crystal structures Simple close packed structures atoms hard spheres problem of structure most efficient packing Donuts * *Proposition made by Goldschmidt 1926. Useful approach for metals, where the chemical bond does not provide geometrical constrains like in diamond for instance

2
hexagonal layers packed in 2 different ways Hexagonal Close-Packed Structure hexagonal close-packed cubic close packed layers stack according to ABAB

3
hexagonal layers are stacked ABC Cubic Close-Packed Structure FCC ( close packed structures - unit cells )

4
* more complicated packing sequence such as ABAC, ABCB, etc * = FCC

5
Computer proof: hcp and fcc have both 74% packing ratio:= Volume of the spheres in the unit cell Volume the unit cell 100% all others including bcc have less packing ratio Johannes Kepler asserted in the early 1600's that no packing can improve the Face-Centered Cubic packing Proof took nearly 400 years 1998 Thomas Hales 1998 Thomas Hales (presently University of Pittsburgh ) announced to have a proof of the Kepler conjecture 250 pages of notes and 3 gigabytes of computer programs, data and results minimizing a function with 150 variables ! ( click to see an e-mail of T.Hales announcing the proof )

6
Lattices which can be considered as 2 interpenetrating fcc lattices diamond lattice: fcc lattice with basis diamond lattice:not packingbutsymmetrically placed valence bonds = two identical atoms at (0,0,0) and (0,0,0) determine the structure

7
What happens if atoms of the basis are different ? ZnS (zincblende), or GaAs Four neighbors all of opposite chemical species ( click here for animations )

8
NaCl : fcc translational symmetry with basis (0,0,0) CsCl : Simple cubic space lattice with basis (0,0,0)

9
The most advantageous crystal structure for ionic solids* NaCl versus CsCl structure Competition between packing and avoiding of e.g. anion-anion contact r0r0 R+R+ R-R- Radius RatioCoordination no.Binary (AB) Structure-type r + /r - = 112 none known 1 > r + /r - > 0.7328CsCl 0.732 > r + /r - > 0.4146NaCl 0.414 > r + /r - > 0.2254ZnS To avoid - contact in NaCl structure (* the explanation in Blakemore page 15 is misleading )

Similar presentations

OK

Bravais Lattices in 2D In 2D there are five ways to order atoms in a lattice Primitive unit cell: contains only one atom (but 4 points?) Are the dotted.

Bravais Lattices in 2D In 2D there are five ways to order atoms in a lattice Primitive unit cell: contains only one atom (but 4 points?) Are the dotted.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on history of vedic maths pdf Marketing mix ppt on nokia phone Ppt on global warming for class 9 download Ppt on javascript events ios Ppt on transport and communication Ppt on different types of houses in india Ppt on product marketing Ppt on circles for class 9th download Ppt on crash fire tender Ppt on dressing etiquettes of life