NON-CRYSTALLINE MATERIALS

Transcription

1 3.012 Fund of Mat Sci: Structure Lecture 21 NON-CRYSTALLINE MATERIALS Images of a silicon nanocrystal removed for copyright reasons. Light amplification for crystalline silicon in a glassy SiO 2 matrix

2 Homework for Fri Dec 2 Study: Chapter 2 of Allen-Thomas until 2.3.1

3 Last time: 1. Tensors, and their transformations 2. Orthogonal matrices 3. Neumann s principle 4. Symmetry constraints on physical properties 5. Curie s principle

4 Physical properties and their relation to symmetry Density (mass, from a certain volume) Pyroelectricity (polarization from temperature) Conductivity (current, from electric field) Piezoelectricity (polarization, from stress) Stiffness (strain, from stress)

5 Curie s Principle a crystal under an external influence will exhibit only those symmetry elements that are common to both the crystal and the perturbing influence

6 Loss of periodic order Liquids ( fluid ) Glasses ( solid ) Oxide glasses (continuous random networks) Polymeric glasses (self-avoiding random walks Oddballs Quasicrystals Superionics

7 Table of the applications of noncrystalline materials removed for copyright reasons.

8 Principle of operation of a CD-RW As Deposited (amorphous) After Initialisation/erase (crystalline) Written mark (amorphous) Erase/Write Readout of data: Difference in %R between amorphous & crystalline states E.g. %R amorphous = 5%; %R cryst = 25% Delta R=20% Figure by MIT OCW.

9 Principle of operation of a CD-RW Writing - Amorphous The active layer is heated above its melting point and quenched into the amorphous phase with a short laser pulse to produce marks. Erasure Crystalline Intermediate laser power is used, so that the active layer does not melt, but rather remains within the crystallization temperature region long enough that the amorphous marks re-crystallize. 800 C Liquid Melting temperature 800 C Liquid Melting temperature o C) 600 Quench o C) 600 Temperature ( A B Amorphous Crystal 99% 1% Temperature ( A B Crystallize 99% 1% Amorphous t min Time (ns) t min Time (ns) Figure by MIT OCW.

10 Erasure: nucleation and growth of crystalline material Figure by MIT OCW.

11 Te-Sb-Ge Alloy 3 Element Phase Diagram Nucleation dominated: 4.7 GB DVD-RAM (Sb 2 Te 3 to GeTe) Growth dominated: CD- RW, DVD-RW, Blu-ray (Sb 69 Te 31 eutectic) Sb 2 Te 3 30 Sb Atomic % Sb 100 Growth dominated SbTeGe Ge GeTe Ge Atomic % Figure by MIT OCW.

12 Structural Descriptors Long-range order Short-range order

13 What do ice and silicon have in common? Source: Wikipedia

14 What do ice and silicon have in common? Photo courtesy of Ansgar Walk.

15 What do ice and silicon have in common? Figure by MIT OCW. Figure by MIT OCW.

16 What do ice and silicon have in common? Compression 11 GPa 13 GPa 16 GPa 36 GPa 42 GPa 79 GPa Si(I) diamond z= Si(II) β-tin z=6 Si(XI) Imma z=6 Si(V) hexagonal Si(VI) orthorhombic Si(VII) hcp Si(X) fcc z=8 z=10 z=12 z=12 Slow Pressure Release 9 GPa 2 GPa >480 K Si(II) β-tin Si(XII) R8 Si(III) BC-8 Si(IV) hex. diamond z=6 z= z= z= Fast Pressure Release Si(VIII) and Si(IX) tetragonal Figure by MIT OCW.

17 What do ice and silicon have in common? Si (Ry/atom) E structure fcc 3 bcc hcp sc β-tin o C) Temperature ( Liquid III Hexagonal Ice II V VI VII VIII X Temperature (K) Diamond Hexagonal Diamond XI IX Volume Figure by MIT OCW. Figure by MIT OCW Pressure (GPa) 0

18 Phase transitions in silicon Energy B A B A Volume

19 Order Parameters for Silicon 1 µ = θi N i N i ¹ σ = θ µ Before compression During compression P = 40 GPa M. J. Demkowicz and A. S. Argon, Phys. Rev. Lett. 93, (2004)

20 Pair correlation functions Graphs of the pair-distribution functions for gas, liquid/gas, and monatomic crystal removed for copyright reasons. See page 41, Figure 2.5 in in Allen, S. M., and E. L. Thomas. The Structure of Materials. New York, NY: J. Wiley & Sons, 1999.

21 Pair correlation function: water Courtesy of Dr. J. Kolafa. Used with Permission. See animation at

22 Pair correlation function: water

23 Count thy neighbours Z r Thickness dr Y X Figure by MIT OCW.

24 Models of disorder: hard spheres Bernal random close packed sphere model Photos of the Bernal random close-packing model removed for copyright reasons. See them at the Science & Society Picture Library: Image 1, Image 2.

25 Models of disorder: hard spheres Voronoi polyhedra (in a crystal: Wigner- Seitz cell) Normal Distance Volume Facial Area Solid Angle Quantitative Definitions of Voronoi Polyhedra Figure by MIT OCW.

26 Mean Square Displacements

27 Mean Square Displacements

28 Mean Square Displacements