P. W. Anderson [Science 1995, 267, 1615]

The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition. This could be the next breakthrough in the coming decade. The solution of the problem of spin glass in the late 1970s had broad implications in unexpected fields like neural networks, computer algorithms, evolution, and computational complexity. The solution of the more important and puzzling glass problem may also have a substantial intellectual spin-off. Whether it will help make better glass is questionable. P. W. Anderson [Science 1995, 267, 1615]

What is a Glass?

What is Glass? A supercooled liquid?

What is a Glass? A glass is a non-ergodic state of matter which has become non-ergodic by virtue of the continuous slow-down of one or more of its degrees of freedom A structural glass is an amorphous solid which is capable of passing into the viscous liquid state, usually, but not necessarily, accompanied by an abrupt increase in heat capacity (the glass transition) An amorphous solid is a solid which lacks long range (crystalline) order

What is a Glass? Structural glasses Spin glasses Orientational glasses Vortex glasses

How can you make a Glass? Rapid cooling of a liquid Vapor deposition Chemical vapor deposition Solvent evaporation Electrochemical deposition In-situ liquid polymerisation reaction Solid state diffusion controlled reaction Hydrolysis of precursor organics and drying (sol-gel) Cold compression of crystal Cold compression of high-p stable crystal Shock, irradiation or intense grinding of crystals

Silica SiO 2 torsional angles O-Si-O intratetrahedral angle Si-O-Si intertetrahedral angle r Si-O

Quartz 20 K, α 793 K, α 1073 K, β

HP Tridymite MD simulation

Vitreous silica

2dsinθ = nλ

k = k' k k = k'

l + l' = k. r k k'. r k' δ = k ( l + l') = k. r

= r k r r d i n A ). )exp( ( ( ) r r k G G r r c b a T T r r G G d i n A i n n w v u n n = = + + = + = ). ( exp ). exp( ) ( ) ( ) (. = 2nπ r k Constructive interference k G r k G = = π 2n ). ( Constructive interference A A I * =

k = G k G

A = n( r)exp( i k. r) dr k. r 2nπ A 0

0.2 0.1 F N (Q) 0.0-0.1-0.2 0 10 20 30 40 Q/Å -1 Neutron diffraction from vitreous SiO 2

F(Q) 3.0 2.0 1.0 0-1.0 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6-0.1 8 10 12 14 15 20 25 30 35 40 45 Q(Å -1 ) Neutron diffraction from vitreous and crystalline SiO 2

0.2 0.1 F N (Q) 0.0-0.1-0.2 0 10 20 30 40 Q/Å -1 Neutron diffraction from vitreous SiO 2

0.6 0.4 0.2 0.0 F X (Q) -0.2-0.4-0.6-0.8 0 5 10 15 20 25 Q/Å -1 X-ray diffraction from vitreous SiO 2 (form factor corrected)

0.6 0.2 0.4 0.1 0.2 F X (Q) 0.0-0.2-0.4 F N (Q) 0.0-0.1-0.6-0.2-0.8 0 5 10 15 20 25 Q/Å -1 0 10 20 30 40 A = n( r)exp( iq. r) dr r) = X-rays f j r j ) Z j j Q/Å -1 n ( f ( r ) ( j j j j Neutrons f ( r ) = Si 14; O - 8 Si 4.15; O 5.8 b j

Intensity 0.4 0.3 0.2 X-ray diffraction 9.1 Warren-Mavel mode Undoped PPG Mg(ClO 4 ) 2 10:1 NaClO 4 5:1 LiClO 4 5:1 0.1 0.0 0 10 20 30 40 2θ X-ray diffraction from a polymer glass (as measured)

A = n( r)exp( i k. r) dr k. r 2nπ A 0 n ( r) = f j ( rj ) j I = A * A

I F ( Q) α β α β αβ i, j ( S ( Q) 1) = c c f f = 2 sin Qr Sαβ ( Q) 1 ρ 4πr αβ 1 Qr ( g ( r) ) dr F(Q) (Q) S αβ (r) g αβ Structure Factor Partial Structure Factor Partial radial distribution function

2.5 2.0 1.5 F(Q) 1.0 0.5 0.0 0 2 4 6 8 10 Q/Å -1 2.5 2.0 1.5 g(r) 1.0 0.5 Peak position average distance Peak area coordination number 0.0 0 5 10 15 20 r/å

Vitreous silica 2 2 2 0 S OO S SiO 0 S SiSi 0-2 -2-4 0 10 20 30 40-2 0 10 20 30 40 0 10 20 30 40 Q/A -1 Q/A -1 Q/A -1

Vitreous silica 6 18 5 16 14 6 4 12 g SiSi 3 g SiO 10 8 g OO 4 2 6 2 1 4 2 0 0 5 10 15 20 0 0 5 10 15 20 0 0 5 10 15 20 r/a r/a r/a

( ) = j i Q S f f c c Q F I, 1 ) ( ) ( αβ β α β α Isotopic subsitution ( ) = j i k k k Q S f f c c Q F, ) ( ) ( ) ( 1 ) ( ) ( αβ β α β α

37 Cl b = 0.25 M Cl b = 0.75 N Cl b = 1.0 35 Cl b = 1.25 Total structure factors F(Q) for molten SrCl 2

Partial structure factors Aij(Q) for molten SrCl2

Partial radial distribution functions g ij (r) for molten SrCl 2

( ) = j i Q S f f c c Q F I, 1 ) ( ) ( αβ β α β α Isotopic subsitution Anomalous scattering Combine techniques Modelling ( ) = j i k k k Q S f f c c Q F, ) ( ) ( ) ( 1 ) ( ) ( αβ β α β α

= 2 sin Qr Sαβ ( Q) 1 ρ 4πr αβ 1 Qr ( g ( r) ) dr

3 g BB (r) 2 1 0 0 2 4 6 8 10 7 6 5 g AB (r) 4 3 2 1 0 0 2 4 6 8 10 r/å

Average structure models Tend to overestimate the geometrical order Tend to ignore the variation in local order, coordination etc. 20 Coordination number distribution for a simple liquid % 15 10 5 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 N

Vitreous silica 6 18 5 16 14 6 4 12 g SiSi 3 g SiO 10 8 g OO 4 2 6 2 1 4 2 0 0 5 10 15 20 0 0 5 10 15 20 0 0 5 10 15 20 r/a r/a r/a

Continuous Random Network (CRN) - Zachariasen

Hand built models

Computer generated models

Molecular dynamics - MD Periodic boundary conditions

Molecular dynamics - MD { r ( ),..., ( )} t r t 1 N Newton s second law of motion: V = m i 2 ri ( t) 2 t δv = δr (3) V ij ( r ) + V ( r, r (2) ij i< j i, j< k ijk i ij jk )

Monte Carlo - MC 3 2 1 V(r) 0-1 -2-3 0 2 4 6 8 10 r/å Interatomic potential

Monte Carlo - MC The energy change U 1 -U 2 /kt drives the simulation

Reverse Monte Carlo - RMC 3 2 g(r) 1 0 0 2 4 6 8 10 r/å Experimental data

Reverse Monte Carlo - RMC The difference between the data and the model χ 12 - χ 22 /σ 2 drives the simulation

Vitreous silica 0.2 0.6 0.4 0.1 0.2 F N (Q) 0.0-0.1 F X (Q) 0.0-0.2-0.4-0.2-0.6 0 10 20 30 40 Q/Å -1-0.8 0 5 10 15 20 25 Q/Å -1 6 18 2 2 2 5 16 14 6 4 12 S OO 0 S SiO 0 S SiSi 0 g SiSi 3 g SiO 10 8 g OO 4-2 -2 2 1 6 4 2 2-4 0 10 20 30 40 Q/A -1-2 0 10 20 30 40 Q/A -1 0 10 20 30 40 Q/A -1 0 0 0 5 10 15 20 r/a 0 0 5 10 15 20 r/a 0 5 10 15 20 r/a

Modified Random Network (MRN) - Greaves Na 2 O-SiO 2 Bridging Oxygen (BO) Non-bridging Oxygen (NBO)

Modified Random Network (MRN) - Greaves

K clusters forming pathways Modified Random Network (MRN) - Greaves (K 2 O) 0.45 (SiO 2 ) 0.55

-CH 2 -CH 2 -

-CF 2 -CF 2 -

-CH 2 -CHCH 3 -O-

Metallic glasses melt spinning Cooling rate > 10 6 K s -1

Bulk Metallic glasses

Magnetic metallic glasses

Magnetic metallic glasses Amorphous alloys having the formula Fe a Co b Ni c S x B y M z are employed as monitoring strips for mechanically oscillating tags, for example for anti-theft protection, together with a source of a pre-magnetization field in which the strip is disposed so as to place the strip in an activated state. In the formula, M denotes one or more elements of groups IV through VII of the periodic table, including C, Ge and P, and the constituents in at % meet the following conditions: a lies between 20 and 74, b lies between 4 and 23, c lies between 5 and 50, with the criterion that b+c>e14, x lies between 0 and 10, y lies between 10 and 20, and z lies between 0 and 5 with the sum x+y+z being between 12 and 21. These alloys have a resonant frequency associated therewith and when passed through an alternating field whose alternation frequency coincides with the resonant frequency, a pulse having a signal amplitude is produced. These alloys can be deactivated by removing the pre-magnetization field, which causes a change in the resonant frequency and the resulting signal amplitude. These alloys exhibit a change in resonant frequency and signal amplitude due to changes in the orientation of the tag in the earth's magnetic field which is smaller than the change occurring upon removal of the pre-magnetization field, so that the tag can be reliably deactivated. An inexpensive multibit magnetic tag is described which uses an array of amorphous wires in conjunction with a magnetic bias field. The tag is interrogated by the use of a ramped field or an ac field or a combination of the two. The magnetic bias is supplied either by coating each wire with a hard magnetic material which is magnetized or by using magnetized hard magnetic wires or foil strips in proximity to the amorphous wires. Each wire switches at a different value of the external interrogation field due to the difference in the magnetic bias field acting on each wire. Fe a Co b Ni c S x B y M z

Magnetic metallic glasses Neutron scattering + X-ray scattering + EXAFS Atomic structure Computer modelling Fe 0.91 Zr 0.09 Neutron scattering Magnetic structure

5 4 AFM-AFM g FeFe (r) 3 2 1 0 0 2 4 6 8 10 r/å

40 Fe 1-x Zr x % of AFM Fe atoms 30 20 10 0 0.0 0.2 0.4 0.6 0.8 1.0 Fe x Zr

% of AFM Fe atoms 40 30 20 10 Fe 0.25 Zr 0.75 Paramagnetic (FM atoms) 0 0.0 0.2 0.4 0.6 0.8 1.0 Fe x Zr

% of AFM Fe atoms 40 30 20 10 Fe 0.40 Zr 0.60 Ferromagnetic (FM atoms) 0 0.0 0.2 0.4 0.6 0.8 1.0 Fe x Zr

% of AFM Fe atoms 40 30 20 10 Fe 0.91 Zr 0.09 Spin glass AFM atoms 0 0.0 0.2 0.4 0.6 0.8 1.0 Fe x Zr

Magnetic metallic glasses Neutron scattering + X-ray scattering + EXAFS Atomic structure Computer modelling Dy 0.7 Fe 0.3 Neutron scattering