1. Amorphous materials at high pressure
Chrystèle Sanloup
CSEC, University of Edinburgh, UK
Université Pierre et Marie Curie
Institut de Physique du Globe de Paris, France

2. High pressure amorphs - Synthesis
▪ Pressure-induced amorphization (PIA)
▪ Amorphous-amorphous transitions (AAT)
Mention traditional synthesis of amorphous materials: ultra-fast quenching, chemical vapor deposition, destructive methods such as irradiation (including in natural conditions) or ball-milling.
Amorphization upon P-release (but still at high P): apparently known since much earlier (Ringwood, CaSiO3 perovskite decompressed from 10GPa EPSL1975,Tsuji JNCS 1992)
Not thermodynamically stable state  choose appropriate c-P-T paths
N.B.: confusion or identification of amorphous forms and quenched liquids (glasses)
cf. example of S upon decompression

3. Basic unit = nanoscale grains
Amorphous materials
▪ Opal (amorphous SiO2) - SEM image
Basic unit = nanoscale grains
 short-order range
Gaillou et al., Am. Min. 2008
Electron microscopy:
Best characterization of amorphous materials but not available at HP,
and can high-pressure amorphs be quenched ?

4. Characterizaton of amorphs at high P
I- Loss of long-range order  Diffuse scattering (X-rays and neutrons)
Sulfur
SnI4
Luo et al. PRB 1993
Fujii et al. JPC:SSP 1985
! Except for heavy elements,
X-ray criteria for PIA
=disappearance of peaks
(misleading)
 Structure unrelated to that of the liquid phase at P0

5. Characterizaton of amorphs at high P
I- Diffuse X-ray scattering:
a-CO2
a-N
Gregoryanz et al., JCP 2007.
Santoro et al., Nature 2006.

6. Characterizaton of amorphs at high P
I- Diffuse X-ray scattering:
amorphous Sulfur
! Very high background/signal ratio
Sanloup et al., PRL 2008

7. Characterizaton of amorphs at high P
I- Diffuse X-ray scattering:
▪ Problems at high P:
1- limited Q-range
2- background substraction
Boehler-Almax anvils
- Empty cell pattern
- Crystalline pattern
▪ Advantages of low T: homogeneous samples 

8. Characterizaton of amorphs at high P
II- Density/volumetric measurements
Deplacement of a piston in a cylinder
Ex: PIA of ice
Mishima Nature 1984
Large volume decrease: ~20%
PIA  large volume reduction
 importance of density measurements on am.

9. Characterizaton of amorphs at high P
II- Density/volumetric measurements - Radiographic techniques
Liu et al, PNAS 2008.
Sato & Funamori, Rev. Sci. Instr
Microtomography: precision claimed= 0.45%, measurements up to 10 GPa
Sato&Funamori: precision claimed=0.5 % at the highest P
Isample = I0 ∙exp(−mdiardiatdia−msamplersampletsample)
3 unknowns
need 3 equations/measurements
measurements up to 60 GPa
Up to 10 GPa
Se: heavy element

10. Characterizaton of amorphs at high P
II- Density measurements - X-ray diffraction technique
a, normalization factor such as
Kaplow et al., Phys. Rev
Access to:
- r: initial slope
- local structure

11. Characteristics of HP amorphs
▪ Crystal-like properties: local structure
Strongly peaked diffraction patterns
Sulfur
H2O
a-ZrW2O8
amorphous
ZrW2O8=zirconium tungstate
Vega et al. Monte Carlo simulations
Tulk et al., X-ray g(r)
ZRW2O8: neutron+Xrays+reverse Monte Carlo
Keen et al. PRL 2007

12. Characteristics of HP amorphs
▪ Crystal-like properties: phonon density of states
Tse Nature 1999
IINS (inelastic incoherent neutron scattering)
 Similarity of LDA and Ice Ih
Differences with hyperquenched water

13. Characteristics of HP amorphs
▪ Crystal-like properties: density
Daisenberg et al., PRB 2007.
Silicon
HAD Si and Si-II
Sulfur
 Compressibility similar to that of the crystalline counter-part

14. Simple molecular systems: CO2, N2
Goncharov et al. PRL 2000
Gregoryanz et al. PRB 2001, JCP 2007
Santoro et al., Nature 2006.
a-CO2
a-N
N: further recrystallization in cg (upon heating, Eremets 2001)
aN discovered by Gonchi, very large hysteresis on decompression (Eremets 2001)
V-CO2: quartz-like (tetrahedral configuration)
High T: molecular to non-molecular transition  high-energy barrier
Low T: molecular crystal to amorphous form transition

15. Simple molecular systems: CO2, N2
▪ Amorphous-amorphous transition:
a-CO2 VI
a-CO2
↑P: PIA, CO2-VI like a-CO2
↓P: AAT, CO2-V like→ CO2-III like a-CO2
↓P: re-crystallization into CO2-I
Santoro et al., Nature 2006.

16. Simple molecular systems: S8
631
521
112
611
Recrystallisation: a-S → S-III
 PIA is the precursor of the phase transition to the high-P polymorph

17. Simple molecular systems: S8
CN=15.0+/-0.4
CN=16.1+/-0.1
LDA is semiconducting (IR measurements); SIII is?
SI is an insulator
SIV is metallic
 Large volume collapse upon PIA
 AAT in conjunction with S-III → S-IV transition, rather 1st order transition
 AAT : Low-density amorph (LDA)  High-density amorph (HDA)

18. Simple molecular systems: S8

19. Simple molecular systems: S8
▪ AAT upon decompression:
 2nd order transition: LDA → liquid-like a-S
Re-crystallization at 0.25 GPa-room T into S-I

20. Cold vs mechanical melting
▪ Crossing of the metastable extension of the melting line
Case of H2O
Dashed line: extrapolated melting curve (by Mishima)
Tse et al: arrow=crossing of the 2 mechanisms
The Lindemann criteria suggests that the onset of an instability is caused when the displacements of atoms exceed a certain threshold, usually a fraction of the interatomic distances.
PIA
Tse et al., Nature 1999.
Mishima et al., Nature 1984.
Mishima, Nature 1996.

21. Cold vs mechanical melting
▪ Crossing of the metastable extension of the melting line
Case of SiO2
Hemley et al., Nature 1988.

22. Cold vs mechanical melting
 Amorphization systematically connected with crystal-crystal transformation just above the amorphisation T.
 Crystalline structures collapse regardless
of their melting behavior
Si et Ge ont points de cristallisation et de fusion a T plus elevees que GaSb
Or c’est le contraire pour T amorphisation (id Hemley et melting curve of SiO2) => Pas logique avec cold melting
Brazhkin et al. JNCS 1997

23. Cold vs mechanical melting
▪ Arguing for mechanical melting: elastic instabilities evidenced before PIA
 Violation of Born criteria
Strässle et al. PRL 2004
Case of H2O
Case of SiO2
Gregoryanz et al. PRL 2000
B3 C11 2 C12C44 2 2C2
14 . 0Strassle: needs to be fitted by a model to extract elastic parameters and get C11-C12
Brazhkin: ! softening is expected to be the most important on the Brillouin zone boundary while ultrasonic measurements registered the behavior of long-wave phonons.
Brazhkin: At least 20% softening of the ½(C11-C12) constant
B3=(C11-C12)∙C44-2C142
Phonon softening in Ice Ih
 PIA predicted at 2.5 GPa
NB: P of PIA by mechanical melting always overestimated by Born criteria

24. Role of defects ▪ Defective X-ray patterns upon approaching PIA
Case of sulfur
S-I 41 GPa – 175 K
(just before amorphization)
S-I 16 GPa – 175 K

25. Role of defects ▪ P-induced reduction of Nb2O5 :
Serghiou et al., PRL 1992.
▪ P-induced reduction of Nb2O5 :
Simultaneous amorphization at 19 GPa-300K
Reduction  O defects in the lattice
Bustingorry and Jagla, PRB 2005.
G’=(C11-C12)/2-P
▪ Numerical simulations:
defect-free: no transformation until
mechanical limit is reached
- sample with one vacancy: transformation starts at lower P
Fecht Nature 1992: when the defect concentration in a cristal reaches a
Critical value, it collapses in a disordered state due to DGv (v:vacancy)
Serghiou: By analogy with ambient P reduction, authors propose that amorph formed by O defects in the lattice (through shear deformation, Crystallographic Shear Plane)
 Defects can destabilize the lattice at pressures much lower
than the instability pressure.

26. Conclusions
▪ a large variety of materials transform into amorphs at high P
▪ PIA occurs if a parent phase is compressed beyond its thermodynamic stability field
▪ Occurs generally at low T: lack of thermal energy
 not enough atomic mobility for the crystalline-crystalline transition to occur
▪ PIA is accompanied by a large volume reduction
Not only tetrahedral frameworks
▪ PIA is the precursor of the phase transition to the high-P polymorph
high-P amorphs have crystal-like properties (distinct from glasses)
▪ high-P amorphs may undergo 1st or 2nd order AAT
▪ high-P amorphs are often difficult to recover at ambient conditions

27. Conclusions
▪ Use of high P to synthesize high quality quenched amorphs
Yu et al., APL, 2009
High quality quench amorphs: without any crystal
Mechanical properties: pliability, stretching
Translucence
Chalcogenide alloys: optical (DVD) and electronic (PCM) applications rely on the fast and reversible phase change between the crystalline and amorphous phase induced by heating either via laser irradiation (DVD) or the Joule effect (PCM). Caravati et al. PRL 2009.
▪ Industry of polymers:
improved kinetic stability, enhanced mechanical properties

29. X-ray amorphs or nanocrystallites ?
a-S 54 GPa
Crystalline S-III
Nanocrystalline S-III?
X-ray amorphs or nanocrystallites ?
Ivashchenko et al. PRB 2007
Nanocrystalline Si
particle size: 2.2 nm
Scherrer equation:
Particle size= Kl
w1/2 cos(q)
Nanocrystalline S-III X-ray amorphous:
If particle size ~ 10 Å
i.e. ~ 3 crystallographic cells
Bustingorry and Jagla PRB 2005
Platelets of the high-P phase nucleate on the vacancy
But growth inhibited  very small crystal size

30. Amorph-amorph transitions
First evidenced in aSi and a-Ge? (Shimomura Philos Mag p547?),
AAT tend to be 1st order transitions (Si, S, H2O?)
LDA and HDA forms have cristalline-like properties (except for complex H2O).
HDA (water) can not be assimilated to a supercooled liquid,
Neither LDA/HDA transition to a 2-state liquids (i.e. liquid-liquid transition)
by way of csqce
Tse:
Differences between high P amorph and glasses
confusion or identification of amorphous forms and quenched liquids (glasses)
cf. example of S upon decompression

31. Amorphous-amorphous transitions
Case of H2O
2- T increase:
High-density amorphous ice (HDA)
→Low-density amorphous ice (LDA)
HDA
LDA
3- P increase:
LDA→HDA
1- Pressure-induced
amorphization
Mishima et al., Nature 1985

32. Amorph-amorph transitions
▪ HDA-LDA: 1st order transition ?
Klotz et al., PRL 2005
Neutron diffraction data (see D>>)
But different picture given by X-rays (see O>>)
very complex phase diagram!!! No wonder every team gets a different picture.
LDA/HDA: not good proxy for LDL/HDL transition since high-P amorphs have crystalline-like properties
▪ HDA water:
- continuous structural changes towards close-packing
- may re-crystallize into different phases
N.B.: very complex H2O phase diagram!!!

33. Amorphous sulphur Pb 1: limited Q-range: Boehler-Almax anvils
Pb 2: the higher the pressure, the more difficult it is to get the background properly
Additional constraint at very high pressures:
 Negligeable on the expal pattern

34. Cold vs mechanical melting
Add P-T phase diagram
(cf Klotz)
Add PIA paths
Tse Nature 1999
Liquid water
Amorphous HDA
Strassle PRL 2007

35. Case of simple molecular systems:
Systematic PIA from molecular to non molecular at low T (not at high T)
Recovery of the amorph down to low P (N, Eremets, us with S)
Case of tetraedrally coordinated systems (classical case)
Case of Si, Ge, III-IV compounds and their solid solutions, etc Tsuji et al., Brazhkin et al.:
PIA upon DECOMPRESSION from METALLIC state.
1- Semi-conductor
zincblende structure
2- Incr.P: metallic b-tin structure
Tsuji JNCS 1996
3- decr.P: amorphization,
T-dependant

36. Characterizaton of amorphs at high P
Hemley et al., Nature 1988
Meade and Jeanloz, PRB 1987
Cr-emulsion mask (1mm lines) on a SiO2-glass
But glass not amorphous silica !
Differences between
high P amorph and glasses
Amorphization is thermodynamically induced

37. Pressure-induced amorphization of Si (porous Si)
Decompression: HDA→LDA transition
(Raman spectroscopy)
Deb et al., Nature 414, 528 (2001)

38. Check that the LDA curve goes on the HAD
Daisenberg et al., PRB 2007
Check that the LDA curve goes on the HAD
(which then coincides with Si-V)
How was LDA formed? Real PIA or Si gel?
Transition predicted at 13.7 GPa,
Between 14 and 16 GPa experimentally

40. Cold vs mechanical melting
Arguing for mechanical melting: elastic instabilities evidenced before PIA
Brief statement on Born criteria
Case of H2O
Strassle: needs to be fitted by a model to extract elastic parameters and get C11-C12
Brazhkin: ! softening is expected to be the most important on the Brillouin zone boundary while ultrasonic measurements registered the behavior of long-wave phonons.
Brazhkin: At least 20% softening of the ½(C11-C12) constant
Brazhkin et al. JNCS 1997
Ultrasonic measurements
Phonon softening in Ice Ih
Strässle et al. PRL 2004
 PIA predicted at 2.5 GPa

41. Characteristics of HP amorphs
high P amorphs have cristalline-like properties (cf Tse PRB 2005 et aS).
Similar thermal conductivity (H2O, Johari PRB2004)
memory of the initial crystallographic orientation or anisotropy of the amorph: single crystal → amorph (incr.P) → single crystal (decr. P) with same orientation (cf AlPO4, Kruger and Jeanloz 1990 or Brillouin scattering on AlPO4 by Polian PRL1993 and a-SiO2 by McNeil PRL1992)

42. High pressure amorphs Case of simple molecular systems:
Systematic PIA from molecular to non molecular at low T (not at high T)
Recovery of the amorph down to low P (N, Eremets, us with S)
Case of tetraedrally coordinated systems (classical case)
Case of Si, Ge, III-IV compounds and their solid solutions, etc Tsuji et al., Brazhkin et al.:
PIA upon DECOMPRESSION from METALLIC state.
But also case of S (cf Wilson, from trigonal state, in the Z. Crist. Paper?)
Tsuji: There are two methods
to obtain amorphous materials using high pressure.
One is amorphization above the thermodynamic transition
pressure Pt, [1,2] and the other is amorphization
from the quenched high-pressure phase below Pt

43. High pressure amorphs - Interests
Interests: synthesis of new materials (properties?),
In particular through high P polyamorphism
Amorphous (industrial interests?)
Theoretical interests:
discussion of polyamorphic transitions, 1st vs 2nd order
amorphs taken as proxies for liquids and the search for 2nd critical points
mechanisms of PIA?

44. Characterizaton of amorphs at high P
II- Density/volumetric measurements
Strain/gauge technique: limited to <10 GPa but very high precision (0.15%)
Tsiok et al., HPR 10, 523 (1992)
Brazhkin et al., JETP 89, 244 (2009)

45. ▪ No long-range order  diffuse X-ray scattering
Amorphous materials
▪ No long-range order  diffuse X-ray scattering
g(r) r 1
I(2)  S(Q), structure factor
S(Q)  g(r), radial distribution fonction
with