Low Melting Point
in Compressed Alkalis
Valentina F Degtyareva
Institute of Solid State Physics,
Chernogolovka, Russia
Liquids under pressure
Outline
• Main factors of crystal structure stability
Concept of the Fermi Sphere - Brillouin Zone
interaction: Cu-Zn alloy system
• Simple sp - metal under pressure:
alkali metals
• Melting of alkali metals under pressure
• Core ionization: increase of the valence
number
Melting curve of the lightest alkali metal: lithium
[Guillaume, Gregoryanz, Degtyareva, Nature Physics, 2011, 7, 211]
Falconi et al. PRL 2005
Cs
Melting of alkalis under pressure
Guillaume, Gregoryanz, Degtyareva et al Nature Physics 6, 211 (2011)
Melting temperature decreases dramatically. K
bcc fcc tI19
liquid
Narygina et al 2011 Phys. Rev. B 84 054111
E. Gregoryanz, O. Degtyareva, M. Somayazulu et al PRL 94,85502(2005)
Phase diagrams Au-Si and Au-Ge
Eutectic composition
at Au-20at%Si z=1.6
at Au-28at%Ge z=1.84
Alkali elements
Li
Na
K
Rb
Cs
High Pressure
Ambient pressure Moderate pressure
Rb-IV, K-III
Rb-VI, Cs-V
[Gregoryanz et al PRL 2005]
[Gregoryanz et al Science 2008]
Alkali elements: Na
[Ma et al Nature 2009]
Alkali metals under pressure:
structural transformations
Li 7.5 39 42 60 70 95
bcc → fcc → hR1 → cI 16 ─► oC88 → oC40 → oC24 < 125
Na 65 104 117 125 180
bcc → fcc → cI 16 ─► oP8 → h-g (tI19*) → hP4 (?) < 200 GPa
K
11.6 20 54 90 96
bcc → fcc ─► h-g (tI19*) → oP 8 → tI 4 → oC16 < 112 GPa
25 35
─► hP4 →
Rb 7 13 17 20 48
bcc → fcc → oC52 ─► h-g (tI19*) → tI 4 → oC16 < 70 GPa
Cs 2.4 4.2 4.3 12 72
bcc → fcc → oC84 ─► tI 4 → oC16 → dhcp < 223 GPa
Large arrows indicate supposed core ionization
(at compression V/Vo equal 0.35 for Li, 0.24 for Na, 0.33 for K, 0.31 for Rb and 0.43 for Cs).
core ionisation s-d electron transfer
Main factors of phase stability
Band structure energy EBS
0
2
2
)(
r
ZeEEwald )q()q(
2
q
BS' ΦSE
Е = Ео + ЕEwald + ЕBS
The crystal energy consists of two terms
electrostatic and electronic band structure
Volume scaling:
~ V −1/3 ~ V −2/3
Enhancement of the Hume-Rothery
arguments at compression
The brass alloy Cu-Zn system
The Age of Bronze A. Rodin
Massalsky (1996)
α (fcc) β (bcc) g (complex cubic) ε (hcp)
1.35 1.5 1.62 1.75 electron/
atom
Hume-Rothery phases:
Fermi sphere – Brillouin zone interaction
Fermi sphere – energy surface of free valence electrons, radius
Brillouin zone – planes in reciprocal space with vector
Interaction (condition of phase stability):
3/123
V
zkF
hkl
hkld
q2
kF ½ qhkl
Alkali metals:
pressure induced complexity
Li-cI16 at 46 GPa (Hanfland et al, Nature 2000)
Crystal structure Electron density of states Brillouin zone Li-cI16
(V Degtyareva 2003)
(b) Schematic diagram of the density of states D(E):
FS – BZ interactions
for the crystalline phase result
in attraction of BZ planes to FS –
in expansion in the real space.
For the liquid phase FS-BZ effects
are uniform for all k wave vectors.
At P>30 GPa liquid can be denser than crystal
FS-BZ effects lead for crystal to more expansion
than for liquid.
Structure factor for liquid elements position of 2kF indicated for z (valence electron number)
0 2 4 6
0
1
2
3
Ga 50 C
Hg -35 C
Si 1440 C
Ag 1000 C
S (
Q)
Q (A-1)
2kF z= 1 2 3 4
Hg melting point 234.3 K (- 38.7 C)
2kF = 2.69
Falconi et al. PRL 2005
Liquid Cs at P>4 GPa is similar to liquid Hg
Cs: core ionization !?
2KF
2KF
s-d-p(core)
hybridization
s-d transfer
Electronic energy levels
vs atomic volume Ross & McMahan,Phys.Rev.B
26, 4088 (1982)
Li Na K Rb Cs
Changes in interatomic distances in Na and K under pressure [Olga Degtyareva, High Pressure Research 2010, 30, 343]
2×ionic radius after [Shannon R D, Acta Cryst. (1976). A32, 751]
for coordination 8
Na 1.18 A
K 1.51 A
High-Pressure Difraction Studies of Rubidium Phase IV
Lars Lundegaard [ Thesis, University of Edinburgh,2007]
Liquid group IVa elements [J. Phys. F: Met. Phys. 14 (1984) 2259-2278.
The structure of the elements in the liquid state
J Hafner and G Kahl ]
Si
12 13 16 38 42 80 сF4 → -Sn, tI 4 → oI 4 → sh → oC16 → hcp → fcc < 250 GPa
Ge
11 75 85 102 160 сF4 → -Sn, tI 4 → oI 4 → sh → oC16 → hcp < 180 GPa
Bi
2.5 2.7 7.7 hR2 → mC4 → host-guest → bcc < 220 GPa → oC16 (>210oC) →
elements of group IV - Si, Ge and V - Bi
K
12 20 54 90 96
bcc → fcc → host-guest → oP8 → t I 4 → oC16 < 112 GPa
hP4
Rb 7 13 17 20 48
bcc → fcc → oC52 → host-guest → t I 4 → oC16 < 70 GPa
Cs 2.4 4.2 4.3 12 72
bcc → fcc → oC84 → t I 4 → oC16 → dhcp < 223 GPa
Structural sequences under pressure:
alkali group I metals s-d transfer s-d-p(core) hybridization
Hanfland et al. PRL 1999
Schwarz et al. PRL 1998
Takemura et al. PRB 2000
Schwarz et al. SSC 1999
Degtyareva V PRB 2000
- “ -
- “ -
Degtyareva et al. PRB 2003
McMahon et al.PRB 2006
Si-VI
Cs-V
Ge
Rb-VI
Bi-IV
Bi - In
Bi - Pb
Bi - Sn
K-IV
Zone filling by valence
electrons is 93%
Orthorhombic Cmca Structure
z = 1 z = 4
no Hume-Rothery effects a Hume-Rothery phase!
[V.F. Degtyareva, Electronic origin of the orthorhombic Cmca structure
in compressed elements and binary alloys Crystals, 3 (2013) 419]
The oC16 structure: 4 valence electrons
Program BRIZ for visualization of Fermi sphere and Brillouin zone interaction
[V. Degtyareva and I. Smirnova, Z. Krist. 2007]
Fermi sphere
intersected by planes
corresponding to a
group of strong
diffraction reflections
Conclusions
• Crystal structures of simple metals under
pressure are determined by valence electron
energy term
• Fermi sphere - Brillouin zone interactions favour
the low-symmetry structures with BZ planes close
to the FS by the Hume-Rothery mechanism
• Formation of low-packing structures is related to
the core ionization
• Melting curve with maximum and negative slope
in alkali metals is defined by Hume-Rothery effect
Thanks for attention
Thanks for collaboration to
Dr Olga Degtyareva
Centre for Science at Extreme Conditions,
University of Edinburgh, UK