in Compressed Alkalis Valentina F Degtyareva Institute of Solid - - PowerPoint PPT Presentation

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

2

2 ) ( r Ze EEwald   

) q ( ) q (

2 q BS

'

Φ S E





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 Ag Age of Bronze ze

• 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 / 1 2

3          V z kF 

hkl hkl

d q  2 

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)

2 4 6 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

El Electroni tronic c energy y le levels ls

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