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