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]

Melting of alkalis under pressure K Melting temperature decreases dramatically. liquid bcc fcc tI 19 Narygina et al 2011 Phys. Rev. B 84 054111 Cs E. Gregoryanz, O. Degtyareva, M. Somayazulu et al PRL 94 ,85502(2005) Guillaume, Gregoryanz, Degtyareva et al Nature Physics 6, 211 (2011) Falconi et al. PRL 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 Rb-IV, K-III Rb-VI, Cs-V Ambient pressure Moderate pressure High Pressure

Alkali elements: Na [Gregoryanz et al PRL 2005] [Ma et al Nature 2009] [Gregoryanz et al Science 2008]

Alkali metals under pressure: structural transformations 7.5 39 42 60 70 95 Li bcc → fcc → hR 1 → cI 16 ─► oC 88 → oC 40 → oC 24 < 125 65 104 117 125 180 Na bcc → fcc → cI 16 ─► oP 8 → h-g ( tI 19*) → hP 4 (?) < 200 GPa 11.6 20 54 90 96 bcc → fcc ─► h-g ( tI 19*) → oP 8 → tI 4 → oC 16 < 112 GPa K 25 35 ─► hP 4 → 7 13 17 20 48 Rb bcc → fcc → oC 52 ─► h-g ( tI 19*) → tI 4 → oC 16 < 70 GPa 2.4 4.2 4.3 12 72 Cs bcc → fcc → oC 84 ─► tI 4 → oC 16 → dhcp < 223 GPa s-d electron transfer core ionisation 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).

Main factors of phase stability Е = Е о + Е Ewald + Е BS The crystal energy consists of two terms electrostatic and electronic band structure 2 ( Ze )  '    2 E Ewald  E S ( q ) Φ ( q ) BS 2 r q 0 Volume scaling: ~ V − 1/3 ~ V − 2/3 Enhancement of the Hume-Rothery arguments at compression Band structure energy E BS

The brass alloy Cu-Zn system The Ag Age of Bronze ze A. Rodin α (fcc)  β (bcc)  g ( complex cubic )  ε (hcp) 1.35  1.5  1.62  1.75 electron/ atom Massalsky (1996)

Hume-Rothery phases: Fermi sphere – Brillouin zone interaction 1 / 3    2 3 z    Fermi sphere – energy surface of free valence electrons, radius k F     V  2  Brillouin zone – planes in reciprocal space with vector q hkl d hkl k F  ½ q hkl Interaction (condition of phase stability):

Alkali metals: pressure induced complexity Li- cI 16 at 46 GPa ( Hanfland et al, Nature 2000 ) Crystal structure Electron density of states Brillouin zone Li- cI 16 ( 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. At P>30 GPa liquid can be denser than crystal For the liquid phase FS-BZ effects FS-BZ effects lead for crystal to more expansion are uniform for all k wave vectors. than for liquid .

Structure factor for liquid elements position of 2kF indicated for z ( valence electron number ) 2k F z= 1 2 3 4 3 Ag 1000 C Hg -35 C Ga 50 C 2 Si 1440 C S (Q) 1 0 0 2 4 6 -1 ) Q (A

Hg melting point 234.3 K (- 38.7 C) 2k F = 2.69

2K F 2K F Falconi et al. PRL 2005 Liquid Cs at P>4 GPa is similar to liquid Hg Cs: core ionization !?

El Electroni tronic c energy y le levels ls vs atomic volume Ross & McMahan, Phys.Rev.B 26 , 4088 (1982) s-d transfer s-d-p(core) hybridization Cs Li Rb Na K

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 ]

Structural sequences under pressure: alkali group I metals s-d transfer s-d-p(core) hybridization 12 20 54 90 96 bcc → fcc → host-guest → oP 8 → t I 4 → oC 16 < 112 GPa K hP 4 7 13 17 20 48 Rb bcc → fcc → oC 52 → host-guest → t I 4 → oC 16 < 70 GPa 2.4 4.2 4.3 12 72 Cs bcc → fcc → oC 84 → t I 4 → oC 16 → dhcp < 223 GPa elements of group IV - Si, Ge and V - Bi 12 13 16 38 42 80 с F 4 →  -Sn, tI 4 → oI 4 → sh → oC 16 → hcp → fcc < 250 GPa Si 11 75 85 102 160 с F 4 →  -Sn, tI 4 → oI 4 → sh → oC 16 → hcp < 180 GPa Ge 2.5 2.7 7.7 hR 2 → mC 4 → host - guest → bcc < 220 GPa Bi → oC16 (>210 o C) →

Orthorhombic Cmca Structure Zone filling by valence electrons is 93% Si-VI Hanfland et al. PRL 1999 Cs-V Schwarz et al. PRL 1998 Ge Takemura et al. PRB 2000 Rb-VI Schwarz et al. SSC 1999 Bi-IV Degtyareva V PRB 2000 z = 1 z = 4 - “ - Bi - In no Hume-Rothery effects a Hume-Rothery phase! - “ - Bi - Pb Bi - Sn Degtyareva et al. PRB 2003 [V.F. Degtyareva, Electronic origin of the orthorhombic Cmca structure K-IV McMahon et al.PRB 2006 in compressed elements and binary alloys Crystals, 3 (2013) 419]

The oC 16 structure: 4 valence electrons Fermi sphere intersected by planes corresponding to a group of strong diffraction reflections Program BRIZ for visualization of Fermi sphere and Brillouin zone interaction [V. Degtyareva and I. Smirnova, Z. Krist. 2007]

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