High-pressure phase of calcium:Prediction of phase Ⅵ

and upper-pressure phases from first principle

Takahiro Ishikawa,Hitose Nagara,Naoshi Suzuki,Taku Tsuchiya,

and Jun Tsuchiya

Shimizu lab. ORII Daisuke

Phys.Rev.B 81,092104(2010)

Contents

• IntroductionWhat’s “High-pressure phase”?⇒An interesting propertyWhat’s “phase ”?ⅥFirst principles calculations

• Motivation• Research• Summary High-pressure phase of calcium:

Prediction of phase Ⅵand upper-pressure phases from first principle

simple cubic

What’s “High-pressure phase”?PressureThe structure change!!

=Structural phase transition(構造相転移 )

Decreasing inter atomic distance by compression

Electronic states change!

bcc

fcc

An interesting propertypressure-induced superconductivity

• Superconductivity(超伝導 )⇒electrical resistance = 0⇒Meissner effect B=0

linear motor car

electrical cable

@ extremely-low-temperature

Normalconductivity (常伝導 )

Superconductivity (超伝導 ) !!

Phase transition!!cool

Matsuoka private communication

①【 Ca- structureⅣ 】Tetragonal P41212 structure with fourfold helical atomic arrangements

②【 Ca- structureⅤ 】Orthorhombic Cmca structure with zigzag atomic arrangement

What’s “phase ”?Ⅵ• Structural phase transitions (構造相転移 ) of calcium

fcc bcc sc (simple cubic) ①

[GPa]20 32 113 139

Ca-I Ca-II Ca-III Ca-IV Ca-V

② ?

　　　　⇒ Highest Tc in simple element!

Transition temperature Tc 25K @ 161GPa (Ca- ?)Ⅴ

Ca

First principles calculations

Input data1. Crystal structure2. Type of atoms

Determination of electronic states

Output data1. Charge density2. Total energy3. Stress4. Inter atomic forceetc…

Motivation

BackgroundInvestigating mechanism of high Tc

superconductivity

Predicting the structure of Ca in which the highest Tc is observed

Computational detailsstructure

1. fcc 2. bcc3. sc (simple cubic)4. hcp5. Cmca6. Cmcm7. Pnma8. I41/amd9. P4121210.I4/mcm(0,0,γ)

The most stable structure @ 0K

Input data1. Making crystal structure (lattice

vectors and atomic coordinates)2. Type of atoms⇒structural optimization⇒electronic states

Comparing the enthalpies up to 200Gpa

(enthalpy)

Comparing enthalpies

figure 1

figure 2

(enthalpy)

The lowest ΔH point⇒Most stable structure

Pnma I4/mcm(00γ)

fcc bcc I41/amd P41212

[GPa]3.5 32 109 135

Cmca Pnma

74 117

Ca-I Ca-II Ca-IV Ca-VCa-Ⅲ Ca-VI? Ca-VII?

I4/mcm(00γ)

[GPa]495

Ca-VII?

hcp

Ca-VIII?

I4/mcm(00γ)

fcc bcc sc (simple cubic) P41212

[GPa]20 32 113 139

Ca-I Ca-II Ca-III Ca-IV Ca-V

Experiment

Calculation in this paper

Cmca

Superconductivity• Theoretically ,Tc=25K

was obtained around the phase boundary between Ca- and Ca-Ⅵ

.Ⅶ

50 100 150pressure(GPa)

J.Phys. Soc. Jpn. 75, 083703 (2006).

0 20 40 60 80 100 120 1400

5

10

15

20

25

30

Prediction

pressure(GPa)

Tc(K

) Ca-Ⅳ

Ca-Ⅴ

Ca-Ⅵ

Ca-Ⅶ

Ca-Ⅰ

Ca-Ⅱ

Ca-Ⅲ

Ca-Ⅵ

158(GPa)Experimental result

( Recently , the structure of ⇒ Ca-Ⅵ was experimentally confirmed.)

(Y.Nakamoto et al , Phys.Rev.B , 81, 140106(R) (2010).)

Summary

• The structures of the phases Ca-Ⅵ and Ca- Ⅶ were predicted.

• The highest TC of 25K inthe Ca-Ⅵ or Ca-Ⅶ phase.