High-pressure phase of calcium: Prediction of phase Ⅵ and upper-pressure phases from first principle Phys.Rev.B 81,092104(2010) Takahiro Ishikawa,Hitose Nagara, Naoshi Suzuki,Taku Tsuchiya, and Jun Tsuchiya Shimizu lab. ORII Daisuke Contents • Introduction What’s “High-pressure phase”? ⇒An interesting property What’s “phase Ⅵ”? First principles calculations • Motivation • Research • Summary High-pressure phase of calcium: Prediction of phase Ⅵ and upper-pressure phases from first principle What’s “High-pressure phase”? The structure change!! =Structural phase transition (構造相転移) Pressure simple cubic bcc fcc Decreasing inter atomic distance by compression Electronic states change! An interesting property pressure-induced superconductivity • Superconductivity(超伝導) ⇒electrical resistance = 0 ⇒Meissner effect B=0 @ extremely-lowtemperature Normalconductivity (常伝導) cool electrical cable Phase transition!! Superconductivity (超伝導) !! linear motor car What’s “phase Ⅵ”? • Structural phase transitions (構造相転移) of calcium Ca-I Ca-II Ca-III Ca-IV fcc bcc sc (simple cubic) 20 32 Ca-V ① 113 ② 139 ? [GPa] ①【Ca-Ⅳ structure】 ②【Ca-Ⅴ structure】 Tetragonal P41212 structure with fourfold helical atomic arrangements Orthorhombic Cmca structure with zigzag atomic arrangement ⇒ Highest Tc in simple element! Transition temperature Tc 25K @ 161GPa (Ca-Ⅴ?) Matsuoka private communication First principles calculations Input data Output data 1. Crystal structure 2. Type of atoms 1. Charge density 2. Total energy 3. Stress 4. Inter atomic force etc… Determination of electronic states Motivation Background Investigating mechanism of high Tc superconductivity Predicting the structure of Ca in which the highest Tc is observed Computational details structure 1. fcc 2. bcc 3. sc (simple cubic) 4. hcp 5. Cmca 6. Cmcm 7. Pnma 8. I41/amd 9. P41212 10.I4/mcm(0,0,γ) 𝐺| 𝑇=0 Input data 1. Making crystal structure (lattice vectors and atomic coordinates) 2. Type of atoms ⇒structural optimization ⇒electronic states Comparing the enthalpies up to 200Gpa 𝐺 = 𝐸 + 𝑃𝑉 − 𝑇𝑆 = 𝐸 + 𝑃𝑉 = 𝑯(enthalpy) The most stable structure @ 0K Comparing enthalpies 𝐺| 𝑇=0 𝐺 = 𝐸 + 𝑃𝑉 − 𝑇𝑆 = 𝐸 + 𝑃𝑉 = 𝑯(enthalpy) The lowest ΔH point ⇒Most stable structure figure 1 figure 2 Experiment Ca-I Ca-II Ca-III Ca-IV Ca-V fcc bcc sc (simple cubic) P41212 Cmca 20 32 113 139 [GPa] Calculation in this paper Ca-I Ca-II fcc bcc 3.5 Ca-IV Ca-V Ca-VI? Ca-Ⅲ I41/amd 32 Ca-VII? I4/mcm(00γ) P41212 74 Ca-VIII? Cmca 109 117 Pnma Ca-VII? I4/mcm(00γ) [GPa] 135 hcp 495 [GPa] Pnma I4/mcm(00γ) Superconductivity Prediction 30 25 20 Tc(K) • Theoretically ,Tc=25K was obtained around the phase boundary between Ca-Ⅵ and CaⅦ. 158(GPa) Ca-Ⅴ Ca-Ⅱ 10 Experimental result Ca-Ⅵ Ca-Ⅳ Ca-Ⅲ 15 Ca-Ⅶ 5Ca-Ⅰ 0 0 20 40 60 80 100 pressure(GPa) Ca-Ⅵ (⇒Recently , the structure of Ca-Ⅵ was experimentally confirmed.) (Y.Nakamoto et al , Phys.Rev.B , 81, 140106(R) (2010).) 50 100 150 pressure(GPa) J.Phys. Soc. Jpn. 75, 083703 (2006). 120 140 Summary • The structures of the phases Ca-Ⅵ and Ca-Ⅶ were predicted. • The highest TC of 25K in the Ca-Ⅵ or Ca-Ⅶ phase.
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