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High Pressure Applications High Pressure Applicaons Haozhe Liu HPSTAR, Changchun/Beijing, China 2015 NXS_ANL 1 Outline • High pressure techniques (brief history) • Pressure calibraon • Equaon of state (EoS) • Cases using synchrotron techniques 2015 NXS_ANL 2 2015 NXS_ANL 3 Unit • Pressure: Force & Area P=F/A • SI unit: Pascal (Pa) • One bar = 100,000 Pa=750.062 torr = 0.9869 atm • 1 atmosphere pressure (sea level) • 1 atm = 760 torr = 14.7 psi • Popular: GPa = 9,870 atm = 10,000 bar. Kbar 2015 NXS_ANL 4 High Pressure Technology • Dynamic HP Shock Wave and Detonation • Static HP 1. Large volume press 2. Small volume cell DAC (Diamond Anvil Cell) 2015 NXS_ANL 5 2015 NXS_ANL 6 Percy Williams Bridgman (1882-1961) • Bridgman published more than 260 papers (only two of which listed a coauthor) and 13 books. • His scien0fic papers have been published in Collected Experimental Papers, 7 vol. (1964). • Among his many books are The Physics of High Pressure (1931) and Reflecons of a Physicist (1950). 2015 NXS_ANL 7 Nobel Lecture, December 11, 1946 Strength of materials! 2015 NXS_ANL 8 Polymorphism Compressibility 2015 NXS_ANL 9 2015 NXS_ANL 10 Large Volume Press (LVP) Novatek Cubic Press 2015 NXS_ANL 11 2015 NXS_ANL 12 HP Applicaons Syntheses via Pressure • Superhard materials Diamond , c-BN, • Superconductor: (Cu, Cr)Sr2Can-1CunO2n+3 n=1--9 (Sr, Ca)3Cu2O4+&Cl2-y • Super “hot” materials: (Mg, Fe)SiO3 2015 NXS_ANL 13 sp2 carbon bonding GRAPHITE π σ sp2 has 3coplanar (strong) sigma-bonds & 2 (week) p-bonds with 360o influence DIAMOND sp3 – carbon bonding 2015 NXS_ANL sp3 has 4 “sigma” (strong) bonds 14 High Pressure Man-made Diamond December 16, 1954, Tracy Hall et al of General Electric F.P Bundy, H.T. Hall, H.M. Strong, R.H. Wentorf, Nature, 176, 51 (1955) 2015 NXS_ANL 15 2015 NXS_ANL 16 2015 NXS_ANL 17 Kimberlitic Diamond Subduction Zone Diamonds 1mm 100 µm 2015 NXS_ANL 18 Diamond anvil cell (DAC) 2015 NXS_ANL 19 2015 NXS_ANL 20 The lever-arm diamond anvil cell, as diagrammed here: by the applicaon of leverage a turn of a screw could create many thousands of atmospheres of pressure • C. E. Weir, E. R. Lippincog, A. Van Valkenburg, and E. N. Bun0ng, Infrared Studies in the 1-to 15-Micron Region to 30,000 Atmospheres, J. Res. Natl. Bur. Stand. 63A, 55-62 (1959). • Alvin Van Valkenburg, Visual Observaons of High Pressure Transi0ons, Rev. Sci. Instrum. 33, 1462 (1962). 2015 NXS_ANL 21 Alvin Van Valkenburg, pictured here in 1963, was a pioneer in using the diamond anvil cell to study materials at high pressure at the Naonal Bureau of Standards (NBS), Washington DC. now the Naonal Ins0tute of Standards and Technology (NIST) 2015 NXS_ANL 22 Distorted anvil face due to plas0c Anvil distor0on and effect on pressure distribu0on deformaon at 1.7 Mbar Mao and Bell, 1978 a,b unbeveled anvils, c,d beveled anvils Mao and Bell, 1978 2015 NXS_ANL 23 Gas driven membrane DAC Cover Membrane Interface disk Upper carbide tungsten rocker 1 Upper rocker support (movable) Guidance pin Gasket (Stainless steel or rhenium) 2 Lower carbide tungsten rocker Lower rocker support (fixed) 3 2 1 4 3 5 4 6 5 7 6 7 8 9 8 Height : 32 mm 9 Diameter : 50 mm 2015 NXS_ANL 24 Screw driver (Hand) driven DAC 2015 NXS_ANL 25 DACs ~160 degree side opening angle Hydrothermal cells Typical symmetric cells ~140 degree side opening angle Panoramic cell Plate cell 2015 NXS_ANL 26 A Powerful and Versatile High-P Technology Electrical Conductivity Experiments Magnetic Susceptibility Experiments Designer Diamond Anvil High-P/High-T Experiments 2015 NXS_ANL 27 In situ Research under High Pressure • Lab XRD • Synchrotron & neutron • Raman sources Dedicated & non-dedicated • IR high pressure staons • Brillouin XRD • Absorp0on Imaging IXS • Electronic and Magne0c PDF Measurement SAS, WAS • … ESAF … 2015 NXS_ANL 28 2015 NXS_ANL 29 High pressure measurement & calibraon • Force • Area • Pressure measurement P=F/A • Higher pressure: totally different story! 2015 NXS_ANL 30 Deformaon • Free rotaon piston-cylinder (deformaon free condi0on) 2015 NXS_ANL 31 Pressure calibraon: Goal Primary calibraon (accuracy) 1- 100 GPa ΔP/P = ±1% 100- 300 GPa ΔP/P = ±1% High temperatures -- at 100 GPa-2500 K ΔP/P = ±1% Secondary calibraon (precision) 10 MPa – 1 GPa ΔP = ±5 MPa 1- 100 GPa ΔP/P = ±0.2% 100- 300 GPa ΔP/P = ±0.2% 2015 NXS_ANL 32 Primary calibraon requires measurements of two independent func0ons related to pressure. Examples: • F and A – free rotation piston-cylinder • US and UP – shock Hugoniot • Vφ and ρ – DAC or LVP 2 Vφ = K/ρ " K = ρ dP/dρ " 2 P = ∫ Vφ dρ. 2015 NXS_ANL 33 Techniques involve • X-ray diffrac0on (axial and radial) • Op0cal spectroscopy (Brillouin, Raman, fluorescence) • Ultrasonic measurement • Inelas0c x-ray scaering spectroscopy 2015 NXS_ANL 34 Pressure calibraon, ΔP/P ±1% Zha, Mao, Hemley, PNAS (2000) ρ from x-ray diffraction Ruby fluorescence shift Calibrated by MgO P-ρ EOS Vφ from Brillouin scattering P-ρ EOS by integration (Primary) (Secondary) 2015 NXS_ANL 35 Brillouin Scaering with synchrotron X-rays at the APS Elas0city Grand Challenge COMPRES Infrastructure Development Project Measure sound veloci0es and density simultaneously “Absolute” or internally consistent Pressure Scales Zha et al., Brillouin on MgO (PNAS, 2000) Isothermal bulk modulus Adiabac elas0c moduli (volume measurements) (velocity measurements) # dP & K = "V% ( 2 $ dV ' µ = !VS 2 2 V K (V) K = "V # (4 /3)"V P = " dV P P #Vo V ! 2015 NXS_ANL 36 ! ! Brillouin scaering § Acous@c waves present in a soliD due to thermal moon of atoms § Laser light interacts with phonons (or density / refracve inDex fluctuaons) anD is scaered with Doppler shied frequency Δω § Brillouin shi is propor@onal to acousc velocity Vi =Δωλ / 2n*sin (θ/2) Platelet (symmetric) geometry Laser Laser beam IN q Original Brillouin Scattered Several Original Light OUT shifted, frequencies frequency Vp or Vs " Analyser ! Frequency 2015 NXS_ANL Vi =Δωλ / 2sin (θ*/2) 37 Schemac diagram of the Brillouin system installed at sector 13-BMD at APS MotorizeD transla@on components (controllable from outsiDe the hatch, blue boxes): HMTS - horizontal motorized translaon stage; VMTS - ver0cal motorized translaon stage; MLFA - motorized laser focusing assembly; MSCA - motorized signal collec0ng assembly; SPOA - sample posi0oning and orientaon assembly; SL-LB - sample light / light block. Observa@on / feeDback elements (reD boxes): VC - video camera; BT - beam target. X-ray components: MAR - MAR Imaging plate; XBS - X-ray beam stop; CS - cleanup slit. 2015 NXS_ANL 38 High Pressure Ultrasonic Experimental Techniques Simultaneous P-V-T Eos and Sound Velocity (Vp,Vs) Measurements! CCD/SSD Press Incident slits Sample NSLS X17B2 Ultrasonic Interferometer YAG and CCD Camera" X-ray Imaging 2015 NXS_ANL 39 Ultrasonic Interferometry Computer i (t) Wave Form Control Generator Amp Ch1 Sync Ch1 Details of SAM 85 IEEE Frequency g(t) cell assembly r(t) Trigger Transduce r Digital Oscilloscope Pt NaCl Buffer Rod P and S wave C-heater Sample travel 0mes TC (tp, ts) inside the sample are TC measured at the Th same 0me e Boronim Cell assembly forsample ultrasonics at High P and T. 2015 NXS_ANL 40 “Pressure” is meaningful only under hydrostatic conditions. Nonhydrostatic stress conditions are difficult to reproduce ... 2015 NXS_ANL 41 Nonhydrostac stress • Stress inhomogeneity (signal) pressure gradients broadening • Uniaxial stress (signal) lattice distortion shift more serious ! 2015 NXS_ANL 42 Deformation under uniaxial stress K. Takemura, JAP 89, 662 (2001). 2015 NXS_ANL 43 Local stress polycrystalline local stress !" single crystal broadening (+ grain boundaries, dislocations, twins, ...) single crystal Ideal hydrostatic conditions can only be achieved with a fluid pressure medium and a perfect single crystal. 2015 NXS_ANL 44 In prac0ce, pressure was measured: •! Powder XRD via well-known EoS of markers (Pt, Au,…) •! Ruby pressure scale Secondary pressure calibraon!! 2015 NXS_ANL 45 Fluorescent spectroscopy •! Ruby (Al O ), YAlO , YAG, MgO, and a few others. 2 3 3 •! Ruby’s main fluorescence lines (the R1 R2 doublet) were intense and sharp, and the lines shited measurably toward the red with increasing pressure R. A. Forman, G. J. Piermarini, J. D. Barneg, and S. Block, Pressure Measurement Made by the U0lizaon of Ruby Sharp- Line Luminescence, Science 176, 284 (1972). 2015 NXS_ANL 46 •! H. K. MAO and P. M. BELL, High-Pressure Physics: The 1- Megabar Mark on the Ruby R1 Static Pressure Scale, Science, Vol. 191. no. 4229, pp. 851 – 852, 1976 •! H. K. MAO and P. M. BELL, High-Pressure Physics: Sustained Static Generation of 1.36 to 1.72 Megabars, Science 200, 1145-1147 1978 •! H.-K. Mao, J. Xu, and P. M. Bell, J. Geophys. Res. 91, 4673 (1986). 2015 NXS_ANL 47 2015 NXS_ANL 48 2015 NXS_ANL 49 DiamonD anvil Raman gauge 2015 NXS_ANL 50 Equaon of State (EoS) •! The relaonships among the pressure, the volume, and the temperature are described by the Equaon of State (EoS). •! Ideal gas: PV=nRT 2015 NXS_ANL 51 •! The volume-temperature relaonship is described by the defini0on of the volume coefficient of expansion •! The relaonship between the pressure and the volume is given by the isothermal bulk modulus Condions For the validity of equaon, it is assumed that the solid is homogeneous, isotropic, nonviscous and has linear elas0city. It is also assumed that the stresses are isotropic; therefore, the principal stresses can be iden0fied as the pressure p = σ1 = σ2 = σ3 . 2015 NXS_ANL 52 A universal EoS must cover the en0re pressure and temperature range; therefore, it is necessary to incorporate all of the derivaves of the volume coefficient of expansion and the isothermal bulk modulus. There is no single expression known for universal! •! The determined values of the volume and the bulk modulus at temperature T can be used as ini0al parameters for an isothermal EoS. •! The isothermal equaon of states follow finite strain, interatomic poten0al, or empirical approach.
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