Experimental and first-principles studies on the elastic properties of α-hafnium metal under pressure

Qi, Xintong; Wang, Xuebing; Chen, Ting; Li, Baosheng

doi:10.1063/1.4945106

Title: Experimental and first-principles studies on the elastic properties of α-hafnium metal under pressure

Abstract

Compressional and shear wave velocities of the a phase of hafnium have been measured up to 10.4GPa at room temperature using ultrasonic interferometry in a multi-anvil apparatus. A finite strain equation of state analysis yielded Ks0 ¼ 110:4 ð5Þ GPa; G0 ¼ 54:7ð5Þ GPa; K0 s0 ¼ 3:7; andG0 0 ¼ 0:6 for the elastic bulk and shear moduli and their pressure derivatives at ambient conditions.Complementary to the experimental data, the single crystal elastic constants, the elastic anisotropy, and the unit cell axial ratio c/a of a-hafnium at high pressures were investigated by Density Functional Theory (DFT) based first principles calculations. A c/a value of 1.605 is predicted for a-Hf at 40GPa, which is in excellent agreement with previous experimental results. The low-pressure derivative of the shear modulus observed in our experimental data up to 10 GPa was found to originate from the elastic constant C44, which exhibits negligible pressure dependence within the current experimental pressure range. At higher pressures (>10GPa), C44 was predicted to soften and the shear wave velocity S trended to decrease with pressure, which can be interpreted as a precursor to the a-x transition similar to that observed in other group IV elements (titanium and zirconium).more »« less

Authors:

^[1]; Wang, Xuebing ^[1]; Chen, Ting ^[1]; Li, Baosheng ^[1]

Stony Brook Univ., Stony Brook, NY (United States)

Publication Date:: Wed Mar 30 00:00:00 EDT 2016

Research Org.:: Stony Brook Univ., NY (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1245457

Alternate Identifier(s):: OSTI ID: 1244607; OSTI ID: 1466776

Grant/Contract Number:: NA0002907; NA0001815

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Applied Physics

Additional Journal Information:: Journal Volume: 119; Journal Issue: 12; Journal ID: ISSN 0021-8979

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; hafnium; high pressure; elasticity; elastic moduli; sound pressure; density functional theory; anisotropy; elasticity, pressure, hafnium

Citation Formats


                    Qi, Xintong, Wang, Xuebing, Chen, Ting, and Li, Baosheng. Experimental and first-principles studies on the elastic properties of α-hafnium metal under pressure.  United States: N. p., 2016. 
Web.  doi:10.1063/1.4945106.

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                    Qi, Xintong, Wang, Xuebing, Chen, Ting, & Li, Baosheng. Experimental and first-principles studies on the elastic properties of α-hafnium metal under pressure.  United States.  https://doi.org/10.1063/1.4945106

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                    Qi, Xintong, Wang, Xuebing, Chen, Ting, and Li, Baosheng. Wed .  
"Experimental and first-principles studies on the elastic properties of α-hafnium metal under pressure".  United States.  https://doi.org/10.1063/1.4945106.  https://www.osti.gov/servlets/purl/1245457.

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@article{osti_1245457,

  title        = {Experimental and first-principles studies on the elastic properties of α-hafnium metal under pressure},

  author       = {Qi, Xintong and Wang, Xuebing and Chen, Ting and Li, Baosheng},

  abstractNote = {Compressional and shear wave velocities of the a phase of hafnium have been measured up to 10.4GPa at room temperature using ultrasonic interferometry in a multi-anvil apparatus. A finite strain equation of state analysis yielded Ks0 ¼ 110:4 ð5Þ GPa; G0 ¼ 54:7ð5Þ GPa; K0 s0 ¼ 3:7; andG0 0 ¼ 0:6 for the elastic bulk and shear moduli and their pressure derivatives at ambient conditions.Complementary to the experimental data, the single crystal elastic constants, the elastic anisotropy, and the unit cell axial ratio c/a of a-hafnium at high pressures were investigated by Density Functional Theory (DFT) based first principles calculations. A c/a value of 1.605 is predicted for a-Hf at 40GPa, which is in excellent agreement with previous experimental results. The low-pressure derivative of the shear modulus observed in our experimental data up to 10 GPa was found to originate from the elastic constant C44, which exhibits negligible pressure dependence within the current experimental pressure range. At higher pressures (>10GPa), C44 was predicted to soften and the shear wave velocity S trended to decrease with pressure, which can be interpreted as a precursor to the a-x transition similar to that observed in other group IV elements (titanium and zirconium). The acoustic velocities, the bulk and shear moduli, and the acoustic Debye temperature (240.1K) determined from the current experiments were all compared well with those predicted by our theoretical DFT calculations.},

  doi          = {10.1063/1.4945106},

  journal      = {Journal of Applied Physics},

  number       = 12,

  volume       = 119,

  place        = {United States},

  year         = {Wed Mar 30 00:00:00 EDT 2016},

  month        = {Wed Mar 30 00:00:00 EDT 2016}

}

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Journal of Applied Physics, Vol. 124, Issue 18
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Title: Experimental and first-principles studies on the elastic properties of α-hafnium metal under pressure

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Simultaneous ultrasonic and synchrotron x-ray studies on pressure induced α-ω phase transition in zirconium journal, January 2008

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Full-potential calculations using the generalized-gradient corrections: structural properties of Ti, Zr and Hf under compression journal, January 1998

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Optical zone-centre phonon modes and macroscopic elasticity in hcp metals journal, July 2000

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The equation of state and structural stability of titanium obtained using the linear muffin-tin orbital band-structure method journal, January 1990

Pressure derivatives of elastic wave velocities from ultrasonic interferometric measurements on jacketed polycrystals journal, October 1989

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Elastic instabilities in crystals from ab initio stress - strain relations
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Homogeneity and constitution of the earth's lower mantle and outer core
journal, August 1975

Phase transitions under shock-wave loading
journal, July 1977

Plane-wave pseudopotential study for the structural stability of Hf: The role of spin–orbit interaction
journal, April 2011

Three-particle forces in the lattice dynamics of some hexagonal close-packed metals
journal, January 1994

Titanium metal at high pressure: Synchrotron experiments and ab initio calculations
journal, May 2004

Study of the Earth’s interior using measurements of sound velocities in minerals by ultrasonic interferometry
journal, August 2014

First-principles investigations on elastic and thermodynamic properties of zirconium under pressure
journal, August 2012

Acoustic travel time gauges for in-situ determination of pressure and temperature in multi-anvil apparatus
journal, August 2015

Omega phase in materials
journal, January 1982

Modern techniques in measuring elasticity of Earth materials at high pressure and high temperature using ultrasonic interferometry in conjunction with synchrotron X-radiation in multi-anvil apparatus
journal, June 2004

Calculation of the P–T phase diagram of hafnium
journal, June 2000

Thermal equations of state of the $α$ , $β$ , and $ω$ phases of zirconium
journal, May 2005

High P-T phase transitions and P-V-T equation of state of hafnium
journal, June 2012

Single-Crystal Elastic Moduli and the hcp → bcc Transformation in Ti, Zr, and Hf
journal, July 1964

Elastic wave velocity measurement in multi-anvil apparatus to 10 GPa using ultrasonic interferometry
journal, November 1996

Calculation of Elastic Properties from Thermodynamic Equation of State Principles
journal, May 1992

First-principles study of high pressure structure phase transition and elastic properties of titanium
journal, August 2010

New high-pressure phase transition in zirconium metal
journal, January 1990

Pressure-induced transition in titanium metal a systematic study of the effects of uniaxial stress
journal, January 2005

Crystal structures of group IVa metals at ultrahigh pressures
journal, October 1990

Crystal structures of Ti, Zr, and Hf under compression: Theory
journal, December 1993

Simultaneous ultrasonic and synchrotron x-ray studies on pressure induced α-ω phase transition in zirconium
journal, January 2008

First-principles calculations of phase transition, elastic modulus, and superconductivity under pressure for zirconium
journal, March 2011

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996

Variation of Elastic Constants and Static Strains with Hydrostatic Pressure: A Method for Calculation from Ultrasonic Measurements
journal, April 1957

Crystal structure from one-electron theory
journal, February 1985

Full-potential calculations using the generalized-gradient corrections: structural properties of Ti, Zr and Hf under compression
journal, January 1998

Lattice dynamics of hcp Hf
journal, July 1981

Reinvestigation of high pressure polymorphism in hafnium metal
journal, June 2014

Optical zone-centre phonon modes and macroscopic elasticity in hcp metals
journal, July 2000

Phase transformations in the Ti-V system under high pressure up to 25 GPa
journal, March 1981

Experimental constraints on the phase diagram of titanium metal
journal, October 2008

Experimental constraints on the phase diagram of elemental zirconium
journal, July 2005

Phase changes and the equation of state of Zr
journal, August 2005

Ultrasonic Phase Velocity by the Pulse‐Echo‐Overlap Method Incorporating Diffraction Phase Corrections
journal, November 1967

The equation of state and structural stability of titanium obtained using the linear muffin-tin orbital band-structure method
journal, January 1990

Pressure derivatives of elastic wave velocities from ultrasonic interferometric measurements on jacketed polycrystals
journal, October 1989

Experimental and theoretical studies on the elasticity of tungsten to 13 GPa
journal, August 2018

Elastic anomalies across phase transitions of praseodymium to 12 GPa
journal, November 2018