Performance of the complete travel-time equation of state at simultaneous high pressure and temperature

Hartmut A. Spetzler, Akira Yoneda

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

The complete travel-time equation of state (CT-EOS) is presented by utilizing thermodynamics relations, such as; {Mathematical expression} The CT-EOS enables us to analyze ultrasonic experimental data under simultaneous high pressure and high temperature without introducing any assumption, as long as the density, or thermal expansivity, and heat capacity are also available as functions of temperature at zero pressure. The performance of the CT-EOS was examined by using synthesized travel-time data with random noise of 10-5 and 10-4 amplitude up to 4 GPa and 1500 K. Those test conditions are to be met with the newly developed GHz interferometry in a gas medium piston cylinder apparatus. The results suggest that the combination of the CT-EOS and accurate experimental data (10-4 in travel time) can determine thermodynamic and elastic parameters, as well as their derivatives with unprecedented accuracy, yielding second-order pressure derivatives (∂2M/∂P2) of the elastic moduli as well as the temperature derivatives of their first-order pressure derivatives ∂2M/∂P∂T). The completeness of the CT-EOS provides an unambiguous criterion to evaluate the compatibility of empirical EOS with experimental data. Furthermore because of this completeness, it offers the possibility of a new and absolute pressure calibration when X-ray (i.e., volume) measurements are made simultaneously with the travel-time measurements.

Original languageEnglish
Pages (from-to)379-392
Number of pages14
JournalPure and Applied Geophysics PAGEOPH
Volume141
Issue number2-4
DOIs
Publication statusPublished - Jun 1993
Externally publishedYes

Fingerprint

Travel time
Equations of state
equation of state
travel time
travel
equations of state
Derivatives
Temperature
completeness
Specific heat
thermodynamics
Thermodynamics
Volume measurement
heat capacity
elastic modulus
EOS
random noise
interferometry
Time measurement
pistons

Keywords

  • acoustic velocity
  • Elastic constant
  • equation of state
  • Grüneisen constant
  • heat capacity
  • high pressure
  • high temperature
  • thermal expansivity
  • thermodynamics

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology

Cite this

Performance of the complete travel-time equation of state at simultaneous high pressure and temperature. / Spetzler, Hartmut A.; Yoneda, Akira.

In: Pure and Applied Geophysics PAGEOPH, Vol. 141, No. 2-4, 06.1993, p. 379-392.

Research output: Contribution to journalArticle

@article{6287175cbdea4b5abd5e8435a8927165,
title = "Performance of the complete travel-time equation of state at simultaneous high pressure and temperature",
abstract = "The complete travel-time equation of state (CT-EOS) is presented by utilizing thermodynamics relations, such as; {Mathematical expression} The CT-EOS enables us to analyze ultrasonic experimental data under simultaneous high pressure and high temperature without introducing any assumption, as long as the density, or thermal expansivity, and heat capacity are also available as functions of temperature at zero pressure. The performance of the CT-EOS was examined by using synthesized travel-time data with random noise of 10-5 and 10-4 amplitude up to 4 GPa and 1500 K. Those test conditions are to be met with the newly developed GHz interferometry in a gas medium piston cylinder apparatus. The results suggest that the combination of the CT-EOS and accurate experimental data (10-4 in travel time) can determine thermodynamic and elastic parameters, as well as their derivatives with unprecedented accuracy, yielding second-order pressure derivatives (∂2M/∂P2) of the elastic moduli as well as the temperature derivatives of their first-order pressure derivatives ∂2M/∂P∂T). The completeness of the CT-EOS provides an unambiguous criterion to evaluate the compatibility of empirical EOS with experimental data. Furthermore because of this completeness, it offers the possibility of a new and absolute pressure calibration when X-ray (i.e., volume) measurements are made simultaneously with the travel-time measurements.",
keywords = "acoustic velocity, Elastic constant, equation of state, Gr{\"u}neisen constant, heat capacity, high pressure, high temperature, thermal expansivity, thermodynamics",
author = "Spetzler, {Hartmut A.} and Akira Yoneda",
year = "1993",
month = "6",
doi = "10.1007/BF00998336",
language = "English",
volume = "141",
pages = "379--392",
journal = "Pure and Applied Geophysics",
issn = "0033-4553",
publisher = "Birkhauser Verlag Basel",
number = "2-4",

}

TY - JOUR

T1 - Performance of the complete travel-time equation of state at simultaneous high pressure and temperature

AU - Spetzler, Hartmut A.

AU - Yoneda, Akira

PY - 1993/6

Y1 - 1993/6

N2 - The complete travel-time equation of state (CT-EOS) is presented by utilizing thermodynamics relations, such as; {Mathematical expression} The CT-EOS enables us to analyze ultrasonic experimental data under simultaneous high pressure and high temperature without introducing any assumption, as long as the density, or thermal expansivity, and heat capacity are also available as functions of temperature at zero pressure. The performance of the CT-EOS was examined by using synthesized travel-time data with random noise of 10-5 and 10-4 amplitude up to 4 GPa and 1500 K. Those test conditions are to be met with the newly developed GHz interferometry in a gas medium piston cylinder apparatus. The results suggest that the combination of the CT-EOS and accurate experimental data (10-4 in travel time) can determine thermodynamic and elastic parameters, as well as their derivatives with unprecedented accuracy, yielding second-order pressure derivatives (∂2M/∂P2) of the elastic moduli as well as the temperature derivatives of their first-order pressure derivatives ∂2M/∂P∂T). The completeness of the CT-EOS provides an unambiguous criterion to evaluate the compatibility of empirical EOS with experimental data. Furthermore because of this completeness, it offers the possibility of a new and absolute pressure calibration when X-ray (i.e., volume) measurements are made simultaneously with the travel-time measurements.

AB - The complete travel-time equation of state (CT-EOS) is presented by utilizing thermodynamics relations, such as; {Mathematical expression} The CT-EOS enables us to analyze ultrasonic experimental data under simultaneous high pressure and high temperature without introducing any assumption, as long as the density, or thermal expansivity, and heat capacity are also available as functions of temperature at zero pressure. The performance of the CT-EOS was examined by using synthesized travel-time data with random noise of 10-5 and 10-4 amplitude up to 4 GPa and 1500 K. Those test conditions are to be met with the newly developed GHz interferometry in a gas medium piston cylinder apparatus. The results suggest that the combination of the CT-EOS and accurate experimental data (10-4 in travel time) can determine thermodynamic and elastic parameters, as well as their derivatives with unprecedented accuracy, yielding second-order pressure derivatives (∂2M/∂P2) of the elastic moduli as well as the temperature derivatives of their first-order pressure derivatives ∂2M/∂P∂T). The completeness of the CT-EOS provides an unambiguous criterion to evaluate the compatibility of empirical EOS with experimental data. Furthermore because of this completeness, it offers the possibility of a new and absolute pressure calibration when X-ray (i.e., volume) measurements are made simultaneously with the travel-time measurements.

KW - acoustic velocity

KW - Elastic constant

KW - equation of state

KW - Grüneisen constant

KW - heat capacity

KW - high pressure

KW - high temperature

KW - thermal expansivity

KW - thermodynamics

UR - http://www.scopus.com/inward/record.url?scp=0042054660&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042054660&partnerID=8YFLogxK

U2 - 10.1007/BF00998336

DO - 10.1007/BF00998336

M3 - Article

VL - 141

SP - 379

EP - 392

JO - Pure and Applied Geophysics

JF - Pure and Applied Geophysics

SN - 0033-4553

IS - 2-4

ER -