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Title: Equation of State Model for the Gamma-Alpha Transition in Ce

ORCiD logo [1]; ORCiD logo [1];  [1]
  1. Los Alamos National Laboratory
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
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DOE Contract Number:
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Resource Relation:
Conference: APS Shock Compression of Condensed Matter ; 2017-07-09 - 2017-07-09 ; St. Louis, Louisiana, United States
Country of Publication:
United States

Citation Formats

Greeff, Carl William, Crockett, Scott, and Honnell, Kevin Guy. Equation of State Model for the Gamma-Alpha Transition in Ce. United States: N. p., 2017. Web.
Greeff, Carl William, Crockett, Scott, & Honnell, Kevin Guy. Equation of State Model for the Gamma-Alpha Transition in Ce. United States.
Greeff, Carl William, Crockett, Scott, and Honnell, Kevin Guy. 2017. "Equation of State Model for the Gamma-Alpha Transition in Ce". United States. doi:.
title = {Equation of State Model for the Gamma-Alpha Transition in Ce},
author = {Greeff, Carl William and Crockett, Scott and Honnell, Kevin Guy},
abstractNote = {},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2017,
month = 9

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  • We present the construction of free energy functions for the {alpha} and {omega} phases of Ti. These free energies combine information from ambient pressure, static high pressure, and shock wave measurements as well as first principles total energy calculations. The Hugoniot data are analyzed in terms of this equation of state. The Hugoniot consists of three segments: a metastable {alpha}-phase region, a transition region, and an {omega}-phase branch. The extent of the metastability and time resolved wave profiles are discussed in terms of a model in which the transformation rate depends exponentially on the pressure, an assumption which is motivatedmore » by static high-pressure data. This picture is consistent with the observed wave shapes and with the observation that the apparent transformation pressure is dependent on the peak shock pressure.« less
  • Foams, porous solids and granular materials have a characteristic Hugoniot locus that for weak shocks is concave in the (particle velocity, shock velocity)-plane. An equation of state (EOS) that has this property can be constructed implicitly from a Helmholtz free energy of the form {Psi}{sub s}(V,T,{phi}) = {Psi}{sub s}(V,T)+B({phi}) where the equilibrium volume fraction {phi}{sub eq} is determined by minimizing {Psi}, i.e., the condition {partial_derivative}{sub {psi}} {Psi} = 0. For many cases, a Hayes EOS for the pure solid {Psi}{sub s}(V,T) is adequate. This provides a thermodynamically consistent framework for the P-{alpha} model. For this form of EOS the volumemore » fraction has a similar effect to an endothermic reaction in that the partial Hugoniot loci with fixed {psi} are shifted to the left in the (V,P)-plane with increasing f. The equilibrium volume fraction can then be chosen to match the concavity of the principal Hugoniot locus. An example is presented for the polymer estane. A small porosity of only 1.4 percent is required to match the experimental concavity in the Hugoniot data. This type of EOS can also be used to obtain the so-called ''universal'' Hugoniot for liquids.« less
  • The noble gas xenon is a particularly interesting element. At standard pressure xenon is an fcc solid which melts at 161 K and then boils at 165 K, thus displaying a rather narrow liquid range on the phase diagram. On the other hand, under pressure the melting point is significantly higher: 3000 K at 30 GPa. Under shock compression, electronic excitations become important at 40 GPa. Finally, xenon forms stable molecules with fluorine (XeF{sub 2}) suggesting that the electronic structure is significantly more complex than expected for a noble gas. With these reasons in mind, we studied the xenon Hugoniotmore » using DFT/QMD and validated the simulations with multi-Mbar shock compression experiments. The results show that existing equation of state models lack fidelity and so we developed a wide-range free-energy based equation of state using experimental data and results from first-principles simulations.« less
  • The [alpha]-[beta] quartz boundary has been re-determined in a diamond anvil cell by using (1) laser interferometry to observe the transition and (2) the equation of state of H[sub 2]O to calculate transition pressures (P[sub tr]) at five measured transition temperatures (T[sub tr]; up to 852 C). The sample chamber, formed by compressing a 125[mu]m-thick rhenium gasket (with a 500[mu]m-diameter hole) between two diamond anvils, was loaded with a doubly-polished quartz platelet (with its c-axis perpendicular to the polished surfaces), distilled-deionized water, and an air bubble. The laser light reflected from the top and bottom surfaces of quartz produces interferencemore » fringes. Both [alpha] to [beta] and [beta] to [alpha] transitions manifest themselves as collective abrupt motions in the interference fringes resulting from the sudden changes in the refractive indices. After each determination of T[sub tr], the sample was cooled nearly isochorically (less than 0.5% variation in volume), and the density of the fluid medium was obtained from the measured homogenization temperature (accurate to [+-] 0.5 C). P[sub tr] was then calculated from T[sub tr] and the density data by using the equation of state of H[sub 2]O. A least-squares fit of the authors data and the 1 atmosphere datum (573 C) yields T[sub tr](C) = 574.3 + 0.2559 P[sub tr] (MP[sub a]) [minus] 6.406 [times] 10[sup [minus]6]P[sub tr]w. This formulation is in excellent agreement with the results of Coe and Paterson at pressures below 500 MPa, and with Mirwald and Massonne at higher pressures. Furthermore, the extrapolation of their equation almost exactly passes through the [alpha]-quartz, [beta]-quartz, and coesite triple point reported by Mirwald and Massonne at 1,380 [+-] 15 C and 3,440 [+-] 20MPa.« less
  • Abstract not provided.