A new equation of state (EoS) is presented for solid argon. The EoS is based on the quasi-harmonic approximation and formulated in terms of the Helmholtz energy, with temperature and molar volume as independent variables. To ensure high accuracy over a wide range of pressures, the static energy is represented semi-analytically by a Buckingham potential with three-body corrections. The vibrational modes are represented by Debye and Einstein contributions, and the EoS includes an anharmonic correction. A comprehensive collection of available experimental data has been used in the parameter optimization, including pressure and volume measurements along the co-existence curves, heat capacities, thermal expansivities and isothermal compressibilites. The EoS reproduces the molar volumes along the sublimation coexistence curve within an estimated uncertainty of 0.03%. For the heat capacity, the uncertainty is estimated to 1% in the range 20–50 K, 2% at higher temperatures, and 6% at lower temperatures. The isentropic and isothermal compressibilities have estimated uncertainties of 4% and 3%. For the thermal expansivity, the EoS has an estimated uncertainty of 2% above, and 5% below 30 K. For the pressure along the phase coexistence curves, the EoS has an estimated uncertainty of 0.4% for melting and 5% for sublimation. For the calculation of pressure as function of temperature and molar volume, the average relative deviation with respect to all available data is 5%. The EoS is valid up to pressures of 16 GPa and temperatures of 300 K, yet extrapolates well at temperatures beyond this range. The EoS represents the coexistence of solid argon in argon–hydrogen and argon–helium fluid mixtures nearly within the experimental uncertainty, provided that the EoS used to represent the fluid phase is sufficiently accurate.
12. References
1.
R.
Agrawal
, D. W.
Woodward
, and T. F.
Yee
, “Argon production from air distillation: Use of a heat pump in a ternary distillation with a side rectifier
,” Gas Sep. Purif.
8
, 37
–43
(1994
).2.
G. E.
Kopchok
, R. A.
White
, G. H.
White
, R.
Fujitani
, J.
Vlasak
, L.
Dykhovsky
, and W. S.
Grundfest
, “CO2 and argon laser vascular welding: Acute histologic and thermodynamic comparison
,” Lasers Surg. Med.
8
, 584
–588
(1988
).3.
D.
Prabhakaran
, A. I.
Coldea
, A. T.
Boothroyd
, and S.
Blundell
, “Growth of large La1−χSrχMnO3 single crystals under argon pressure by the floating-zone technique
,” J. Cryst. Growth
237
, 806
–809
(2002
).4.
A.
Friedland
and S. W.
Li
, “Understanding the energy resolution of liquid argon neutrino detectors
,” Phys. Rev. D
99
, 036009
(2019
).5.
P. M.
Hewitt
, J.
Zhao
, J.
Akhter
, and D. L.
Morris
, “A comparative laboratory study of liquid nitrogen and argon gas cryosurgery systems
,” Cryobiology
35
, 303
–308
(1997
).6.
E. R.
Dobbs
and G. O.
Jones
, “Theory and properties of solid argon
,” Rep. Prog. Phys.
20
, 516
(1957
).7.
B. F.
Figgins
, “The specific heats of solid argon and an equimolar argon-krypton mixture
,” Proc. Phys. Soc.
76
, 732
(1960
).8.
O. G.
Peterson
, D. N.
Batchelder
, and R. O.
Simmons
, “Measurements of x-ray lattice constant, thermal expansivity, and isothermal compressibility of argon crystals
,” Phys. Rev.
150
, 703
(1966
).9.
R. K.
Crawford
, M. L.
Klein
, and J. A.
Venables
, Rare Gas Solids
(Academic Press
, London
, 1977
).10.
A.
Dewaele
, A. D.
Rosa
, N.
Guignot
, D.
Andrault
, J. E. F.
Rodrigues
, and G.
Garbarino
, “Stability and equation of state of face-centered cubic and hexagonal close packed phases of argon under pressure
,” Sci. Rep.
11
, 15192
(2021
).11.
M.
Grimsditch
, P.
Loubeyre
, and A.
Polian
, “Brillouin scattering and three-body forces in argon at high pressures
,” Phys. Rev. B
33
, 7192
(1986
).12.
C.
Tian
, F.
Liu
, L.
Cai
, H.
Yuan
, H.
Chen
, and M.
Zhong
, “Ab initio calculations of many-body interactions for compressed solid argon
,” J. Chem. Phys.
143
, 174506
(2015
).13.
T.
Iitaka
and T.
Ebisuzaki
, “First-principles calculation of elastic properties of solid argon at high pressures
,” Phys. Rev. B
65
, 012103
(2001
).14.
M.
Ross
, H. K.
Mao
, P. M.
Bell
, and J. A.
Xu
, “The equation of state of dense argon: A comparison of shock and static studies
,” J. Chem. Phys.
85
, 1028
–1033
(1986
).15.
M. S.
Anderson
and C. A.
Swenson
, “Experimental equations of state for the rare gas solids
,” J. Phys. Chem. Solids
36
, 145
–162
(1975
).16.
J. A.
Barker
, “High pressure equation of state for solid argon from interatomic potentials
,” J. Chem. Phys.
86
, 1509
–1511
(1987
).17.
N.
Van Nghia
, H. K.
Hieu
, and D. D.
Phuong
, “Equation-of-state and melting curve of solid neon and argon up to 100 GPa
,” Vacuum
196
, 110725
(2022
).18.
P.
Schwerdtfeger
, K. G.
Steenbergen
, and E.
Pahl
, “Relativistic coupled-cluster and density-functional studies of argon at high pressure
,” Phys. Rev. B
95
, 214116
(2017
).19.
S.
Yang
and X.
Ren
, “Phase stability of the argon crystal: First-principles study based on random phase approximation plus renormalized single excitation corrections
,” New J. Phys.
24
, 033049
(2022
).20.
J. P. M.
Trusler
, “Equation of state for solid phase I of carbon dioxide valid for temperatures up to 800 K and pressures up to 12 GPa
,” J. Phys. Chem. Ref. Data
40
, 043105
(2011
).21.
A.
Jäger
and R.
Span
, “Equation of state for solid carbon dioxide based on the Gibbs free energy
,” J. Chem. Eng. Data
57
, 590
–597
(2012
).22.
X.
Xiao
, J. P. M.
Trusler
, X.
Yang
, M.
Thol
, S. Z. S.
Al Ghafri
, D.
Rowland
, and E. F.
May
, “Equation of state for solid benzene valid for temperatures up to 470 K and pressures up to 1800 MPa
,” J. Phys. Chem. Ref. Data
50
, 043104
(2021
).23.
P.
Stringari
, M.
Campestrini
, and S.
Hoceini
, “Gibbs free energy equation of state for phase I of solid benzene from 15 to 488 K and up to 1165 MPa
,” J. Chem. Eng. Data
66
, 4603
–4617
(2021
).24.
R.
Feistel
and W.
Wagner
, “A new equation of state for H2O ice Ih
,” J. Phys. Chem. Ref. Data
35
, 1021
–1047
(2006
).25.
S. Z. S.
Al Ghafri
, S.
Munro
, U.
Cardella
, T.
Funke
, W.
Notardonato
, J. P. M.
Trusler
, J.
Leachman
, R.
Span
, S.
Kamiya
, G.
Pearce
et al, “Hydrogen liquefaction: A review of the fundamental physics, engineering practice and future opportunities
,” Energy Environ. Sci.
15
, 2690
–2731
(2022
).26.
A.
Yokozeki
, “Analytical equation of state for solid–liquid–vapor phases
,” Int. J. Thermophys.
24
, 589
–620
(2003
).27.
A.
Yokozeki
, “Phase equilibria of benzene–cyclohexane binary mixtures using a solid–liquid–vapor equation-of-state
,” Appl. Energy
81
, 334
–349
(2005
).28.
M.
Campestrini
, P.
Stringari
, and P.
Arpentinier
, “Solid–liquid equilibrium prediction for binary mixtures of Ar, O2, N2, Kr, Xe, and CH4 using the LJ-SLV-EoS
,” Fluid Phase Equilib.
379
, 139
–147
(2014
).29.
C.
Mo
, G.
Zhang
, Z.
Zhang
, D.
Yan
, and S.
Yang
, “A modified solid–liquid–gas phase equation of state
,” ACS Omega
7
, 9322
–9332
(2022
).30.
H. S.
Kang
, T.
Ree
, and F. H.
Ree
, “A perturbation theory of classical solids
,” J. Chem. Phys.
84
, 4547
–4557
(1986
).31.
N. S.
Ramrattan
, “Simulation and theoretical perspectives of the phase behaviour of solids, liquids and gases using the Mie family of intermolecular potentials
,” Ph.D. thesis, Imperial College London
, London
, 2013
.32.
P.
Stringari
, M.
Campestrini
, S.
Hoceini
, and D.
Atig
, “Gibbs free energy equation of state for solid methane from 21 to 300 K and up to 5000 MPa
,” J. Chem. Eng. Data
66
, 1157
–1171
(2021
).33.
E.
Brosh
, R. Z.
Shneck
, and G.
Makov
, “Explicit Gibbs free energy equation of state for solids
,” J. Phys. Chem. Solids
69
, 1912
–1922
(2008
).34.
A.
Dewaele
, F.
Datchi
, P.
Loubeyre
, and M.
Mezouar
, “High pressure–high temperature equations of state of neon and diamond
,” Phys. Rev. B
77
, 094106
(2008
).35.
K.
Asaumi
, “High-pressure x-ray diffraction study of solid xenon and its equation of state in relation to metallization transition
,” Phys. Rev. B
29
, 7026
(1984
).36.
P.
Loubeyre
, R.
LeToullec
, D.
Hausermann
, M.
Hanfland
, R. J.
Hemley
, H. K.
Mao
, and L. W.
Finger
, “X-ray diffraction and equation of state of hydrogen at megabar pressures
,” Nature
383
, 702
–704
(1996
).37.
M. T.
Dove
, Introduction to Lattice Dynamics
(Cambridge University Press
, Cambridge
, 1993
), Vol. 4
.38.
P. I.
Dorogokupets
and A. R.
Oganov
, “Ruby, metals, and MgO as alternative pressure scales: A semiempirical description of shock-wave, ultrasonic, x-ray, and thermochemical data at high temperatures and pressures
,” Phys. Rev. B
75
, 024115
(2007
).39.
P. I.
Dorogokupets
and A.
Dewaele
, “Equations of state of MgO, Au, Pt, NaCl-B1, and NaCl-B2: Internally consistent high-temperature pressure scales
,” High Pressure Res.
27
, 431
–446
(2007
).40.
F.
Birch
, “Elasticity and constitution of the Earth’s interior
,” in Elastic Properties and Equations of State
(American Geophysical Union
, 1988
), Vol. 26
, pp. 31
–90
.41.
F. D.
Stacey
, B. J.
Brennan
, and R. D.
Irvine
, “Finite strain theories and comparisons with seismological data
,” Geophys. Surv.
4
, 189
–232
(1981
).42.
J.-P.
Poirier
and A.
Tarantola
, “A logarithmic equation of state
,” Phys. Earth Planet. Inter.
109
, 1
–8
(1998
).43.
P.
Schwerdtfeger
and A.
Hermann
, “Equation of state for solid neon from quantum theory
,” Phys. Rev. B
80
, 064106
(2009
).44.
P.
Schwerdtfeger
, A.
Burrows
, and O. R.
Smits
, “The Lennard-Jones potential revisited: Analytical expressions for vibrational effects in cubic and hexagonal close-packed lattices
,” J. Phys. Chem. A
125
, 3037
–3057
(2021
).45.
A.
Burrows
, S.
Cooper
, E.
Pahl
, and P.
Schwerdtfeger
, “Analytical methods for fast converging lattice sums for cubic and hexagonal close-packed structures
,” J. Math. Phys.
61
, 123503
(2020
).46.
C.
Cervinka
, M.
Fulem
, R. P.
Stoffel
, and R.
Dronskowski
, “Thermodynamic properties of molecular crystals calculated within the quasi-harmonic approximation
,” J. Phys. Chem. A
120
, 2022
–2034
(2016
).47.
A.
Aasen
, M.
Hammer
, Å.
Ervik
, E. A.
Müller
, and Ø.
Wilhelmsen
, “Equation of state and force fields for Feynman–Hibbs-corrected Mie fluids. I. Application to pure helium, neon, hydrogen, and deuterium
,” J. Chem. Phys.
151
, 064508
(2019
).48.
A.
Aasen
, M.
Hammer
, E. A.
Müller
, and Ø.
Wilhelmsen
, “Equation of state and force fields for Feynman–Hibbs-corrected Mie fluids. II. Application to mixtures of helium, neon, hydrogen, and deuterium
,” J. Chem. Phys.
152
, 074507
(2020
).49.
A.
Aasen
, M.
Hammer
, S.
Lasala
, J.-N.
Jaubert
, and Ø.
Wilhelmsen
, “Accurate quantum-corrected cubic equations of state for helium, neon, hydrogen, deuterium and their mixtures
,” Fluid Phase Equilib.
524
, 112790
(2020
).50.
A.
Otero-de-la Roza
, D.
Abbasi-Pérez
, and V.
Luaña
, “Gibbs2: A new version of the quasiharmonic model code. II. Models for solid-state thermodynamics, features and implementation
,” Comput. Phys. Commun.
182
, 2232
–2248
(2011
).51.
S.
Stølen
and T.
Grande
, Chemical Thermodynamics of Materials: Macroscopic and Microscopic Aspects
(John Wiley & Sons
, Chichester
, 2004
).52.
L.
Finegold
and N. E.
Phillips
, “Low-temperature heat capacities of solid argon and krypton
,” Phys. Rev.
177
, 1383
(1969
).53.
R. H.
Beaumont
, H.
Chihara
, and J. A.
Morrison
, “Thermodynamic properties of krypton. Vibrational and other properties of solid argon and solid krypton
,” Proc. Phys. Soc.
78
, 1462
(1961
).54.
V. A.
Rabinovich
, A.
Vasserman
, V.
Nedostup
, and L. S.
Veksler
, Thermophysical Properties of Neon, Argon, Krypton, and Xenon
(Hemisphere Publishing Corporation
, Washington
, 1988
), Vol. 10
.55.
P.
Vinet
, J. H.
Rose
, J.
Ferrante
, and J. R.
Smith
, “Universal features of the equation of state of solids
,” J. Phys.: Condens. Matter
1
, 1941
(1989
).56.
P.
Bose Roy
and S.
Bose Roy
, “Applicability of isothermal three-parameter equations of state of solids—A reappraisal
,” J. Phys.: Condens. Matter
17
, 6193
(2005
).57.
B.
Jäger
, R.
Hellmann
, E.
Bich
, and E.
Vogel
, “Ab initio virial equation of state for argon using a new nonadditive three-body potential
,” J. Chem. Phys.
135
, 084308
(2011
).58.
J.
Lang
, M.
Przybytek
, and M.
Lesiuk
, “Thermophysical properties of argon gas from improved two-body interaction potential
,” Phys. Rev. A
109
, 052803
(2024
).59.
G.
Marcelli
and R. J.
Sadus
, “Molecular simulation of the phase behavior of noble gases using accurate two-body and three-body intermolecular potentials
,” J. Chem. Phys.
111
, 1533
–1540
(1999
).60.
G.
Marcelli
and R. J.
Sadus
, “A link between the two-body and three-body interaction energies of fluids from molecular simulation
,” J. Chem. Phys.
112
, 6382
–6385
(2000
).61.
P. J.
Walker
, T.
Zhao
, A. J.
Haslam
, and G.
Jackson
, “Ab initio development of generalized Lennard-Jones (Mie) force fields for predictions of thermodynamic properties in advanced molecular-based SAFT equations of state
,” J. Chem. Phys.
156
, 154106
(2022
).62.
A. R.
Oganov
and P. I.
Dorogokupets
, “Intrinsic anharmonicity in equations of state and thermodynamics of solids
,” J. Phys.: Condens. Matter
16
, 1351
(2004
).63.
J. A.
Nelder
and R.
Mead
, “A simplex method for function minimization
,” Comput. J.
7
, 308
–313
(1965
).64.
P.
Virtanen
, R.
Gommers
, T. E.
Oliphant
, M.
Haberland
, T.
Reddy
, D.
Cournapeau
, E.
Burovski
, P.
Peterson
, W.
Weckesser
, J.
Bright
et al, “SciPy 1.0: Fundamental algorithms for scientific computing in Python
,” Nat. Methods
17
, 261
–272
(2020
).65.
P.
Flubacher
, A. J.
Leadbetter
, and J. A.
Morrison
, “A low temperature adiabatic calorimeter for condensed substances. Thermodynamic properties of argon
,” Proc. Phys. Soc.
78
, 1449
(1961
).66.
C. R.
Tilford
and C. A.
Swenson
, “Thermal expansions of solid argon, krypton, and xenon above 1 K
,” Phys. Rev. B
5
, 719
(1972
).67.
W. H.
Hardy
, R. K.
Crawford
, and W. B.
Daniels
, “Experimental determination of the P–T melting curve of argon
,” J. Chem. Phys.
54
, 1005
–1010
(1971
).68.
V. M.
Cheng
, W. B.
Daniels
, and R. K.
Crawford
, “Molar volume of argon along the melting curve up to 10 kbar
,” Phys. Lett. A
43
, 109
–110
(1973
).69.
R. K.
Crawford
and W. B.
Daniels
, “Melting in argon at high temperatures
,” Phys. Rev. Lett.
21
, 367
(1968
).70.
C. W.
Leming
and G. L.
Pollack
, “Sublimation pressures of solid Ar, Kr, and Xe
,” Phys. Rev. B
2
, 3323
(1970
).71.
H. H.
Chen
, C. C.
Lim
, and R. A.
Aziz
, “The enthalpies of sublimation and internal energies of solid argon, krypton, and xenon determined from vapor pressures
,” J. Chem. Thermodyn.
10
, 649
–659
(1978
).72.
L. A.
Schwalbe
, R. K.
Crawford
, H. H.
Chen
, and R. A.
Aziz
, “Thermodynamic consistency of vapor pressure and calorimetric data for argon, krypton, and xenon
,” J. Chem. Phys.
66
, 4493
–4502
(1977
).73.
G. K.
Horton
, “Ideal rare-gas crystals
,” Am. J. Phys.
36
, 93
–119
(1968
).74.
C.
Tegeler
, R.
Span
, and W.
Wagner
, “A new equation of state for argon covering the fluid region for temperatures from the melting line to 700 K at pressures up to 1000 MPa
,” J. Phys. Chem. Ref. Data
28
, 779
–850
(1999
).75.
A. G. M.
Ferreira
and L. Q.
Lobo
, “The sublimation of argon, krypton, and xenon
,” J. Chem. Thermodyn.
40
, 1621
–1626
(2008
).76.
A. T.
Macrander
, “Constant-volume x-ray study of solid argon and solid krypton
,” Phys. Rev. B
21
, 2549
(1980
).77.
W. F.
Lewis
, D.
Benson
, R. K.
Crawford
, and W. B.
Daniels
, “Isochoric measurement of the equation of state of solid argon at high pressure
,” J. Phys. Chem. Solids
35
, 383
–391
(1974
).78.
L. W.
Finger
, R. M.
Hazen
, G.
Zou
, H. K.
Mao
, and P. M.
Bell
, “Structure and compression of crystalline argon and neon at high pressure and room temperature
,” Appl. Phys. Lett.
39
, 892
–894
(1981
).79.
C. S.
Barrett
and L.
Meyer
, “X-ray diffraction study of solid argon
,” J. Chem. Phys.
41
, 1078
–1081
(1964
).80.
Y.
Fujii
, N. A.
Lurie
, R.
Pynn
, and G.
Shirane
, “Inelastic neutron scattering from solid 36Ar
,” Phys. Rev. B
10
, 3647
(1974
).81.
L. A.
Schwalbe
and R. W.
Wilkins
, “High-temperature thermal expansion characteristics of solid argon and krypton
,” J. Chem. Phys.
72
, 3130
–3133
(1980
).82.
B. L.
Smith
and C. J.
Pings
, “Optical determination of the compressibility of solid argon
,” J. Chem. Phys.
38
, 825
–827
(1963
).83.
A. O.
Urvas
, D. L.
Losee
, and R. O.
Simmons
, “The compressibility of krypton, argon, and other noble gas solids
,” J. Phys. Chem. Solids
28
, 2269
–2281
(1967
).84.
S.
Gewurtz
, H.
Kiefte
, D.
Landheer
, R. A.
McLaren
, and B. P.
Stoicheff
, “Elastic constants of argon and neon by Brillouin scattering from single crystals near their triple points
,” Phys. Rev. Lett.
29
, 1454
(1972
).85.
G. J.
Keeler
and D. N.
Batchelder
, “Measurement of the elastic constants of argon from 3 to 77 degrees K
,” J. Phys. C: Solid State Phys.
3
, 510
(1970
).86.
V. G.
Manzhelii
, V. G.
Gavrilko
, and E. I.
Voitovich
, “Thermal expansion of solidified rare gases
,” Sov. Phys. Solid State
9
, 1157
(1967
).87.
M.
Gsänger
, H.
Egger
, and E.
Lüscher
, “Determination of the elastic constants of argon
,” Phys. Lett. A
27
, 695
–696
(1968
).88.
B.
Dorner
and H.
Egger
, “Elastic constants of argon at 4.2 °K from phonon measurements
,” Phys. Status Solidi B
43
, 611
–617
(1971
).89.
D. N.
Batchelder
, M. F.
Collins
, B. C. G.
Haywood
, and G. R.
Sidey
, “Lattice dynamics of argon at 4 degrees K
,” J. Phys. C: Solid State Phys.
3
, 249
(1970
).90.
H. R.
Moeller
and C. F.
Squire
, “Ultrasonic velocities in solid argon
,” Phys. Rev.
151
, 689
(1966
).91.
K.
Clusius
, “Atomwärmen und schmelzwärmen von neon, argon, und krypton
,” Z. Phys. Chem.
31B
, 459
–474
(1936
).92.
I. S.
Grigoriev
and E. Z.
Meilikhov
, Handbook of Physical Quantities
(CRC Press
, Boca Raton, FL
, 1997
).93.
V. G.
Manzhelii
, E. A.
Kosobutskaya
, V. V.
Sumarokov
, A. N.
Aleksandrovskii
, Y. A.
Freiman
, V. A.
Popov
, and V. A.
Kostantinov
, “Hindered rotation of linear molecules in atomic cryocrystals and thermal properties of solutions
,” Sov. J. Low Temp. Phys.
12
, 86
–97
(1986
).94.
H. H.
Chen
, R. A.
Aziz
, and C. C.
Lim
, “On the vapor pressure of solid argon
,” Can. J. Phys.
49
, 1569
–1581
(1971
).95.
G.
Boato
, G.
Scoles
, and M. E.
Vallauri
, “Vapour pressure of isotopic solids by a steady flow method: Argon between 72 °K and triple point
,” Il Nuovo Cimento
23
, 1041
–1053
(1962
).96.
M. W.
Lee
, S.
Fuks
, and J.
Bigeleisen
, “Vapor pressures of 36Ar and 40Ar. Intermolecular forces in solid and liquid argon
,” J. Chem. Phys.
53
, 4066
–4076
(1970
).97.
H.
Shakeel
, H.
Wei
, and J. M.
Pomeroy
, “Measurements of enthalpy of sublimation of Ne, N2, O2, Ar, CO2, Kr, Xe, and H2O using a double paddle oscillator
,” J. Chem. Thermodyn.
118
, 127
–138
(2018
).98.
J.
Ancsin
, “Studies of phase changes in argon
,” Metrologia
9
, 147
(1973
).99.
W.
van Witzenburg
and J. C.
Stryland
, “Density measurements of compressed solid and liquid argon
,” Can. J. Phys.
46
, 811
–816
(1968
).100.
S. M.
Stishov
, “The thermodynamics of melting of simple substances
,” Sov. Phys. Usp.
17
, 625
(1975
).101.
P. W.
Bridgman
, “The melting parameters of nitrogen and argon under pressure, and the nature of the melting curve
,” Phys. Rev.
46
, 930
–933
(1934
).102.
A.
Michels
and C.
Prins
, “The melting lines of argon, krypton and xenon up to 1500 atm; representation of the results by a law of corresponding states
,” Physica
28
, 101
–116
(1962
).103.
H.
Shimizu
, H.
Tashiro
, T.
Kume
, and S.
Sasaki
, “High-pressure elastic properties of solid argon to 70 GPa
,” Phys. Rev. Lett.
86
, 4568
(2001
).104.
R. W.
Wilkins
, “Low-temperature bulk-modulus of solid argon
,” Ph.D. thesis, University of Illinois at Urbana-Champaign
, 1973
.105.
R. D.
Dick
, R. H.
Warnes
, and J.
Skalyo
, Jr., “Shock compression of solid argon
,” J. Chem. Phys.
53
, 1648
–1651
(1970
).106.
J. W.
Stewart
, “Compression of solidified gases to 20 000 kg/cm2 at low temperature
,” J. Phys. Chem. Solids
1
, 146
–158
(1956
).107.
S.
Ono
, “Fate of subducted argon in the deep mantle
,” Sci. Rep.
10
, 1393
(2020
).108.
C.-S.
Zha
, R.
Boehler
, D. A.
Young
, and M.
Ross
, “The argon melting curve to very high pressures
,” J. Chem. Phys.
85
, 1034
–1036
(1986
).109.
F.
Datchi
, P.
Loubeyre
, and R.
LeToullec
, “Extended and accurate determination of the melting curves of argon, helium, ice (H2O), and hydrogen (H2)
,” Phys. Rev. B
61
, 6535
(2000
).110.
J. W.
Leachman
, R. T.
Jacobsen
, S. G.
Penoncello
, and E. W.
Lemmon
, “Fundamental equations of state for parahydrogen, normal hydrogen, and orthohydrogen
,” J. Phys. Chem. Ref. Data
38
, 721
(2009
).111.
D. O.
Ortiz Vega
, K. R.
Hall
, J. C.
Holste
, A. H.
Harvey
, and E. W.
Lemmon
, “An equation of state for the thermodynamic properties of helium
,” Technical Report No. NISTIR 8474
, 2023
, https://doi.org/10.6028/NIST.IR.8474.112.
R.
Beckmüller
, I. H.
Bell
, M.
Thol
, E. W.
Lemmon
, and R.
Span
, “New fundamental equations of state for binary hydrogen mixtures containing argon, helium, and neon
,” Cryogenics
140
, 103817
(2024
).113.
J.
Tkaczuk
, I. H.
Bell
, E. W.
Lemmon
, N.
Luchier
, and F.
Millet
, “Equations of state for the thermodynamic properties of binary mixtures for helium-4, neon, and argon
,” J. Phys. Chem. Ref. Data
49
, 023101
(2020
).114.
D.
Augood
, “The separation of HD and H2 by absorptive fractionation
,” Trans. Inst. Chem. Eng.
35
, 394
–408
(1957
).115.
J. C. G.
Calado
and W. B.
Streett
, “Liquid–vapor equilibrium in the system H2-Ar at temperatures from 83 to 141 K and pressures to 52 MPa
,” Fluid Phase Equilib.
2
, 275
–282
(1979
).116.
J.
Mullins
and W.
Ziegler
, “Phase equilibria in the argon-helium and argon-hydrogen systems from 68 to 108 K and pressures to 120 atmospheres
,” in Proceedings of the Int. Adv. Cryog. Eng. Conf.
(McGraw-Hill, New York
, 1965
), Vol. 10
, pp. 171
–181
.You do not currently have access to this content.
