We present quantum molecular dynamics calculations of thermophysical properties of solid and liquid zirconium in the vicinity of melting. An overview of available experimental data is also presented. We focus on the analysis of thermal expansion, molar enthalpy, resistivity, and normal spectral emissivity of solid and liquid Zr. Possible reasons of discrepancies between the first-principles simulations and experiments are discussed. Our calculations reveal a significant volume change on melting in agreement with electrostatic levitation experiments. Meanwhile, we confirm a low value of enthalpy of fusion obtained in some pulse-heating experiments. Electrical resistivity of solid and liquid Zr is systematically underestimated in our simulations, however, the slope of resistivity temperature dependencies agrees with experiments. Our calculations predict almost constant normal spectral emissivity in liquid Zr.
REFERENCES
1.
E. Y.
Tonkov
and E.
Ponyatovsky
, Phase Transformations of Elements Under High Pressure
(CRC Press
, 2018
).2.
S.
Sikka
, Y.
Vohra
, and R.
Chidambaram
, Prog. Mater. Sci.
27
, 245
(1982
). 3.
J. S.
Pigott
, N.
Velisavljevic
, E. K.
Moss
, D.
Popov
, C.
Park
, J. A. V.
Orman
, N.
Draganic
, Y. K.
Vohra
, and B. T.
Sturtevant
, J. Phys.: Condens. Matter.
32
, 12LT02
(2019
). 4.
A.
Dewaele
, V.
Stutzmann
, J.
Bouchet
, F.
Bottin
, F.
Occelli
, and M.
Mezouar
, Phys. Rev. B
91
, 134108
(2015
). 5.
S.
Anzellini
, F.
Bottin
, J.
Bouchet
, and A.
Dewaele
, Phys. Rev. B
102
, 184105
(2020
). 6.
P.
Parisiades
, F.
Cova
, and G.
Garbarino
, Phys. Rev. B
100
, 054102
(2019
). 7.
O.
Hellman
, I.
Abrikosov
, and S.
Simak
, Phys. Rev. B
84
, 180301
(2011
). 8.
D. W.
Bonnell
, Ph.D. thesis (Rice University, Houston, TX, 1972). 9.
R.
Hixson
and M.
Winkler
, Int. J. Thermophys.
14
, 409
(1993
). 10.
M.
Boivineau
, H.
Colin
, J.
Vermeulen
, and T.
Thévenin
, Int. J. Thermophys.
17
, 1001
(1996
). 11.
W.
Obendrauf
, E.
Kaschnitz
, G.
Pottlacher
, and H.
Jäger
, Int. J. Thermophys.
14
, 417
(1993
). 12.
A.
Seifter
, F.
Sachsenhofer
, S.
Krishnan
, and G.
Pottlacher
, Int. J. Thermophys.
22
, 1537
(2001
). 13.
G. R.
Gathers
, Rep. Prog. Phys.
49
, 341
(1986
). 14.
M.
Boivineau
and G.
Pottlacher
, Int. J. Mater. Product Technol.
26
, 217
(2006
). 15.
W.-K.
Rhim
, S. K.
Chung
, D.
Barber
, K. F.
Man
, G.
Gutt
, A.
Rulison
, and R. E.
Spjut
, Rev. Sci. Instrum.
64
, 2961
(1993
). 16.
T.
Ishikawa
, P.-F.
Paradis
, T.
Itami
, and S.
Yoda
, Meas. Sci. Technol.
16
, 443
(2005
). 17.
R.
Bradshaw
, D.
Schmidt
, J.
Rogers
, K.
Kelton
, and R.
Hyers
, Rev. Sci. Instrum.
76
, 125108
(2005
). 18.
N.
Mauro
and K.
Kelton
, Rev. Sci. Instrum.
82
, 035114
(2011
). 19.
G. W.
Lee
, S.
Jeon
, and D.-H.
Kang
, Cryst. Growth Des.
13
, 1786
(2013
). 20.
P.-F.
Paradis
, T.
Ishikawa
, G.-W.
Lee
, D.
Holland-Moritz
, J.
Brillo
, W.-K.
Rhim
, and J. T.
Okada
, Mater. Sci. Eng.
76
, 1
(2014
). 21.
F.
Millot
, J.-C.
Rifflet
, V.
Sarou-Kanian
, and G.
Wille
, Int. J. Thermophys.
23
, 1185
(2002
). 22.
G.
Wille
, F.
Millot
, and J.
Rifflet
, Int. J. Thermophys.
23
, 1197
(2002
). 23.
I.
Egry
, High Temperatures-High Pressures
32
, 127
(2000
). 24.
G. W.
Lee
, S.
Jeon
, C.
Park
, and D.-H.
Kang
, J. Chem. Thermodyn.
63
, 1
(2013
). 25.
T.
Ishikawa
, P.-F.
Paradis
, and S.
Yoda
, Rev. Sci. Instrum.
72
, 2490
(2001
). 26.
T.
Ishikawa
, P.-F.
Paradis
, T.
Itami
, and S.
Yoda
, J. Chem. Phys.
118
, 7912
(2003
). 27.
E.
Wimmer
, R.
Najafabadi
, G. A.
Young, Jr
, J. D.
Ballard
, T. M.
Angeliu
, J.
Vollmer
, J. J.
Chambers
, H.
Niimi
, J. B.
Shaw
, C.
Freeman
, M.
Christensen
, W.
Wolf
, and P.
Saxe
, J. Phys.: Condens. Matter.
22
, 384215
(2010
). 28.
I.
Schnell
and R. C.
Albers
, J. Phys.: Condens. Matter.
18
, 1483
(2006
). 29.
Y.-J.
Hao
, L.
Zhang
, X.-R.
Chen
, L.-C.
Cai
, Q.
Wu
, and D.
Alfè
, Phys. Rev. B
78
, 134101
(2008
). 30.
Y.-J.
Hao
, L.
Zhang
, X.-R.
Chen
, Y.-H.
Li
, and H.-L.
He
, J. Phys.: Condens. Matter.
20
, 235230
(2008
). 31.
X.
Zhu
, X.
Gao
, H.
Song
, G.
Han
, and D.-Y.
Lin
, Mater. Des.
119
, 30
(2017
). 32.
C.-E.
Hu
, Z.-Y.
Zeng
, L.
Zhang
, X.-R.
Chen
, and L.-C.
Cai
, Comput. Mater. Sci.
50
, 835
(2011
). 33.
S.
Zhang
, X.
Zhang
, Y.
Zhu
, S.
Zhang
, L.
Qi
, and R.
Liu
, Comput. Mater. Sci.
61
, 42
(2012
). 34.
M. I.
Mendelev
, D. J.
Sordelet
, and M. J.
Kramer
, J. Appl. Phys.
102
, 043501
(2007
). 35.
M. I.
Mendelev
and B. S.
Bokstein
, Philos. Mag.
90
, 637
(2010
). 36.
A.
Poty
, J.-M.
Raulot
, H.
Xu
, J.
Bai
, C.
Schuman
, J.-S.
Lecomte
, M.-J.
Philippe
, and C.
Esling
, J. Appl. Phys.
110
, 014905
(2011
). 37.
E.
Zarkadoula
, R.
Devanathan
, W. J.
Weber
, M. A.
Seaton
, I. T.
Todorov
, K.
Nordlund
, M. T.
Dove
, and K.
Trachenko
, J. Appl. Phys.
115
, 083507
(2014
). 38.
H.
Wang
, S.
Yang
, L.
Hu
, and B.
Wei
, Chem. Phys. Lett.
653
, 112
(2016
). 39.
M. I.
Mendelev
and G. J.
Ackland
, Philos. Mag. Lett.
87
, 349
(2007
). 40.
H. S.
Huang
, L. Q.
Ai
, A. C. T.
van Duin
, M.
Chen
, and Y. J.
Lü
, J. Chem. Phys.
151
, 094503
(2019
). 41.
S.
Becker
, E.
Devijver
, R.
Molinier
, and N.
Jakse
, Phys. Rev. B
102
, 104205
(2020
). 42.
H.
Fang
, X.
Hui
, G.
Chen
, R.
Öttking
, Y.
Liu
, J.
Schaefer
, and Z.
Liu
, Comput. Mater. Sci.
43
, 1123
(2008
). 43.
N.
Jakse
and A.
Pasturel
, Phys. Rev. Lett.
91
, 195501
(2003
). 44.
N.
Jakse
, O.
Le Bacq
, and A.
Pasturel
, J. Non-Cryst. Solids
353
, 3684
(2007
). 45.
M.
French
and T. R.
Mattsson
, Phys. Rev. B
90
, 165113
(2014
). 46.
D. V.
Minakov
, M. A.
Paramonov
, and P. R.
Levashov
, AIP Adv.
8
, 125012
(2018
). 47.
D. V.
Minakov
, M. A.
Paramonov
, and P. R.
Levashov
, Phys. Rev. B
103
, 184204
(2021
). 48.
D. V.
Minakov
, M. A.
Paramonov
, and P. R.
Levashov
, Phys. Rev. B
97
, 024205
(2018
). 49.
D. V.
Minakov
, M. A.
Paramonov
, and P. R.
Levashov
, High Temperatures–High Pressures
49
, 211
(2020
). 50.
J.
Clérouin
, P.
Renaudin
, and P.
Noiret
, Phys. Rev. E
77
, 026409
(2008
). 51.
L.
Miljacic
, S.
Demers
, Q.-J.
Hong
, and A.
van de Walle
, Calphad
51
, 133
(2015
). 52.
J.
Clérouin
, P.
Noiret
, V. N.
Korobenko
, and A. D.
Rakhel
, Phys. Rev. B
78
, 224203
(2008
). 53.
N. D.
Mermin
, Phys. Rev.
137
, A1441
(1965
). 54.
G.
Kresse
and J.
Hafner
, Phys. Rev. B
47
, 558
(1993
). 55.
G.
Kresse
and J.
Hafner
, Phys. Rev. B
49
, 14251
(1994
). 56.
G.
Kresse
and J.
Furthmüller
, Phys. Rev. B
54
, 11169
(1996
). 57.
G.
Kresse
and J.
Furthmüller
, Comput. Mater. Sci.
6
, 15
(1996
). 58.
P. E.
Blöchl
, Phys. Rev. B
50
, 17953
(1994
). 59.
J. P.
Perdew
, K.
Burke
, and M.
Ernzerhof
, Phys. Rev. Lett.
77
, 3865
(1996
). 60.
J. P.
Perdew
, K.
Burke
, and M.
Ernzerhof
, Phys. Rev. Lett.
78
, 1396
(1997
). 61.
S.
Nosé
, J. Chem. Phys.
81
, 511
(1984
). 62.
CRC Handbook of Chemistry and Physics, Internet Version 2005, edited by D. R. Lide (CRC Press, Boca Raton, FL, 2005).
63.
A.
Baldereschi
, Phys. Rev. B
7
, 5212
(1973
). 64.
R.
Armiento
and A. E.
Mattsson
, Phys. Rev. B
72
, 085108
(2005
). 65.
D. M.
Ceperley
and B. J.
Alder
, Phys. Rev. Lett.
45
, 566
(1980
). 66.
D. V.
Knyazev
and P. R.
Levashov
, Contrib. Plasma Phys.
59
, 345
(2018
). 67.
M. P.
Desjarlais
, J. D.
Kress
, and L. A.
Collins
, Phys. Rev. E
66
, 025401
(2002
). 68.
D. V.
Knyazev
and P. R.
Levashov
, Comput. Mater. Sci.
79
, 817
(2013
). 69.
P. M.
Kowalski
, S.
Mazevet
, D.
Saumon
, and M.
Challacombe
, Phys. Rev. B
76
, 075112
(2007
). 70.
H. J.
Monkhorst
and J. D.
Pack
, Phys. Rev. B
13
, 5188
(1976
). 71.
J. S.
Toll
, Phys. Rev.
104
, 1760
(1956
). 72.
A.
Peterson
, H.
Kedesdy
, P.
Keck
, and E.
Schwarz
, J. Appl. Phys.
29
, 213
(1958
). 73.
74.
M. A. Maurakh, Trans. Indian Inst. Met.
14
, 209 (1964).75.
D.
Steinberg
, Metall. Mater. Trans. B
5
, 1341
(1974
). 76.
77.
P.-F.
Paradis
and W.-K.
Rhim
, J. Mater. Res.
14
, 3713
(1999
). 78.
H.
Yoo
, C.
Park
, S.
Jeon
, S.
Lee
, and G. W.
Lee
, Metrologia
52
, 677
(2015
). 79.
T.
Ishikawa
, P.-F.
Paradis
, and S.
Yoda
, Rev. Sci. Instrum.
72
, 2490
(2001
). 80.
V. N.
Korobenko
and A. I.
Savvatimskii
, High Temp.
39
, 525
(2001
). 81.
T.
Schenk
, D.
Holland-Moritz
, V.
Simonet
, R.
Bellissent
, and D. M.
Herlach
, Phys. Rev. Lett.
89
, 075507
(2002
). 82.
T. H.
Kim
and K. F.
Kelton
, J. Chem. Phys.
126
, 054513
(2007
). 83.
J.
Hafner
, J. Comput. Chem.
29
, 2044
(2008
). 84.
J.
Harl
and G.
Kresse
, Phys. Rev. Lett.
103
, 056401
(2009
). 85.
Y. S.
Touloukian
, R.
Kirby
, R.
Taylor
, and P.
Desai
, Thermophysical Properties of Matter—The TPRC Data Series. Volume 12. Thermal Expansion Metallic Elements And Alloys
(IFI/Plenum
, New York
, 1975
).86.
T.
Itami
and M.
Shimoji
, J. Phys. F: Met. Phys.
14
, L15
(1984
). 87.
M. W.
Chase
, NIST-JANAF Thermochemical Tables
, 4th ed. (American Institute of Physics for the National Institute of Standards and Technology
, Washington, DC
, 1998
).88.
J.
Arblaster
, Calphad
43
, 32
(2013
). 89.
L. V.
Gurvich
, I. V.
Veits
, and V. A.
Medvedev
, Thermodynamic Properties of Individual Substances. Volume 4
(Nauka
, Moscow
, 1982
) (in Russian).90.
V. N.
Korobenko
, A. I.
Savvatimski
, and K. K.
Sevostyanov
, High Temperatures – High Pressures
33
, 647
(2001
). 91.
C.
Brunner
, C.
Cagran
, A.
Seifter
, and G.
Pottlacher
, AIP Conf. Proc
. 684, 771 (2003). 92.
93.
V.
Korobenko
, M.
Agranat
, S.
Ashitkov
, and A.
Savvatimskiy
, Int. J. Thermophys.
23
, 307
(2002
). 94.
G.
Gathers
, Rep. Prog. Phys.
49
, 341
(1986
). 95.
T. B.
Douglas
and A. C.
Victor
, J. Res. Natl. Bur. Stand.
61
, 13
(1958
). 96.
A.
Cezairliyan
and F.
Righini
, J. Res. Natl. Bur. Stand., Sect. A
78
, 509
(1974
). 97.
I. I.
Petrova
, V. E.
Peletskii
, and B. N.
Samsonov
, High Temp.
38
, 560
(2000
). 98.
M.
Rösner-Kuhn
, K.
Drewes
, H.
Franz
, and M. G.
Frohberg
, J. Alloys Compd.
316
, 175
(2001
). 99.
G. V.
Belov
, S. A.
Dyachkov
, P. R.
Levashov
, I. V.
Lomonosov
, D. V.
Minakov
, I. V.
Morozov
, M. A.
Sineva
, and V. N.
Smirnov
, J. Phys.: Conf. Ser.
946
, 012120
(2018
). 100.
F.
Jaeger
and W.
Veenstra
, Recl. Trav. Chim. Pays-Bas
53
, 677
(1934
). 101.
J.
Coughlin
and E.
King
, J. Am. Chem. Soc.
72
, 2262
(1950
). 102.
G. B.
Skinner
, J. W.
Edwards
, and H. L.
Johnston
, J. Am. Chem. Soc.
73
, 174
(1951
). 103.
104.
R.
Redmond
and J.
Lones
, “Enthalpies and heat capacities of stainless steel (316), zirconium, and lithium at elevated temperatures,” Technical Report (Oak Ridge National Laboratory, 1952).105.
I.
Fieldhouse
and J.
Lang
, “Armour research foundation report,” Technical Report No. WADD-TR-60-904, 1961.106.
107.
J.
Qin
, M.
Rösner-Kuhn
, K.
Drewes
, U.
Thiedemann
, G.
Kuppermann
, B.
Camin
, R.
Blume
, and M. G.
Frohberg
, High Temp. Mater. Sci.
37
, 129
(1997
).108.
V.
Elyutin
, M.
Maurakh
, and G.
Sverdlov
, Izv. Vyssh. Ucheb. Zaved., Tsvet. Met.
2
, 87
–88
(1967
).109.
H. B.
Radousky
, M. R.
Armstrong
, R. A.
Austin
, E.
Stavrou
, S.
Brown
, A. A.
Chernov
, A. E.
Gleason
, E.
Granados
, P.
Grivickas
, N.
Holtgrewe
, H. J.
Lee
, S. S.
Lobanov
, B.
Nagler
, I.
Nam
, V.
Prakapenka
, C.
Prescher
, P.
Walter
, A. F.
Goncharov
, and J. L.
Belof
, Phys. Rev. Res.
2
, 013192
(2020
). 110.
J. S.
Pigott
, N.
Velisavljevic
, E. K.
Moss
, N.
Draganic
, M. K.
Jacobsen
, Y.
Meng
, R.
Hrubiak
, and B. T.
Sturtevant
, J. Phys.: Condens. Matter.
32
, 355402
(2020
). 111.
D.
Smirnova
, S.
Starikov
, and I.
Gordeev
, Comput. Mater. Sci.
152
, 51
(2018
). 112.
V.
Stutzmann
, A.
Dewaele
, J.
Bouchet
, F. M. C.
Bottin
, and M.
Mezouar
, Phys. Rev. B
92
, 224110
(2015
). 113.
P. D.
Desai
, H. M.
James
, and C. Y.
Ho
, J. Phys. Chem. Ref. Data
13
, 1097
(1984
). 114.
V. E.
Peletskii
and E. A.
Bel’skaya
, Elektricheskoe Soprotivlenie Tugoplavkikh Metallov (Electrical Resistance of Refractory Metals)
(Energoizdat
, Moscow
, 1981
).115.
N. D.
Milošević
and K. D.
Maglić
, Int. J. Thermophys.
27
, 1140
(2006
). 116.
I. I.
Petrova
, V. E.
Peletskii
, and B. N.
Samsonov
, High Temp.
38
, 560
(2000
). 117.
118.
S. C.
Furman
and P. A.
McManus
, “Metal-water reactions: Ix. the kinetics of metal-water reactions- feasibility study of some new techniques,” Technical Report GEAP-3338 (General Electric Co. Vallecitos Atomic Laboratory, Pleasanton, CA, 1960).119.
D.
Cubicciotti
, J. Am. Chem. Soc.
73
, 2032
(1951
). 120.
R. K.
Koch
, J.
Hoffman
, and R. A.
Beall
, Liquid State Spectral Emissivities of Titanium, Vanadium, Zirconium, Molybdenum, and Platinum in an Electron-Beam Furnace
(U.S. Department of Interior, Bureau of Mines
, 1973
), Vol. 7743.121.
C.
Cagran
, C.
Brunner
, A.
Seifter
, and G.
Pottlacher
, High Temp. High Pressures
34
, 669
(2002
). 122.
S.
Krishnan
, C. D.
Anderson
, and P. C.
Nordine
, Phys. Rev. B
49
, 3161
(1994
). 123.
A.
Cezairliyan
, J.
McClure
, and A.
Miiller
, Int. J. Thermophys.
15
, 993
(1994
). 124.
J. A.
Coffman
, G. M.
Kibler
, T. F.
Lyon
, and B. D.
Acchione
, “Carbonization of plastics and refractory materials research,” Technical Report WADD-TR-60-646 (Pt.II); AD-2979 (General Electric Co. Flight Propulsion Laboratory Department, Cincinnati, OH, 1961).125.
Y. V.
Petrov
, K. P.
Migdal
, N.
Inogamov
, and S. I.
Anisimov
, JETP Lett.
104
, 431
(2016
). 126.
M. P.
Desjarlais
, C. R.
Scullard
, L. X.
Benedict
, H. D.
Whitley
, and R.
Redmer
, Phys. Rev. E
95
, 033203
(2017
). 127.
128.
C.
Ronchi
, J. P.
Hiernaut
, and G. J.
Hyland
, Metrologia
29
, 261
(1992
). 129.
D. N.
Baria
and R. G.
Bautista
, Metall. Trans.
5
, 555
(1974
). 130.
A.
Cezairliyan
and F.
Righini
, J. Res. Natl. Bur. Stand., Sect. A
78A
, 509
(1974
). 131.
A. I.
Savvatimskii
and V. N.
Korobenko
, High-Temperature Properties of Metals of Atomic Power Engineering (Zirconium, Hafnium, and Iron in Melting and Liquid State)
(Izd. dom MEI
, 2012
) (in Russian).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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