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The Na–H system: from first-principles calculations to thermodynamic modeling

  • Caian Qiu , Susanne M. Opalka EMAIL logo , Gregory B. Olson and Donald L. Anton
Published/Copyright: January 11, 2022
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International Journal of Materials Research
From the journal International Journal of Materials Research Volume 97 Issue 6

Abstract

The Na–H system thermodynamic properties were assessed using Gibbs free energy model parameters obtained from best fit optimizations to combined experimental and first-principles predicted data. The first-principles finite temperature thermodynamic property predictions, based upon density functional theory ground state minimizations and direct method lattice dynamics, were used to supplement the Na–H dataset wherever experimental information was unavailable or unattainable. The predictions proved to be important for extending the evaluation of the heat capacity of the stable NaH phase to cover the complete 0 – 2000 K temperature range. The predicted thermodynamic properties of the hypothetical NaH3 end-member representing complete interstitial H substitution in solid body-centered cubic Na, provided a physical basis for modeling H dissolution in the Na lattice. The modeling also showed satisfactory agreement with experimental measurements of NaH enthalpies of formation, NaH decomposition pressures, and H solubility in liquid Na.

Keywords: Thermodynamics; Phase diagram; First-principles; Density functional theory; Direct method lattice dynamics
Susanne M. Opalka, Ph.D. United Technologies Research Center, 411 Silver Lane, MS 129-30 East Hartford, CT, USA 06108 Tel.: +1 860 610 7195 Fax: +1 860 610 1661

  1. This work was financially supported by the U.S. Department of Energy under contract DE–FC36–02AL67610, managed by United Technology Research Center, East Hartford, Connecticut, USA. S. M. Opalka gratefully acknowledges valuable discussions with Paul Saxe of Materials Design, Inc., Taos, New Mexico.

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Appendix

Summary of Thermodynamic Parameters Describing the Na–H System

Values are given in SI units (Joule, mole, Kelvin, and Pa) and correspond to one mole of formula units of the phases. The parameters marked with an asterisk (*) were evaluated in the present work. The parameters for elemental Na are from Ref. [20]. The parameters for the gas phase are from Ref. [17].

Liquid with formula (Na, H)

°GNaliq=+2581.491−6.951225T−2.67339×10−18T7                + GHSERNA for 298.15 K<T<371.00 K            =+2609.079−7.029303T−1.60713×1023T−9                + GHSERNA for 371.00 K<T<2300.00 K
(*) °GHliq=8035+25T+2Tln(T)+0.5×F10784 T
(*) 0LH,Naliq=−70264+45.2458T
(*) 1LH,Naliq=−56577+21.8825T

bcc_A2 with formula (Na)1(H, Va)3

°GNa:Hbcc=215965+3RTln[exp(0.5×215/T)                   −exp(−0.5×215/T)]−0.0095113T2

for 0 K < T < 298.15 K (*)

= 206 754 + 258.2187T– 42.90288T ln T– 0.004047T2 + 1.889 × 10 –7T3 + 696 986/T

for 298.15 K < T < 2000 K (*)

°GNa:Vabcc= GHSERNA 

NaH with formula (Na)1(H)1

°GNaa:HNaH=−66593+3RTln[exp(0.5×268/T)                      −exp(−0.5×268/T)]−0.0188755T2

for 0 K < T < 298.15 K (*)

= – 75 768 + 293.7188T–48.6935T ln T–2.614 × 10 –4T2 + 1.8048 × 10– 8T3 + 632 658/T

for 298.15 K < T < 2000 K (*)

Gas with formula (H, H2, H1Na1, Na, Na2)

°GHgas=F10383 T+RTln(10−5P)°GH2gas=F10784 T+RTln(10−5P)°GH1Na1gas=F10562 T+RTln(10−5P)°GNagas=F12933 T+RTln(10−5P)°GNa2 gas =F12977 T+RTln(10−5P)

Symbols:

GHSERNA

– 11 989.434 + 260.548708T– 51.0393608T ln(T) + 0.072306633T2– 4.3638283 × 10 –5T 3 + 132 154/T

for 298.15 K < T < 371.00 K

– 11 009.557 + 199.61918T– 38.1198801T ln(T) + 0.009745854T2– 1.70664 × 10 –6T3 + 34 342/T + 1.60713 × 1023T– 9

for 371.00 K < T < 2300.00 K

F10383T

+ 211 801.621 + 24.4989821T– 20.78611T ln(T) F10562T

+ 132 553.465– 16.1455876T– 24.82785T ln(T) – 0.010652725T2 + 1.5821195 × 10– 6T3 + 2238.863/T

for 298.15 K < T < 800.00 K

+ 129 256.792 + 35.5334784T– 32.81208T ln(T) – 0.0026811235T2 + 1.59482667 × 10– 7T3 + 223 972.1/T

for 800.00 K < T < 2500.00 K

+ 52 224.6946 + 343.223031T– 71.12485T ln(T) + 0.00541529T2 – 1.38711217 × 10 –7T3 + 28 391 720/T

for 2500.00 K < T < 5800.00 K

+ 307 909.677– 276.144986T + 1.091352T ln(T) – 0.003663472T2 + 7.54038833 × 10– 8T3 – 1.4180265 × 108/T

for 5800.00 K < T < 6000.00 K

F10784T

– 9522.9741 + 78.5273879T– 31.35707T ln(T) + 0.0027589925T2 – 7.46390667 × 10 –7T3 + 56 582.3/T

for 298.15 K < T < 1000.00 K

+ 180.108664– 15.6128256T– 17.84857T ln(T) – 0.00584168T2 + 3.14618667 × 10– 7T3– 1 280 036/T

for 1000.00 K < T < 2100.00 K

– 18 840.1663 + 92.3120255T– 32.05082T ln(T) –0.0010728235T2 + 1.14281783 × 10– 8T3 + 3 561 002.5/T

for 2100.00 K < T < 6000.00 K

F12933T

+ 101 202.044– 12.9290068T– 21.02539T ln(T) + 1.9194285 × 10– 4T2– 2.37558167 × 10– 8T3 + 6714.165/T

for 298.15 K < T < 2700.00 K

+ 123 818.458 – 80.8203215T– 13.00233T ln(T) – 6.87485 × 10 –4T2 –3.3153 × 10– 8T3– 10 435 685/T

for 2700.00 K < T < 5500.00 K

+ 200 317.377 – 314.322311T + 14.94379T ln(T) – 0.0049580625T2 + 8.45444167 × 10– 8T3– 45 680 820/T

for 5500.00 K < T < 9600.00 K

– 248 549.945 + 382.618817T– 61.81729T ln(T) + 8.73722 × 10 –4T2 + 1.54938383 × 10 –9T3 + 4.4661115 × 108/T

for 9600.00 K < T < 10 000.00 K

F12977T

+ 131 697.685 + 6.55101085T– 35.05636T ln(T) – 0.0039954535T2 + 5.82776667 × 10– 7T3– 20 127.66/T

for 298.15 K < T < 800.00 K

+ 123 510.411 + 75.1001481T– 44.47351T ln(T) – 5.345085 × 10– 4T2 + 6.400745 × 10 –7T3 + 1 150 765/T

for 800.00 K < T < 1500.00 K

+ 79 657.0271 + 417.408691T– 91.76357T ln(T) + 0.022097085T2– 1.3875195 × 10 –6T3 + 8 765 605/T

for 1500.00 K < T < 3100.00 K

+ 841 444.171 – 2436.16812T + 261.4099T ln(T) – 0.0509968T2 + 1.46319 × 10– 6T3– 3.005069 × 108/T

for 3100.00 K < T < 4800.00 K

– 471 200.866 + 911.74126T– 131.5149T ln(T) + 0.0011608825T2 + 1.68225167 × 10 –7T3 + 5.200375 × 108/T

for 4800.00 K < T < 6000.00 K
Received: 2005-06-13
Accepted: 2005-10-17
Published Online: 2022-01-11

© 2006 Carl Hanser Verlag, München

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  2. Microstructure and mechanical behavior of Pt-modified NiAl diffusion coatings
  3. Evolution of C-rich SiOC ceramics
  4. Evolution of C-rich SiOC ceramics
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  17. Knudsen effusion mass spectrometric studies of the Al–Ni system: Thermodynamic properties over {AlNi + Al3Ni2} and {Al3Ni2 + Al3Ni}
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  24. The Na–H system: from first-principles calculations to thermodynamic modeling
  25. Personal
  26. Conferences
  27. Frontmatter
  28. Basic
  29. Microstructure and mechanical behavior of Pt-modified NiAl diffusion coatings
  30. Evolution of C-rich SiOC ceramics
  31. Evolution of C-rich SiOC ceramics
  32. Nanostructured SiC/BN/C ceramics derived from mixtures of B3N3H6 and [HSi(Me)C≡C]n
  33. Thermodynamic analysis of structural transformations induced by annealing of amorphous Si–C–N ceramics derived from polymer precursors
  34. Thermodynamic modelling of the Ce–Ni system
  35. Thermodynamic assessment of the Ce–O system in solid state from 60 to 67 mol.% O
  36. Phase transformations of iron nitrides at low temperatures (< 700 K) – application of mechanical mixtures of powders of nitrides and iron
  37. Effect of organic self-assembled monolayers on the deposition and adhesion of hydroxyapatite coatings on titanium
  38. Reconstruction and structural transition at metal/diamond interfaces
  39. Applied
  40. Microstructure, hardness, and fracture toughness evolution of hot-pressed SiC/Si3N4 nano/micro composite after high-temperature treatment
  41. High-temperature plasticity of SiC sintered with Lu2O3-AlN additives
  42. Interaction of functionalised surfaces on silica with dissolved metal cations in aqueous solutions
  43. XRD and TEM study of NiO–LSGM reactivity
  44. Microstructure and dielectric properties of nanoscale oxide layers on sintered capacitor-grade niobium and V-doped niobium powder compacts
  45. Knudsen effusion mass spectrometric studies of the Al–Ni system: Thermodynamic properties over {AlNi + Al3Ni2} and {Al3Ni2 + Al3Ni}
  46. Aqueous solution deposition of indium hydroxide and indium oxide columnar type thin films
  47. Thermodynamic properties of B2-AlFeNi alloys: modelling of the B2-AlFe and B2-AlNi phases
  48. Regular Articles
  49. Kinetics of precipitate formation in (TixWyCrz)B2 solid solutions: influence of Cr concentration and Co impurities
  50. On the mechanisms governing the texture and microstructure evolution during static recrystallization and grain growth of low alloyed zirconium sheets (Zr702)
  51. Out-of-pile chemical compatibility of Pb–Bi eutectic alloy with Graphite
  52. Microstructural characterisation of a Co–Cr–Mo laser clad applied on railway wheels
  53. The Na–H system: from first-principles calculations to thermodynamic modeling
  54. Notifications
  55. Personal
  56. Conferences
https://doi.org/10.1515/ijmr-2006-0136
Keywords for this article
Thermodynamics; Phase diagram; First-principles; Density functional theory; Direct method lattice dynamics

Articles in the same Issue

  1. Frontmatter
  2. Microstructure and mechanical behavior of Pt-modified NiAl diffusion coatings
  3. Evolution of C-rich SiOC ceramics
  4. Evolution of C-rich SiOC ceramics
  5. Nanostructured SiC/BN/C ceramics derived from mixtures of B3N3H6 and [HSi(Me)C≡C]n
  6. Thermodynamic analysis of structural transformations induced by annealing of amorphous Si–C–N ceramics derived from polymer precursors
  7. Thermodynamic modelling of the Ce–Ni system
  8. Thermodynamic assessment of the Ce–O system in solid state from 60 to 67 mol.% O
  9. Phase transformations of iron nitrides at low temperatures (< 700 K) – application of mechanical mixtures of powders of nitrides and iron
  10. Effect of organic self-assembled monolayers on the deposition and adhesion of hydroxyapatite coatings on titanium
  11. Reconstruction and structural transition at metal/diamond interfaces
  12. Microstructure, hardness, and fracture toughness evolution of hot-pressed SiC/Si3N4 nano/micro composite after high-temperature treatment
  13. High-temperature plasticity of SiC sintered with Lu2O3-AlN additives
  14. Interaction of functionalised surfaces on silica with dissolved metal cations in aqueous solutions
  15. XRD and TEM study of NiO–LSGM reactivity
  16. Microstructure and dielectric properties of nanoscale oxide layers on sintered capacitor-grade niobium and V-doped niobium powder compacts
  17. Knudsen effusion mass spectrometric studies of the Al–Ni system: Thermodynamic properties over {AlNi + Al3Ni2} and {Al3Ni2 + Al3Ni}
  18. Aqueous solution deposition of indium hydroxide and indium oxide columnar type thin films
  19. Thermodynamic properties of B2-AlFeNi alloys: modelling of the B2-AlFe and B2-AlNi phases
  20. Kinetics of precipitate formation in (TixWyCrz)B2 solid solutions: influence of Cr concentration and Co impurities
  21. On the mechanisms governing the texture and microstructure evolution during static recrystallization and grain growth of low alloyed zirconium sheets (Zr702)
  22. Out-of-pile chemical compatibility of Pb–Bi eutectic alloy with Graphite
  23. Microstructural characterisation of a Co–Cr–Mo laser clad applied on railway wheels
  24. The Na–H system: from first-principles calculations to thermodynamic modeling
  25. Personal
  26. Conferences
  27. Frontmatter
  28. Basic
  29. Microstructure and mechanical behavior of Pt-modified NiAl diffusion coatings
  30. Evolution of C-rich SiOC ceramics
  31. Evolution of C-rich SiOC ceramics
  32. Nanostructured SiC/BN/C ceramics derived from mixtures of B3N3H6 and [HSi(Me)C≡C]n
  33. Thermodynamic analysis of structural transformations induced by annealing of amorphous Si–C–N ceramics derived from polymer precursors
  34. Thermodynamic modelling of the Ce–Ni system
  35. Thermodynamic assessment of the Ce–O system in solid state from 60 to 67 mol.% O
  36. Phase transformations of iron nitrides at low temperatures (< 700 K) – application of mechanical mixtures of powders of nitrides and iron
  37. Effect of organic self-assembled monolayers on the deposition and adhesion of hydroxyapatite coatings on titanium
  38. Reconstruction and structural transition at metal/diamond interfaces
  39. Applied
  40. Microstructure, hardness, and fracture toughness evolution of hot-pressed SiC/Si3N4 nano/micro composite after high-temperature treatment
  41. High-temperature plasticity of SiC sintered with Lu2O3-AlN additives
  42. Interaction of functionalised surfaces on silica with dissolved metal cations in aqueous solutions
  43. XRD and TEM study of NiO–LSGM reactivity
  44. Microstructure and dielectric properties of nanoscale oxide layers on sintered capacitor-grade niobium and V-doped niobium powder compacts
  45. Knudsen effusion mass spectrometric studies of the Al–Ni system: Thermodynamic properties over {AlNi + Al3Ni2} and {Al3Ni2 + Al3Ni}
  46. Aqueous solution deposition of indium hydroxide and indium oxide columnar type thin films
  47. Thermodynamic properties of B2-AlFeNi alloys: modelling of the B2-AlFe and B2-AlNi phases
  48. Regular Articles
  49. Kinetics of precipitate formation in (TixWyCrz)B2 solid solutions: influence of Cr concentration and Co impurities
  50. On the mechanisms governing the texture and microstructure evolution during static recrystallization and grain growth of low alloyed zirconium sheets (Zr702)
  51. Out-of-pile chemical compatibility of Pb–Bi eutectic alloy with Graphite
  52. Microstructural characterisation of a Co–Cr–Mo laser clad applied on railway wheels
  53. The Na–H system: from first-principles calculations to thermodynamic modeling
  54. Notifications
  55. Personal
  56. Conferences
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