Skip to main content
SpringerLink
Log in

Features of contraction of solids: cooling vs pressing

  • Research
  • Published:
Structural Chemistry Aims and scope Submit manuscript

Abstract

Contraction of solid elements and compounds by cooling from room temperature to 0 K or by mechanical pressing to the same volume at 298 K is experimentally determined. We found that the energy cost of cold compression exceeds the energy of mechanical compression on average by two orders of magnitude. This fact is caused by the different mechanisms of contraction: pressing directly reduces interatomic distances, cooling mainly reduces the amplitudes of harmonic vibrations of atoms, whereas the anharmonic part of the vibration energy, responsible for the thermal contraction, is very small, ca. 1%.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Data availability

No datasets were generated or analysed during the current study.

References

  1. Lennard-Jones JE (1931) Cohesion. Proc Phys Soc 43:461–482

    Article  CAS  Google Scholar 

  2. Heinz H, Vaia RA, Farmer BL, Naik RR (2008) Accurate simulation of surfaces and interfaces of face-centered cubic metals using 12–6 and 9–6 Lennard-Jones potentials. J Phys Chem C 112:17281–17290

    Article  CAS  Google Scholar 

  3. Morse PM (1929) Diatomic molecules according to the wave mechanics. Vibrational levels. Phys Rev 34:57–65

    Article  CAS  Google Scholar 

  4. Girifalco LA, Weizer VG (1959) Application of the Morse potential function to cubic metals. Phys Rev 114:687–690

    Article  CAS  Google Scholar 

  5. Rassoulinejad-Mousavi SM, Zhang Y (2018) Interatomic potentials transferability for molecular simulations: a comparative study for platinum, gold and silver. Sci Rep 8:2424

    Article  PubMed  PubMed Central  Google Scholar 

  6. Birch F (1978) Finite strain isotherm and velocities for single crystal and polycrystalline NaCl at high-pressures and 300 K. J Geophys Res B83:1257–1268

    Article  Google Scholar 

  7. Vinet P, Rose JH, Ferrante J, Smith JR (1989) Universal features of the equation of state of solids. J Phys Condens Matter 1:1941–1964

    Article  CAS  Google Scholar 

  8. Schlosser H, Ferrante J (1993) High-pressure equation of state for partially ionic solids. Phys Rev B 48:6646–6649

    Article  CAS  Google Scholar 

  9. Holzapfel WB (1998) Equations of state for solids under strong compression. High Pressure Res 16:81–126

    Article  Google Scholar 

  10. Ponkratz U, Holzapfel WB (2004) Equations of state for wide ranges in pressure and temperature. J Phys Condens Matter 16:S963–S972

    Article  CAS  Google Scholar 

  11. Villars P, Daams JLC (1993) Atomic-environment classification of the chemical elements. J Alloys Compd 197:177–196

    Article  CAS  Google Scholar 

  12. Batsanov SS, Batsanov AS (2012) Introduction to structural chemistry. Springer, Dordrecht, New York

    Book  Google Scholar 

  13. Young DA, Cynn H, Söderlind P, Landa A (2016) Zero-Kelvin compression isotherms of the elements 1 ≤ Z ≤ 92 to 100 GPa. J Phys Chem Ref Data 45:043101

    Article  Google Scholar 

  14. Thermal Constants of Substances Database, Version 2 (2012) Joint Institute of High Temperatures RAS & Chemistry Department, Moscow State University, Moscow, Russia. https://www.chem.msu.ru/cgi-bin/tkv.pl

  15. Dewaele A (2019) Equations of state of simple solids (including Pb, NaCl and LiF) compressed in helium or neon in the Mbar range. Minerals 9:684

    Article  CAS  Google Scholar 

  16. Akahama Y, Kamiue K, Okawa N, Kawaguchi S, Hirao N, Ohishi Y (2021) Volume compression of period 4 elements: Zn, Ge, As, and Se above 200 GPa: ordering of atomic volume by atomic number. J Appl Phys 129:025901

    Article  CAS  Google Scholar 

  17. Anderson MS, Swenson CA, Peterson DT (1990) Experimental equations of state for calcium, strontium, and barium metals to 20 kbar from 4 to 295 K. Phys Rev B 41:3329–3338

    Article  CAS  Google Scholar 

  18. Takemura K (1997) Structural study of Zn and Cd to ultrahigh pressure. Phys Rev B 56:5170–5179

    Article  Google Scholar 

  19. Anderson MS, Swenson CA (1985) Experimental equations of state for cesium and lithium metals to 20 kbar and the high-pressure behavior of the alkali metals. Phys Rev B 31:668–680

    Article  CAS  Google Scholar 

  20. Dewaele A, Loubeyre P, Occelli F, Mezouar M, Dorogokupets PI, Torrent M (2006) Quasihydrostatic equation of state of iron above 2 Mbar. Phys Rev Lett 97:215504

    Article  PubMed  Google Scholar 

  21. Pandey KK, Gyanchandani J, Somayazulu M, Dey GK, Sharma SM, Sikka SK (2014) Reinvestigation of high-pressure polymorphism in hafnium metal. J Appl Phys 115:233513

    Article  Google Scholar 

  22. Takemura K, Fujihisa H (1993) High-pressure structural phase transition in indium. Phys Rev B 47:8465–8470

    Article  CAS  Google Scholar 

  23. Cynn H, Klepeis JE, Yoo C-S, Young DA (2002) Osmium has the lowest experimentally determined compressibility. Phys Rev Lett 88:135701

    Article  PubMed  Google Scholar 

  24. Winzenick M, Vijayakumar U, Holzapfel WB (1994) High-pressure X-ray diffraction on potassium and rubidium up to 50 GPa. Phys Rev B 50:12381–12385

    Article  CAS  Google Scholar 

  25. Chen W, Semenok DV, Troyan IA, Ivanova AG, Huang X, Oganov AR, Cui T (2020) Super-conductivity and equation of state of lanthanum at megabar pressures. Phys Rev B 102:134510

    Article  CAS  Google Scholar 

  26. Hanfland M, Loa I, Syassen K, Schwarz U, Takemura K (1999) Equation of state of lithium to 21 GPa. Solid State Comm 112:123–127

    Article  CAS  Google Scholar 

  27. Sinton GW, MacLeod SG, Cynn H, Errandonea D, Evans WJ, Proctor JE, Meng Y, McMahon MI (2014) Equation of state and high-pressure/high-temperature phase diagram of magnesium. Phys Rev B 90:134105

    Article  Google Scholar 

  28. Fujihisa H, Takemura K (1995) Stability and the equation of state of α-manganese under ultrahigh pressure. Phys Rev B 52:13257–13260

    Article  CAS  Google Scholar 

  29. Hanfland M, Loa I, Syassen K (2002) Sodium under pressure: bcc to fcc structural transition and pressure-volume relation to 100 GPa. Phys Rev B 65:184109

    Article  Google Scholar 

  30. Takemura K, Singh AK (2006) High-pressure equation of state for Nb with a helium-pressure medium: powder X-ray diffraction experiments. Phys Rev B 73:224119

    Article  Google Scholar 

  31. Vohra YK, Ruoff AL (1990) Static compression of metals Mo, Pb, and Pt to 272 GPa: comparison with shock data. Phys Rev B 42:8651–8654

    Article  CAS  Google Scholar 

  32. Frost M, Smith D, McBride EE, Smith JS, Glenzer SH (2023) The equations of state of statically compressed palladium and rhodium. J Appl Phys 134:035901

    Article  CAS  Google Scholar 

  33. Zhao YC, Porsch F, Holzapfel WB (1996) Evidence for the occurrence of a prototype structure in Sc under pressure. Phys Rev B 54:9715–9720

    Article  CAS  Google Scholar 

  34. Anzellini S, Wharmby MT, Miozzi F, Kleppe A, Daisenberger D, Wilhelm H (2019) Quasi-hydrostatic equation of state of silicon up to 1 megabar at ambient temperature. Sci Reports 9:15537

    Google Scholar 

  35. Salamat A, Briggs R, Bouvier P, Petitgirard S, Dewaele A, Cutler ME, Cora F, Daisenberger D, Garbarino G, McMillan PF (2013) High-pressure structural transformations of Sn up to 138 GPa: angle-dispersive synchrotron X-ray diffraction study. Phys Rev B 88:104104

    Article  Google Scholar 

  36. Mast DS, Kim E, Siska EM, Pointau F, Czerwinski KR, Lavina B, Forster PM (2016) Equation of state for technetium from X-ray diffraction and first-principle calculations. J Phys Chem Solids 95:6–11

    Article  CAS  Google Scholar 

  37. Vohra YK, Holzapfel WB (1993) Thorium under strong compression – a test case for the evaluation of EOS data by different forms and procedures. High Pressure Res 11:223–237

    Article  Google Scholar 

  38. Dewaele A, Stutzmann V, Bouchet J, Bottin F, Occelli F, Mezouar M (2015) High pressure-temperature phase diagram and equation of state of titanium. Phys Rev B 91:134108

    Article  Google Scholar 

  39. Cazoria C, MacLeod SG, Errandonea D, Munro KA, McMahon MI, Popescu C (2016) Thallium under extreme compression. J Phys Cond Matter 28:445401

    Article  Google Scholar 

  40. Dewaele A, Bouchet J, Occelli FM, Hanfland M, Garbarino G (2013) Refinement of the equation of state of α-uranium. Phys Rev B 88:134202

    Article  Google Scholar 

  41. Errandonea D, MacLeod SG, Burakovsky L, Santamaria-Perez D, Proctor JE, Cynn H, Mezouar M (2019) Melting curve and phase diagram of vanadium under high-pressure and high-temperature conditions. Phys Rev B 100:094111

    Article  CAS  Google Scholar 

  42. Qi X, Cai N, Wang S, Li B (2020) Thermoelastic properties of tungsten at simultaneous high pressure and temperature. J Appl Phys 128:105105

    Article  CAS  Google Scholar 

  43. Pace EJ, Finnegan SE, Storm CV, Stevenson M, McMahon MI, MacLeod SG, Plekhanov E, Bonini N, Weber C (2020) Structural phase transitions in yttrium up to 183 GPa. Phys Rev B 102:094104

    Article  CAS  Google Scholar 

  44. Zhao Y, Zhang J, Pantea C, Qian J, Daemen LL, Rigg PA, Hixson RS, Gray GT, Yang Y, Wang L, Wang Y, Uchid T (2005) Thermal equations of state of the α, β, and ω phases of zirconium. Phys Rev B 71:184119

    Article  Google Scholar 

  45. Batsanov SS (2006) Relationships between the molar volumes of mixtures of elements and their compounds. Russ J Inorg Chem 51:1299–1301

    Article  Google Scholar 

  46. Liu X, Wang H, Wang W, Fu Z (2021) A prediction model of thermal expansion coefficient for cubic inorganic crystals by the bond valence model. J Solid State Chem 299:122111

    Article  CAS  Google Scholar 

  47. Batsanov SS (2020) Harmonic phase transition in solids under high pressures. J Phys Chem Solids 144:109508

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The author thanks Prof. Dr. R. Hoffmann (Cornell University, USA), Dr. A.S. Batsanov (Durham University, UK), and Dr. A. R. Oganov (Skolkovo Institute of Science and Technology, Russia) for useful discussions.

Author information

Authors and Affiliations

  1. National Research Institute for Physical-Technical Measurements, Moscow Region, Mendeleevo, 141570, Russia

    Stepan S. Batsanov

Authors
  1. Stepan S. Batsanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

SSB is the sole author of this manuscript; therefore, Stepan S. Batsanov is the corresponding author.

Corresponding author

Correspondence to Stepan S. Batsanov.

Ethics declarations

Conflict of interest

The author declares no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Batsanov, S.S. Features of contraction of solids: cooling vs pressing. Struct Chem (2024). https://doi.org/10.1007/s11224-024-02315-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11224-024-02315-3

Keywords

Search

Navigation