Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials
Founded at 2009

To the problem of applicability of the Tamman temperature concept to nanosized objects: to the 160th anniversary of Gustav Tamman

V.M. Samsonov, I.V. Talyzin, V.V. Puitov, S.A. Vasilyev

Tver State University

DOI: 10.26456/pcascnn/2021.13.503

Original article

Abstract: The introduction provides a brief critical review of the available definitions and interpretations of the Tamman temperature, usually defined as TT(∞)=0,5Tm(∞), and of the Hüttig temperature TH(∞)=0,5Tm(∞) where Tm(∞) is the macroscopic value of the melting point of the material. For a nanoparticle we propose to replace in the above relations Tm(∞) by the melting temperature of the small object Tm , i.e. to define TT as 0,5Tand TH as 0,3Tm. In our molecular dynamics experiments on Au nanoparticles, carried out using the LAMMPS program, we found that at the temperature T=TT, in both the central part of the fcc nanoparticle (the core) and in its surface layer (the shell), some local species of a quasicrystalline structure appear which are alternately identified either as crystalline or as non-crystalline by the OVITO program. However, contrary to opinion of E. Rukenstein (1984), at T=TT, a liquid layer on the surface of the crystalline nanoparticle is not formed yet. However, a liquid-like layer was gradually developed in the course of the further temperature elevation. At the same time, in our molecular dynamics experiments we did not reveal any manifestation of the Hüttig temperature TH in the structure of crystalline Au nanoparticles reproduced in our molecular dynamics experiments. It is also of interest that in our molecular dynamics experiments the nanoparticle sintering took place not only above the Tammann temperature but below it as well.

Keywords: Tamman temperature, Hüttig temperature, metal nanoparticles, surface melting, sintering, molecular dynamics

  • Vladimir M. Samsonov – Dr. Sc., Full Professor, General Physics Department, Tver State University
  • Igor V. Talyzin – Ph. D., Researcher, Management of Scientific Research, Tver State University
  • Vladimir V. Puitov – Laboratory Assistant, Scientific Research Department, Tver State University
  • Sergey A. Vasilyev – Senior Lecturer, Applied Physics Department, Researcher, Scientific Research Department, Tver State University


Samsonov, V.M. To the problem of applicability of the Tamman temperature concept to nanosized objects: to the 160th anniversary of Gustav Tamman / V.M. Samsonov, I.V. Talyzin, V.V. Puitov, S.A. Vasilyev // Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials. — 2021. — I. 13. — P. 503-512. DOI: 10.26456/pcascnn/2021.13.503. (In Russian).

Full article (in Russian): download PDF file


1. Samsonov V.M., Talyzin I.V., Vasilyev S.A., Alymov M.I. On the mechanisms of coalescence of nanodroplets and sintering of solid particles, Colloid Journal, 2020, vol. 82. issue 5, pp. 573-583. DOI: 10.1134/S1061933X20050154.
2. Tkachenko S.V., Zhukov A.P. Gustav Tamman: vklad v metallovedeniye [Gustav Tamman: contribution to metal science], Uspekhi v khimii i khimicheskoy tekhnologii [Advances in Chemistry and Chemical Technology], 2009, vol. 23, no. 5 (98), pp.114-117. (In Russian).
3. Dai Yu., Lu P., Cao Zh., Campbell C.T., Xia Y. The physical chemistry and material science behind sinter- resistant catalysts, Chemical Society Reviews, 2018, vol. 47, issue 12, pp. 4314-4331. DOI: 10.1039/C7CS00650K.
4. Tammann G. Die temperatur des beginns innerer diffusion in kristallen, Zeitschrift für anorganische und allgemeine Chemie, 1926. vol. 157, issue 1, pp. 321-325. DOI: 10.1002/zaac.19261570123.
5. Tammann G., Mansuri Q.A. Metallographische mitteilungen aus dem institut für physikalische chemie der universität göttingen cxiii. zur rekristallisation von metallen und salzen, Zeitschrift für anorganische und allgemeine Chemie, 1923, vol. 126, issue 1, pp. 119-128. DOI: 10.1002/zaac.19231260109.
6. Hüttig G.F., Theimer H., Breuer W. Über reaktionen fester stoffe: 126. Mitteilung. Über die entgasung fester stoffe, Zeitschrift für anorganische und allgemeine Chemie, 1942, vol. 249, issue 2, pp. 134-145. DOI: 10.1002/zaac.19422490202.
7. Finch G.I., Sinha K.P. On Reaction in the solid state, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1957, vol. 239, issue 1217, pp. 145-153. DOI: 10.1098/rspa.1957.0028.
8. Roshchin A.V. Mekhanizm tverdofaznogo karbotermicheskogo vosstanovleniya vkraplennykh khromovykh rud [Mechanism of solid-phase carbothermal reduction of disseminated chromium ores], Cand. tech. sci. diss. Abstr. Chelyabinsk, SUSU Publ., 2002, 24 p. (In Russian).
9. Roshchin V.E., Roshchin A.V. Fizika pirometallurgicheskikh protsessov [Physics of pyrometallurgical processes], Moscow-Vologda, Infra-Engineering Publ., 2021, 304 p. (In Russian).
10. Ruckenstein E. The effect of interactions among metal, support and atmosphere on the behaviour of supported metal catalysts, Materials Science Research, ed. by G.C. Kuczynski, A.E. Miller, G.A. Sargent. – Boston, MA: Springer, 1984. – P. 199-221. DOI: 10.1007/978-1-4613-2761-5_15.
11. Sun J., Ma D., Zhang H. et al. Toward monodispersed silver nanoparticles with unusual thermal stability, Journal of the American Chemical Society, 2006, vol. 128, issue 49, pp. 15756-15764. DOI: 10.1021/ja064884j.
12. Castro T., Reifenberger R., Choi E., Andres R.P. Size-dependent melting temperature of individual nanometer-sized metallic clusters, Physical Review B, 1990, vol. 42, issue 13, pp. 8548-8556. DOI: 10.1103/PhysRevB.42.8548.
13. Kofman R., Cheyssac P., Lereach Y., Stella A. Melting of clusters approaching 0D , The European Physical Journal D. Atomic, molecular and optical physics, 1999, vol. 9, pp. 441-444. DOI: 10.1007/978-3-642-88188-6_88.
14. Dick K., Dhanasekaran T., Zhang Zh., Meisel D. Size-dependent melting of silica-encapsulated gold nanoparticles, Journal of the American Chemical Society, 2002, vol. 124, issue 10, pp. 2312-2317. DOI: 10.1021/ja017281a.
15. Samsonov V.M., Kharechkin S.S., Gafner S.L., Redel' L.V., Gafner Yu.Ya. Molecular dynamics study of the melting and crystallization of nanoparticles, Crystallography Reports, 2009, vol. 54, issue 3, pp. 526-531. DOI: 10.1134/S1063774509030250.
16. Sdobnyakov N.Yu., Sokolov D.N. Izuchenie termodinamicheskikh i strukturnykh kharakteristik nanochastits metallov v protsessakh plavleniya i kristallizatsii: teoriya i komp'yuternoe modelirovanie: monografiya [Study of the thermodynamic and structural characteristics of metal nanoparticles in the processes of melting and crystallization: theory and computer modeling: monograph]. Tver, Tver State University Publ., 2018, 176 p. (In Russian).
17. Sdobnyakov N.Yu., Sokolov D.N., Bazulev A.N. et al. Relation between the size dependences of the melting and crystallization temperatures of metallic nanoparticles, Russian Metallurgy (Metally), 2013, no. 2, pp. 100-105. DOI: 10.1134/S0036029513020110.
18. Samsonov V.M., Sdobnyakov N.Y., Bembel’ A.G. et al. Complex approach to the computer simulation of the melting and crystallization of gold nanoclusters, Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta «MIFI» [Bulletin of the National Research Nuclear University «MEPhI»], 2013, vol. 2, no. 4, pp. 448-451. (In Russian).
19. Sdobnyakov N.Yu., Repchak S.V., Samsonov V.M. et al. Correlation between the size-dependent melting and crystallization temperatures of metal nanoparticles, Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques, 2011, vol. 5, issue 3, pp. 508-511. DOI: 10.1134/S1027451011050120.
20. Samsonov V.M., Vasilyev S.A., Nebyvalova K.K. et al. Melting temperature and binding energy of metal nanoparticles: size dependences, interrelation between them, and some correlations with structural stability of nanoclusters, Journal of Nanoparticle Research, 2020, vol. 22, issue 8, art. № 247, 15 p. DOI: 10.1007/s11051- 020-04923-6.
21. Adams J.B., Foiles S.M., Wolfer W.G. Self-diffusion and impurity diffusion of fcc metals using the five- frequency modeland the embedded atom method, Journal of Materials Research, 1989, vol. 4, issue 1, pp. 102-112. DOI: 10.1557/JMR.1989.0102.
22. Nosé S. A unified formulation of the constant temperature molecular dynamics methods, The Journal of Chemical Physics, 1984, vol. 81, issue 1, pp. 511-519. DOI: 10.1063/1.447334.
23. Stukowski A. Visualization and analysis of atomistic simulation data with OVITO – the open visualization tool, Modelling and Simulation in Materials Science and Engineering, 2010, vol. 18, issue 1, pp. 015012-1- 015012-7. DOI: 10.1088/0965-0393/18/1/015012.

⇐ Prevoius journal article | Content | Next journal article ⇒