Kinetic Phase Diagrams as an Enforced Consequence of Rapid Changing Temperature or Diminishing Particle Size: Thermodynamic Fundamentals and Limits

  • Jaroslav ŠestákEmail author
Part of the Hot Topics in Thermal Analysis and Calorimetry book series (HTTC, volume 11)


The innovative sphere of kinetic phase diagrams as a special domain of routine thermodynamic determined diagrams is re-evaluated while accentuating its specificity and practical impact when studying system under rapid changes of temperature (e.g., cooling). Requirement for a certain driving force in order to accomplish transformations is explored. It involves merger of heating–cooling as a nonequilibrium thermodynamic state of a certain sample ‘autonomy.’ The meaning of temperature is discussed when measured during inconstant thermal experiments. Thermodynamic legitimacy when assuming the effect of programmed temperature changes at the constant heating rate is examined and approved. Query about the implication of the term ‘temperature’ under rapid quenching results in a proposal of new tem ‘tempericity.’ Size as another degree of thermodynamic freedom is observed and investigated for the issue of nanomaterials providing the apparent analogy between the temperature-dependent kinetic phase diagrams and those obtained for diminishing particle size. Specific behavior of nanocomposites is explored regarding the particle curvature, temperatures of transformation, dissolution or phase separation, etc. Extension of kinetic phase diagram to the nanostate determinability, involving thermodynamics expanded by ‘one dimension’ as a result of severely contracted particle surface, is dealt with. The chapter contains 92 references.


Cool Rate Solidification Front Kinetic Phase Thomson Equation Irreversible Heat Transfer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The present work was also supported by Institutional Research Plan of Institute of Physics ASCR, v.v.i., as developed at its Join Research Laboratory with the New Technologies Centre of the University of West Bohemia in Pilzen (the CENTEM project, reg. no. CZ.1.05/2.1.00/03.0088 that is cofunded from the ERDF as a part of the MEYS—Ministry of Education, Youth and Sports OP RDI Program and, in the follow-up sustainability stage supported through the CENTEM PLUS LO 1402). Deep thanks are due to long-lasting collaboration activity by J.J. Mareš, P. Hubík, Z. Kožíšek, Z. Chvoj (Institute of Physics), P. Holba + , M. Holeček (West Bohemian University), J. Málek (University of Pardubice), N Koga (Hiroshima University in Japan), J. Leitner (University of Chemical Technology in Prague), and P. Šimon (President of the Slovak Chemical Society with Technical University in Bratislava).


  1. 1.
    Šesták J (1979) Thermodynamic basis for the theoretical description and correct interpretation of thermoanalytical experiments. Thermochim Acta 28:197CrossRefGoogle Scholar
  2. 2.
    Jou D, Casas-Vázquez J, Lebon G (1993) Extended irreversible thermodynamics. Springer, BerlinCrossRefGoogle Scholar
  3. 3.
    Šesták J (1984) Thermophysical properties of solids: their measurements and theoretical thermal analysis. Elsevier, Amsterdam; and (1987) Teoretičeskij termičeskij analysis. Mir, Moscow (in Russian)Google Scholar
  4. 4.
    Šesták J, Mareš JJ, Hubík P, Proks I (2009) Contribution by Lazare and Sadi Carnot to the caloric theory of heat and its inspirative role in thermodynamics. J Thermal Anal Calorim 97:679–683CrossRefGoogle Scholar
  5. 5.
    Curzon FL, Ahlborn B (1975) Efficiency of a Carnot engine a maximum power output. Am J Phys 43:22–24Google Scholar
  6. 6.
    Glicksmann ME (2011) Principles of solidification. Springer, BerlinCrossRefGoogle Scholar
  7. 7.
    Šesták J, Chvoj Z (1987) Thermodynamics of kinetic phase diagrams. J Thermal Anal 32:325–333CrossRefGoogle Scholar
  8. 8.
    Chvoj Z, Kožíšek Z, Šesták J (1989) Non-equilibrium processes of melt solidification and metastable phases formation. Thermochim Acta 153 (Spec Issue)Google Scholar
  9. 9.
    MacFarlane DR (1982) Continuous cooling (CT) diagrams and critical cooling rates: a direct method of calculation using the concept of additivity. J Non-Cryst Sol 53:61Google Scholar
  10. 10.
    Grange K, Kiefer J (1941) The transformation of austenite by continuous cooling and its relation to transformation at constant temperature. Trans ASM 29:85Google Scholar
  11. 11.
    Farahany S, Ourdjini A, Idris MH, Shabestari SG (2013) Computer aided cooling curve thermal analysis of near eutectic Al–Si–Cu–Fe alloy. J Therm Anal Calorim 114:705–717CrossRefGoogle Scholar
  12. 12.
    Saleh AM, Clemente RA (2004) A simple model for solidification of undercooled metallic samples. Jpn J Appl Phys 43:3624–3628CrossRefGoogle Scholar
  13. 13.
    Xu JF, Liu F, Zhang D, Jian ZY (2015) An analytical model for solidification of undercooled metallic melts. J Therm Anal Calorim 119:273–280Google Scholar
  14. 14.
    Šesták J, Chvoj Z, Proks I, Bárta Č (1990) Thermodynamic applications concerning constrained (kinetic) states. Institute of Physics- internal report, available on websites:
  15. 15.
    Chvoj Z, Šesták J, Tříska A (eds) (1991) Kinetic phase diagrams: non-equilibrium phase transitions. Elsevier, AmsterdamGoogle Scholar
  16. 16.
    Chvoj Z, Šesták J, Fendrych F (1995) Nonequilibrium (kinetic) phase diagrams in the PbCl2-AgCl eutectic system. J Therm Anal 43:439–448CrossRefGoogle Scholar
  17. 17.
    Stefanescu DM, Upadhya G, Bandyopadhyay D (1990) Heat transfer solidification kinetics: modeling of solidification of castings. Metall Trans 21A:997–1005CrossRefGoogle Scholar
  18. 18.
    Šesták J, Chvoj Z (2003) Irreversible thermodynamics and kinetic thermal state dynamics in view of generalized solid-state reactions. Thermochim Acta 388:427–439Google Scholar
  19. 19.
    Lipton J, Glicksman ME, Kurz W (1984) Dendritic growth into undercooled alloy melts. Mater Sci Eng 65:57–63CrossRefGoogle Scholar
  20. 20.
    Elliot RS (1989) Eutectic solidification processing: crystalline and glassy alloys. Butterworth, LondonGoogle Scholar
  21. 21.
    Saunders N, Miodownik AP (1998) CALPHAD (Calculation of phase diagrams): a comprehensive guide. Elsevier, AmsterdamGoogle Scholar
  22. 22.
    Zhao J-C (2007) Methods for phase diagram determination. Elsevier, AmsterdamGoogle Scholar
  23. 23.
    Hillert M (2007) Phase equilibria, phase diagrams and phase transformations. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  24. 24.
    Šesták J (2000) Art and horizon of nonequilibrated states by quenching and the methods of formation. Glass Sci Tech 70C:153–161; and (2000) Miracle of reinforced states of matter Glasses: ancient and innovative materials for the third millennium. J Thermal Anal Calorim 61:305–323Google Scholar
  25. 25.
    Šesták J (1988) Thermophysical properties of solids: theoretical thermal analysis. Elsevier, Amsterdam (1984 and Russian translation: Mir, Moscow)Google Scholar
  26. 26.
    Rossiter BW, Beatzold RC (eds) (1992) Determination of thermodynamic properties. Wiley, New YorkGoogle Scholar
  27. 27.
    Herlach DM (1994) Non-equilibrium solidification of undercooled metallic melts. Mater Sci Eng R 12:177–272CrossRefGoogle Scholar
  28. 28.
    Stávek J, Šesták J (2002) The application of the principle of least action to some self-organized chemical reactions. Thermochim Acta 388:441–450CrossRefGoogle Scholar
  29. 29.
    Šesták J, Barta Č (2001) Invited plenary lecture: thermophysical research under microgravity: kinetic phase diagrams determination inspace lab. In: CD Proceedings of the 3rd IPMM (Inteligent Processing and Manufacturing of Materials, J. Meech. edt), Vancouver, CanadaGoogle Scholar
  30. 30.
    Šesták J, Queiroz CA, Mareš JJ (2013) Some aspects of quenching, vitrification, amorphization, disordering and the extent of nano-crystallinity, Chapter 4 in the book “Glassy, Amorphous and Nano-crystalline Materials” (J. Šesták, J. Mareš, P. Hubík, editors). pp 59–76,. Springer, Berlin, ISBN 978-90-481-2881-5Google Scholar
  31. 31.
    Šesták J (2015) Kinetic phase diagrams as a consequence of radical changing temperature or particle size. J Thermal Anal Calor 120:129–137CrossRefGoogle Scholar
  32. 32.
    Los JH, Van den Heuvel M, van Enckevort WJP, Vlieg E, Oonk HAJ, Matovic M, van Miltenburg JC (2006) Models for the determination of kinetic phase diagrams and kinetic phase separation domains. Calphad 30:216–224CrossRefGoogle Scholar
  33. 33.
    Šesták J, Kozmidis-PetrovicA, Živković Ž. (2011) Crystallization kinetics accountability and the correspondingly developed glass-forming criteria. J Min Metall Sect B-Metall 47B:229–239; and Kozmidis-Petrovic A, Šesták J. (2012) Forty years of the Hruby’ glass-forming coefficient via DTA when comparing other criteria in relation to the glass stability and vitrification ability. J Thermal Anal Calor 110:997–1004Google Scholar
  34. 34.
    Šesták J (2016) Measuring “hotness”: should the sensor’s readings for rapid temperature changes be named “tempericity”?. J Thermal Anal Calorim 125:991–999CrossRefGoogle Scholar
  35. 35.
    Adamovsky AS, Minakov AA, Schick C (2003) Scanning microcalorimetry at high cooling rate. Thermochim Acta 403:55–63CrossRefGoogle Scholar
  36. 36.
    Minakov A, Morikawa J, Hashimoto T, Huth H, Schick C (2006) Temperature distribution in a thin-film chip utilized for advanced nanocalorimetry. Meas Sci Technol 17:199–207CrossRefGoogle Scholar
  37. 37.
    Šesták J (2010) Invited plenary lecture: Macro-, meso-, micro- and nano-world: significance of temperature and allied thermal physics. In: Joint Middle European GEFTA Symposium (Modeling and experiments for solving calorimetry and kinetics)) Dresden, (Abstracts pp 15–16)Google Scholar
  38. 38.
    Flynn JH (1970) An analytical evaluation of DSC. In: Menis O (ed) Status of thermal analysis. Special NBS Publication No. 338, p 119Google Scholar
  39. 39.
    Adamovsky S, Schick C (2004) Ultra-fast isothermal calorimetry using thin film sensors Thermochim Acta. 415:1–7Google Scholar
  40. 40.
    Mareš JJ, Hubík P, Šesták J, Špička V, Krištofik J, Stávek J (2008) A Phenomenological approach to the caloric theory of heat: an alternative thermodynamics. Thermochim Acta 474:16–24CrossRefGoogle Scholar
  41. 41.
    Mareš JJ, Šesták J, Hubík P (2013) Transport constitutive relations, quantum diffusion and periodic reactions. In: Šesták J, Mareš J, Hubík P (eds) Glassy, amorphous and nano-crystalline materials: thermal physics, analysis, structure and properties. Springer, Berlin, pp. 227–245. ISBN 978-90-481-2881-5Google Scholar
  42. 42.
    Andeson S (1983) On the description of complex inorganic crystal structures. Angewandte Chem 22:69–81CrossRefGoogle Scholar
  43. 43.
    Lehn JM (1995) Supramolecular chemistry: concepts and perspectives, Weiheim CWCHGoogle Scholar
  44. 44.
    Naivz O, Arndt M, Zeilinger A (2003) Quantum interference experiments with large molecules. Amer J Phys 7:319–325Google Scholar
  45. 45.
    Mareš JJ, Šesták J (2005) An attempt at quantum thermal physics. J Thermal Anal Calor 82:681–686CrossRefGoogle Scholar
  46. 46.
    Šesták J, Mareš JJ (2014) Invited plenary lecture: composite materials and nanostructured systems thermodynamics. In: ICCE-22 international conference on composite nano-engineering). Saint J, Malta; and Šesták J (2015) at 20 RCCT (international conferewnce on chemical thermodynamics) Nizhni Novgord (Russia)Google Scholar
  47. 47.
    Šesták J (2014) Invited award lecture: peculiarities of nano-structured systems: thermodynamic (top-down) and quantum (bottom-up) issues. In: At the 40th anniversary GEFTA conference (Thermal analysis in industry and research), BerlinGoogle Scholar
  48. 48.
    Wautelet M, Shyrinian AS (2009) Thermodynamics: nano vs. macro. Pure Appl Chem 81:1921–1930CrossRefGoogle Scholar
  49. 49.
    Schevchenko VYA (2011) Search in chemistry, biology and physics of the nanostate. Lema, St.Petersburg (Rusia)Google Scholar
  50. 50.
    Hill TL (2002) Thermodynamics of small systems. Courier Dover PublicationsGoogle Scholar
  51. 51.
    Jiang Q, Wen Z (2011) Thermodynamics of materials. In: Thermodynamics of interfaces., Springer, Berlin, p 207Google Scholar
  52. 52.
    Fiala J, Kraus I (2009) Povrchy a rozhraní (Surfaces and interfaces). ČVUT, Praha (in Czech)Google Scholar
  53. 53.
  54. 54.
    Leitner J. (2011) Structure of nanometarials (Struktura nanomateriálů), Textbook by the Prague Institute of Chemical Technology (in Czech)
  55. 55.
    Leitner J, Kamrádek M (2003) Termodynamický popis nanosytémů (Thermodynamic description of nanosystem) Chem. Listy 107:606–613 (in Czech)Google Scholar
  56. 56.
    Bustamante C, Liphardt J, Ritort F (2005) The nonequilibrium thermodynamics of small systems. Phys Today 58:43–48CrossRefGoogle Scholar
  57. 57.
    Thomas Y (1805) An essay on the cohesion of fluids. Philos Trans R Soc Lond 95:65CrossRefGoogle Scholar
  58. 58.
    Laplace PS (1805) Traité de Mécanique Céleste, vol 4. Courcier, Supplément au dixième livre du Traité de Mécanique Céleste, Paris, France, pp 1–79Google Scholar
  59. 59.
    Thomson JJ (1888) Applications of dynamics to physics and chemistry. Macmillan and Co., LondonGoogle Scholar
  60. 60.
    McDonald JE (1953) Homogeneous nucleation of supercooled water drops. J Meteorology 10:416–433CrossRefGoogle Scholar
  61. 61.
    Křemenáková D, Mishra R, Militký J, Mareš JJ, Šesták J (eds) (2013) Selected properties of functional materials. OSP, Liberec-Plzeň. ISBN 978-80-87269-28-2Google Scholar
  62. 62.
    Bhushan B, Luo D, Schricker SR, Sigmund W, Zauscher S (eds) (2014) Handbook of nanomaterials properties. Springer, Berlin. ISBN 978-3-642-31107-9Google Scholar
  63. 63.
    Leitner J (2011) Teplota tání nanočástic (Melting temperatures of nanoparticles) Chem. Listy 105:174–185 (in Czech)Google Scholar
  64. 64.
    Roduner E, Cronin L (2006) Nanoscopic materials: size-dependent phenomena. RSC-Publications, CambridgeGoogle Scholar
  65. 65.
    Jiang Q, Yang CC (2008) Size effect on the phase stability of nanostructures. Curr. Nanosc. 4:179–200CrossRefGoogle Scholar
  66. 66.
    Guisbiers G (2010) Size-dependent materials properties toward a universal equation. Nanoscale Res Lett 5:1132–1136CrossRefGoogle Scholar
  67. 67.
    Wautelet M, Duvivier D (2007) The characteristic dimensions of the nanoworld. Er J Phys. 28:953–959Google Scholar
  68. 68.
    Babuk VA, Zelikov AD, Salimullin RM (2013) Nanothermodynamics as a tool to describe small objects of nature. Zhurnal Tekhnicheskoi Fiziki, 2013; 83, 1–7, transl. Tech Phys 58:151–157CrossRefGoogle Scholar
  69. 69.
    Barnard AS, Zapol P (2004) A model for the phase stability of arbitrary nanoparticles as a function of size and shape. J. Chem Phys 121:4276–4283CrossRefGoogle Scholar
  70. 70.
    Sheng HW, Xu J, Yu LG, Sun KX, Hu ZQ, Lu K (1996) Melting process of nanometer-sized in particles embedde in an Al matrix synthesized by ball milling. J Mater Res 11:2841–2851CrossRefGoogle Scholar
  71. 71.
    Sheng HW, Ren G, Peng LM, Hu ZQ, Lu K (1997) Epitaxial dependence of the melting behavior of In nanoparticles embedded in an Al matrices. J Mater Res 12:119–123CrossRefGoogle Scholar
  72. 72.
    Schick C (2014) Invited award lecture: calorimetry on scales from microseconds to days. In: At the 40th anniversary GEFTA conference (Thermal analysis in industry and research) BerlinGoogle Scholar
  73. 73.
    Xiao S, Hu W, Luo W, Wu Y, Li X, Deng H (2006) Size effect on alloying ability and phase stability of immiscible bimetallic nanoparticles. Eur Phys J B 54:479–484CrossRefGoogle Scholar
  74. 74.
    Ouyang Q, Tan X, Wang CX, Yang GW (2006) Solid solubility limit in alloying nanoparticles. Nanotechnology 17:4257–4262CrossRefGoogle Scholar
  75. 75.
    Martinez JMM, La Hoz De, Callejas Tovar R, Balbuena PB (2009) Size effect on the stability of Cu–Ag nanoalloys. Mol Simul 35:785–794CrossRefGoogle Scholar
  76. 76.
    Qi WH, Huang BY, Wang MP (2009) Size and shape-dependent formation enthalpy of binary alloy nanoparticles. Phys B 404:1761–1765CrossRefGoogle Scholar
  77. 77.
    Zhao M, Jiang Q (2010) Size effect on thermal properties in low-dimensional materials. Key Eng Mater 444:189–217Google Scholar
  78. 78.
    Romero M, Kováčová M, Rincón JMa.(2008) Effect of particle size on kinetics crystallization of an iron-rich glass. J Mater Sci 43:4135–4142Google Scholar
  79. 79.
    Höhne GWH (2003) Calorimetry on small systems a thermodynamic contribution. Thermochim Acta 403:25–36CrossRefGoogle Scholar
  80. 80.
    Staszczuk P (2005) World of nanostructures nanotechnology, surface properties of chosen nanomaterials. J Thermal Anal Calor 79:545–554CrossRefGoogle Scholar
  81. 81.
    Wunderlich B (2007) Calorimetry of nanophases of macromolecules. Int J Thermophys 28:958–967CrossRefGoogle Scholar
  82. 82.
    Garden JL, Guillou H, Lopeandia AF, Richard J, Heron JS, Souche GM, Ong FR, Vianay B, Bourgeois O (2009) Thermodynamics of small systems by nanocalorimetry: From physical to biological nano-objects. Thermochim Acta 492:16–28CrossRefGoogle Scholar
  83. 83.
    Perepezko JH, Glendenning TW, Wang J-Q (2015) Nanocalorimnetry measurements ofmetastable states. Thermochim Acta 603:24–28CrossRefGoogle Scholar
  84. 84.
    Leitner J (2010) Využití kalorimetrie při studiu nanočástic (Use of calorimetry for studying nanoparticles) KS2011_Leitner.ppt
  85. 85.
    Šesták J, Holba P (2013) Heat inertia and temperature gradient in the treatment of DTA peaks: existing on every occasion of real measurements but until now omitted. J Thermal Anal Calorim 113:1633–1643CrossRefGoogle Scholar
  86. 86.
    Holba P, Šesták J (2014) Imperfections of Kissinger evaluation method and crystallization kinetics. Glass Physics and Chemistry. 40: 486–495. ISSN 1087–6596. doi: 10.1134/S1087659614050058) and on Russian: Fizika I Khimiya Stekla, 2014; 40:645–657; and Šesták J, Holba P, Živkovič Ž, (2014) Doubts on Kissinger’s method of kinetic evaluation based on several conceptual models showing the difference between the maximum of reaction rate and the extreme of a DTA. J Min Metall Sect B-Metall 50:77–81. doi: 10.2298/JMMB130902006S
  87. 87.
    Holba P, Šesták J (2015) Heat inertia and its role in thermal analysis. J Thermal Anal Calor 121:303–307CrossRefGoogle Scholar
  88. 88.
    Holba P (2013) Equilibrium background of processes initiated by heating and Ehrenfest’s classification of phase transitions. In: Šesták J, Šimon P, (ed) Thermal analysis of micro, nano- and non-crystalline materials. Springer, Berlin, pp 29–52. ISBN 978-90-481-3149-5); and (2015) Ehrenfest equations for calorimetry and dilatometry. J Thermal Anal Calorim 120:175–181Google Scholar
  89. 89.
    Holba P, Šesták J (1972) Kinetics with regard to the equilibrium of processes studied by non-isothermal techniques. Zeit physik Chem N.F 80:1–20Google Scholar
  90. 90.
    Cantwell PR, Tang M, Dillon SJ, Luo J, Rohrer GS, Harmer MP (2014) Grain boundary complexions (overview No. 152). Acta Mater 62:1–48; and Kang YB (2015) Relationship between surface tension and Gibbs energy, and application of constrained Gibbs energy minimization. Calphad 50:23–31Google Scholar
  91. 91.
    Kaptay G (2008) A unified model for the cohesive enthalpy, critical temperature, surface tension and volume thermal expansion coefficient of liquid metals of bcc, fcc and hcp crystals. Mater Sci Eng A 495:19–26 and 501:255 as well as (2011) The extension of the phase rule to nanosystems and on the quaternary point in one-component nano-phase diagrams. J Nanosci Nanotechnol 12:1–9; and (2016) Modeling equilibrium grain boundary segregation, grain boundary energy and grain boundary segregation transitive by the extended Butler equation. J Mater Sci 51:1738–175Google Scholar
  92. 92.
    Boltachev GS, Schmelzer WPJ (2010) On the definition of temperature and its fluctuations in small systems. J Chem Phys 133:134509; and Schmelzer WPJ, Boltachev GS, Abyzov AS (2013) Temperature of critical clusters in nucleation theory: generalized Gibbs’ approach. J Chem Phys 139:034702. doi: 10.1063/1.4813238

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.New Technologies Research Centre (NTC-ZČU)University of West BohemiaPilsenCzech Republic

Personalised recommendations