Sir Joseph John Thomson derived Kelvin's equation (page 163) and the depression of the melting point of ice by pressure (page 258), but he did not derive the Gibbs–Thomson equation. However, on pages 251–252, Thomson considered the effects of temperature and surface tension on the solubility of salts in spherical droplets, and he obtained an equation for that phenomenon which has a form similar to that of the Gibbs–Thomson equation. See: Thomson, J.J., Applications of dynamics to physics and chemistry (London, England: Macmillan and Co., 1888).
Sir Joseph John Thomson derived Kelvin's equation (page 163) and the depression of the melting point of ice by pressure (page 258), but he did not derive the Gibbs–Thomson equation. However, on pages 251–252, Thomson considered the effects of temperature and surface tension on the solubility of salts in spherical droplets, and he obtained an equation for that phenomenon which has a form similar to that of the Gibbs–Thomson equation. See: Thomson, J.J., Applications of dynamics to physics and chemistry (London, England: Macmillan and Co., 1888).
Jeong-Myeong Ha, Crystallization and Thermotropic Properties of Organic Solids in Nanoscopic Reactors, Ph.D. thesis: University of Minnesota, 2006, pages 26–28[permanent dead link].
Robert von Helmholtz (1886) "Untersuchungen über Dämpfe und Nebel, besonders über solche von Lösungen" (Investigations of vapors and mists, especially of such things from solutions), Annalen der Physik, 263 (4) : 508–543. On pages 523–525, Robert von Helmholtz converts Kelvin's equation to the Ostwald–Freundlich equation.
Josiah Willard Gibbs (1878) "On the equilibrium of heterogeneous substances", Transactions of the Connecticut Academy of Arts and Sciences, 3 : 343–524. The equation for the energy that's required to create a surface between two phases appears on page 483. Reprinted in: Josiah Willard Gibbs with Henry Andrews Bumstead and Ralph Gibbs van Name, ed.s, The Scientific Papers of J. Willard Gibbs, ..., vol. 1, (New York: Longmans, Green and Co., 1906), page 315.
See, for example: Martin Eden Glicksman, Principles of Solidification, (New York: Springer Science + Business Media, 2011), pages 199–201.
J. G. McLean et al., "A model and simulation of the decay of isolated nanoscale surface features" in: M.C. Tringides, ed., Surface Diffusion: Atomistic and collective processes (New York: Plenum Press, 1997), page 378.
M. W. Barsoum, Fundamentals of Ceramics (New York: Taylor & Francis, 2003), page 346.
Robert von Helmholtz (1886) "Untersuchungen über Dämpfe und Nebel, besonders über solche von Lösungen" (Investigations of vapors and mists, especially of such things from solutions), Annalen der Physik, 263 (4) : 508–543. From page 525: "Eine zufällig von mir gemachte Beobachtung dürfte vielleicht eine experimentelle Bestätigung dieser Resultate enthalten: Wenn nämlich auf einer Glasscheibe ein feiner Beschlag gebildet ist, über den dickere Tropfen zerstreut sind, so bildet sich bald um die letzteren herum eine Scheibe, welche vom feineren Beschlag befreit ist, ein Beweis, dass die kleinen in die grossen Tropfen überdestillirt sind." (An observation that I made by chance perhaps might contain an experimental confirmation of this result: namely, if a fine mist forms on a pane of glass, over which large drops are scattered, then around the latter, a disk soon forms, which is free of fine mist — evidence that the small [droplets] are "distilled" into the big ones.)
Friedrich Wilhelm Küster (1906) Lehrbuch der allgemeinen physikalischen und theoretischen Chemie ... [Textbook of general physical and theoretical chemistry ... ] (Heidelberg, Germany: Carl Winter, 1906), v.1, p. 189. The relevant passage is reprinted on page 189 of volume 1 of the 1913 edition: § 127. Schmelzen feinster Pulver. (Melting of the finest powder). From page 189: "Folglich ist die Schmelztemperatur des Pulvers, t1°, niedriger als die der Kristalle, t°. Der Unterschied ist jedoch so gering, daß er noch nicht zur Beobachtung gelangt ist (vgl. weiter unter §. 131)." (Consequently, the melting temperature of the powder, t1°, is lower than that of the [bulk] crystal, t°. However, the difference is so small that it still hasn't been observed (compare §. 131 below).)
As early as 1906, the Austrian mineralogist Cornelio August Doelter (1850-1930) had attempted to determine the melting points of various minerals via a microscope and had observed that finely powdered silicates melted over a range of as much as 100°C. See pp. 618-619 of: Doelter. C (17 August 1906) "Bestimmung der Schmelzpunkte vermittelst der optischen Methode" (Determination of melting points by means of an optical method), Zeitschrift für Elektrochemie und angewandte physikalische Chemie, 12 (33) : 617-621. From p. 618: " … wir erkennen, dass zwischen Beginn der Schmelzung und diesem Punkt bei manchen Silikaten ein erheblicher Temperaturunterschied — bis 100° — liegen kann, … " ( … we discern that between the beginning of melting and this point [i.e., at which molten droplets join together] there can lie, in the case of some silicates, a considerable difference in temperature — up to 100°C … )
See: Kubelka, Paul (July 1932) "Über den Schmelzpunkt in sehr engen Capillaren" (On the melting point in very narrow capillaries), Zeitschrift für Elektrochemie und angewandte physikalische Chemie (Journal for Electrochemistry and Applied Physical Chemistry), 38 (8a) : 611–614. Available on-line in English translation at: National Research Council CanadaArchived 2016-02-06 at the Wayback Machine. From page 614: "Tests which will be reported in detail by the author elsewhere enable us to prove ... that iodine in activated charcoal is still liquid at room temperature, i.e., approximately 100° below the melting point."
See: Kubelka, Paul (July 1932) "Über den Schmelzpunkt in sehr engen Capillaren" (On the melting point in very narrow capillaries), Zeitschrift für Elektrochemie und angewandte physikalische Chemie (Journal for Electrochemistry and Applied Physical Chemistry), 38 (8a) : 611–614. Available on-line in English translation at: National Research Council CanadaArchived 2016-02-06 at the Wayback Machine. From page 614: "Tests which will be reported in detail by the author elsewhere enable us to prove ... that iodine in activated charcoal is still liquid at room temperature, i.e., approximately 100° below the melting point."
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This derivation of the Gibbs–Thomson equation appears on pages 417–418 of: James E. McDonald (December 1953) "Homogeneous nucleation of supercooled water drops", Journal of Meteorology, 10 : 416–433. Available on-line at: Princeton.eduArchived 2014-03-09 at the Wayback Machine
See: Kubelka, Paul (July 1932) "Über den Schmelzpunkt in sehr engen Capillaren" (On the melting point in very narrow capillaries), Zeitschrift für Elektrochemie und angewandte physikalische Chemie (Journal for Electrochemistry and Applied Physical Chemistry), 38 (8a) : 611–614. Available on-line in English translation at: National Research Council CanadaArchived 2016-02-06 at the Wayback Machine. From page 614: "Tests which will be reported in detail by the author elsewhere enable us to prove ... that iodine in activated charcoal is still liquid at room temperature, i.e., approximately 100° below the melting point."
See: Kubelka, Paul (July 1932) "Über den Schmelzpunkt in sehr engen Capillaren" (On the melting point in very narrow capillaries), Zeitschrift für Elektrochemie und angewandte physikalische Chemie (Journal for Electrochemistry and Applied Physical Chemistry), 38 (8a) : 611–614. Available on-line in English translation at: National Research Council CanadaArchived 2016-02-06 at the Wayback Machine. From page 614: "Tests which will be reported in detail by the author elsewhere enable us to prove ... that iodine in activated charcoal is still liquid at room temperature, i.e., approximately 100° below the melting point."
This derivation of the Gibbs–Thomson equation appears on pages 417–418 of: James E. McDonald (December 1953) "Homogeneous nucleation of supercooled water drops", Journal of Meteorology, 10 : 416–433. Available on-line at: Princeton.eduArchived 2014-03-09 at the Wayback Machine
