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Applied Sciences
, Volume 11 (1) – Dec 23, 2020

/lp/multidisciplinary-digital-publishing-institute/contact-melting-of-metals-explained-via-the-theory-of-quasi-liquid-WeBSlPKK2J

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- 2076-3417
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- 10.3390/app11010051
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applied sciences Communication Contact Melting of Metals Explained via the Theory of Quasi-Liquid Layer Alexey V. Melkikh Institute of Physics and Technology, Ural Federal University, 62002 Yekaterinburg, Russia; melkikh2014@gmail.com; Tel.: +7-343-3759349 Abstract: It has been shown that the contact melting rate for metals is determined by the fact that at least one of them has a quasi-liquid layer on the surface. As a result, the diffusion of metal atoms occurs in the liquid phase, and not in the solid phase, which determines the characteristic contact melting time (seconds and minutes). Keywords: premelting; mass transfer; diffusion 1. Introduction The processes underlying the appearance and growth of the intermediate phases that occur during the alloying of various metals to obtain intermetallic compounds and heterogeneous mixtures have not yet been fully studied. Moreover, of particular theoretical and practical interest is the clariﬁcation of the conditions required for mass transfer to occur at the boundaries of coexisting phases. Contact melting is a phenomenon in which two metals that are initially in a solid state begin to melt upon contact. The reason for this melting is that metal atoms diffuse into each other; as a result, the melting temperature of such a solution decreases. This phenomenon is characteristic of metals with a eutectic phase, in which the melting point of the mixture Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 4 is lower than the melting point of the individual pure substances. The contact melting rate has yet to be fully elucidated. According to experimental Citation: Melkikh, A.V. Contact Melt- data [1–7], contact melting of samples occurs on a timescale of seconds. However, in ing of Metals Explained via the The- explaining this characteristic time, a contradiction arises. Indeed, in order for metal atoms ory of Quasi-Liquid Layer. Appl. Sci. to diffuse into each other, both metals , must = alr1+ eady be liquid, since the diffusion rate in (3 a) 2021, 11, 51. https://dx.doi.org/ solid is negligible. 10.3390/app11010051 where 2. Results and Discussion Received: 26 November 2020 = − (4) Accepted: 20 December 2020 The statement of this problem has the√following form (Figure 1): Published: 23 December 2020 Publisher’s Note: MDPI stays neu- tral with regard to jurisdictional claims in published maps and institutional afﬁliations. Copyright: © 2020 by the author. Li- censee MDPI, Basel, Switzerland. This Figure Figure 1. 1. Mutual Mutual diffusion of diffusion of atoms atoms of two of two substances. substances. article is an open access article distributed under the terms and conditions of the Diffusion equation: The chemical potential of an atom in this case can be written as: Creative Commons Attribution (CC BY) ¶c ¶ c = +, (5) license (https://creativecommons.org/ = D , (1) ¶t ¶x licenses/by/4.0/). where does not depend on the concentration of substances. In this formulation of the problem, we neglect the chemical reactions between the components, as well as various cross effects. However, until diffusion occurs, the metals cannot become liquid, because, being in- Appl. Sci. 2021, 11, 51. https://dx.doi.org/10.3390/app11010051 https://www.mdpi.com/journal/applsci itially in a pure state, they are both solid. According to Einstein’s formula, the mean square displacement can be written as: (6) = √2 where D is the coefficient of mutual diffusion for two metals, and t is the time. For liquid −9 2 metals, diffusion coefficients are approximately 10 m /s; however, for solid metals, dif- −20 2 fusion coefficients are approximately 10 m /s. It is easy to see that for typical experi- mental times of the order of a minute, solids will not have time to diffuse, and the root mean square displacement will be smaller than the size of an atom. Thus, contact melting of metals should occur slowly, i.e., it should be determined by diffusion in a solid. Existing contact melting models (see, for example, refs. [8–10]) cannot explain this contradiction. To solve this problem, we will take into account that at temperatures close to the melting temperature a quasi-liquid layer (film) is located on the surface of a solid. Such quasi-liquid layers have been repeatedly recorded experimentally for different substances (see, for example, refs. [11–14]). When calculating the volumetric thermodynamic charac- teristics of a substance, such a layer can be neglected; however, for some cases in which the surface condition is important, its presence is crucial. The temperature at which a quasi-liquid layer (premelting) is formed can be approx- imately estimated by taking into account the fact that an atom has a smaller number of neighbors on the surface of a solid compared with the atoms inside a sample (Figure 2). Figure 2. Atoms on the surface of a metal. Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 4 Appl. Sci. 2021, 11, 51 2 of 4 , = 1+ (3) where Initial and boundary conditions for a homogeneous case (liquid or solid): = − (4) cj = 1, cj = 0, cj = h(x), (2) x!¥ x!¥ t=0 where h(x) is a Heaviside step function. The solution of the equation, taking into account the initial and boundary conditions, has the form: 1 x c(x, t) = 1 + er f p (3) 2 Dt where er f (x) = p exp x dx (4) The chemical potential of an atom in this case can be written as: Figure 1. Mutual diffusion of atoms of two substances. m = m + kTlnc, (5) The chemical potential of an atom in this case can be written as: = +, (5) where m does not depend on the concentration of substances. In this formulation of the where does not depend on the concentration of substances. In this formulation of the problem, we neglect the chemical reactions between the components, as well as various cr problem, we oss effects. neglect the chemical reactions between the components, as well as various cross e However ffects. , until diffusion occurs, the metals cannot become liquid, because, being initially in a pure state, they are both solid. According to Einstein’s formula, the mean However, until diffusion occurs, the metals cannot become liquid, because, being in- square displacement can be written as: itially in a pure state, they are both solid. According to Einstein’s formula, the mean square displacement can be written as: 2 1/2 hx i = 2Dt (6) = 2 (6) where D is the coefficient of mutual diffusion for two metals, and t is the time. For liquid where D is the coefﬁcient of mutual diffusion for two metals, and t is the time. For liquid −9 2 metals, diffusion coefficients are approximately 10 m 9 /s; however, for 2 solid metals, dif- metals, diffusion coefﬁcients are approximately 10 m /s; however, for solid metals, −20 2 fusion coefficients are approximately 10 m20 /s. It is 2 easy to see that for typical experi- diffusion coefﬁcients are approximately 10 m /s. It is easy to see that for typical mental times of the order of a minute, solids will not have time to diffuse, and the root experimental times of the order of a minute, solids will not have time to diffuse, and the mean square displacement will be smaller than the size of an atom. root mean square displacement will be smaller than the size of an atom. Thus, contact melting of metals should occur slowly, i.e., it should be determined by Thus, contact melting of metals should occur slowly, i.e., it should be determined by diffusion in a solid. Existing contact melting models (see, for example, refs. [8–10]) cannot diffusion in a solid. Existing contact melting models (see, for example, refs. [8–10]) cannot explain this contradiction. explain this contradiction. To solve this problem, we will take into account that at temperatures close to the To solve this problem, we will take into account that at temperatures close to the melting temperature a quasi-liquid layer (film) is located on the surface of a solid. Such melting temperature a quasi-liquid layer (ﬁlm) is located on the surface of a solid. Such quasi-liquid layers have been repeatedly recorded experimentally for different substances quasi-liquid layers have been repeatedly recorded experimentally for different substances (see, for example, refs. [11–14]). When calculating the volumetric thermodynamic charac- (see, for example, refs. [11–14]). When calculating the volumetric thermodynamic charac- teristics of a substance, such a layer can be neglected; however, for some cases in which teristics of a substance, such a layer can be neglected; however, for some cases in which the surface the surfcondition ace conditis ion important, is important its ,pr itesence s presence is cris c ucial. rucial. The The t temperatur emperature e at at which which a a quasi-liquid quasi-liquid l layer ayer (preme (premelting) lting) is is fo formed rmed c can an be be app appr rox- ox- imately estimated by taking into account the fact that an atom has a smaller number of imately estimated by taking into account the fact that an atom has a smaller number of neighbors neighbors on on the the sur surface face of of a a solid solid com compar pared ed wit with h t the he at atoms oms inside inside a a s sample ample ( (Figur Figure e 2 2) ).. Figure 2. Atoms on the surface of a metal. Figure 2. Atoms on the surface of a metal. Let V(x) be the potential energy of the interaction of the selected atom with one of its nearest neighbors. The potential energy for the interaction with N atoms is equal to NV(x). Appl. Sci. 2021, 11, 51 3 of 4 Each atom residing deep in the solid has six nearest neighbors, and an atom lying on the surface has ﬁve nearest neighbors. Therefore, the energies of this atom in such potential wells will be related by a 5/6 ratio. The energy required for melting should be proportional to the depth of the potential well; therefore, the temperature at which the quasi-liquid layer (premelting) appears in the ﬁrst approximation is 5/6 of the melting temperature in the volume: T T . (7) ql In this regard, we consider contact melting experiments for some pairs of metals (Pb-Sn [6], Sn-In [7], Tl-Bi, Tl-Sn [2,7]), and show that when such metals contact each other, at least one of them has a quasi-liquid ﬁlm on their surface. According to [2,7], contact melting was performed in a thermostat. The samples were cylinders with a diameter of ~3 mm and a length of ~2 cm. The contact surfaces of the samples were polished. From the moment of contact between the samples, the diffusion time begins. The growth of the liquid layer was observed visually using a microscope. From Table 1 we can conclude that when the samples come into contact with each other, at least one of them (or both) has a quasi-liquid ﬁlm on its surface. That is, upon contact between these metals, dissolution occurs of the solid metal in this quasi-liquid layer (the dissolution of solid metals in liquid is characteristic of most of the listed metals). As a result of the enrichment of the quasi-liquid layer with the second component, the melting temperature of the next metal layer decreases (for the same reasons as the decrease in the volume), i.e., it also becomes a liquid. Table 1. Experimental contact melting temperature and quasi-liquid layer temperature for some metals. Maximum Minimum Sample Materials Used in the Experimental Where is the Pre-Melting Pre-Melting Experiment and Their Contact Melting Quasi-Liquid Temperature Temperature Melting Points, K [2,6,7] Temperature, K Film Located? (First Metal) (Second Metal) Pb (601)–Sn (505) 463 501 421 Sn Sn (505)–In (430) 400 421 358 In Tl (577)–Bi (545) 483 480 454 Tl, Bi Tl (577)–Sn (505) 455 480 421 Sn Note that the proposed model is simpliﬁed because it does not take into account the real structure of the crystal lattice of both contacting substances. An atom on a material’s surface may have more or less than the usual 5 neighbors. However, the model is in qualitative agreement with the experiment and explains the rate of contact melting. A similar phenomenon is observed upon contact between ice (snow) and salt. In this case, a quasi-liquid ﬁlm is formed on the surface of the snow at temperatures above 45 C. 3. Conclusions Thus, the reason for such rapid contact melting of metals is that a quasi-liquid layer is located on the surface of one of the metals. When the metals come into contact with each other, the atoms in the second metal dissolve sufﬁciently quickly, as a result of which the next layer becomes liquid (in the case of a phase diagram with a eutectic). Following the motion of the layer, diffusion also occurs. Thus, the contact melting rate is limited by the rate of mutual diffusion in liquid metals, although both metals are in a solid state before contact. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest. Appl. Sci. 2021, 11, 51 4 of 4 References 1. Savvin, V.S.; Mikhaleva, O.V.; Povzner, A.A. Contact Melting Studies of the Phase Composition of the Pb-Bi Diffusion Zone. Inorg. Mater. 2002, 38, 683–687. [CrossRef] 2. Savvin, V.S.; Aitukaev, A.D. Sintering of Bi–Tl, Bi–In, Bi–Pb, and Hg–In Contacts. Inorg. Mater. 2004, 40, 147–151. [CrossRef] 3. Savvin, V.S.; Azavi, A.K.; Kadochnikova, A.S.; Povzner, A.A. Investigation of the Phase Composition of the Diffusion Zone of the Bismuth Indium System upon Contact Melting. Phys. Met. Metallogr. 2005, 99, 520–526. 4. Savvin, V.S.; Mikhaleva, O.V.; Zubova, Y.A. Atomic Diffusion from Liquid to Solid Phase during Contact Melting. Tech. Phys. Lett. 2007, 33, 417–419. [CrossRef] 5. Savvin, V.S.; Kazachkova, Y.A.; Povzner, A.A. Phase formation in contact of dissimilar metals. J. Phys. Conf. Ser. 2008, 98, 052002. [CrossRef] 6. Savvin, V.S.; Pomytkina, Y.Y.; Anokhina, N.N. Contact Melting in Simple Eutectic System. EPJ Web Conf. 2011, 15, 01020. [CrossRef] 7. Savvin, V.S.; Anokhina, N.N.; Povzner, A.A. Processes at the Liquid/Crystal Boundary upon Contact Melting in the System with Intermediate Solid Phases. Phys. Met. Metallogr. 2012, 113, 406–410. [CrossRef] 8. Savitskii, A.P.; Martsunova, L.S.; Zhdanov, V.V. Contact Melting in Intermetallic Systems. Adgez. Rasplavov Paika Mater. 1977, 2, 55–57. 9. Zalkin, V.M. Nature of Eutectic Alloys and Contact Melting Effect; Metallurgiya: Moscow, Russia, 1987. 10. Gufan, A.Y.; Akhkubekov, A.A.; Zubkhadzhiev, M.A.V.; Kumykov, Z.M. Adhesion theory of contact melting. Bull. RAS Phys. 2005, 69, 632–638. 11. Dash, J.G.; Fu, H.; Wettlaufe, J.S. The premelting of ice and its environmental consequences. Rep. Prog. Phys. 1995, 58, 115–167. [CrossRef] 12. Doppenscmidt, A.; Butt, H.-J. Measuring the Thickness of the Liquid-like Layer on Ice Surfaces with Atomic Force Microscopy. Langmuir 2000, 16, 6709–6714. [CrossRef] 13. Sazaki, G.; Zepeda, S.; Nakatsubo, S.; Yokomine, M.; Furukawa, Y. Quasi-liquid layers on ice crystal surfaces are made up of two different phases. Proc. Natl. Acad. Sci. USA 2012, 109, 1052–1055. [CrossRef] 14. Benet, J.; Llombart, P.; Sanz, E.; MacDowell, L.G. Premelting-Induced Smoothening of the Ice-Vapor Interface. Phys. Rev. Lett. 2016, 117, 096101. [CrossRef]

Applied Sciences – Multidisciplinary Digital Publishing Institute

**Published: ** Dec 23, 2020

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