Materials science Calculation of surface tension and its temperature dependence for liquid Cu-20Ni-20Mn alloy Pavlo Prysyazhnyuk Ph. D. In Engineering Ivano-Frankivsk National Technical University of Oil and Gas Ivano-Frankivsk, Ukraine E-mail: [email protected] Dmytro Lutsak E-mail: [email protected] Aristid Vasylyk Ph. D. In Engineering Ivano-Frankivsk National Technical University of Oil and Gas Ivano-Frankivsk, Ukraine Thaer Shihab Ivano-Frankivsk National Technical University of Oil and Gas Ivano-Frankivsk, Ukraine Myroslav Burda Ivano-Frankivsk National Technical University of Oil and Gas Ivano-Frankivsk, Ukraine 346 Metallurgical and Mining Industry No.12 — 2015 Materials science Abstract Temperature dependence of surface tension of manganese cupronickel Cu-20Ni-20Mn is defined for triplex system Cu-Ni-Mn with the use of Butler model and thermodynamic functions of liquid phase calculated according to CALPHAD methodology. For calculation of temperature dependence of surface tension of specified alloy there suggested the equation γ ()TTCu60 Ni 20 Mn 20 =−−1384,5 0,1735( 1323) , which describes the results of experimental research to high precision. Key words: SURFACE TENSION, BUTLER EQUATION, MANGANESE CUPRONICKEL, COMPUTING THERMODYNAMICS, CERMETS 1. Introduction in a gas bubble only in the range of temperatures Dispersive hardening alloys of the system of 1260 - 1280°C are presented. As the temperature Cu-Ni-Mn are widely used as matrix alloys [1] in the range of receiving the products and coatings with hardwearing composite materials and coatings on the use of an alloy of Cu-20Ni-20Mn is much wider [3], base of high-melting compounds or hard alloys, which there is a need of an assessment of its surface tension are obtained mostly in the presence of liquid phase within the temperatures of 1050 - 1400°C. From according to the technologies of furnace welding there, the aim of the work is the development of (for coatings) or during preservation of presintered analytical model for calculation of a surface tension porous ceramic frames (for products). When of manganese cupronickel Cu-20Ni-20Mn alloy with choosing technological parameters of such processes, the use of Butler equation [4] and thermodynamic one of the necessary conditions is the estimation of functions of liquid phase in Cu-Ni-Mn system [5] surface tension of binding alloy in the wide range of within the CALPHAD method [6]. temperatures, which defines the growth kinetics of 2. Calculation model soaked layer depth. This in its turn allows to avoid According to Butler’s equation the surface excessive isothermal holding, when uncontrolled tension (γ) for multicomponent fusion is the diffusion processes, leading to the reduction of the function of physical properties of components and level of mechanical properties, are being developed. thermodynamic parameters of their interaction. Thus Literary data on surface tension of alloys of the surface monoatomic layer is considered as the Cu-Ni-Mn system are limited, for example, in work independent phase, which is in balance with other [2] the results of experimental studies on measurement volume of fusion. For the system consisting of n of a surface tension of an alloy of MNMTs 60-20-20 components the equation for a surface tension (γn) can (Cu-20Ni-20Mn) by method of a maximum pressure be written as follows: RT cS 1 γγ++i ES S − EB B = (1) n(T) = i ln B { Gii( Tc, ) G ii( Tc,)} ,( i 1,2... n) Ai cAii th E B where γі – is a surface tension of the і component, energy of the system ( G ) according to the equation: 2 J/ m ; R – is a multiple-purpose gas constant, EB J/mol · K; A – is a surface area of a monoatomic EB B EB B∂ G i Gii( Tc,1) = G +−( ci) layer of a liquid component, m2; c C and c B – are the i i ∂ci (3) surface and volume concentration of components, in its turn excess energy of system in the form of respectively, at. fraction; E S E B Gi and Gi – are Redlikha-Kister’s polynoms [8] is determined by a superficial and volume partial pressure free energy of formula: 23 1 a component, respectively, J/mol. v The value A according to [7] is calculated as EB= BB v − i G∑∑ cci j ∑ L ij( T)( c i c j ) follows: ij=>=11 v 0 12 (4) 33 A=ii1,091 NV (2) where Lij – are the interaction parameters. At the known value of EG B, value EG S is suggested to where N – Avogadro constant; V – molar volume of i i i be determined by a formula[9]: pure component, cubic meters. E B ES EB The value Gi is determined with the help of excess GG≈ 0,83 (5) No.12 — 2015 Metallurgical and Mining Industry 347 Materials science 3. Results and their discussion looks as follows: For the threefold Cu-Ni-Mn system the equation (1) RT 1−−ccSS 1 γγ++Ni Mn ES S S − EB B B CuNiMn (T) = Cu lnBB { GCu( Tc,, Ni c Mn) G Cu( Tc ,, Ni c Mn )} ACu 1−−ccNi Mn A Cu RT cS 1 =++γ Ni ES S S − EB B B Ni lnB { GNi( Tc,, Ni c Mn) G Ni( Tc ,, Ni c Mn )} ANi cANi Ni RT cS 1 =++γ Mn ES S S − EB BB (6) Mn ln B { GMn( Tc,, NicG Mn ) Mn(Tc,, Ni c Mn )} AMn cAMn Mn Temperature dependences of a surface tension for are мJ/ m2: pure Cu, Ni and Mn according to work [10] γ Cu =−−1355 0,19(T 1358) ; γ Ni =−−1796 0,35(T 1728) ; (7) γ Mn =−−1100 0,35(T 1519) . Partial pressure of Gibbs’s energy of components in fusion may be presented according to [9] in the form: EB EB EB B B EB B∂∂GGB GCu( Tc,, Mn c Ni ) =−− G cMn cNi ∂∂ccMn Ni EB EB EB B B EB B ∂∂GGB GMn( Tc,, Mn c Ni ) = G +−( 1 cMn ) − cNi ∂∂ccMn Ni EB EB EB B B EB B∂∂GGB GNi( Tc,, Mn c Ni ) = G − cMn +−(1cNi ) (8) ∂∂ccMn Ni where EGB for the system Cu-Ni-Mn after substitution looks as follows: EB BB BB BB BBB (9) G=+++ ccLCu Ni Cu: Ni cc Cu Mn L Cu: Mn ccL Mn Ni Mn: Ni cccL Cu Ni Mn Cu:: Ni Mn Temperature dependences of parameters of interaction (L) according to work [5] look as follows: BB LCu: Ni =(11760 + 1,084T ) +− ( 1672)( ccCu − Ni ); BB LCu: Mn =(1800 − 2, 28T ) +− ( 6500 − 2,91Tc )(Cu − c Mn ); BB LNi: Mn =−( 85853 + 22,715T ) +− ( 1620 + 4,902Tc )(Ni − c Mn ); =−BB + − +− + B LCu:: Ni Mn ( 7000)cCu (25000 50Tc )Ni ( 111000 50Tc )Mn . (10) Surface areas of monoatomic layers of components after substitution of values in the equation (2) will be: 12 1 2 12 A=1,091(6⋅⋅ 1023 )33 (7,1 10−−−6 ) ; A= 1,091(6 ⋅⋅ 1023 )3 (6,5 106 ) 3 ; A = 1,091(6 ⋅⋅ 1023 )33 (7,1 106 ) . Cu Ni Mn (11) For manganese cupronickel the composition in surface tension was defined under set temperature T B B atomic fraction was accepted as: cCu =0,57259; cNi with the help of this system. The values thus obtained B =0,20664; cMn =0,22077. Thus, after substitution of were compared with experimental data of work [2]. values of the equation (7-11) into the equation (6) the Results (fig. 1) show that calculation data with high S system of the equations with two unknown values cNi precision describe the results of experiment (devia- S and cMn was obtained. Temperature dependence of tion does not exceed 1%). Thus temperature depen- 348 Metallurgical and Mining Industry No.12 — 2015 Materials science dence of surface tension of an alloy of Cu-20Ni- 4. Conclusions 20Mn is described with the value of corrected deter- It is shown that the use of the equation of Butler mination coefficient, which is equal to 0.99987 by the for fusions of Cu-Ni-Mn system allows to calculate equation, mJ/m2: with high precision the value of a surface tension of an alloy of the MNMTs 60-20-20 grade within the γ ()TTCu60 Ni 20 Mn 20 =−−1384,5 0,1735( 1323) (12) temperature range 1050 – 1400 ºС. At temperature increase there observed the reduction of surface tension of the specified alloy on linear dependence. Thus the major part of Mn is concentrated in surface coating (which is also typical for manganese steels [12]). It creates prerequisites for wettability improve- ment by manganese cupronickel of ceramic materials and whereby it promotes obtaining of cermet in the system: ceramics – Cu-20Ni-20Mn. References 1. Sukhovaya E. V. (2013). Structural approach to the development of wear-resistant compos- ite materials. Journal of Superhard Materials. V. 35, No 5, p.p. 277–283. 2. Myshko Yu. D., Klibus A. V. , Gapchenko Figure 1. Temperature dependence of surface tension of M. N. , Ishchuk N. Ya. (1974). Wetting of manganese cupronickel Cu-20Ni-20Mn: ■ – calculation; some hard alloys by Melchior MNMts20-20. ● – the values obtained at immersion of restrictor on 4, 10 Soviet Powder Metallurgy and Metal Cera- and 16 mm2 [2]; ♦ – average result according to [2] mics. V. 13, No 9, p.p. 731-734. It should be also marked that according to results 3. Prysyazhnyuk P.M., Kryl Ya.A. Kermet na of calculation, distribution of elements in the volume osnove karbida hroma s medno-nikel’-mar- and on surface significantly differs especially accord- gancevoj svjazkoj [Cermet on the base of ing to the content of manganese (fig. 2), which con- chromium carbide with copper-nickel-man- centration in surface layer is nearly 1.4 times higher.