July, 1956
SURFACE TENSION OF NICKELAT ELEVATED TEMPERATURES
Equations 8 and 12 can now be compared. For equation 12 F is plotted versus l / t B . For equation 8 dt/dNB is plotted as a functioii of N B at constant F. Integrating graphically from NB = ( N B ) t o to N B = 0, gives f~ for each F (see Fig. 5 ) . A comparison of the simplified and general expressions is given in Fig. 6. The curves have a similar shape except for an important distinction. The simplified equation 12 suggests no critical force, while the more precise equation 8 predicts a critical force a t G7.5 g. A rough indication of the effect of the variables WA and FT on the apparent bond strength can be
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obtained by calculation. Figures 7 and 8 show the results. Note that work of adhesion has a profound effect on time to breakage for a given load, although it represents a small fraction of the energy expended. The free energy of activation for viscoelastic flow of the adhesive also has a marked effect. Although, admittedly, experimental confirniation is lacking, i t is felt that the absolute rate theory affords a new point of view for examining adhesion and may suggest experiments which could lead to a true understanding of the effect of the variables governing the process.
SURFACE TENSION AT ELEVATED TEMPERATURES. 111. EFFECT OF Cr, In, Sn AND Ti ON LIQUID NICKEL SURFACE TENSION AND INTERFACIAL ENERGY WITH A1203 BY C. R. KURKJIAN AND W. D. KINGERT Ceramics Division, 1 Department of Metallurgy, Massachusetts Institute of Technology, Cambridge, Massachusetts Received Januarv BO, 1966
The sessile drop method has been employed to study the surface tension and interface energy of dilute solutions of indium, tin, chromium and titanium in nickel for the system Ni(l)-A120a(s). The surface tension of pure liquid nickel was found to be 1725 dyne cm.-l. Indium and tin concentrate a t the liquid-gas interface, lowering the surface tension; chromium and titailium concentrate at the solid-liquid interface, lowering the interface energy. Adsorption a t the solid-liquid interface is closely related to the free energy of metal-oxygen bond formation.
Introduction Although the importance of surface and interface energies in determining wetting behavior, in studying joining phenomena, and in determining equilibrium microstructure of polyphase systems is well knowq2S3 there have been few quantitative measurements at elevated temperatures. It has previously been reported that small amounts of osygen and sulfur are markedly surface active in liquid irons4 I n the present paper, the surface and interface energy of the solutions in liquid nickel of iiidium and tin, which have low surface tensions, large atomic size and might be expected to be surface active, and of chromium and titanium, which are known to enhance wetting behavior, are reported. Data previously reported for the surface tension of liquid nickel give values from 1505-1760 dynes/ cm. under various atmospheres and in contact with various supports.6 The higher value would be expected t o be closest t o the value for pure nickel, lower values being due to various sources of minor conta~nination.~No data are available in the literature for solutions of other constituents in nickel. Experimental
in contact with aluminum oxide. The maximum experimental deviations in measured values for a given composition varied between 1 and 3%. Interface energies were calculated from the following relation between the liquidsolid, solid-vapor and liquid-vapor interface energies and the contact angle, e taking a value of 930 erg/cm.2 for YLS = Yay - YLV cos B (1) the solid surface energy of A1203 a t 1475O.O An error in this value, or a change due to the presence of liquid nickel, will shift the absolute value of interfacial energy reported, but will not affect the slope of the curves or the calculation of interfacial adsorption if it can be assumed that small solute additions have no effect on the solid surface ener y. High-purity vacuum-melted nickel (Vacuum detals Corporation) was employed as the base material for all compositions prepared. This material has the following impurities: 0.004% C, 0.0043 0, 0.000042 N, 0.0023 S, 0.002 Cu, 0.025 Fe, 0.01 Mg, 0.009 Si. Compositions were prepared by vacuum melting this material with various additions of high-purity tin, indium, chromium and titanium hydride. From these ingots, samples were prepared with hemispherical bases to ensure a uniform advancing contact angle. Sessile drops were melted on A403 plaques prepared from calcined aluminuni oxide (J. T. Baker, reagent grade), sintered zn vucuo a t 1830", and polished. Indium-nickel and tin-nickel compositions were studied in a purified helium atmosphere; chromium-nickel and titanium-nickel compositions were heated in pure dry hydrogen and then melted zn vacuo (0.005 p). No differences in liquid surface tension were found between measuretnents in hydrogen, helium, or vacuo, indicating that The sessile drop method which previously has been de- previous variations in different atmospheres6 (which gave scribed in detai14is was employed to simultaneously deter- lower surface tenRion values than reported here) must be mine liquid surface tension and contact angle of the liquid attributed to small amounts ot impurities. In view of the known effects of small amounts on metal (1) With funds from the United States Atoniio Energy Commissurface tension,4 all compositions were analyzed for oxygen sion under Contract No. AT(30-1)-1192. as well as for the added constituent. Results of experi(2) C.9. Smith, Trans. A.I.M.E., Tech. Paper No. 2387 (1948). mental surface tension measurements, contact angles, ( 3 ) A. Bondi, Cham. Reus., 52, 417 (1953). and interface energies calculated from equation 1 are listed (4) F. A. Hrtlden and W. D. Kingery, THIS JOURNAL, 89,557 (1955). in Table I. ( 5 ) W. (1953).
D. Kingery and M. Humenik, Jr., i b X , 67, 359
(6)
W. D. Kingery, J . Am. Cer. SOC.,57, 42(1954).
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C. R. KURKJIAN AND W. D. KINGERY
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Vol. 60
TABLE I polation of the molar volume us. temperature for indium13 gives a surface area of 10 X cm.2/ SURFACE TENSION A N D CONTACT ANGLEMEASUREMENTS AT atom a t 1475”. Crude extrapolations of surface ten1475” Wt. % added constituent
0.05 I n 0.53 In 0.90 In 3.32 In 0.007 Sn 0.047 Sn 0 . 5 6 Sn 1.86 Sn 0.027 Cr 0 . 1 4 Cr 0.89 Cr 3.61 Cr 8.72 Cr 0.004 Ti 0.015 T i 0.025 T i 0.051 Ti 0.87 Ti
wt’ % oxygen
Surface tension, dyne om.-’
Contact angle degree
Interface energy, erg cm.-z
0.0048 ,0044 ,0060 .0037 ,005 .005 ’ .003 ,002 .006 .007 .0006 .003 .0075 .002 .001 .001 .001 < .0001
1510 1329 1277 1251 1627 1540 1494 1422 1725 1725 1725 1725 1725 1725 1725 1725 1725 1725
136.7 140.9 141.8 143.1 141.1 145.8 145.4 148.8 136.1 135.2 135.2 118.2 108.8 137.8 125.1 123.6 121.3 90.0
2030 1960 1935 1930 2196 2202 2160 2136 2171 2156 2155 1746 1485 2205 1920 1885 1450 930
Discussion A. Liquid Surface Tension.-In two component systems, the relation between surface tension and composition for ideal mixtures is given by
sion data from much lower temperatures give estimates of 400 dyne/cm. for the surface tension of tin and 150 dyne/cm. for the surface tension of indium a t 1475’. Results of these calculations are shown as solid lines in Fig. 1 together with measured surface tensions. Tin shows negative deviations from ideal solution behavior,14 so that a smaller surface activity is expected than that calculated. Deviations of Ni-In solutions from ideal solution behavior are not known. Additions above 0.5% show surface tensions of the magnitude t o be expected, with deviations for tin occurring in the right direction to be accounted for by deviations from ideality. The lower concentrations show surface tensions which are considerably lower than can be accounted for by ideal solution behavior, and can hardly be accounted for by deviations from ideality since they deviate in the opposite directions from higher concentrations. We have no satisfactory explanation of these results for low concentrations. They are probably in part, and may be completely, due to the 0.005% oxygen present. About this same amount of oxygen is present in the Ni-Cr and Ni-Ti solutions, but would have a lower activity there. The surface tension of pure nickel may be taken from these results as equal to 1725 dyne/cm. a t 1475’. This value is close to the value of 1720 dyne/cm. at 1570” previously reported for pure liquid iron.4 B. Interfacial Energy with A1203.-The interfacial energies of the compositions studied are shown in Fig. 2, plotted against log weight per cent. addition. Over the range of compositions studied, additions of tin and or indium have little effect on the interface energy. I n contrast, both titanium and chromium markedly lower the interface energy. The excess surface concentrations can be derived from the Gibbs isotherm
where y1 and y z are the surface tensions of the pure components el and e2 are the molal surface areas, and x” and X b are the surface and bulk mole fractions, respe~tively.7-~ If solutions are not ideal, an additional term must be included in equation 2 to take into account the mutual interaction of the two components. Surface adsorption of the solute is favored by positive deviations from Raoult’s law as well as by a lowering of the surface ten~ion.~-~ As indicated in Table I, small additions of chromium and titanium have no appreciable effect on the surface tension of nickel. This is not unexpected, since various empirical ~ o r r e l a t i o n s ~ ~ ~ 0 ~ ~ ’ indicate that the surface tensions of titanium and chromium should be similar t o that of nickel. The surface tension of nickel is markedly lowered by small additions of indium and tin. These effects have been calculated from equation 2. The measured density (8.0 g./cc.) and surface tension (1725 dyne/cm.) were employed for liquid nickel in these calculations, taking surface area as equal to the (molal voIume)’/8. The density of tin is known12 a t 1475’ (6.18 g./cc.), giving a surface area of 10.0 x 10-lB cm.2/atom. A linear extra(7)R . Defay and I. Prigogine, Trans. Faraday SOC.,46,199 (1950).
r=-
Io00
0
05
RTdlna
10 15 WEIGHT PERCENT ADDITION.
(3)
20
R. L. Scott, “Solubility of Non-Electrolytes,” Reinhold Publ. Corp., New York, N . Y., 1950. (9) E. A. Guggenheim, “Mixtures,” Oxford Univ. Press, Cambridge,
Fig. 1.-Effect
1952. (10) C. J. Leadbeater, “Selected Gov’t. Res. Rept., Powder Metallurgy,’’ Ministry of Supply, 1951. ( 1 1 ) I
