Elastic Moduli of Some Eutectic Alloy Systems

By B. Subrahmanyam*

The variation of elastic wave velocities with composition has been measured for four eutectic binary systems, namely, Pb-Sn, Cu-Ag, Pb-Sb and Sn-Zn alloys, using the ultrasonic wedge-method. The variation of the calculated moduli is illustrated graphically. The moduli are found to vary continuously with a change in rate of variation at the eutectic composition. Hence the course of the moduli (Young's and rigidity moduli) curves can be taken as a helpful guide in corroborating metallurgical data on the composition at which eutectic formation occurs. A qualitative explanation of the change in rate of variation at the eutectic composition is offered by considering the behaviour of alloy at the eutectic composition as a composite metal. (Received July 19, 1971)

I. Introduction Elastic properties of metallic alloys in the polycry- stalline state whether of binary or of higher types have their own importance in industrial applications. With this view in mind an extensive study of elastic properties of the various types of alloy systems have been undertaken. The present paper reports the concentra- Fig. 1 Optical arrangement for the diffraction of light by ultrasonic waves. tion variation of elastic moduli at room temperature for four eutectic binary alloy systems, namely Pb-Sn, Cu-Ag, Pb-Sb and Sn-Zn, throughout the entire composition range. Some of the alloys of the eutectic systems Pb-Sn and Pb-Sb are of considerable industrial importance. Pb-Sn alloys are used as solders. Pb-Sb alloys are used as bearings and bullets, etc. The propor- tions of the metals have been varied over a wide range to include as many of the commercial alloys as possible. The investigations were mainly concerned with the determination of longitudinal and transverse wave Fig. 2 Crystal holder velocities and the calculation of Young's modulus (Y) and rigidity modulus (n) at 5 or 6 compositions. The variation is illustrated graphically together with phase diagrams. A qualitative explanation of the variation of moduli with composition is proposed.

II. Experimental The method employed is the ultrasonic-wedge method(1) using optical diffraction for the determination of the fundamental frequencies of the alloy specimens. The principle and essential details have been given below for completeness and ready reference. The sufficient power (10W) excites the quartz wedge. In experimental set-up is illustrated in Fig. 1. view of the varying thickness of the wedge, an ultrasonic Asmall wedge of about 2cm×1cm and gradient of frequency spectrum is generated by it when the oscillator 1/10 is prepared from quartz or tourmaline. It is put frequency is gradually varied by rotating the condenser. over the experimental specimen and is acoustically The limits of frequencies depend on the end thicknesses cemented to the specimen surface by putting a small of the wedge. The specimen in contact with the wedge drop of transformer oil between the two. This doublet picks up one or the other of the frequencies produced is mounted on a suitable holder (see Fig. 2). A glass by the wedge and is then thrown into vibration. The cell, 3/4 filled with dust free, doubly distilled water, picked-up frequencies may coincide either to the funda- is suitably mounted on a wooden platform so that the mental or to one of the harmonics of the specimen. surface of the water just makes contact with the bottom The ultrasonic wave so generated by the vibration of the surface of the specimen. An electronic oscillator of specimen is transmitted through the liquid as a travelling

*Department of Physics , Indian Institute of Technology, (1) S. Bbagavantam and J. Bhimasenachar: Proc. Ind. Acad. Sci., Madras-36. India. 20 (1944), 298.

Trans. JIM 1972 Vol.13 90 Elastic Moduli of Some Eutectic Alloy Systems

or standing wave, depending on the depth of the water ground to uniform thickness are annealed for 10 hours in the glass cell and creates a phase grating in the for homogenization at 200℃. Alloys of Cu-Ag system liquid. A collimated monochromatic beam coming from were annealed at 600℃. The values reported are the a linear slit and passing through the liquid in a direc- average ones from the specimens cut in various direc- tion perpendicular to that of the ultrasonic wave gets tions. diffracted by the phase grating provided by the liquid, Check measurements were also made by preparing and the diffraction maxima can be observed visually, the same composition twice or thrice. In all cases good after being brought into focus on a screen. The appear- reproducibility of both concentration and velocity values ance of the diffraction pattern is an indication of the have been obtained. The disparity in velocity and specimen vibrating at its fundamental or at one of its moduli values is in no case greater than 5 percent. The harmonic frequencies. Hence as the oscillator frequency densities of the specimens were determined by hydro- is continuously varied, a series of diffraction patterns static method. appears in succession. By means of an accurate and sensitive frequency meter the frequencies at which the IV. Results patterns appear sharply and intensely can be noted. The frequencies so noted include those belonging to 1. Pb-Sn system longitudinal and transverse modes. The fundamental The variation of moduli with composition is illustrated frequencies of vibration can be arrived at by assigning in Fig. 3. The phase diagram of the system is repro- them to their different modes and different harmonics duced over the Young's modulus vs composition curve in a mode. The patterns belonging to the transverse in Fig. 3. Y and n show a continuous increase with mode are relatively faint. This is because a transverse increasing Sn content. The rate of increase is slow wave is communicated to the liquid in the form of a and is almost linear up to about 60 percent of Sn in consequential longitudinal strain produced by coupling the case of n. Beyond these compositions, the rates of due to edge effects or other inherent causes. increase of Y and n are greater. It is interesting to From the fundamental frequencies so determined the note that the rate of variation increases at a composition velocities and elastic moduli can be determined from the near the eutectic composition which is 61.9 percent of following relations: Sn for this system.

(1)

(2)

(3) where V1is the longitudinalwave velocity, Vt the transverse wave velocity,f1 the longitudinal fundamental frequency,ft transverse fundamental frequency, d the thickness of the specimen, C11 is the longitudinal principle elastic constant, Y the Young's modulus, n the rigidity modulus and ρ the density of the specimen.

III. Preparation of the Specimens

The various alloy systems studied have been prepared as follows:-Weighed quantities of the component metals required for a desired composition have been molten in a cylindrical crucible of about 4cm diameter in a 'Therelek' crucible furnace. The necessary precau- tions as specified in the A.S.M. Hand Book(2) have been Fig.3 Variationof elasticmoduli (Y: Young'smodulus, n: observed scrupulously to avoid oxidation, voltalization, rigiditymodulus) of Pb-Snalloys with compositionat etc. during melting. The melt is furnace cooled to room roomtemperature. Y curvesuperposed on the Pb-Sn temperature. Thin circular sections of about 1.5mm phasediagram. thickness are cut out and ground to uniform thickness. 2. Cu-Ag system The actual composition of the specimens have been fixed after chemical analysis by the methods given in standard The variation of moduli with composition is illu- chemical analysis by Scot(3). The sections after being strated in Fig. 4. The phase diagram of the system is reproduced over the Young's modulus vs the composition (2) A. S. M. Hand Book: Publishd by A. S. M. curve in Fig. 4. In this system also the Y and n decrease (3) W. S. Wilfered: Standard Methods of Chemical Analysis, Vol.2, 5th Ed. by D. Van Nostrand Comp. Inc. Princeton, with content of Ag almost linearly on either side of a N.J. (1966), p.868. composition (about 73 percent of Ag) which is a very B. Subrahmanyam 91

crease with increasing content of Sb a little beyond 10% Sb. After this composition the moduli rise almost linearly. 4. Sn-Zn system The variation of moduli are illustrated in Fig. 6. The phase diagram is reproduced over the variation of Young's modulus with composition curve in Fig. 6. This case is analogous to Pb-Sb system. The eutectic is at 9 percent of Zn. The Y and n curves exhibit changes in the rate of increase at a composition a little over 10 percent of Zn. Beyond that composition the moduli increase almost linearly.

Fig. 4 Variation of elastic moduli (Y: Young's modulus, n: rigidity modulus) of Cu-Ag alloys with composition at room temperature. Y curve superposed on the Cu-Ag phase diagram. nearly eutectic composition and the rate of decrease of moduli changes at that composition.

3. Pb-Sb system The variation of moduli are illustrated in Fig. 5. The phase diagram is reproduced over the variation of Young's modulus vs composition curve in Fig. 5. In this case the eutectic composition is 11.2 percent of Sb. Fig. 6 Variation of elastic moduli (Y: Young's modulus, n: The Y and n curves show a change in the rate of in- rigidity modulus) of Sn-Zn alloys with composition at room temperature. Y curve superposed on the Sn-Zn phase diagram.

V. Discussion

A comprehensive view of the elastic behaviour of the eutectic alloy systems investigated would lead to the following conclusions. The moduli vary continuously and almost linearly with composition. But at a concentration very near to eutectic composition the rate of variation changes as evinced by the change in gradients of the moduli curves. The following table gives the compositions for the changes of the rate of variation of the moduli and actual eutectic composition taken from phase diagrams of the respective alloy systems. It is to be noted from Table 1 that the compositions at which the linear variations of moduli changes its rate coincide approximately with the eutectic compositions.

Table 1 Comparison of eutectic compositions.

Fig. 5 Variation of elastic moduli (Y: Young's modulus, n: rigidity modulus)of Pb-Sb alloys with composition at room temperature. Y curve superposedon the Pb-Sb phase diagram. 92 Elastic Moduli of Some Eutectic Alloy Systems

It might therefore be suggested that the course of as a composite metal with its own individual elastic moduli vs composition curve may be utilized as an aid properties as distinct from those of the component to obtain the eutectic composition in case it is otherwise metals and the other alloys of that series. Therefore difficult from conventional metallurgical studies. This the eutectic system can be imagined as consisting of 3 general feature of the change of rate of variation of the metals in all. Let us say metal A and metal B at the moduli at the eutectic composition, or a composition very ends of the series, and the composite metal AB at the near that, is corroborated by similar results obtained by eutectic composition. So, between the metal A and the Koster(4) for the Pb-Sn eutectic system. In this case metal AB the moduli curve varies almost linearly with the change in rate of variation is at about 45% of Sn a rate of variation of its own. Between the composite and the eutectic composition is about 61.8% of Sn. metal AB and the metal B in a series which is sligthly, But in the present work the composition where the rate different from previous series, the moduli again vary of variation changes in a Pb-Sn system (60 to 65% of nearly linearly with an altered variation. Sn) is much nearer to the eutectic composition and hence is in better agreement. The influence of eutectic composition on the course Acknowledgments of the moduli vs composition curve can be realized as The author expresses his thanks to Prof. Bh. follows. At the eutectic composition the alloy behaves Krishnamurthy, College of Engineering, Andhra Uni- versity for suggesting the problem and his continued (4) W. Koster: Physical Metallurgy for Engineers, by Albert G. Guy, (1962), p.279. encouragement.