Iron and Steel Division - Use of Electrical Resistance Measurements to Determine the Solidus of the Lead-tin System

The solidus is usually the least satisfactorily determined portion of a phase diagram. Cooling curves, which succeed well with the liquidus, show the solidus inaccurately or not at all because of segregation which occurs during freezing. Heating curves of carefully homogenized alloys might be expected to indicate accurately the solidus, but they are seldom used. Dynamic methods involving heating or cooling are never completely satisfactory because of uncertainty as to whether equilibrium is attained. A static method in which the specimen may be allowed hours, days, or even weeks to attain equilibrium is to be preferred. In a static method a solid solution, for example, is first made thoroughly homogeneous, then heated to successively higher temperatures. After sufficient time at each temperature to assure equilibrium, some property is measured which should alter strikingly when melting begins. Microscopic examination can be used to detect the beginning of melting, but the method is tedious since the specimen must be quenched, sectioned, polished, and etched before each examination. Of all the physical properties which change on melting, electrical resistance is probably the most satisfactory to measure. The measurement may be made while the specimen is at temperature without damage to the specimen. It may be repeated indefinitely to ascertain when equilibrium has been achieved. Measurements may be made on a single specimen over the whole range of temperature. Most metals approximately double their resistance on melting. Since an accuracy of a few tenths of a percent is easy to achieve, the method is highly sensitive to the beginning of melting. In spite of these advantages, which have been perceived for a long time,l,2 a reasonable search of the literature has failed to reveal a single case in which the method has been satisfactorily applied in practice to the determination of solidus temperatures. The use of electrical resistance measurements appears to have been confined in practice to changes in the solid state. In the work described in the following pages we have applied the electrical resistance method to the solidus of the lead-tin system. We have found the method to be convenient, reproducible, and highly sensitive. We chose the lead-tin system because it leads to few technical difficulties. Furthermore, a number of determinations of solidus have been made in this system by various methods and results could be checked against them. However, all published results are not in good agreement with one another, so this work should help in determining the solidus more precisely. The Lead-tin Diagram Because of its commercial importance, there have been numerous investigations of the lead-tin diagram. The results of the most recent work on the solidus are indicated in Fig 7, as well as the results of the present work. The works of Honda and Abe3 and of Stockdale4 agree fairly well with each other and with the present work. Jeffery's5 data indicate the solidus to be about 50°C lower. Honda and Abe3 used differential thermal analysis on both heating and cooling cycles. Stockdale4 used the microscopic method and also differential heating curves. Stockdale's results were about 4" higher than those of Honda and Abe at low tin contents and lower at higher tin contents. These results also agree with those of Rosen-hain and Tucker.= Jeffery5 used electrical resistance measurements of the alloy as it was being heated or cooled. Apparently he did not attain equilibrium as his results are about 40°C lower than those of Stockdale4 or Honda and Abe.3 MATERIALS AND METHODS The lead and tin used were of high purity. They were supplied by the American Smelting and Refining Co., who gave the following analyses: Lead: silver, 0.0016 oz per ton; copper, 0.0008 pct; cadmium, 0.0007 pct; zinc, 0.0002 pct; arsenic, 0.0003 pct; antimony, 0.0002 pct; bismuth, 0.0005 pct; tin, 0.0001 pct; iron, 0.0020 pct; lead (by difference), 99.995 pct. Tin: antimony, 0.037 pct; arsenic, 0.020 pct; bismuth, 0.004 pct; cadmium, trace; copper, 0.025 pct; iron, 0.004 pct; lead, 0.020 pct; nickel and cobalt, 0.005 pct; silver, 0.0005 pct; sulphur, 0.005 pct; tin (by .-difference). 99.88 pct. One hundred grams of metal with the desired proportions of lead and tin was weighed out to the nearest one-tenth of a milligram. The mixture was placed in a silica crucible, covered with charcoal, and melted in a reducing atmosphere in a gas-fired furnace. The alloy was well stirred. Chemical analysis of two of the alloys checked closely with the weighed portions. The compositions of the remainder of the alloys were taken directly from the weighings, without chemical analysis.