Phase Diagram Determination - Laboratory Report 10 | MATSE 471, Lab Reports of Materials science

Download Phase Diagram Determination - Laboratory Report 10 | MATSE 471 and more Lab Reports Materials science in PDF only on Docsity! MatSE 471 Laboratory 10 Phase Diagram Determination 1. Objective The objective of this laboratory is to determine a portion of the lead-tin phase diagram using thermal analysis. 2. Background The cooling of a material takes place at a rate that is dependent on its heat capacity. If no phase transitions occur, we observe a cooling curve (temperature vs. time) that is smooth and monotonically decreasing, as shown below. Figure 1. Cooling curve for a material that does not undergo a phase transformation. If, however, phase transformations occur during cooling, the cooling curve experiences a discontinuity at the temperature at which the phase transformation takes place (see Figure 2). There are two reasons for this phenomenon. The first is that the new phase often has a heat capacity that is different from the old phase, so the slope of the cooling curve will change as a result of the transformation. A second, more important reason is that most phase transformations that occur on cooling give off heat. For instance, a complete description of the freezing of water would be H2O(l)  H2O(s)+ heat (This heat is why farmers in Florida spray their orange trees with water during a freeze: when the water freezes, it gives off heat that warms the trees so the trees don't die.) When heat is given off during a phase transformation, the cooling rate during the transformation is significantly decreased. Thus, a sudden, significant decrease in the slope of a cooling curve often signals the onset of a phase transformation. When the phase transformation is complete, cooling resumes at a normal rate. Note that phase transformations that give off only very small amounts of heat are hard to detect by thermal analysis, for the change in cooling rates in these cases is slight. T t Figure 2. Cooling of a material that is undergoing a L  S phase transformation. During this transformation, the rate of cooling is noticeably decreased, due to the heat of fusion evolved. When the L  S reaction is complete, cooling resumes at a faster rate, but the rate of cooling of the solid is somewhat different than that of the prior liquid, due to the difference in heat capacities of solids and liquids. There are some conditions under which a phase transformation will cause cooling to stop entirely, resulting in a thermal arrest of the cooling curve, as shown in Figure 3. These conditions can be predicted by the condensed Gibbs phase rule: P + F = C + l. In this equation, P is the number of phases present, C is the number of components (= 2 in a binary alloy), and F is the number of degrees of freedom. If F = 0, then the temperature cannot change during the phase transformation, and we get a horizontal line on the cooling curve. Thus, for a eutectic transformation in a binary alloy (say, Pb- Sn), P = 3, C = 2, and so F = 0. The result is a thermal arrest during the eutectic transformation, as is observed. The freezing (L  S) transformation of a pure metal will also exhibit a thermal arrest (P = 2 and C = l, so F = 0 in this case also). Figure 3. Cooliing of a material undergoing a eutectic transformation. Note that, during the eutectic transformation, the cooling curve exhibits a thermal arrest.