Engineering Chemistry 3(2+1)

Lesson 2. Phase rule and its application to two component system

2.1.2 THERMAL ANALYSIS

The shape of the freezing point curves for any system especially those involving metals can be determined by thermal analysis a method involving study of the cooling curves of various compositions of systems during solidification.  The form of the cooling curve indicates the composition of the solid. The principle of the method can be understood from the following considerations

1. When a pure substance in the fused or liquid state is allowed to cool slowly and the temperature noted at definite time, the graphic representation of the rate of cooling will be continuous curve (fig.7a) . When the freezing point is reached and the solid makes it appearances, it is indicated by a break in the continuity of the cooling curve and the temperature will remain constant until is completely solidified.  Thereafter, the fall in the temperature will again become continuous. FIGURE  

2. If a mixture of two solids in the fused state be cooled slowly and the cooling curve is obtained in a similar manner. We likewise obtain a continuous cooling curve, so long as the mixture (solution) is in the liquid state. When a solid phase begins to form, the rate of cooling abruptly alters and the cooling curve exhibits a break. However, the temperature dose not remained constant, as in the previous case of cooling of the pure substance. They temperature decreases continuously, but at a different rate and if the mixture forms an eutectic, the fall of temperature continues, till the eutectic point is reached. The system now becomes in variant from the point of the view of the phase rule and the temperature remains content, until solidification is complete.  (see Fig -7b page -403) there after the fall of the temperature becomes uniform but the rate of fall is quite different than the previous one.   

From the cooling curve for any mixture of a definite composition, it is possible to obtain its freezing point and eutectic point.

1. The freezing point varies with the composition of the system, but the eutectic point remains constant for given system.

2. The nearer the composition of the system to the eutectic, the shorter is the portion bc and the more prolonged is the halt cd.

3. If the mixture coincides with the eutectic composition, the curve shows no break corresponding to bc, but the break appears only at the eutectic point, c.

4. If the cooling curve of a series of a alloys of known compositions are worked out and their freezing point are noted,  by plotting freezing point against composition, T-C curve is obtained for the alloy system. However, in order to complete the diagram it is necessary to the freezing point s of the pure components also.

5. Now the cooling curve of an alloy of the same metals, but of unknown composition is determined and its freezing point located in the T – C diagram. The composition corresponding to this freezing point yields the composition of the alloy.

6. The thermal analysis procedure can be used to derive the phase diagram of any two component system

2.1.3 Construction of phase diagram:

            The thermal analysis method (i.e. by studying the cooling rates) can be used to construct the phase diagram of a binary alloy system. It involves the study of temperature – time curves of the various compositions of alloy system during solidification. From theser curves, it is possible to detect the temperatures at which transformation and transitions occure. Let us illustrate it to determine the phase diagram for the binary alloy system of bismuth (Bi) – cadmium (Cd).

 Method:

prepar a number of mixtures of Bi and Cd ranging in composition 100% Bi to 100% Cd. These mixtures are spaced at 10% interval and of equal eight. Place each of these mixtures separately in fireclay or graphite crucible and then melt in an electric furnace in an inert atmosphere of nitrogen. After melting and thorough agitation, a thermocouple is inserted in each melt and the furnace is allowed to cool slowly. Temperature and time reading are taken, until the charge in the crucible is completely solidified. Then prepare the plots of temperature versus time for each mixture. Figure-8  shows a set of cooling curves obtained for various compositions of Bi-Cd mixtures.

 Explanation of cooling curves:

when a body is cooled slowly and uniformly, a smooth cooling curve is obtained, till the temperature approaches that of room. However when some transformation (or transition) that liberates heat occur during cooling, the slope of the curve is reduced suddenly. The nature of the reduction depends on the degree of freedom (F) of the system. A single phase (p=1) with F=2 exhibits a continuous curve, but when a phase appears, the degree of freedom (F) is reduced to one and the heat liberated by the formation of the new phase results in the discontinuity in the curve, due to the change of slope for the cooling of one phase to a lesser slope corresponding to the cooling of two phases. Again, when the third phase appears, F=0, the temperature of the system must remain constant, until one of the phases disappears. This in-turn results in a flat portion on the cooling curve. Finally, when solidification is complete, thesystem regains a degree of freedom, thereby the cooling curves once again exhibit continuous variation of temperature versus time.

In the light of the above facts:

1. Abreak (or arrest) in a cooling curve indicates the appearance of second phase, usually the separation of a solid from the melt, and

2. A horizontal portion in a cooling curve indicates the existence of three phases. With these consideration in mind we can conclude from the cooling curve in Fig. That  the arrests indicated by t_i signifies the appearance of a second phase in the system and the horizontal portions results from the existence of three phases. In the system under consideration, solid phase are pure Bi and pure Cd, so the horizontal portions indicate the simultaneous occurrence of these solid plus melt. It may be noted that in curves (a) and (h) the horizontal portions are due to two phases.

Construction of equilibrium diagram:

      From the cooling curves, the initial solidification temperatures (t_i) and final solidification temperature (t_f) for various concentrations are plotted on a temperature – concentration diagram. Smooth curves drawn through all the t_i and t_f to yield the phase diagram shown in Figure -9 in this diagram:

1. ABC represents the initial freezing point, while DBE represent the final freezing points of metals of various compositions

2. Curve AB indicates the temperatures at which Bi begins to separate from the various concentrations of melt. This line may be looked as the solubility curve of Bi in molten Cd.

3. Curve BC indicates the temperatures at which Cd begins to separate from the various concentration of melt. This line may be looked as the solubility curve of Cd in molten Bi.

4. Point A 9271oC) and C (321oC) represent the freezing (or melting) point of Bi and Cd respectively.

5. Point  B (144oC) represents the solution is saturated with respects to both solids.

2.2 EUTECTIC SYSTEM

            A binary system consisting of two substances, which are miscible in all proportion in the liquid phase, but which do not react chemically, is known as the eutectic (easy to melt) system, e.g. a mixture of lead and silver comprises of such a system.

            Eutectic Mixture is a solid solution of two or more substances having the lowest freezing point of all the possible mixture of the components. This is taken advantage of in alloys of low melting point which are generally eutectic mixtures.

            Eutectic point: Two or more solid substances capable of forming solid solutions with each other tave the property of lowering each other’s freezing point; and the minimum freezing point attainable corresponding to the eutectic mixture is termed the eutectic point (means lowest melting point).

 

Components (m.p., oC)		Eutectic composition	Eutectic Temperature
Ag  (960o)	Cu  (1083o)	71.8 % Ag	778 oC
Pb  (327o)	Ag  (961o)	97.4 % Pb	303 oC
Bi  (271o)	Cd  (321o)	60.0 % Bi	144 oC
Cd  (323o)	Zn  (419o)	67.0 % Zn	270 oC
Zn  (419o)	Al  (659o)	95.6 % Zn	381 oc

 

Application of eutectics: Low-melting alloy are used in safety devices (e.g. as pluge in automobiles), fire-sprinklers device in boilers). By suitable choice of metals, very low melting alloys can be obtained e.g. wood’s metal (alloy containing 50% Bi, 25 % Pb, 12.5 % Cd and 12.5 % Cd) melts at 65 ^oC only.

 2.3 SAFTY FUSES AND SOLDERS

Safety Fuse is a protective device containing a piece of low melting alloy that melts under heat produced either by excess heating or by an excess current in the  circuit , thereby, breaking the circuit. Main objectives of using safety fuses are (i) protection of the equipment by excessive heating or electric current, and (ii) to avoid the chances of accidents.

 Examples:

1. Pressure cooker, used for cooking domestic food items, is provided with a safety fuse made of an alloy, having a definite composition and definite eutectic temperature. Below its eutectic temperature, the alloy exists in the solid form; while above the eutectic temperature it melts to liquid form. Consequently, whenever the cooker is heated above the eutectic temperature due to some reason, the safety fuse melts, thereby avoiding any chace of accident due to overheating of cooker. From these discussions, it is clear that the melting point of the fuse used must be lower than safety limit temperature of the equipment itself.

2. Safety Fuses (as plugs) are employed in buildings to protect them against any fire the hazards. When a building catches fire, the heat melts fusible alloy and water rushes out from the pipe. This controls the fire automatically.

3. Fuses are also used for protecting the cable in an electric circuit against damage from any excusive current than normal. The safety fuse ( in the form of fuse wire ) can carry normal working current safely, without heating, but when current is exceeded than the normal value, it gets heated upto the melting point of fuse alloy, thereby the circuit gets broken. In this way fuse protects the wires in the circuit from over – heating.

4. Safety fuse in the form of plug is fitted in steam boiling in order to avoid any accident caused, due to blockage of high pressure steam in the boiler. Whenever, steam pressure exceeds the limiting value of pressure, safety plug gets over – heated and melts, thereby permitting excessive steam to escape out of the boiler.

Important safety fuse making alloys:

a. Wood metal contains Bi (50%), Pb(25%), Sn(12.5%) and Cd(12.5%). It meets at 70 ^oC and used for making fire – alarms, automatic sprinklers, safety plugs in cookers, milk pot, electric fuses and boiler fuses.

b. Rose metal contains Bi(50%), Pb(28%) and Sn (22%). It melts at 89 ^oC and used for making fire – alarms, electric fuse wires and in automobile sprinklers.

c. Fuse wires for 1.small currents are made of Pb-Sn alloy, 2. high currents are made of Pb,Sn,Zn,Sb,Cu,Al etc.

 2.4 SOLDERS:

are various readily fusible alloys which are applied to the point between metal object to unite them closely and without heating the objects to the melting point. The capability of a solder to join the metal objects closely and intimately depends on the surface alloy formation between the solder and metal objects being joined. The selection of solder for a particular joining purpose depends on the melting point of alloy at which the solder form close and intimate surface alloy with the metal objects to be joined. Solders usually contain Pb and Sn as main components.