Solidification & Binary Phase Diagrams II. Solidification & Binary Phase Diagrams II

Transcription

1 Module 19 Solidification & inary Phase Diagrams II ecture 19 Solidification & inary Phase Diagrams II 1 NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

2 Keywords : Three phase equilibrium, eutectic and peritectic system, cooling curves & evolution of structure during solidification, estimation of phases present using lever rule, free energy composition diagram Introduction In the last module we learned about the solidification of a binary alloy consisting of two hypothetical metals & having unlimited solubility in each other in both liquid and solid state. We have seen that in such a system the structure of the solid evolves over a range of temperature. The compositions of the solid and the liquid keep changing during the process. This is possible only if the alloy is cooled under an equilibrium rate of cooling. It was explained how by plotting the temperatures at which the solidification begins and ends as a function of composition you could construct the phase diagram of such a system. In this module we would look at the solidification behavior of a binary alloy where the two components ( & ) have unlimited solubility in the liquid state but limited solubility in the solid state. et denote the solid solution of in and denotes the solid solution of in. In the previous case we had only one solid and one liquid. The phase diagram consisted of two single phase regimes separated by a two phase regime. In this case since there are 3 single phases (,, ); there must be 3 two phase fields (+, +, +). The subsequent part of this module explains how these regions should be arranged in a phase diagram describing the stability of various phases in a temperature composition space. Three phase equilibrium: In this binary system since if there are 3 phases there must be a situation when the 3 phases must coexist. When can this happen? What is the degree of freedom for 3 phase equilibrium in a binary system? Recall that the number of components C = 2, and the number of phases P = 3. Therefore the degree of freedom (F) according to ibb s Phase Rule is given by; F = C+1 P = = 0. It means such equilibrium is possible only at a fixed temperature between three phases of fixed composition. If we write this in the form of a chemical reaction there are only three possibilities. These are given below. = + + = + = 2 The equation 1 represents a case where solidification takes place by simultaneous formation of two phases at a fixed temperature. Note that its degree of freedom is zero. This means such equilibrium can exist at a fixed temperature between a liquid having a fixed composition and two solids of fixed compositions. The amount of liquid would keep decreasing as the solidification continues. The temperature would remain constant during the entire solidification process like that of a pure metal. The alloy which solidifies in this manner is called eutectic. Its cooling curve is exactly same as that of a pure metal. Therefore such a binary system has three compositions (pure, eutectic and pure ) that NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

3 solidify at a fixed temperature. et us assume that the melting points of & are & T and the eutectic temperature is T E. The weight fractions in and that form at the eutectic temperature are X 1 and X 2 respectively. The weight fraction in the eutectic is X E. typical phase diagram of such a system is given in fig 1. This gives a graphical representation of the stability of all the possible phases in a simple binary eutectic system in a temperature composition plane at a constant pressure. Temperature + + a e b X 1 X E X 2 1 Composition T T E Fig 1: typical eutectic phase diagram showing the stability of phases as a function of temperature and composition. It has 3 single phase and 3 two phase regimes. The point e is called the eutectic point and aeb is the eutectic reaction isotherm. t this temperature having X E amount of is in equilibrium with having X 1 amount of and having X 2 amount of are in equilibrium. Just above T E the alloy is totally liquid and just below T E it is a solid made of two phase and. Note that in this type of 3 phase equilibrium the isotherm denoting three phase equilibrium is at a temperature lower than the melting points of both and. The two phase and are known as terminal solid solutions as these are located in the two ends of the diagram. The temperature range over which they solidify is lower than the melting points of both and. However there may be cases (if >> T ) where the solidification range of terminal solid solution may higher than T. This may be represented by equation 2 or 3. The equations 2 & 3 represent a different type of 3 phase equilibrium in a binary alloy. The degree of freedom in this case too is zero. It means that at a fixed temperature having a fixed amount of is in equilibrium with two phase and having fixed amounts of. The temperature remains constant during solidification until the entire amount or a part of reacts with to produceas per equation 2. The temperature at which such equilibrium exists is known as peritectic reaction isotherm (T P ). inary alloy having such an isotherm is known as a peritectic system. et compositions of, and coexisting at this temperature be X P, X 1 and X 2 respectively. typical binary peritectic phase diagram is given by fig 2. lthough the equations 2 & 3 appear to be different they represent exactly similar type of 3 phase equilibrium in a binary alloy system. 3 T + a b p + T P T + T P the alloy consists of liquid and and just below T P NPTE 0 Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept it is made of Metallurgical of. and Materials Engineering 0 X 1 X 2 X P 1 W Fig 2: typical peritectic phase diagram showing the stability of phases as a function of temperature and composition. It has 3 single phase and 3 two phase regimes. The point p is called the peritectic point and abp is the peritectic reaction isotherm. t this temperature having X P amount of is in equilibrium with having X 1 amount of and having X 2 amount of are in equilibrium. Just above

4 Note that in this type of binary phase diagram the isotherm denoting three phase equilibrium is at a temperature lower than the melting points of but higher than that of. The solidification range for the two terminal solid solutions is lower than the melting point of but it is higher than that of. inary eutectic system: Figure 3 represents a phase diagram of a typical binary eutectic system. It gives the temperature range over which solidification takes place in an alloy belonging to this system. It has 3 two phase and 3 single phase regions separated by boundaries having specific names. The line above which the alloy is totally liquid is known as liquidus. The boundary between the terminal solid solutions and the region having both liquid and solid are known as solidus. The boundary between the single phase domains and the one having both and is known as solvus. Temperature + a Solidus iquidus Eutectic e + b + + Solvus 0 X 1 X E X 2 1 Composition T T E Fig 3: typical binary eutectic phase diagram showing the stability of phases as a function of temperature and composition. ine e & T e are known as liquidus. The line a & T b are known as solidus. The line ab is the eutectic reaction isotherm. The line ax 1 & bx 2 are known as solvus. The eutectic reaction is given by (e weight fraction ) = (a weight fraction ) + (b weight fraction ). T E denotes eutectic temperature. inary eutectic system T Eutectic T E + a e + b T T E Slide 1 + Eutectic Eutectic X 1 X 1 W X 2 Time % in eutectic = (eb/ab)x100 at T E NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

5 Slide 1: Shows the solidification of a eutectic. Its cooling curve is exactly same as that of a pure metal. Solidification begins as the temperature reaches T E with simultaneous nucleation and growth of two solids and. It is shown as alternate plates of &. The volume fraction of eutectic keeps increasing at the cost of liquid. The temperature however remains constant as long as the process continues. Once it is totally solid the temperature again keeps dropping. The compositions of & change because the solubility in this case decreases with temperature. The proportion of the two at any temperature is given by the lever rule. It also shows how the structure evolves during solidification. It takes place at a constant temperature. Solid with W = a and with W = b keep precipitating from the liquid. The process consists of two steps; nucleation and growth. The former represents the formation of new crystals or platelets of &. The latter represents the growth of the nodules of eutectic already formed. The eutectic consists of an intimate mixture of two phases. Here it is shown as consisting of alternate layers of & whose weight fractions are given by the lever rule. % 100 % (4) Once the entire liquid transforms into randomly oriented eutectic nodules, the temperature again starts falling. During this the composition of & keeps changing. s a result the proportion of & in the eutectic would change. Note that the boundary between solid and the two phase regime gives the solubility of in. It decreases with temperature. The solvus line on the right of the phase diagram gives the solubility of in. The amount of & in the eutectic at room temperature is given by the following equation: % 100 % (5) If the composition of the alloy is such that a < W < e; it is known as a hypoeutectic alloy. If it lies between e < W < b; it is known as a hypereutectic alloy. Solidification behavior of a hypoeutectic alloy has been explained with the help of slide 2. 5 NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

6 Hypo eutectic alloys: evolution of structure T + T T T Slide 2 a e b T E Hypoeutectic + eutectic 0 X 1 X X E X 2 1 Time % eutectic in the alloy = (ax/ae) x Slide 2: The sketch on the left shows the phase diagram of a binary eutectic system. The dotted line at W = X intersects the liquidus at T. This denotes the temperature at which the alloy begins to solidify during cooling from its molten state. The cooling curve on the right shows that there is a change in the slope at T. s soon as T drops below this temperature; crystals of phase form. The composition of is given by the point of intersection of the tie line at this temperature with the solidus. The amount of increases until it reaches T E when the remaining liquid transforms into eutectic. It also explains how the structure of a hypoeutectic alloy evolves during solidification. Note that the cooling curve of such an alloy has three distinct stages. It cools at a constant rate until T when there is a change in the slope. The cooling rate thereafter is a little slower because of the heat released during solidification. There is a step in the cooling curve at T = T E. During this stage eutectic begins to form with simultaneous precipitation of &. The transformation that takes place during cooling has been illustrated with the help of sketches superimposed on the cooling curve. bove T it is totally liquid. Solidification begins when T drops below T with the formation crystals of. The composition of the first to form is given by the point of intersection of the tie line at T with the solidus. Note that it has much less W than that of the gross alloy (W << X). Consequently the liquid becomes richer in. s T keeps dropping below T the amount of keeps increasing and it becomes relatively richer in. The solvus line describes how the composition of should change. The composition of the liquid too keeps changing. The process continues until the temperature reaches T E. t this stage (W ) = a & (W ) = e = X E and the temperature drop stops until the remaining amount of liquid solidifies as a mixture of &. Thereafter the temperature starts dropping again. schematic microstructure of the alloy immediately after solidification is shown in slide 2. It is made of primary grains (crystals) of and eutectic (shown as alternate layers of &). The grains of that form before the eutectic begins to form are known as pro eutectic. part from this; is present in the eutectic as well. The amount of total, pro eutectic & eutectic in the alloy just after solidification can be estimated using the lever rule. % 100 (6) NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

7 % 100 (7) % 100 (8) % 100 (9) The above set of equations gives the amount different constituents immediately after solidification (just below T E ). s the alloy cools further the composition of pro eutectic (also known as primary) and that in the eutectic would change. The composition of as well would change. The amounts of & in the eutectic too at room temperature would be different from those at T E. Slide 3: The sketch on the left shows phase diagram of a binary eutectic system. The dotted line at W = X intersects the liquidus at T. This denotes the temperature at which the alloy begins to solidify during cooling from its molten state. The cooling curve on the right shows that there is a change in the slope at T. s T drops below this temperature; crystals of phase form. The composition of is given by the point of intersection of the tie line at this temperature with the solidus. The amount of increases until T reaches T E when the remaining liquid transforms into eutectic. Hyper-eutectic alloys: evolution of structure T T Slide 3 a e X b T E Eutectic 0 X 1 X E X X 2 1 Time % eutectic in the alloy = (Xb/eb)100 7 n alloy where e < W < b is known as a hypereutectic alloy. Slide 3 illustrates the solidification behavior of such an alloy. The process of solidification is exactly similar to that of a hypoeutectic alloy. Only difference is that in place of the primary phase here is. schematic microstructure of the alloy NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

8 immediately after solidification is shown in slide 3. It is made of primary grains (crystals) of and eutectic (shown as alternate layers of &). The grains of that form before the eutectic begins to form are known as pro eutectic also known as primary). part from this; is present in the eutectic as well. The amount of total, pro eutectic & eutectic in the alloy just after solidification can be estimated using the lever rule (see equation 10 13). % 100 (10) % 100 (11) % 100 (12) % 100 (13) The cooling curve and the evolution of structure in alloys beyond the eutectic reaction isotherm are exactly same as those of an isomorphous system unless the composition line intersects the solvus. In this stage the cooling rate may become a little slower once precipitation of from begins. The final structure in such a case would consist of grains of & precipitates of along the grain boundaries. The amounts of & in the structure can be estimated by the lever rule. inary peritectic system: et us now look at the solidification behavior of an alloy belonging to a binary peritectic system. Slide 4 describes the nature of the cooling curve of such an alloy and explains how the structure evolves during solidification. 8 NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

9 inary Peritectic system T Solidus + Peritectic isotherm a X b iquidus p + T P Slide 4 0 X X 2 1 X 1 Solvus Solidus W % at peritectic temperature = (xb/ab) x 100 T Slide 4: The sketch on the left shows the phase diagram of a binary pertectic system. The dotted line at W = X intersects the liquidus at T. This denotes the temperature at which the alloy begins to solidify during cooling from its molten state. The cooling curve on the right shows that there is a change in the slope at T. s the alloy cools & temperature drops below T grains of forms. The composition of is given by the point of intersection of the tie line at this temperature with the solidus. The amount of increases until T reaches T P when the liquid begins to react with to form. part of is left behind because the amount of liquid is not enough to consume the entire amount of. The lever rule gives the amount of & in the alloy at T P just before the onset of the peritectic reaction. % 100 (14) % 100 (15) Once the peritectic reaction sets in, (W = a) reacts with the liquid (: W = p) to form (W = b). The most likely location for the reaction is the ( interface. s long as the reaction continues the temperature remains constant. The amount of & as predicted by equation would keep decreasing and the amount of that forms would increase. Depending on the magnitude of X we may come across three situations X = b where the amounts of & are in such a proportion that on the completion of the peritectic reaction the entire amounts of and get consumed in the formation of a new phase (). The final structure immediately after the peritectic reaction is 100%. NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

10 2. a < X < b where the amount of the phase is in excess of that could be consumed by the peritectic reaction with the liquid to form. Therefore on completion of the reaction some amount of is still left behind. The alloy immediately after solidification would therefore consist of two solids. 3. b < X < p where the amount of the liquid is in excess of that could be consumed by the peritectic reaction with solid to form. Therefore on completion of the reaction some amount of liquid is left behind. Immediately after the peritectic reaction the alloy would consist of &. The process of solidification continues even after the pretectic reaction. s it cools (or the temperature drops) the remaining amount of the liquid transforms into solid. The slide 4 therefore represents the case 2. Immediately after the peritectic reaction the alloy consists of two solids (phase) &. The entire amount of the liquid is consumed by the reaction. The relative amounts of the two solids & are given by the lever rule: % 100 (16) % 100 (17) inary peritectic system T + T + a b p + T P Slide 5 T 0 X1 W X X 2 1 Time 10 Slide 5: The sketch on the left shows the phase diagram of a binary pertectic system. The dotted line at W = X intersects the liquidus at T. This denotes the temperature at which the alloy begins to solidify during cooling from its molten state. The cooling curve on the right shows that there is a change in the slope at T. s the alloy cools & temperature drops below T grains of form. The composition of is given by the point of intersection of the tie line at this temperature with the solidus. The amount of NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

11 increases until it reaches T P when the liquid reacts with to form. Here the amount of liquid is just enough to consume the entire amount of. The lever rule could be used to estimate the amount of & in the alloy at T P before the onset of the peritectic reaction. % 100 (18) % 100 (19) The above equations give the amounts of & just enough to form 100%. Drawing an analogy of the eutectic reaction this represents a true peritectic alloy. The peritectic reaction can be described as: (wt % a) + (wt % p) = (wt% b) (20) The evolution of structure in this alloy has been illustrated with the help of the sketches on the right hand side of slide 5. Note that before the onset of the peritectic reaction it consists of + (the white region). Just after the reaction it is made of 100 % (denoted with grey color). With further cooling the composition of should change (Note that the solvus is not vertical) according to the solvus curve. Therefore some amount of comes out of as precipitates. The most favorable sites are the grain boundaries. The white boundary in the microstructure shown in slide 5 denotes. Weight % & % at any given temperature (say 0 C) can be estimated from the phase diagram using the lever rule. inary Peritectic system + a b X p + T T P + + Slide 6 + T + X1 X 2 W X 1 Time 11 Slide 6: This explains the solidification behavior of in a binary peritectic system where the composition of the alloy is given by b < W < p. The vertical dotted line at W = X represents the location of the alloy in the phase diagram. The sketch on the right is a typical cooling curve for such an alloy. Solidification begins with the precipitation of solid when the temperature drops below T. Note that there is a NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

12 change in the slope of the cooling curve given in slide 6. During this stage grains of are formed within the liquid. The structure as shown consists of floating in the liquid. The compositions of the two at a given temperature between T & T P are given by the points of intersections of the tie line with the corresponding solidus and the liquidus. The precipitation of solid during cooling continues until T reaches T P. t this stage the peritectic reaction sets in. This is described by equation 20. Note that the existing solid having a definite composition reacts with the surrounding liquid of fixed composition to form solid having a fixed composition. Until the reaction is over the temperature remains constant. In this case the composition of the alloy is such that even after the entire amount of solid is consumed some amount of liquid is still left behind. When this happens, the peritectic reaction is complete. The temperature of the alloy now consisting of solid and liquid begins to drop again. During this stage solid keeps precipitating out of the remaining liquid. The amount of liquid keeps decreasing until the alloy becomes 100% solid Note that there is a change in the slope of the cooling curve given in slide 6. This denotes the temperature at which solidification is complete. Thereafter as it cools there is no change in the microstructure of the alloy. It is made of several grains of solid having the same composition. Terminal solid solution: oth the eutectic and the peritectic systems may have regions where the reactions involving three phases do not take place. These are known as terminal solid solutions. We would later come across binary alloys where there may be intermediate solid solutions as well. Solidification of terminal alloys begins with the precipitation of either solid or. When this happens the solute gets partitioned between the liquid and the solid. lthough the gross composition of the alloy remains the same, the compositions of the solid and the liquid are different. These are given by the points of intersection of the tie line and the corresponding solidus and the liquidus. Note that during solidification both the solid and the liquid become richer in solute. When the temperature approaches the solidus the composition of the solid tends to approach the gross composition of the alloy where as the liquid has solute far in excess of the gross composition. However the amount of liquid at this stage is negligible. T S T Sol 0 X 1 T + X Tie line + W Eutectic / Peritectic T T S T Sol Time Fig 4: Solidification behavior of a terminal solid solution in any binary phase diagram. 12 Figure 4 illustrates the solidification behavior of a terminal solid solution. The sketch on the left gives a part of the phase diagram. Note that the firm horizontal line could represent either a eutectic or a peritectic reaction. The dotted line at W = X is the alloy whose cooling curve is given on the right. T is the temperature at which solidification begins and Ts is the temperature at which it becomes totally NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

13 solid. t T > T > T S the alloy is partly solid and partly liquid as shown in fig 4. t T S > T > T Sol the alloy consists of solid only. T Sol is the temperature at which the composition line intersects the solvus. Once the temperature drops below T Sol sold starts precipitating out. The composition of that forms is given by the point of intersection of the dotted horizontal tie line at T Sol with the solvus curve for the phase (not shown in the fig 4). s the temperature drops further the amount of in the alloy increases. schematic structure of the alloy is shown in fig 4. There are several commercial alloys having similar features. We shall look at them in details in a subsequent module. Free energy composition diagram: We know that ibb s free energy is a measure of the stability of a phases The one having the lowest free energy is the most stable phase at a given pressure and temperature. In the previous module we looked at free energy composition diagrams at different temperatures for a binary isomorphous system where we compared the stability of two phases (liquid & solid). et us see how such diagrams would look like where 3 phases can coexist. This is illustrated in subsequent slides. T T + + Common tangent to & W + W + % Common tangent to & Slide 7 13 Slide 7: The sketch at the top shows a binary eutectic phase diagram. Consider the stability of the three phases (, and ) involved at a given temperature shown by the horizontal dotted line superimposed on this diagram. The sketch at the bottom gives the free energy composition plots for each of the three phases (, and ) at this temperature. Note that the plots for the solids ( and are much steeper than that of the liquid. Draw a common tangent to the free energy plots of solid ( ) and liquid ( ). The intercepts of a tangent to a free energy curve (say ) with the axes representing pure gives the partial molar free energy of in that phase (. This is also a measure of chemical potential of in. NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

14 Since it coincides with the intercept of the tangent to it satisfies the condition of thermodynamic equilibrium. It means at this temperature a liquid having W weight % can coexist with solid having W weight %. Draw a vertical line at W. If you extend the same it would pass through the point of intersection of the horizontal dotted line on the phase diagram with the solidus line. In the same manner if a vertical line is drawn on the free energy composition diagram at W it would pass through the point of intersection of the horizontal dotted line in the phase diagram with the liquidus. Thus the points on the free energy plots of phases through which a common tangent can be drawn represent the compositions the respective phases that can remain in equilibrium. The common tangent to the free energy plots of solid and liquid too gives similar results. T + + T T E Slide 8 Common tangent W % W W Slide 8 shows the free energy composition curves for the three phases in a binary system at the eutectic temperature. The sketch at the top is a typical binary eutectic phase diagram having two terminal solid solutions ( & ). The sketch at the bottom gives free energy composition curves for the three phases:, &. Note that in this case it is possible to draw a line which is tangent to each of the three phases. This signifies that the chemical potentials of in each of the three phases are equal. The chemical potentials of too in each of the three phases are equal. 14 Free energy composition plots for the three phases in a binary pertiectic system are given in slide 9. The sketch at the top represents a binary peritectic phase diagram. The sketch at the bottom gives the free energy composition curves for the three phases, & at a given temperature T shown with the help of a horizontal dotted line super imposed on the phase diagram. NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

15 T T Common tangent to & + + W % W W W Common tangent to & Slide 9 Note that there is a similarity between the free energy composition plots given in slide 7 & 9. The only difference is in the locations of the plots for &. In slide 9 the plot for is in the central region whereas in slide 7 the plot for is in the middle. In a peritectic system the two solids are relatively more stable than the liquid below the peritectic temperature. The relations between partial molar free energy of each of the three phases are indicated on the diagram. In principle if the free energies of the three phases are known the composition of the phases that could co exist can be calculated in the same way as illustrated in the previous module. In addition it is also possible to find the temperature at which the phases (& ) can coexist. This will be taken up in one of the subsequent modules of this course. Summary: 15 In this module we looked at the main features of a binary phase diagram when the two constituents are soluble in the liquid state but have limited solubility in the solid state. During solidification some of the alloys must pass through a stage where three phases could co exist. Using ibb s phase rule it has been shown that the degree of freedom for such equilibrium is zero. When it happens the temperature and the compositions of the phases must remains constant. Once the reaction involving 3 phases is complete the temperature of the alloy system begins to drop again. There could be two types of cases. In one a liquid of fixed composition transforms into a mixture of two solids () having fixed compositions. This is known as eutectic ( = ). In the other a liquid having a definite composition reacts with a solid having a fixed composition to give a different solid having a fixed composition. This is known as peritectic ( + = or + = ). We have seen if the phase diagram of such a system is known it is possible to visualize what would its structure look like once it has solidified. There is a close relation between a phase diagram and the temperatures at which phase transformations take places. In fact phase diagrams are constructed from the cooling curves of alloys having different compositions. The concept of free energy can also be used to explore the existence of equilibrium between different NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

16 phases. If thermodynamic parameters are known it is possible to construct free energy composition diagrams for different phases at a given temperature. ooking at the trends of these plots it is possible to find the compositions of the phases that could coexist at a given temperature. In this lecture we have learnt how to draw free energy composition curves of the three phases at a given temperature if the phase diagram is given. Exercise: 1. binary alloy having 28 wt % Cu & balance g solidifies at 779⁰C. The soild consists of two pahses &. Phase has 9% Cu whereas phase has 8% g at 779⁰C. t room temperature these are pure g & Cu respectively. Sketch the phase diagram. abel all fields & lines. Melting points of Cu & g are 1083⁰ & 960⁰C respectively. Estimate the amount of & in the above alloy at 779⁰C & at room temperature. 2. molten g Cu (20%) alloy is allowed to cool slowly till room temperature. Refer to the diagram in problem 1 and plot its cooling curve. Estimate % just after it has solidified at 779⁰C & room temperature. Sketch its microstructure and find % Eutectic. 3. diffusion couple consisting of g & Cu was kept at just below its euectic temperature. Show with the help of a schematic diagram the concentration profile along its length at different lengths of hold time. ssume that the couple is queched to suppress any transformation below its eutectic temperature. 4. Two alloys belonging to a binary system have the following microstructures. One having 25% consists of 50% & 50% eutectic and the other having 0.75% has 50% & 50% eutectic. Microstructrural examination shows that eutectic is made of 50% & 50%. Estimate the composition of, & eutectic. 5. Draw the phase diagram for a binary alloy system having following features. Melting point of the two metals ( & ) are widely different. These are partially soluble in each other. There is one three phase reaction isotherm at a temperature higher than the melting point of but lower than that of. Write down the equation representing the 3 phase reaction. What is it commonly known as? 16 NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

17 nswer: 1. The process of solidification at 779⁰C can be represented as =. This involves equlibrium between 3 phases. Such a system is known as eutectic. The phase diagram is as follows: 960⁰ Solvus g iquidus ⁰ 8 28 Wt% Cu 92 Cu 1083⁰ Eutectic reaction isotherm Solvus 28% Cu is a eutectic alloy. % phases are given by lever rule. % % at 779⁰C. t room temperature % % The cooling curve is as follows & refer to the diagram above. Temp + iquidus + Eutectic time Eutectic The microstructure will consist of proeutectic & eutectic. 779 : % % Note that is present as primary phase & within eutectic. t room temperature 20 0 % % g will diffuse into Cu & vice versa. The concentration profile will depend on hold time. These are given for different lengths of time assuming that length of both g & Cu are infinite. g Cu g : Cu: t time = 0 % Cu % g t time = % Cu % g et the eutectic reaction be represented as (X1) = (X2) + (X3). Composition of the three phases are given with brackets. The eutectic reaction isotherm is shown in the following diagram. There are 3 unknowns. Therefore we need three equations to find these. These can be formulated as follows. NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

18 lloy 1 lloy 2 1: X1 X2 X3 2: : ; ; ; These equations can be solved by eliminating the unknown variables one after the other. nswer: X1 =0, X3 = 1 & X2= The diagram is shown below. The 3 phase reaction in case must be + = This is called prectic reaction. + + Note the melting points of the two metals are widely different. The peritectic isotherm lies between these two. T 18 NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering