Coordinates of Phase Diagram and Experimental Methods
Phase diagrams are usually plotted with temperature as the ordinate, and the alloy composition in weight percentage as the abscissa. Sometimes alloy composition is expressed in atomic percentage for certain type of scientific work as it is more convenient that way. The data for the construction of equilibrium diagrams are determined experimentally by a variety of methods, the most common methods are as under.
Metallographic Methods
This method is applied by heating samples of an alloy to different temperatures, waiting for equilibrium to be established, and then quickly cooling to retain their high-temperature structure. The samples then examined microscopically. This method is difficult to apply to metals at high temperatures because the rapidly cooled samples do not always retain their high-temperature structure, and considerable skill is then required to interpret the observed microstructure correctly.
X-ray Diffraction Technique
This method is applied by measuring the lattice dimensions and indicating the appearance of a new phase either by the change in lattice dimension or by the appearance of a new crystal structure. This method is very precise and very useful in determining the changes in solid solubility with temperature.
Thermal Analysis
This is by far the most widely used experimental method. It relies on the information obtained from the cooling curves. In this method, alloys mixed at different compositions are melted and then the temperature of the mixture is measured at a certain time interval while cooling back to room temperature. This method seems to be best for determining the initial and final temperature of solidification. Phase changes occurring solely in the solid state generally involve only small heat changes, and other methods give more accurate results.
Two Metals Completely Soluble in the Liquid and Solid States (Type I)
Since the two metals are completely soluble in the solid state, the only type of solid phase formed will be a substitutional solid solution. The two metals will generally have the same type of crystal structure and differ in atomic radii by less than 8 percent.
Construction of Phase Diagram
The result of running a series of cooling curves for various combinations or alloys between metals A and B, varying in composition from 100 percent A & 0 percent B to 0 percent A & 100 percent B is shown in the diagram at LHS in the figure given below.
It may be noted that each cooling curve is a separate experiment starting from zero time. The cooling curves for the pure metals A and B show only a horizontal line because the beginning and end of solidification take place at a constant temperature. However, since intermediate compositions form a solid solution, these cooling curves shows two breaks or change in slope. For an alloy containing 80A and 20B, the first break is at temperature T1, which indicates the beginning of solidification, and the lower break at T2 indicates the end of solidification. All intermediate alloy compositions will show a similar type of cooling curve. It is now possible to construct actual phase diagram by plotting temperature vs. composition. The appropriate points are taken from the series of cooling curves and plotted on the new diagram as shown by the diagram at RHS in the above figure. Since the left axis represents the pure metal A, TA is plotted along this line. Similarly, TB is plotted. Since all intermediate compositions are percentages of A and B, for simplicity the percent sign is omitted. A vertical line representing the alloy 80A-20B is drawn, and T1 and T2 from cooling curve are plotted along this line. The same procedure is used for the other compositions.
The phase diagram consists of two points, two lines, and three areas. The two points TA and TB represent the freezing points of the two pure metals. The upper line, obtained by connecting the points showing the beginning of solidification, is called the liquidus; and the lower line, determined by connecting the points showing the end of solidification, is called the solidus line. The area above the liquidus line is a single-phase region, and any alloy in that region will consist of a homogeneous liquid solution. Similarly, the area below the solidus line is a single-phase region, and any alloy in this region will consist of a homogeneous solid solution. It is common practice, in labeling of equilibrium diagrams, to represent solid solution and sometimes intermediate alloys by Greek letters. In this case, it is labeled the solid solution alpha (α). Upper case letters A and B are used to represent the pure metals. Between the liquidus and solidus lines there exists a two-phase region. Any alloy in this region will consist of a mixture of a liquid solution and a solid solution. Specification of temperature and composition of an alloy in a two-phase region indicates that the alloy consists of a mixture of two phases but does not give any information about the actual chemical composition and the relative amounts of the two phases that are present. They can be determined as under.
Chemical Composition of Phases
To determine the actual chemical composition of the phases of an alloy, draw a horizontal temperature line, called a tie line, to the boundaries of the field as shown in the figure given below.
The points of intersection are dropped to the base line, and the composition is read directly. In the above figure, consider the alloy composed of 80A-20B at the temperature T. The alloy is in a two-phase region. To find the composition, draw the tie line mo to the boundaries of the field. Point m, the intersection of tie line with the solidus line, when dropped to the base line, gives the composition of the phase that exists at that boundary. In this case, the phase is a solid solution of α of composition 90A-10B. Similarly, point o, when dropped to the base line, will give the composition of the other phase constituting the mixture, in this case the liquid solution of composition 74A-26B.
Relative Amounts of Each Phase (The Lever Rule)
To determine the relative amounts of the two phases, draw a vertical line representing the alloy and a horizontal temperature line to the boundaries of the field (tie line). The vertical line will divide the horizontal line into two parts whose lengths are inversely proportional to the amount of the phases present. This is also known as the Lever Rule. The point where the vertical line intersects the horizontal line may be considered as the fulcrum of a lever system. The relative lengths of the lever arms multiplied by the amounts of the phases present must balance. In the above figure, the vertical line, representing the alloy 20B, divides the horizontal tie line into two parts, mn and no. If the entire length of the tie line mo is taken to represent 100 percent, or the total weight of the two phases present at temperature T, the lever rule may be expressed mathematically as:
Liquid (percent) = (mn / mo) x 100
Solid α (percent) = (no / mo) x 100
By inserting the numerical values, we get
Liquid (percent) = (10 / 16) x 100 = 62.5
Solid α (percent) = (6 / 16) x 100 = 37.5
The above may be summarized as; the alloy of composition 80A-20B at temperature T consists of a mixture of two phases. One is liquid solution of composition 74A-26B consisting 62.5 percent of all the material present and the other a solid solution of composition 90A-10B making up 37.5 percent of the material present. Note that the right side of the tie line gives the proportion of the phase on the left (α phase in this example) and left side of the tie line gives the proportion of the phase to the right (liquid phase in this example).
Equilibrium Cooling of a Solid Solution Alloy
Phase changes that occur at various stages during equilibrium cooling of a solid solution alloy from liquid state to solid state are explained below. The process is explained with reference to the phase diagram given below by showing what happens in a particular alloy 70A-30B as it is cooled from liquid state to solid state.
The alloy at temperature T0 is a homogeneous single-phase liquid solution and remains so until temperature T1 is reached. Since T1 is on the liquidus line, freezing/solidification now begins. The first nuclei of solid solution to form, α1, will be very rich in the higher-melting-point metal A and will be composed of 95A-5B. Since the solid solution in forming takes material very rich in A from the liquid, the liquid must get richer in B. In view of this, just after the solidification, the composition of the liquid is approximated as 69A-31B.
When the lower temperature T2 is reached, the liquid composition is at L2. The only solid solution in equilibrium with L2 and therefore the only solid solution forming at T2 is α2. It can be seen from the diagram that α2 is composed of 10B. Hence, as the temperature is decreased, not only does the liquid composition become reach in B but also the solid solution. At T2, crystals of α2 are formed surrounding the α1 composition cores (primary dendrites α1) and also separate dendrites of α2 as shown in the figure given below.
In order for the equilibrium to be established at T2, the entire solid phase must be a composition α2. This requires diffusion of B atoms to the A rich core not only from the solid just formed but also from the liquid. This is possible only if the cooling is extremely slow so that diffusion may keep pace with crystal growth. At any temperature, the relative amounts of the liquid and solid solution may be determined by Lever Rule.
As the temperature falls, the solid solution continues to grow at the expense of the liquid. At T3, the solid solution will make up approximately three-fourths of all the material present. Finally, the solidus line is reached at T4 and the last liquid L4, very rich in B, solidifies primarily at the grain boundaries. However, diffusion will take place and all the solid solution will be of uniform composition α (70A-30B), which is the overall composition of the alloy.
Two Metals Completely Soluble in the Liquid State and Completely Insoluble in the Solid State (Type II)
Technically, no two metals are completely insoluble in each other. However, in some cases the solubility is so restricted that for practical purpose they may be considered insoluble. The series of cooling curves for the pure metals and various alloys are shown in the figure given below.
As expected, the cooling curves for the pure metals A and B show a single horizontal line at their freezing points. As B is added to A, the temperature for the beginning of solidification is lowered. As A is added to B, the temperature for the beginning of solidification for those alloys is also lowered. Therefore, since each metal lowers the freezing point of the other, the line connecting the points showing the beginning of solidification, the liquidus line, must show a minimum. This is shown by the upper dotted line in the above figure, showing a minimum at point E, known as the eutectic point, for a composition of 40A-60B. It can be seen that over a wide range of compositions, a portion of the cooling curve that shows the end of solidification occurs at a fixed temperature. The lower horizontal line at TE, shown dotted in the above figure, is known as eutectic temperature. In one alloy, the eutectic composition 40A-60B, complete solidification occurs at a single temperature, the eutectic temperature. Although the freezing of the eutectic composition alloy thus resembles that of a pure metal, it is not congruent melting alloy since the resulting solid is composed of two phases (we will study this shortly in this article). The end product of a congruent melting alloy shall have only one phase. The actual phase diagram may now be constructed by transferring the breaks on the cooling curves to a plot of temperature vs. composition, as shown in the figure given below.
The melting points of the two pure metals, points M and N, are plotted on the vertical lines that represent the pure metals A and B. For an alloy having composition 80A-20B, the points showing the beginning of solidification T1 and end of solidification TE are plotted as shown. The same procedure is followed for all other alloys. The upper lines on the phase diagram connecting the points M, E and N is the liquidus line and shows the beginning of solidification. The point, at which the liquidus lines intersect, the minimum point E, is known as the eutectic point. TE is called the eutectic temperature and 40A-60B the eutectic composition. As solidus line is a continuous line connecting the melting points of pure metals, the complete solidus line is MFGN. The phase diagram consists of four areas. The area above the liquidus line is a single-phase homogeneous liquid solution, since the two metals are soluble in the liquid state (labeled as Liquid solution). The remaining three areas are two-phase areas.
Every two-phase area on a phase diagram must be bounded along a horizontal line by single phases. Thus, if single-phase areas are labeled first, than the two-phase areas may be easily determined. To determine the phases that exist in the two-phase area MFE in the above diagram, a horizontal tie line OL is drawn. This line intersects the liquidus at L, which means that liquid is one of the phases existing in the two-phase area and intersects the left axis at point O. The left axis represents a single phase, the pure metal A, which below melting point is solid. Therefore, the two phases existing in the area MFE are liquid and solid A (labeled as Liquid + Solid A). By the same logic, the two phases that exist in area NEG are liquid and solid B (labeled as Liquid + Solid B).
Since the two metals are assumed to be completely insoluble in the solid state, when freezing starts, the only solid that can form is a pure metal. Thus, every alloy when completely solidified must be a mixture of the two pure metals. Thus the area below FEG line in above diagram will be a mixture of two solid pure metals A and B (labeled as Solid A + Solid B). It is common practice to consider alloys to the left of the eutectic composition as hypoeutectic alloys and those to the right as hypereutectic alloys. The way solidification takes place and resulting microstructures at various stages can be studied by following the slow cooling of different alloys. The process is explained by study of slow cooling of Alloy 1 (eutectic composition), Alloy 2 (hypoeutectic alloys) and Alloy 3 (hypereutectic alloys) in the figure given below.
Alloy 1 (Eutectic Composition)
Alloy 1 is the eutectic composition 40A-60B. As it is cooled from temperature T0, it remains a uniform liquid solution until it reaches point E, on the horizontal eutectic temperature line. Since this is the intersection of the liquidus and solidus lines, the liquid must now start to solidify, and the temperature cannot drop until the alloy is completely solid. The liquid will solidify into a mixture of two phases. These phases are always the ones that appear at either end of the horizontal eutectic-temperature line, in this case point F, which is pure metal A, and point G, the pure metal B. Let us assume that a small amount of pure metal A solidified. This leaves the remaining liquid richer in B; the liquid composition has shifted slightly to the right. To restore the liquid composition to equilibrium value, B will solidify. If slightly too much B is solidified, the liquid composition will have shifted to the left, requiring A to solidify to restore equilibrium. Therefore, at constant temperature, the liquid solidifies alternately pure A and pure B, resulting in extremely fine mixture usually visible only under the microscope. This is known as eutectic mixture shown at (4) in the above figure. In the above figure at (1), the alloy is in liquid state. At (2), as the alloy starts to solidify, it forms alternate layers of pure A and pure B. This layered microstructure is known as lamellar microstructure and the layers are often only of the order of 1 micron across. The reason that a eutectic alloy forms in this way has to do with the diffusion times required to form the solid. The grains grow by adding A to A and B to B until they encounter another grain as shown at (3). Further nucleation sites will also continue to form within the liquid parts of the mixture and solidification completes as shown at (4). This solidification happens very rapidly as the liquid reaches the eutectic temperature. It may be noted that though the points (2), (3) and (4) are shown separately, actually they are at the same location (all are pointed to E).
The change of this liquid of composition E into two solids at constant temperature is known as the eutectic reaction and may be written as
Since solidification of eutectic alloy occurs at constant temperature, its cooling curve would be the same as that for a pure metal or any congruent melting alloy. The eutectic solidification however is not congruent as there is a difference in composition between the liquid and the individual solid phases.
Alloy 2 (Hypoeutectic Alloys)
Alloy 2, a hypoeutectic alloy composed of 80A-20B, remains a uniform liquid solution as shown at (1) until the liquidus line temperature T1 is reached. At this point the liquid L1, is saturated in A, and as the temperature is dropped slightly, the excess A must solidify as shown at (2). The liquid by depositing crystals of pure A must become richer in B. It can be seen that at temperature T2, solid is pure A and liquid composition L2 is 70A-30B. The amount of A and L2 can be calculated using the Lever Rule as under.
A (percent) = (x2L2 / T2L2) x 100 = (10 / 30) x 100 = 33 percent
L2 (percent) = (T2x2 / T2L2) x 100 = (20 / 30) x 100 = 63 percent
The microstructure would appear as shown at (3). As the solidification continues, the amount of pure solid A increases gradually by continued precipitation from the liquid. The liquid composition, becoming richer in B, is slowly travelling downward and to the right along the liquidus curve, while the amount of liquid is gradually decreasing. When the alloy reaches xE, the eutectic line, the liquid is at point E. The conditions existing just a fraction of a degree above TE are: The microstructure would appear as shown at (4). The remaining liquid (33 percent), having reached the eutectic point, now solidifies into the fine intimate mixture of A and B as described under alloy 1. When solidified, the alloy will consist of 67 percent of grains of primary or proeutectic A (which formed between T1 and TE or before the eutectic reaction) and 33 percent eutectic (A + B) mixture as shown at (5). Every alloy to the left of the eutectic point E, when solidified, will consist of grains of proeutectic A and the eutectic mixture. The closer the alloy composition is to the eutectic composition, the more eutectic mixture will be present in the solidified alloy.
Alloy 3 (Hypereutectic Alloys)
Alloy 3, a hypereutectic alloy composed of 10A-90B, undergoes the same cooling process as alloy 2 except that when the liquidus line is reached at temperature T3 the liquid deposits crystals of pure B instead of A as shown at (2). As the temperature is decreased, more and more of B will solidify, leaving the liquid richer in A. The amount of liquid gradually decreases, and its composition gradually moves down and to the left along the liquidus line until the point E is reached at the eutectic temperature. The remaining liquid now solidifies into the eutectic (A + B) mixture as shown at (5). After solidification the alloy will consist of 75 percent grains of primary B or proeutectic B and 25 percent eutectic (A + B) mixture.
Every alloy to the right of eutectic point, when solidified, will consist of grains of proeutectic B and the eutectic mixture (A + B). The area below the solidus line and to the left of the eutectic composition is labeled Solid A + Eutectic mixture and that to the right, Solid B + Eutectic mixture.
Thus it is apparent that, regardless of alloy composition, the same reaction takes place whenever the eutectic-temperature line is reached, namely,
The above reaction applies specifically to the figure (diagram) given above. However, the eutectic reaction may be written in general as,
The only requirement being that the eutectic mixture consists of two different solid phases. This mixture may be two pure metals, two solid solutions, two intermediate phases, or any combination of the above.
Two Metals Completely Soluble in the Liquid State but only Partly Soluble in the Solid State (Type III)
Since most metals have some solubility for each other in the solid state, this type is the most common alloy system. The phase diagram of this type is shown in the figure given below.
The melting points of the pure metals A and B are shown as TA and TB respectively. The liquidus line is TAETB, and the solidus line is TAFEGTB.
The single-phase areas are now labeled. Above the liquidus line, there is only single-phase liquid solution. At the melting points of pure metals (at melting point of A and melting point of B), where the liquidus and solidus lines meet, the diagram resembles the cigar-shaped diagram of Type I (complete solid solubility), and since these metals are partly soluble in the solid state, a solid solution must be formed. Alloys in this system never solidify crystals of pure A or pure B but always a solid solution or mixture of solid solutions. Thus the areas below melting points of pure metal A and pure metal B are the areas of single-phase α (alpha) and β (beta) solid-solutions. Since these solid solutions are next to the axes, they are known as terminal solid solutions. The remaining three two-phase areas may now be labeled as liquid + α, liquid + β and α + β.
At TE, the α solid solution dissolves a maximum of 20 percent B as shown by point F and the β solid solution a maximum of 10 percent A as shown by point G. With decreasing temperature, the maximum amount of solute that can be dissolved decreases, as indicated by lines FH and GJ. These lines are called solvus lines and indicate the maximum solubility (saturated solution) of B in A (α solution) or A in B (β solution) as a function of temperature. Point E, where the liquidus lines meet at a minimum, as in Type II, is known as the eutectic point.
The way solidification takes place and resulting microstructures at various stages can be studied by following the slow cooling of different alloys as under.
Alloy 1
Alloy 1 composed of 95A-5B, when slowly cooled, will follow a process exactly the same as any alloy in Type I. When liquidus line is crossed at T1, it will begin to solidify by forming crystals of α solid solution extremely rich in A. The process continues, with the liquid getting richer in B and gradually moving down along the liquidus line. The α solid solution, also getting richer in B, is moving down along the solidus line. When the solidus line is finally crossed at T4 and with diffusion keeping pace with crystal growth, the entire solid will be a homogeneous α solid solution and will remain that way down to room temperature.
Alloy 2
Alloy 2, 30A-70B is the eutectic composition and remains liquid until the eutectic temperature is reached at point E. Since this is also the solidus line, the liquid now undergoes the eutectic reaction, at constant temperature, forming a very fine mixture of two solids. The two solids that make up eutectic mixture are given by the extremities of the eutectic-temperature line, α of composition F and β of composition G. The eutectic reaction may be written as
This reaction is the same as the one which occurred in the Type II diagram, except for the substitution of solid solutions for pure metals. The relative amounts of α and β in the eutectic mixture may be determined by the Lever Rule as under.
α (percent) = (EG / FG) x 100 = (20 / 70) x 100 = 28.6 percent
β (percent) = (EF / FG) x 100 = (50 / 70) x 100 = 71.4 percent
Because of the change in solubility of B in A, line FH, and of A in B, line GJ, there will be a slight change in the relative amounts of α and β as the alloy is cooled to room temperature. The relative amounts of α and β at room temperature are,
α (percent) = (KJ / HJ) x 100 = (25 / 85) x 100 = 29.4 percent
β (percent) = (HK / HJ) x 100 = (60 / 85) x 100 = 70.6 percent
Compositions of the two solid solutions that make up eutectic mixture are given by the composition existing on either end of the tie line HKJ, α of composition H (90A-10B) and β of composition J (5A-95B).
Alloy 3
Alloy 3, 60A-40B, remains liquid until the liquidus line is reached at T3. The liquid starts to solidify crystals of primary α solid solution very rich in A. As the temperature decreases the liquid becomes richer and richer in B, gradually moving down and to the right along the liquidus line until it reaches point E. Just above the eutectic temperature TE, there exist two phases as under. Since the remaining liquid (40 percent) is at point E, the right temperature and composition to form the eutectic mixture, it now solidifies by forming alternately crystals of α and β of the composition appearing at the ends of the eutectic temperature line (points F and G). The temperature does not drop until solidification is complete.
As the alloy cools to room temperature because of the change in solubility, as shown by the solvus line FH, some excess β is precipitated from the solution.
Alloy 4
Alloy 4, 85A-15B, initially follows the same process as described for Alloy I. Solidification starts at T2 and is complete at T5, the resultant solid being a homogeneous single phase, the α solid solution (85A-15 B). At M, the solution is unsaturated. The solvus line FH as explained previously, shows the decrease in solubility of B in A with decreasing temperature. As the alloy cools, the solvus line is reached at point N. The α solution is saturated in B. Below this temperature, under slow cooling, the excess B comes out of solution. Since A is soluble in B, the precipitate does not come out as the pure metal B but as β solid solution. At room temperature, the alloy will consist mostly of α with a small amount of excess β, primarily along the grain boundaries. The excess β can be determined by applying the Lever Rule at the line HJ as under.
β (percent) = (HP / HJ) x 100 = (5 / 85) x 100 = 5.88 percent
If the β phase is relatively brittle, the alloy will not be very strong or ductile. The strength of an alloy to a large extent is determined by the phase that is continuous through the alloy. In this case, although the β solution constitutes only about 6 percent of the alloy, it exists as a continuous network along the grain boundaries. Therefore, the alloy will tend to rupture along these boundaries. This alloy, however, may be made to undergo a significant change in strength and hardness after being properly heat treated.
Phase diagrams are usually plotted with temperature as the ordinate, and the alloy composition in weight percentage as the abscissa. Sometimes alloy composition is expressed in atomic percentage for certain type of scientific work as it is more convenient that way. The data for the construction of equilibrium diagrams are determined experimentally by a variety of methods, the most common methods are as under.
Metallographic Methods
This method is applied by heating samples of an alloy to different temperatures, waiting for equilibrium to be established, and then quickly cooling to retain their high-temperature structure. The samples then examined microscopically. This method is difficult to apply to metals at high temperatures because the rapidly cooled samples do not always retain their high-temperature structure, and considerable skill is then required to interpret the observed microstructure correctly.
X-ray Diffraction Technique
This method is applied by measuring the lattice dimensions and indicating the appearance of a new phase either by the change in lattice dimension or by the appearance of a new crystal structure. This method is very precise and very useful in determining the changes in solid solubility with temperature.
Thermal Analysis
This is by far the most widely used experimental method. It relies on the information obtained from the cooling curves. In this method, alloys mixed at different compositions are melted and then the temperature of the mixture is measured at a certain time interval while cooling back to room temperature. This method seems to be best for determining the initial and final temperature of solidification. Phase changes occurring solely in the solid state generally involve only small heat changes, and other methods give more accurate results.
Two Metals Completely Soluble in the Liquid and Solid States (Type I)
Since the two metals are completely soluble in the solid state, the only type of solid phase formed will be a substitutional solid solution. The two metals will generally have the same type of crystal structure and differ in atomic radii by less than 8 percent.
Construction of Phase Diagram
The result of running a series of cooling curves for various combinations or alloys between metals A and B, varying in composition from 100 percent A & 0 percent B to 0 percent A & 100 percent B is shown in the diagram at LHS in the figure given below.
It may be noted that each cooling curve is a separate experiment starting from zero time. The cooling curves for the pure metals A and B show only a horizontal line because the beginning and end of solidification take place at a constant temperature. However, since intermediate compositions form a solid solution, these cooling curves shows two breaks or change in slope. For an alloy containing 80A and 20B, the first break is at temperature T1, which indicates the beginning of solidification, and the lower break at T2 indicates the end of solidification. All intermediate alloy compositions will show a similar type of cooling curve. It is now possible to construct actual phase diagram by plotting temperature vs. composition. The appropriate points are taken from the series of cooling curves and plotted on the new diagram as shown by the diagram at RHS in the above figure. Since the left axis represents the pure metal A, TA is plotted along this line. Similarly, TB is plotted. Since all intermediate compositions are percentages of A and B, for simplicity the percent sign is omitted. A vertical line representing the alloy 80A-20B is drawn, and T1 and T2 from cooling curve are plotted along this line. The same procedure is used for the other compositions.
The phase diagram consists of two points, two lines, and three areas. The two points TA and TB represent the freezing points of the two pure metals. The upper line, obtained by connecting the points showing the beginning of solidification, is called the liquidus; and the lower line, determined by connecting the points showing the end of solidification, is called the solidus line. The area above the liquidus line is a single-phase region, and any alloy in that region will consist of a homogeneous liquid solution. Similarly, the area below the solidus line is a single-phase region, and any alloy in this region will consist of a homogeneous solid solution. It is common practice, in labeling of equilibrium diagrams, to represent solid solution and sometimes intermediate alloys by Greek letters. In this case, it is labeled the solid solution alpha (α). Upper case letters A and B are used to represent the pure metals. Between the liquidus and solidus lines there exists a two-phase region. Any alloy in this region will consist of a mixture of a liquid solution and a solid solution. Specification of temperature and composition of an alloy in a two-phase region indicates that the alloy consists of a mixture of two phases but does not give any information about the actual chemical composition and the relative amounts of the two phases that are present. They can be determined as under.
Chemical Composition of Phases
To determine the actual chemical composition of the phases of an alloy, draw a horizontal temperature line, called a tie line, to the boundaries of the field as shown in the figure given below.
The points of intersection are dropped to the base line, and the composition is read directly. In the above figure, consider the alloy composed of 80A-20B at the temperature T. The alloy is in a two-phase region. To find the composition, draw the tie line mo to the boundaries of the field. Point m, the intersection of tie line with the solidus line, when dropped to the base line, gives the composition of the phase that exists at that boundary. In this case, the phase is a solid solution of α of composition 90A-10B. Similarly, point o, when dropped to the base line, will give the composition of the other phase constituting the mixture, in this case the liquid solution of composition 74A-26B.
Relative Amounts of Each Phase (The Lever Rule)
To determine the relative amounts of the two phases, draw a vertical line representing the alloy and a horizontal temperature line to the boundaries of the field (tie line). The vertical line will divide the horizontal line into two parts whose lengths are inversely proportional to the amount of the phases present. This is also known as the Lever Rule. The point where the vertical line intersects the horizontal line may be considered as the fulcrum of a lever system. The relative lengths of the lever arms multiplied by the amounts of the phases present must balance. In the above figure, the vertical line, representing the alloy 20B, divides the horizontal tie line into two parts, mn and no. If the entire length of the tie line mo is taken to represent 100 percent, or the total weight of the two phases present at temperature T, the lever rule may be expressed mathematically as:
Liquid (percent) = (mn / mo) x 100
Solid α (percent) = (no / mo) x 100
By inserting the numerical values, we get
Liquid (percent) = (10 / 16) x 100 = 62.5
Solid α (percent) = (6 / 16) x 100 = 37.5
The above may be summarized as; the alloy of composition 80A-20B at temperature T consists of a mixture of two phases. One is liquid solution of composition 74A-26B consisting 62.5 percent of all the material present and the other a solid solution of composition 90A-10B making up 37.5 percent of the material present. Note that the right side of the tie line gives the proportion of the phase on the left (α phase in this example) and left side of the tie line gives the proportion of the phase to the right (liquid phase in this example).
Equilibrium Cooling of a Solid Solution Alloy
Phase changes that occur at various stages during equilibrium cooling of a solid solution alloy from liquid state to solid state are explained below. The process is explained with reference to the phase diagram given below by showing what happens in a particular alloy 70A-30B as it is cooled from liquid state to solid state.
The alloy at temperature T0 is a homogeneous single-phase liquid solution and remains so until temperature T1 is reached. Since T1 is on the liquidus line, freezing/solidification now begins. The first nuclei of solid solution to form, α1, will be very rich in the higher-melting-point metal A and will be composed of 95A-5B. Since the solid solution in forming takes material very rich in A from the liquid, the liquid must get richer in B. In view of this, just after the solidification, the composition of the liquid is approximated as 69A-31B.
When the lower temperature T2 is reached, the liquid composition is at L2. The only solid solution in equilibrium with L2 and therefore the only solid solution forming at T2 is α2. It can be seen from the diagram that α2 is composed of 10B. Hence, as the temperature is decreased, not only does the liquid composition become reach in B but also the solid solution. At T2, crystals of α2 are formed surrounding the α1 composition cores (primary dendrites α1) and also separate dendrites of α2 as shown in the figure given below.
In order for the equilibrium to be established at T2, the entire solid phase must be a composition α2. This requires diffusion of B atoms to the A rich core not only from the solid just formed but also from the liquid. This is possible only if the cooling is extremely slow so that diffusion may keep pace with crystal growth. At any temperature, the relative amounts of the liquid and solid solution may be determined by Lever Rule.
As the temperature falls, the solid solution continues to grow at the expense of the liquid. At T3, the solid solution will make up approximately three-fourths of all the material present. Finally, the solidus line is reached at T4 and the last liquid L4, very rich in B, solidifies primarily at the grain boundaries. However, diffusion will take place and all the solid solution will be of uniform composition α (70A-30B), which is the overall composition of the alloy.
Two Metals Completely Soluble in the Liquid State and Completely Insoluble in the Solid State (Type II)
Technically, no two metals are completely insoluble in each other. However, in some cases the solubility is so restricted that for practical purpose they may be considered insoluble. The series of cooling curves for the pure metals and various alloys are shown in the figure given below.
As expected, the cooling curves for the pure metals A and B show a single horizontal line at their freezing points. As B is added to A, the temperature for the beginning of solidification is lowered. As A is added to B, the temperature for the beginning of solidification for those alloys is also lowered. Therefore, since each metal lowers the freezing point of the other, the line connecting the points showing the beginning of solidification, the liquidus line, must show a minimum. This is shown by the upper dotted line in the above figure, showing a minimum at point E, known as the eutectic point, for a composition of 40A-60B. It can be seen that over a wide range of compositions, a portion of the cooling curve that shows the end of solidification occurs at a fixed temperature. The lower horizontal line at TE, shown dotted in the above figure, is known as eutectic temperature. In one alloy, the eutectic composition 40A-60B, complete solidification occurs at a single temperature, the eutectic temperature. Although the freezing of the eutectic composition alloy thus resembles that of a pure metal, it is not congruent melting alloy since the resulting solid is composed of two phases (we will study this shortly in this article). The end product of a congruent melting alloy shall have only one phase. The actual phase diagram may now be constructed by transferring the breaks on the cooling curves to a plot of temperature vs. composition, as shown in the figure given below.
The melting points of the two pure metals, points M and N, are plotted on the vertical lines that represent the pure metals A and B. For an alloy having composition 80A-20B, the points showing the beginning of solidification T1 and end of solidification TE are plotted as shown. The same procedure is followed for all other alloys. The upper lines on the phase diagram connecting the points M, E and N is the liquidus line and shows the beginning of solidification. The point, at which the liquidus lines intersect, the minimum point E, is known as the eutectic point. TE is called the eutectic temperature and 40A-60B the eutectic composition. As solidus line is a continuous line connecting the melting points of pure metals, the complete solidus line is MFGN. The phase diagram consists of four areas. The area above the liquidus line is a single-phase homogeneous liquid solution, since the two metals are soluble in the liquid state (labeled as Liquid solution). The remaining three areas are two-phase areas.
Every two-phase area on a phase diagram must be bounded along a horizontal line by single phases. Thus, if single-phase areas are labeled first, than the two-phase areas may be easily determined. To determine the phases that exist in the two-phase area MFE in the above diagram, a horizontal tie line OL is drawn. This line intersects the liquidus at L, which means that liquid is one of the phases existing in the two-phase area and intersects the left axis at point O. The left axis represents a single phase, the pure metal A, which below melting point is solid. Therefore, the two phases existing in the area MFE are liquid and solid A (labeled as Liquid + Solid A). By the same logic, the two phases that exist in area NEG are liquid and solid B (labeled as Liquid + Solid B).
Since the two metals are assumed to be completely insoluble in the solid state, when freezing starts, the only solid that can form is a pure metal. Thus, every alloy when completely solidified must be a mixture of the two pure metals. Thus the area below FEG line in above diagram will be a mixture of two solid pure metals A and B (labeled as Solid A + Solid B). It is common practice to consider alloys to the left of the eutectic composition as hypoeutectic alloys and those to the right as hypereutectic alloys. The way solidification takes place and resulting microstructures at various stages can be studied by following the slow cooling of different alloys. The process is explained by study of slow cooling of Alloy 1 (eutectic composition), Alloy 2 (hypoeutectic alloys) and Alloy 3 (hypereutectic alloys) in the figure given below.
Alloy 1 (Eutectic Composition)
Alloy 1 is the eutectic composition 40A-60B. As it is cooled from temperature T0, it remains a uniform liquid solution until it reaches point E, on the horizontal eutectic temperature line. Since this is the intersection of the liquidus and solidus lines, the liquid must now start to solidify, and the temperature cannot drop until the alloy is completely solid. The liquid will solidify into a mixture of two phases. These phases are always the ones that appear at either end of the horizontal eutectic-temperature line, in this case point F, which is pure metal A, and point G, the pure metal B. Let us assume that a small amount of pure metal A solidified. This leaves the remaining liquid richer in B; the liquid composition has shifted slightly to the right. To restore the liquid composition to equilibrium value, B will solidify. If slightly too much B is solidified, the liquid composition will have shifted to the left, requiring A to solidify to restore equilibrium. Therefore, at constant temperature, the liquid solidifies alternately pure A and pure B, resulting in extremely fine mixture usually visible only under the microscope. This is known as eutectic mixture shown at (4) in the above figure. In the above figure at (1), the alloy is in liquid state. At (2), as the alloy starts to solidify, it forms alternate layers of pure A and pure B. This layered microstructure is known as lamellar microstructure and the layers are often only of the order of 1 micron across. The reason that a eutectic alloy forms in this way has to do with the diffusion times required to form the solid. The grains grow by adding A to A and B to B until they encounter another grain as shown at (3). Further nucleation sites will also continue to form within the liquid parts of the mixture and solidification completes as shown at (4). This solidification happens very rapidly as the liquid reaches the eutectic temperature. It may be noted that though the points (2), (3) and (4) are shown separately, actually they are at the same location (all are pointed to E).
The change of this liquid of composition E into two solids at constant temperature is known as the eutectic reaction and may be written as
Since solidification of eutectic alloy occurs at constant temperature, its cooling curve would be the same as that for a pure metal or any congruent melting alloy. The eutectic solidification however is not congruent as there is a difference in composition between the liquid and the individual solid phases.
Alloy 2 (Hypoeutectic Alloys)
Alloy 2, a hypoeutectic alloy composed of 80A-20B, remains a uniform liquid solution as shown at (1) until the liquidus line temperature T1 is reached. At this point the liquid L1, is saturated in A, and as the temperature is dropped slightly, the excess A must solidify as shown at (2). The liquid by depositing crystals of pure A must become richer in B. It can be seen that at temperature T2, solid is pure A and liquid composition L2 is 70A-30B. The amount of A and L2 can be calculated using the Lever Rule as under.
A (percent) = (x2L2 / T2L2) x 100 = (10 / 30) x 100 = 33 percent
L2 (percent) = (T2x2 / T2L2) x 100 = (20 / 30) x 100 = 63 percent
The microstructure would appear as shown at (3). As the solidification continues, the amount of pure solid A increases gradually by continued precipitation from the liquid. The liquid composition, becoming richer in B, is slowly travelling downward and to the right along the liquidus curve, while the amount of liquid is gradually decreasing. When the alloy reaches xE, the eutectic line, the liquid is at point E. The conditions existing just a fraction of a degree above TE are: The microstructure would appear as shown at (4). The remaining liquid (33 percent), having reached the eutectic point, now solidifies into the fine intimate mixture of A and B as described under alloy 1. When solidified, the alloy will consist of 67 percent of grains of primary or proeutectic A (which formed between T1 and TE or before the eutectic reaction) and 33 percent eutectic (A + B) mixture as shown at (5). Every alloy to the left of the eutectic point E, when solidified, will consist of grains of proeutectic A and the eutectic mixture. The closer the alloy composition is to the eutectic composition, the more eutectic mixture will be present in the solidified alloy.
Alloy 3 (Hypereutectic Alloys)
Alloy 3, a hypereutectic alloy composed of 10A-90B, undergoes the same cooling process as alloy 2 except that when the liquidus line is reached at temperature T3 the liquid deposits crystals of pure B instead of A as shown at (2). As the temperature is decreased, more and more of B will solidify, leaving the liquid richer in A. The amount of liquid gradually decreases, and its composition gradually moves down and to the left along the liquidus line until the point E is reached at the eutectic temperature. The remaining liquid now solidifies into the eutectic (A + B) mixture as shown at (5). After solidification the alloy will consist of 75 percent grains of primary B or proeutectic B and 25 percent eutectic (A + B) mixture.
Every alloy to the right of eutectic point, when solidified, will consist of grains of proeutectic B and the eutectic mixture (A + B). The area below the solidus line and to the left of the eutectic composition is labeled Solid A + Eutectic mixture and that to the right, Solid B + Eutectic mixture.
Thus it is apparent that, regardless of alloy composition, the same reaction takes place whenever the eutectic-temperature line is reached, namely,
The above reaction applies specifically to the figure (diagram) given above. However, the eutectic reaction may be written in general as,
The only requirement being that the eutectic mixture consists of two different solid phases. This mixture may be two pure metals, two solid solutions, two intermediate phases, or any combination of the above.
Two Metals Completely Soluble in the Liquid State but only Partly Soluble in the Solid State (Type III)
Since most metals have some solubility for each other in the solid state, this type is the most common alloy system. The phase diagram of this type is shown in the figure given below.
The melting points of the pure metals A and B are shown as TA and TB respectively. The liquidus line is TAETB, and the solidus line is TAFEGTB.
The single-phase areas are now labeled. Above the liquidus line, there is only single-phase liquid solution. At the melting points of pure metals (at melting point of A and melting point of B), where the liquidus and solidus lines meet, the diagram resembles the cigar-shaped diagram of Type I (complete solid solubility), and since these metals are partly soluble in the solid state, a solid solution must be formed. Alloys in this system never solidify crystals of pure A or pure B but always a solid solution or mixture of solid solutions. Thus the areas below melting points of pure metal A and pure metal B are the areas of single-phase α (alpha) and β (beta) solid-solutions. Since these solid solutions are next to the axes, they are known as terminal solid solutions. The remaining three two-phase areas may now be labeled as liquid + α, liquid + β and α + β.
At TE, the α solid solution dissolves a maximum of 20 percent B as shown by point F and the β solid solution a maximum of 10 percent A as shown by point G. With decreasing temperature, the maximum amount of solute that can be dissolved decreases, as indicated by lines FH and GJ. These lines are called solvus lines and indicate the maximum solubility (saturated solution) of B in A (α solution) or A in B (β solution) as a function of temperature. Point E, where the liquidus lines meet at a minimum, as in Type II, is known as the eutectic point.
The way solidification takes place and resulting microstructures at various stages can be studied by following the slow cooling of different alloys as under.
Alloy 1
Alloy 1 composed of 95A-5B, when slowly cooled, will follow a process exactly the same as any alloy in Type I. When liquidus line is crossed at T1, it will begin to solidify by forming crystals of α solid solution extremely rich in A. The process continues, with the liquid getting richer in B and gradually moving down along the liquidus line. The α solid solution, also getting richer in B, is moving down along the solidus line. When the solidus line is finally crossed at T4 and with diffusion keeping pace with crystal growth, the entire solid will be a homogeneous α solid solution and will remain that way down to room temperature.
Alloy 2
Alloy 2, 30A-70B is the eutectic composition and remains liquid until the eutectic temperature is reached at point E. Since this is also the solidus line, the liquid now undergoes the eutectic reaction, at constant temperature, forming a very fine mixture of two solids. The two solids that make up eutectic mixture are given by the extremities of the eutectic-temperature line, α of composition F and β of composition G. The eutectic reaction may be written as
This reaction is the same as the one which occurred in the Type II diagram, except for the substitution of solid solutions for pure metals. The relative amounts of α and β in the eutectic mixture may be determined by the Lever Rule as under.
α (percent) = (EG / FG) x 100 = (20 / 70) x 100 = 28.6 percent
β (percent) = (EF / FG) x 100 = (50 / 70) x 100 = 71.4 percent
Because of the change in solubility of B in A, line FH, and of A in B, line GJ, there will be a slight change in the relative amounts of α and β as the alloy is cooled to room temperature. The relative amounts of α and β at room temperature are,
α (percent) = (KJ / HJ) x 100 = (25 / 85) x 100 = 29.4 percent
β (percent) = (HK / HJ) x 100 = (60 / 85) x 100 = 70.6 percent
Compositions of the two solid solutions that make up eutectic mixture are given by the composition existing on either end of the tie line HKJ, α of composition H (90A-10B) and β of composition J (5A-95B).
Alloy 3
Alloy 3, 60A-40B, remains liquid until the liquidus line is reached at T3. The liquid starts to solidify crystals of primary α solid solution very rich in A. As the temperature decreases the liquid becomes richer and richer in B, gradually moving down and to the right along the liquidus line until it reaches point E. Just above the eutectic temperature TE, there exist two phases as under. Since the remaining liquid (40 percent) is at point E, the right temperature and composition to form the eutectic mixture, it now solidifies by forming alternately crystals of α and β of the composition appearing at the ends of the eutectic temperature line (points F and G). The temperature does not drop until solidification is complete.
As the alloy cools to room temperature because of the change in solubility, as shown by the solvus line FH, some excess β is precipitated from the solution.
Alloy 4
Alloy 4, 85A-15B, initially follows the same process as described for Alloy I. Solidification starts at T2 and is complete at T5, the resultant solid being a homogeneous single phase, the α solid solution (85A-15 B). At M, the solution is unsaturated. The solvus line FH as explained previously, shows the decrease in solubility of B in A with decreasing temperature. As the alloy cools, the solvus line is reached at point N. The α solution is saturated in B. Below this temperature, under slow cooling, the excess B comes out of solution. Since A is soluble in B, the precipitate does not come out as the pure metal B but as β solid solution. At room temperature, the alloy will consist mostly of α with a small amount of excess β, primarily along the grain boundaries. The excess β can be determined by applying the Lever Rule at the line HJ as under.
β (percent) = (HP / HJ) x 100 = (5 / 85) x 100 = 5.88 percent
If the β phase is relatively brittle, the alloy will not be very strong or ductile. The strength of an alloy to a large extent is determined by the phase that is continuous through the alloy. In this case, although the β solution constitutes only about 6 percent of the alloy, it exists as a continuous network along the grain boundaries. Therefore, the alloy will tend to rupture along these boundaries. This alloy, however, may be made to undergo a significant change in strength and hardness after being properly heat treated.
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