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# Lecture 15 ## Phase Diagrams ### Phase Rule The number of degrees of freedom $(F)$ i.e. the number of independent variables that must be specified to define the state of the system is given by the phase rule: $F = C - P + 2$ where $C$ is the number of components and $P$ is the number of phase...
# Lecture 15 ## Phase Diagrams ### Phase Rule The number of degrees of freedom $(F)$ i.e. the number of independent variables that must be specified to define the state of the system is given by the phase rule: $F = C - P + 2$ where $C$ is the number of components and $P$ is the number of phases. ### Cooling Curves #### Pure Metal * On the diagram, a is the melting point. * Between b and c the metal is solidifying and the temperature remains constant. * Between c and d the metal is cooling as a solid. #### Solid Solution Alloy * Solid solution alloys freeze over a range of temperatures between b and c as shown on the diagram * There is no sharp melting point. ### Example 1: The Cu-Ni System In this system we have: $C = 2$ (Cu and Ni) $P = 2$ (Liquid and Solid) Thus: $F = 2 - 2 + 2 = 2$ To define the system, we need to define 2 intensive variables e.g. Temperature and Composition. If we define just one variable e.g. Composition, then: $F = 2 - 2 + 1 = 1$ and the system is defined by specifying the Temperature. The diagram shows the phase diagram for the Cu-Ni system. * Liquidus line: The line above which only liquid exists. * Solidus line: The line below which only solid exists. #### Lever Rule The lever rule is used to determine the composition of the liquid and solid phases at a given temperature. $\% \text{ solid } = \frac{c-b}{a-b} \times 100$ $\% \text{ liquid } = \frac{a-c}{a-b} \times 100$ Where: * a is the overall composition of the alloy * b is the composition of the solid phase * c is the composition of the liquid phase ### Example 2: The Iron-Carbon System This is an important system as it is the basis for steel production. In this system we have: $C = 2$ (Fe and $Fe_3C$) $P = 2$ (Liquid and Solid) Thus: $F = 2 - 2 + 2 = 2$ To define the system, we need to define 2 intensive variables e.g. Temperature and Composition. The diagram shows the phase diagram for the Fe-$Fe_3C$ system. #### Key points on the diagram * A: Austenite ($\gamma$-Fe): This is a solid solution of carbon in $\gamma$-Fe. It has an FCC structure and exists between 912 and $1394^\circ C$. The maximum solubility of carbon in austenite is 2.14 wt$\%$ at $1147^\circ C$. * $Fe_3C$: Cementite: This is an intermetallic compound with a fixed composition of 6.7 wt$\%$ C. It is hard and brittle * $\alpha$-Ferrite: This is a solid solution of carbon in $\alpha$-Fe. It has a BCC structure and exists below $912^\circ C$. The maximum solubility of carbon in $\alpha$-ferrite is 0.022 wt$\%$ at $727^\circ C$. * $\delta$-Ferrite: This is a solid solution of carbon in $\delta$-Fe. It has a BCC structure and exists above $1394^\circ C$. The maximum solubility of carbon in $\delta$-ferrite is 0.09 wt$\%$ at $1493^\circ C$. #### Reactions * Eutectic: $L \xrightarrow{\text{cooling}} \gamma + Fe_3C$ * occurs at $1147^\circ C$ * $C = 4.30 \text{ wt} \%$ * Eutectoid: $\gamma \xrightarrow{\text{cooling}} \alpha + Fe_3C$ * occurs at $727^\circ C$ * $C = 0.76 \text{ wt} \%$ * Peritectic: $\delta + L \xrightarrow{\text{cooling}} \gamma$ * occurs at $1493^\circ C$ * $C = 0.16 \text{ wt} \%$ #### Microstructures * Pearlite: This is a eutectoid mixture of $\alpha$-ferrite and cementite. It has a lamellar structure. * Hypoeutectoid steel: A steel with a carbon content less than 0.76 wt$\%$. It consists of primary $\alpha$-ferrite and pearlite. * Hypereutectoid steel: A steel with a carbon content greater than 0.76 wt$\%$. It consists of primary cementite and pearlite. #### Isothermal Transformation Diagrams These diagrams are used to predict the microstructure of a steel after a given heat treatment. They plot the time required for a phase transformation to begin and end at a constant temperature. ##### Example For a eutectoid steel, the diagram shows the time required for the austenite to transform to pearlite at a given temperature. The nose of the curve is at around $550^\circ C$. * Cooling rapidly (quenching) results in the formation of martensite. Martensite is a hard and brittle phase. * Cooling slowly results in the formation of coarse pearlite. Coarse pearlite is a soft and ductile phase.
