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— | tutorials:t7 [2019/05/14 11:39] – [Complimentary files] pwarczok | ||
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+ | ===== T7: Calculating phase boundaries ===== | ||
+ | //This tutorial was tested on\\ | ||
+ | MatCalc version 6.01 rel 1.003\\ | ||
+ | license: free\\ | ||
+ | database: mc_fe.tdb// | ||
+ | |||
+ | ==== Complimentary files ==== | ||
+ | |||
+ | Click {{: | ||
+ | |||
+ | ==== Contents ==== | ||
+ | |||
+ | * Using " | ||
+ | * Determining austenite <-> ferrite transformation temperatures | ||
+ | * Finding phase boundaries for carbide phases in terms of temperature and element content | ||
+ | * Tracing a phase boundary on axes of temperature versus element content | ||
+ | |||
+ | It was seen in [[tutorials: | ||
+ | |||
+ | ===== Setting up the system ===== | ||
+ | |||
+ | Create a new workspace file and set up the system with elements **Fe**, **C** and **Nb** and phases **FCC_A1**, **BCC_A2**, **LIQUID** and **CEMENTITE**. Enter the composition as **0.1 wt.%C**, **0.3 wt.% Nb** and calculate an equilibrium at 1000°C (Refer to [[tutorials: | ||
+ | |||
+ | Note the results in the **' | ||
+ | |||
+ | < | ||
+ | #### /FCC_A1/ moles: 0,996502, gm: -62324,3 (-62324,3) | ||
+ | Phasestatus: | ||
+ | FE +9, | ||
+ | |||
+ | #### /FCC_A1#01/ moles: 0,00349803, gm: -114284 (-114284) | ||
+ | Phasestatus: | ||
+ | NB +5, | ||
+ | |||
+ | |||
+ | ### inactive ### | ||
+ | |||
+ | #### /BCC_A2/ moles: 0, gm: -62253,7 (-62253,7) | ||
+ | Phasestatus: | ||
+ | FE +9, | ||
+ | |||
+ | #### /LIQUID/ moles: 0, gm: -58549,4 (-58549,4) | ||
+ | Phasestatus: | ||
+ | FE +9, | ||
+ | |||
+ | #### /CEMENTITE/ moles: 0, gm: -52497,4 (41843,3) | ||
+ | Phasestatus: | ||
+ | FE +7, | ||
+ | </ | ||
+ | |||
+ | It is the following line in the database file **mc_fe.tdb** which causes the second FCC_A1 phase to be created: | ||
+ | |||
+ | < | ||
+ | |||
+ | This creates that a **new phase of type FCC_A1** with Ti, Nb or V as the major constituents on the first sublattice and C or N as the major constituents on the second when the system contains these elements. The **' | ||
+ | |||
+ | {{: | ||
+ | |||
+ | ===== Calculating phase boundaries ===== | ||
+ | |||
+ | ==== Solidus and liquidus temperatures ==== | ||
+ | |||
+ | The solidus temperature is defined by zero phase fraction of liquid. To calculate this, choose **' | ||
+ | |||
+ | {{: | ||
+ | |||
+ | The following message appears in the console window. | ||
+ | |||
+ | < | ||
+ | |||
+ | The liquidus temperature is the dissolution temperature of the last solid phase, which in this case is BCC_A2. Selecting **' | ||
+ | |||
+ | < | ||
+ | |||
+ | Of course, this is not a liquidus temperature, | ||
+ | The liquidus phase can be easily found if an equilibrium calculation in the liquid system is performed first. Calculate an equlibrium at 1600°C (or any temperature in which system contains only a liquid) and search again for the phase boundary of BCC_A2 phase. This time the following result should be given: | ||
+ | |||
+ | < | ||
+ | |||
+ | **In general, the correct phase boundaries are found if the initial equilibrium describes the system in the neighbouring phase field which does not contain the searched phase** - in the case presented above, the liquidus temperature (which is phase boundary of ' | ||
+ | |||
+ | ==== Austenite-ferrite transformation temperatures ==== | ||
+ | |||
+ | Low-alloy steels undergo a ferrite - austenite phase transformation between 700 and 800°C (see, for example, [[tutorials: | ||
+ | |||
+ | < | ||
+ | |||
+ | The zero-phase boundary of BCC_A2 for this transformation can be identified by calculating an equilibrium at 900°C and then searching for the boundary. | ||
+ | |||
+ | < | ||
+ | |||
+ | ==== Dissolution temperatures of carbides ==== | ||
+ | |||
+ | Cementite is only stable to relatively low temperatures, | ||
+ | |||
+ | < | ||
+ | |||
+ | Note that this is the same temperature as the zero-phase boundary of FCC_A1. Niobium carbide, by contrast, remains stable at higher temperatures. Calculate an equilibrium at 1500°C before searching for the boundary. | ||
+ | |||
+ | < | ||
+ | |||
+ | ==== Element content for zero-phase fractions ==== | ||
+ | |||
+ | Phase boundaries can also be found in terms of element content at a fixed temperature. To illustrate this, the zero-phase boundary of cementite at 700°C will be evaluated in terms of carbon content. Calculate an equilibrium at 700°C, then open the **' | ||
+ | |||
+ | {{: | ||
+ | |||
+ | The output gives the carbon content for zero phase fraction of cementite in mole fraction and in weight percent. | ||
+ | |||
+ | < | ||
+ | iter: 2, time used: 0,03 s, GibbsEnergy: | ||
+ | X(C): 0, | ||
+ | </ | ||
+ | |||
+ | **Note: After the search for the phase boundary with element content variation, the composition of the system is changed to the found value! (check ' | ||
+ | |||
+ | In the same way, the zero phase fraction boundary for niobium carbide at 1000°C can be evaluated in terms of the niobium content. Firstly, open **' | ||
+ | |||
+ | {{: | ||
+ | |||
+ | The output in the console shows the Nb content above which the carbide phase is thermodynamically stable. | ||
+ | |||
+ | < | ||
+ | iter: 7, time used: 0,03 s, GibbsEnergy: | ||
+ | X(NB): 1, | ||
+ | </ | ||
+ | |||
+ | ==== Tracing phase boundaries ==== | ||
+ | |||
+ | Once a point on a phase boundary has been identified using the process described above, the boundary can be traced as a function of element content. In the following example, the effect of the niobium content on the temperature of the FCC_A1#01 (NbC) zero-phase boundary will be calculated.\\ | ||
+ | Having established the zero phase fraction boundary for niobium carbde at 1000°C, open the **' | ||
+ | In the **' | ||
+ | |||
+ | {{: | ||
+ | |||
+ | |||
+ | Create a new X-Y plot window ([[tutorials: | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | Right-click in the plot window outside the plot area and choose **' | ||
+ | Change the carbon content of the system to 0.05 wt.% C, calculate an equilibrium at 1000°C and search again for the same phase boundary, then make a stepped calculation using the same conditions as before. The phase boundary for 0.05 wt.% C should follow the green curve in the plot below, which also shows the same phase boundary for 0.01 wt.%C - as an exercise you can try to format the plot as shown below. | ||
+ | |||
+ | {{ : | ||
+ | |||
+ | ===== Consecutive articles ===== | ||
+ | |||
+ | The tutorial is continued in article [[tutorials: | ||
+ | |||
+ | Go to [[: |