T3: Stepped equilibrium calculations
 
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—tutorials:t3 [2019/05/08 16:36] – [Complimentary files] pwarczok
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 +===== T3: Stepped equilibrium calculations =====
  
 +//This tutorial was tested on \\
 +MatCalc version 6.01 rel 1.003 \\
 +license: free \\
 +database: mc_fe.tdb //
 +
 +==== Complimentary files ====
 +
 +Click {{:tutorials:t3:script:t3_6021003.mcs|here}} to view the script for this tutorial.
 + 
 +
 +==== Contents ====
 +
 +  * Re-opening a saved file and loading a calculation state
 +  * Calculating a stepped equilibrium with varying temperature
 +  * Understanding the results in the Output window
 +  * Working with multiple buffers
 +  * Calculating a stepped equilibrium with varying composition
 +  * The "Edit buffer states" window
 +
 +===== Before starting... =====
 +
 +Re-open the file saved from [[tutorials:T2 |Tutorial 2]] and load the calculation state **'Equil @ 600°C'**.
 +
 +===== Stepped equilibrium calculation with varying temperature =====
 +
 +==== Running the stepped calculation ====
 +
 +In phase status window, remove graphite phase. Select **'Stepped calculation...'** from the **'Calc'** menu or click on the {{:tutorials:t3:img:icon_calc_stepped.png| MatCalc stepped calculation}} icon. The **'Step equilibrium'** window will appear. Select **'Temperature'** (the uppermost choice in the left-hand column). \\
 +In the **'Range'** box, the default **'Start'**, **'Stop'** and **'Step interval'** values are 400, 1600 and 25 respectively. Keep these values and verify that the **'Temperatures in Celsius'** option has been selected. The step direction is unimportant, and it is not necessary to enter the interval as **'-25'** if stepping in a negative direction. The contents of the **'Vary'** and **'Boundary conditions'** boxes are currently greyed-out because they are not applicable to a temperature-step calculation. Click on the **'Go'** button at the bottom right of the window.
 + 
 +{{:tutorials:t3:img:t3_step_equilibrium_2016.png| MatCalc step equilibrium}}
 +
 +==== Output ====
 +
 +The **'console'** window should show the following series of messages:
 +
 +<code>
 +1, 0,00 s, 600,00 C (873,15 K), its 2,  BCC_A2 CEMENTITE - OK -
 +2, 0,00 s, 625,00 C (898,15 K), its 4,  BCC_A2 CEMENTITE - OK -
 +3, 0,00 s, 650,00 C (923,15 K), its 4,  BCC_A2 CEMENTITE - OK -
 +4, 0,00 s, 675,00 C (948,15 K), its 4,  BCC_A2 CEMENTITE - OK -
 +5, 0,00 s, 700,00 C (973,15 K), its 4,  BCC_A2 CEMENTITE - OK -
 +6, 0,00 s, 725,00 C (998,15 K), its 4,  BCC_A2 CEMENTITE - OK -
 +Tsol 'FCC_A1': 726,53 C (999,68 K) iter: 4, time used: 0,00 s
 +Tsol 'CEMENTITE': 726,53 C (999,68 K) iter: 5, time used: 0,00 s
 +7, 0,01 s, 750,00 C (1023,15 K), its 5,  FCC_A1 BCC_A2 - OK -
 +8, 0,00 s, 775,00 C (1048,15 K), its 5,  FCC_A1 BCC_A2 - OK -
 +Tsol 'BCC_A2': 787,14 C (1060,29 K) iter: 4, time used: 0,00 s
 +9, 0,00 s, 800,00 C (1073,15 K), its 4,  FCC_A1 - OK -
 +10, 0,00 s, 825,00 C (1098,15 K), its 2,  FCC_A1 - OK -
 +11, 0,00 s, 850,00 C (1123,15 K), its 2,  FCC_A1 - OK -
 +12, 0,00 s, 875,00 C (1148,15 K), its 2,  FCC_A1 - OK -
 +13, 0,00 s, 900,00 C (1173,15 K), its 2,  FCC_A1 - OK -
 +14, 0,00 s, 925,00 C (1198,15 K), its 2,  FCC_A1 - OK -
 +15, 0,00 s, 950,00 C (1223,15 K), its 2,  FCC_A1 - OK -
 +16, 0,00 s, 975,00 C (1248,15 K), its 2,  FCC_A1 - OK -
 +17, 0,00 s, 1000,00 C (1273,15 K), its 2,  FCC_A1 - OK -
 +18, 0,00 s, 1025,00 C (1298,15 K), its 2,  FCC_A1 - OK -
 +19, 0,00 s, 1050,00 C (1323,15 K), its 2,  FCC_A1 - OK -
 +20, 0,00 s, 1075,00 C (1348,15 K), its 2,  FCC_A1 - OK -
 +21, 0,00 s, 1100,00 C (1373,15 K), its 2,  FCC_A1 - OK -
 +22, 0,00 s, 1125,00 C (1398,15 K), its 2,  FCC_A1 - OK -
 +23, 0,00 s, 1150,00 C (1423,15 K), its 2,  FCC_A1 - OK -
 +24, 0,00 s, 1175,00 C (1448,15 K), its 2,  FCC_A1 - OK -
 +25, 0,00 s, 1200,00 C (1473,15 K), its 2,  FCC_A1 - OK -
 +26, 0,00 s, 1225,00 C (1498,15 K), its 2,  FCC_A1 - OK -
 +27, 0,00 s, 1250,00 C (1523,15 K), its 2,  FCC_A1 - OK -
 +28, 0,00 s, 1275,00 C (1548,15 K), its 2,  FCC_A1 - OK -
 +29, 0,00 s, 1300,00 C (1573,15 K), its 2,  FCC_A1 - OK -
 +30, 0,00 s, 1325,00 C (1598,15 K), its 2,  FCC_A1 - OK -
 +31, 0,00 s, 1350,00 C (1623,15 K), its 2,  FCC_A1 - OK -
 +32, 0,00 s, 1375,00 C (1648,15 K), its 2,  FCC_A1 - OK -
 +33, 0,00 s, 1400,00 C (1673,15 K), its 2,  FCC_A1 - OK -
 +34, 0,00 s, 1425,00 C (1698,15 K), its 2,  FCC_A1 - OK -
 +35, 0,00 s, 1450,00 C (1723,15 K), its 2,  FCC_A1 - OK -
 +Tsol 'LIQUID': 1453,06 C (1726,21 K) iter: 3, time used: 0,00 s
 +36, 0,00 s, 1475,00 C (1748,15 K), its 3,  LIQUID FCC_A1 - OK -
 +Tsol 'FCC_A1': 1494,61 C (1767,76 K) iter: 4, time used: 0,00 s
 +Tsol 'BCC_A2': 1494,61 C (1767,76 K) iter: 5, time used: 0,00 s
 +37, 0,00 s, 1500,00 C (1773,15 K), its 5,  LIQUID BCC_A2 - OK -
 +Tsol 'BCC_A2': 1505,65 C (1778,80 K) iter: 4, time used: 0,00 s
 +38, 0,00 s, 1525,00 C (1798,15 K), its 4,  LIQUID - OK -
 +39, 0,00 s, 1550,00 C (1823,15 K), its 2,  LIQUID - OK -
 +40, 0,00 s, 1575,00 C (1848,15 K), its 2,  LIQUID - OK -
 +41, 0,00 s, 1600,00 C (1873,15 K), its 2,  LIQUID - OK -
 +changing step direction ...
 +42, 0,00 s, 575,00 C (848,15 K), its 5,  BCC_A2 CEMENTITE - OK -
 +43, 0,00 s, 550,00 C (823,15 K), its 5,  BCC_A2 CEMENTITE - OK -
 +44, 0,00 s, 525,00 C (798,15 K), its 5,  BCC_A2 CEMENTITE - OK -
 +45, 0,00 s, 500,00 C (773,15 K), its 5,  BCC_A2 CEMENTITE - OK -
 +46, 0,00 s, 475,00 C (748,15 K), its 5,  BCC_A2 CEMENTITE - OK -
 +47, 0,00 s, 450,00 C (723,15 K), its 5,  BCC_A2 CEMENTITE - OK -
 +48, 0,00 s, 425,00 C (698,15 K), its 5,  BCC_A2 CEMENTITE - OK -
 +49, 0,00 s, 400,00 C (673,15 K), its 5,  BCC_A2 CEMENTITE - OK -
 +Steps: 50, CalcTime: 0,11 s
 +AktStepVal: 673,150000
 +- OK -
 +</code>
 +
 +Each line corresponds to an equilibrium calculated at a single temperature value and comprises a line number, the calculation time, the temperature, the number of iterations, the stable phases at that temperature and an **'- OK -'** message indicating that the equilibrium calculation was successful. \\
 +Note that the temperature-stepping starts from the equilibrium at 600°C loaded from the calculation state. Initially, the temperature is increased by the **'Step interval'** each time until the upper temperature limit is reached. \\ Then, a **'changing step direction'** message is displayed and, again starting from the equilibrium at 600°C, the temperature is decreased until the lower limit is reached.
 +Also note the lines beginning with **'Tsol'**: phase solubility temperatures are automatically evaluated during the stepped calculation. Thus it is seen in the output above that from **600°C to 726.53°C**, the two stable phases are **BCC_A2** (ferrite) and **CEMENTITE**. At **726.53°C**, **FCC_A1** (austenite) becomes stable, and cementite becomes unstable. The two phases in equilibrium are ferrite and austenite between this temperature and **787.14°C**, when ferrite becomes unstable. Austenite is then the only stable phase, and this situation persists up to the liquid solubility temperature of **1453.06°C**. The **BCC_A2** phase known as delta-ferrite is stable in a narrow temperature range at high temperature, and by **1600°C** the only equilibrium phase is **liquid**. There are no changes in phase stability between 600°C and 400°C, as can be seen from the block of lines below **'changing step direction ...'**.\\
 +The final three lines of output give the number of steps and total calculation time, the current value of the stepped variable (673.15 K = 400°C) and an **'OK'** message indicating that the calculation was carried out successfully. \\
 +The contents of the **'Phase summary'** and **'Phase details'** are not modified during the stepped calculation, but still display the information loaded from the calculation state **'Equil @ 600°C'**.
 +
 +==== Buffers ====
 +
 +All the equilibria listed above are stored in a buffer. In other words, a buffer is a collection of calculation states, with each calculation state created at a different temperature. The default buffer is named **'_default_'**, and its contents are overwritten when a new stepped calculation is carried out. \\
 +To be able to keep more than one set of stepped equilibria, additional buffers must be created. Firstly, rename the existing default buffer using **'Global > Buffers > Rename'**. Type **'T=400 to 1600°C'** into the **'New buffer name'** box and click **'OK'**. Then, create a new buffer using **'Global > Buffers > Create'**. This new buffer will contain the results from a new stepped equilibrium calculation in which the carbon content is varied from 0 to 1.5 wt.% at 500°C, so enter the name **'C=0 to 1.5 at 500°C'**. Note that buffers can be selected from the drop-box in the toolbar area or using 'Global > Buffers > Select'.
 +
 +{{:tutorials:t3:img:t3_buffer_toolbox_2016.png| MatCalc buffer toolbox}}
 +
 +===== Stepped equilibrium calculation with varying carbon content =====
 +
 +==== Running the calculation ====
 +
 +Calculate an equilibrium at 500°C. Open the **'Step equilibrium'** window again, but this time select **'Element content'** instead of **'Temperature'** in the **'Type'** box. Enter **'0'**, **'1.5'** and **'0.05'** respectively as the start, stop and step interval values. (Note that, as shown in the image below, MatCalc accepts either a decimal point or a comma as the decimal separator.)
 +In the **'Boundary conditions'** box, ensure that the element selected is **'C'**, and enter the temperature as **'500'**. Ensure that in the **'vary'** box, **'global comp'** is selected, and that in the **'Options'** column, **'Temperatures in Celsius'** and **'Composition in weight percent'** are both selected, then click on **'Go'**.
 + 
 +{{:tutorials:t3:img:t3_step_equilibrium_element_2016.png| MatCalc step equilibrium}}
 + 
 +The contents of the **'console'** window should appear as follows:
 + 
 +<code>
 +1, 0,00 s, 0,4, its 9,  BCC_A2 CEMENTITE - OK -
 +2, 0,00 s, 0,45, its 2,  BCC_A2 CEMENTITE - OK -
 +3, 0,00 s, 0,5, its 2,  BCC_A2 CEMENTITE - OK -
 +4, 0,00 s, 0,55, its 2,  BCC_A2 CEMENTITE - OK -
 +5, 0,00 s, 0,6, its 2,  BCC_A2 CEMENTITE - OK -
 +6, 0,00 s, 0,65, its 2,  BCC_A2 CEMENTITE - OK -
 +7, 0,00 s, 0,7, its 2,  BCC_A2 CEMENTITE - OK -
 +8, 0,00 s, 0,75, its 2,  BCC_A2 CEMENTITE - OK -
 +9, 0,00 s, 0,8, its 2,  BCC_A2 CEMENTITE - OK -
 +10, 0,00 s, 0,85, its 2,  BCC_A2 CEMENTITE - OK -
 +11, 0,00 s, 0,9, its 2,  BCC_A2 CEMENTITE - OK -
 +12, 0,01 s, 0,95, its 2,  BCC_A2 CEMENTITE - OK -
 +13, 0,00 s, 1, its 2,  BCC_A2 CEMENTITE - OK -
 +14, 0,00 s, 1,05, its 2,  BCC_A2 CEMENTITE - OK -
 +15, 0,00 s, 1,1, its 2,  BCC_A2 CEMENTITE - OK -
 +16, 0,00 s, 1,15, its 2,  BCC_A2 CEMENTITE - OK -
 +17, 0,00 s, 1,2, its 2,  BCC_A2 CEMENTITE - OK -
 +18, 0,00 s, 1,25, its 2,  BCC_A2 CEMENTITE - OK -
 +19, 0,00 s, 1,3, its 2,  BCC_A2 CEMENTITE - OK -
 +20, 0,00 s, 1,35, its 2,  BCC_A2 CEMENTITE - OK -
 +21, 0,00 s, 1,4, its 2,  BCC_A2 CEMENTITE - OK -
 +22, 0,00 s, 1,45, its 2,  BCC_A2 CEMENTITE - OK -
 +23, 0,00 s, 1,5, its 2,  BCC_A2 CEMENTITE - OK -
 +changing step direction ...
 +24, 0,00 s, 0,35, its 2,  BCC_A2 CEMENTITE - OK -
 +25, 0,00 s, 0,3, its 2,  BCC_A2 CEMENTITE - OK -
 +26, 0,00 s, 0,25, its 2,  BCC_A2 CEMENTITE - OK -
 +27, 0,00 s, 0,2, its 2,  BCC_A2 CEMENTITE - OK -
 +28, 0,00 s, 0,15, its 2,  BCC_A2 CEMENTITE - OK -
 +29, 0,00 s, 0,1, its 2,  BCC_A2 CEMENTITE - OK -
 +30, 0,00 s, 0,05, its 2,  BCC_A2 CEMENTITE - OK -
 +Xsol 'CEMENTITE': 
 +X(C): 5,7389141e-005, WP(C): 0,0012343224
 + - OK -
 +31, 0,00 s, 1e-012, its 4,  BCC_A2 - OK -
 +Steps: 32, CalcTime: 0,07 s
 +AktStepVal: 0,000000
 +- OK -
 +</code>
 + 
 +Similarly to the temperature-step calculation, the output consists of a series of equilibria evaluated at the specified step-values. The first of these corresponds to the carbon content of 0.4 wt.% entered in the **'System composition'** box in [[tutorials:T2 | Tutorial 2]]. The carbon content is then increased in 0.05 wt.% steps up to the maximum value of 1.5 wt.%. The 'Changing step direction' line marks the beginning of the second set of equilibria, in which the carbon content is decreased.
 +At 500°C, the stable phases are BCC_A2 and CEMENTITE across almost the whole composition range, but between the final two equilibria there is a line beginning with **'Xsol'**. The line below this gives the carbon content at which cementite becomes unstable, both in mole fraction **'X(C)'** and in weight percent **'WP(C)'**.\\
 +Create a third buffer named **'C=0 to 1.5 at 800°C'** and perform a stepped calculation with the same composition range but at a temperature of 800°C. The output in this case includes three **'Xsol'** lines, corresponding to changes in phase stability:
 + 
 +<code>
 +1, 0,00 s, 0,4, its 23,  FCC_A1 - OK -
 +2, 0,00 s, 0,45, its 3,  FCC_A1 - OK -
 +3, 0,00 s, 0,5, its 3,  FCC_A1 - OK -
 +4, 0,00 s, 0,55, its 3,  FCC_A1 - OK -
 +5, 0,00 s, 0,6, its 3,  FCC_A1 - OK -
 +6, 0,00 s, 0,65, its 3,  FCC_A1 - OK -
 +7, 0,00 s, 0,7, its 3,  FCC_A1 - OK -
 +8, 0,00 s, 0,75, its 3,  FCC_A1 - OK -
 +9, 0,00 s, 0,8, its 3,  FCC_A1 - OK -
 +10, 0,00 s, 0,85, its 3,  FCC_A1 - OK -
 +11, 0,00 s, 0,9, its 3,  FCC_A1 - OK -
 +Xsol 'CEMENTITE': 
 +X(C): 0,042617353, WP(C): 0,94829227
 + - OK -
 +12, 0,00 s, 0,95, its 4,  FCC_A1 CEMENTITE - OK -
 +13, 0,00 s, 1, its 2,  FCC_A1 CEMENTITE - OK -
 +14, 0,00 s, 1,05, its 2,  FCC_A1 CEMENTITE - OK -
 +15, 0,00 s, 1,1, its 2,  FCC_A1 CEMENTITE - OK -
 +16, 0,00 s, 1,15, its 2,  FCC_A1 CEMENTITE - OK -
 +17, 0,00 s, 1,2, its 2,  FCC_A1 CEMENTITE - OK -
 +18, 0,00 s, 1,25, its 2,  FCC_A1 CEMENTITE - OK -
 +19, 0,00 s, 1,3, its 2,  FCC_A1 CEMENTITE - OK -
 +20, 0,00 s, 1,35, its 2,  FCC_A1 CEMENTITE - OK -
 +21, 0,01 s, 1,4, its 2,  FCC_A1 CEMENTITE - OK -
 +22, 0,00 s, 1,45, its 2,  FCC_A1 CEMENTITE - OK -
 +23, 0,00 s, 1,5, its 2,  FCC_A1 CEMENTITE - OK -
 +changing step direction ...
 +24, 0,00 s, 0,35, its 3,  FCC_A1 - OK -
 +Xsol 'BCC_A2': 
 +X(C): 0,015675087, WP(C): 0,3413233
 + - OK -
 +25, 0,00 s, 0,3, its 4,  FCC_A1 BCC_A2 - OK -
 +26, 0,00 s, 0,25, its 2,  FCC_A1 BCC_A2 - OK -
 +27, 0,00 s, 0,2, its 2,  FCC_A1 BCC_A2 - OK -
 +28, 0,00 s, 0,15, its 2,  FCC_A1 BCC_A2 - OK -
 +29, 0,00 s, 0,1, its 2,  FCC_A1 BCC_A2 - OK -
 +30, 0,00 s, 0,05, its 2,  FCC_A1 BCC_A2 - OK -
 +Xsol 'FCC_A1': 
 +X(C): 0,00055593532, WP(C): 0,011961706
 + - OK -
 +31, 0,00 s, 1e-012, its 4,  BCC_A2 - OK -
 +Steps: 32, CalcTime: 0,07 s
 +AktStepVal: 0,000000
 +- OK -
 +</code>
 +
 +==== Edit buffer states ====
 +
 +The **'console'** window provides information on which phases are stable at a given temperature and carbon content, but not on the phase fractions or compositions. However, this detailed information is stored in the buffers and can be found by selecting **'Global > Buffers > Edit buffer states'**.
 +
 +{{:tutorials:t3:img:t3_edit_and_load_buffer_states_6001000.png| MatCalc edit and load the buffer states}}
 +
 +The upper part of the **'step value...'** area contains a drop-box for selecting a buffer, and the lower part gives a list of the step-values at which equilibria have been evaluated. These are either temperature or carbon content values, depending on the buffer chosen, and their units are those specified in the **'Step equilibrium'** window when setting up the calculation. The **'Tsol'** or **'Xsol'** values are also stored. If the **'auto load'** box at the bottom left is ticked, clicking on a step-value loads the equilibrium, and the contents of the **'Phase summary'** and **'Phase details'** are immediately updated with phase fraction and composition details for this equilibrium.
 +The next two tutorials demonstrate how to produce graphical plots of phase fractions, compositions and many other quantities as a function of the stepped variable.
 +
 +===== To finish... =====
 +
 +Save the workspace file - it will be needed again in [[tutorials:T4 | Tutorial 4]].
 +
 +===== Consecutive articles =====
 +
 +The tutorial is continued in article [[tutorials:T4 | T4 - Graphical presentation and export of results]]
 +
 +Go to [[:tutorials|MatCalc tutorial index]].
tutorials/t3.txt · Last modified: 2023/08/01 12:39 by pwarczok
 
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