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Calculation of liquidus contours and primary phase fields for a multicomponent system

This application is used for the calculation of liquidus contours and primary phase fields for a triangular cut in composition through the phase diagram of a multicomponent, multiphase system (contours generated from calculated liquidus temperatures for compositions defined on a triangular grid).

Various forms of output can be obtained depending on the options requested. For example in addition to carrying out the calculations, the application will replot previously calculated diagrams eg liquidus temperature points, jagged and smoothed liquidus temperature contours, liquidus primary phase names or numbers at grid points and jagged and smoothed liquidus primary phase boundaries. This application can also be used to produce a solidus surface.

Before asking for the liquidus contours and primary phase fields to be calculated it is necessary to define a datafile for the multicomponent system (for three or more components), to classify any phases required to be absent or identified as giving rise to miscibility gaps and to specify the pressure. All this can be set up using the normal APPLICATION commands within MTDATA. Also it is necessary to define the range of temperatures to be covered by the scan for the liquidus valleys

range t 500 1200 0.1 !

The third value here represents the tolerance in temperature ie the accuracy required for each calculation of the liquidus temperature. A value of 0.1 will achieve a high degree of accuracy, although calculations might be a little slow. On the other hand a value of 10 might be suitable for obtaining a rough quick view of the liquidus surface.

The application is designed for a multicomponent system (ie with at least three components). The following example, however, is for a three component system. In this case the ternary section is identical to a the liquidus projection for an ordinary ternary diagram. To calculate sections in higher order systems it is necessary simply to add more components to the composition groups.

set 'A' 0.9998 0.0001 0.0001 !
set 'B' 0.0001 0.9998 0.0001 !
set 'C' 0.0001 0.0001 0.9998 !

The density of calculations is set through use of the user variable "number_of_steps" (maximum of 100).

set user_v(number_of_steps) 30 !

and the corners of the diagram assigned to the composition groups.

set user_v(group_lower_left) 'A' !
set user_v(group_top) 'B' !
set user_v(group_lower_right) 'C' !

It is also necessary to specify how the diagram should be labelled. Two different options are available The default option (0) is for the temperatures to be printed out at point on the triangular grid on the "jagged" temperature plot. Alternatively the phase field names or numbers may be given (option 1). eg:

set user_v(labelling_option) 0 !

Calculation is initiated by entering the compute command.

compute !

Plotting options are also available when displaying the results of the calculation. Potting option 0 (the default) is required for the calculation to be carried out and this dispays the full set of graphical output. Results are then stored in a ".liq" file. The other plotting options provide the means to plot some or all of the graphs from results stored in the ".liq" file. eg.

set user_v(plotting_option) 3 !

Plotting options 3 and 4 provide the full range of graphs as is displayed immediately following the calculation. With plotting option 4, however, the labelling of the smoothed primary phase boundaries is suppressed. Plotting options 0 to 4 all provide a plot of the temperature or primary phase number at each grid point depending on the value set for the labelling_option. Option 1 also provides a plot of the "jagged" temperature contours over the array of grid points and a plot of the smoothed, labelled, temperature contours. Option 2, on the other hand, provides a plot of the "jagged" primary phase boundaries over the array of grid points and a plot of the smoothed, named primary phase fields. Plotting options 5 and 6 provide a highly restricted selection of output. Option 5 provides a plot of the smoothed, labelled, temperature contours while option 6 provides a plot of the smoothed, named primary phase fields.

Further refinement to the calculations is possible by using the user variable "defn_method". By default the value of "defn_method" is set to 0 and the calculations proceed assuming that it is the boundary at the highest temperature that is required. However if "defn_method" is 1 then the user is asked to define whether a LIQUIDUS or SOLIDUS surface is required and then to categorise each phase according to whether it should be treated as a liquid or as a solid or to be ignored with respect to finding a phase boundary.

If "defn_method" is 2, further refinement is possible:

set user_v(defn_Method) = 2 !

Further user variables, Liq_Solidus, liq_phs_nos and ign_phs_nos provide the extra control.

The user variable Liq_Solidus allows a resticted set of the available lines to be calculated and plotted, liq_phs_nos allow a particular phase (or phases) to be assigned as the liquid phase and ign_phs_nos allows certain phases to ignored in terms of the definition of the phase boundaries although still present in the calculations.

0   just the liquidus curve is calculated defined as the highest temperature at which a solid is still present or at which a liquid miscibility gap is still present
1   just the liquidus curve is required defined as the highest temperature at which a solid is still present
2   just the solidus curve is required defined as the highest temperature at which no liquid is present.
3   all boundaries are required except those corresponding to those phases that are to be ignored, defined by the user variable ign_phs_nos

The user variables liq_phs_nos and ign_phs_nos should be entered within quotes. If a list of numbers is given they be separated by + signs. Multiple numbers for liq_phs_nos allows both liquid and gas phases to be assigned as high temperature phases eg '2+4'.

The results from a LIQSECT calculation may be displayed as a three dimensional image using the LIQSURF application.

Liquidus projections may also be calculated using other MTDATA applications ie. LIQPROJ and LIQCONT. They use different ways to delineate the liquidus valley. LIQCONT may give better temperature contours than LIQSECT while LIQCONT may give better indication of the primary phase boundaries for the liquidus but take longer. LIQPROJ is limited to ternary systems.


Updated 7 May 2010