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Calculation of liquidus temperature contours for a multicomponent system

This application is used for the calculation of a triangular cut in composition through the phase diagram of a multicomponent, multiphase system for compositions defined on a triangular grid. The application works by calculating the phase boundaries at a set of temperatures and interpreting the results in terms of liquidus contours. The application can also be used to produce a solidus contours.

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 20 !

The third value here represents the contour step interval in temperature. The number of contours calculated by this application is limited to 55. For most purposes a value of 50 for the step interval will be sufficient but for low melting systems where great complexity may arise over a narrow temperature range, a smaller value might be more appropriate.

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' !

Extra calculations to be carried out in regions where phase boundaries meet. This can be turned off using the "refine" user variable. By default this variable is set to 1. However if extra calculations are not required the change can be initiated with:

set user_v(refine) = 0 !

Calculation is initiated by entering the compute command.

compute !

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'.

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


Updated 7 May 2010