The Phase Equilibrium Section contains one large table field and one large graph field. The section displays the values (tabularly and graphically) of properties related to phase equilibria between solid, liquid, and vapor phases.

1	Property Control: this control shows the property whose values are currently displayed in the section's table and graph controls.
2	Type Control: this control shows what type of values are currently displayed in the section's table and graph controls. The different types of values are: curve points, data values, equations, and estimates.
3	Table Control: displays the selected physical property's values. A green triangle in the table control's upper right corner indicates that additional data are available. (See below.)
4	Graph Control: displays the selected physical property's data values, estimated values, and curve points. Note that the Phase Equilibria Section's graph control is a compound graph control, i.e., it contains both an XY graph and a triangular graph.

Note that the table control contains several additional controls enabling you to select units for temperature, pressure, and composition.

5	Temperature Units Control: this control shows the units in which temperature values are displayed.
6	Pressure Units Control: this control shows the units in which pressure values are displayed.
7	Composition Units Control: this control shows the units in which composition values are displayed.

1	Properties List Control: Displays all physical properties dependent upon temperature and composition.
2	Values Type List Control: Displays the type of values available in this section.

Selecting Data Values from the Type Control will display the chosen physical property's data values. The data values are displayed in the units shown in the units rows near the top of the table. A green triangle in the upper right corner of the property data box indicates that additional data are available. (See documentation on the Phase Equilibria All Data Dialog for details on managing data of different status.)

Clicking the left mouse button on the data values table control activates the Phase Equilibria Data Edit Dialog enabling you to enter temperature, pressure, composition values, accuracies, units, a reference and comments. (See here for documentation.)

Clicking the right mouse button within the data table control displays the field's data commands menu.

The menu's commands enable you to copy, cut and paste values to and from the data table control. See Common Menu Commands for documentation on the commands commonly found on command menus. Some of this field's more specific commands are:

• Edit All Data: uses the All Data dialog to enable editing data having status values of passive, rejected or unknown. See All Data Dialog for documentation.)
• Edit Data: enables you to view and mofidy the current physical property's datum. See Data Edit Dialog for detailed documentation. (Clicking the left mouse button on the table control will also execute this command.)

  Each property field runs a set of verification tests to check the validity of an entered value. For example, the temperature must be a number greater than 0 K. Cranium or Synapse will signal an error if the entered value fails a physical property verification test.

1. Open a "working" copy of the MKS Sample Knowledge Base document or create a copy of the document. See here for details on how to create copies of documents.
2. Change to the Mixtures Chapter and navigate to the '1-butanol + n-octane' mixture. (See the Navigation Overview documentation for details on navigating chapters and pages.)
3. Scroll down to the Phase Equilibria section and click the left mouse button in the property control. The application activates the Properties - f(T,P,X) dialog.
4. Select 'SLE, Liquidus Point - f(T,P,X)' from the list of properties and Data Values from the list of values types.
5. Press the OK button. The application will close the dialog and display any current data.
6. Click on each of the Units Control in the section's table and select the following units from the Set Units dialog:

   Attribute	Units
   Temperature	K
   Pressure	atm
   Composition	mol frac

   The section's table control will display the new units.
7. Click the left mouse button anywhere in the large values area of the section's table control. The application activates the Property Data edit dialog.
8. Click the left mouse button on an empty row in the dialog's table control. Press the Edit button. The application activates the Property Datum dialog.
9. Enter the following values into the dialog's controls. (Note that required values are highlighted in yellow.)

   Control Section	Attribute	Value
   Composition	X,1-butanol	0.1975
   Composition	X,n-octane	0.8025
   Datum	Temperature	216.07 K
   Datum	Pressure	1 atm

   For an actual data entry, we recommend also entering values for the references and some comments as shown in the figure below.
10. Press the OK button when finished. The new datum is added to the Property Data edit dialog.

    Note that datum entry dialogs manage data in their original units. Data dialogs and fields display manage data in their current, converted units.

11. Press the Save button to store these values in the document and display them in the field's table control.

See documentation for the Phase Equilibrium Data Dialog for further details on the use of the data and datum entry dialogs.

In Cranium and Synapse, the temperature and pressure attribute of each phase equilibria property can be estimated. For example, for the VLE, Bubble Point - f(T,P,X) property, you can estimate both the pressure value, given the temperature and composition, or the temperature value, given the pressure and composition.

Selecting either 'Pressure Estimates' or 'Temperature Estimates' from the Value Type Control (see above) will display the chosen physical property's estimated values. Estimated values are displayed in the units shown in the units rows near the top of the table.

Before state variable dependent estimates can be generated, you must enter one or more sets of state variable values. Clicking the left mouse button on the estimated values table control activates an Estimates Edit Dialog. The specific dialog activated depends upon if the temperatures or pressures are being estimated.

Estimates Type	Estimates Edit Dialog
Temperature Estimates	Temperature Estimates Dialog
Pressure Estimates	Pressure Estimates Dialog

Clicking the right mouse button on the estimated values table control displays the estimated values table control's command menu.

The menu's commands enable you to copy, cut and clear values from the estimate control and manage the property's estimation techniques. (You can paste composition values but you cannot paste estimated values into the control.) See Common Menu Commands for documentation on the commands commonly found on command menus. Some of this field's more specific commands are:

• Edit Variables & Detail Estimates: activates the Property Estimates dialog.

  The Estimates dialog enables you to view estimation details, enter state variables for new estimations, copy values, regress values and use Goal Seek to find state variables giving specified estimated values. See Temperature Estimates Edit Dialog or Pressure Estimates Edit Dialog for documentation on these capabilities.

• Select Technique: enables you to specify the estimation mode and the estimation technique used to estimate the current physical property. Selecting this command activates the Estimation Technique Information dialog.

  The dialog lists two estimation modes: Automatic and Manual. By default all estimations are initially set to Automatic Mode. Once you choose Manual Mode, the list of estimation techniques is enabled allowing you to choose any application estimation technique. See documentation for the Manual Techniques Dialog for more details about manually setting estimation techniques.
• Compute Estimates: activates the Property Estimation dialog which enables you to estimate the current physical property. The functionality of this command is similar to that of the Commands menu Compute Estimates command. The key difference is that the estimates control's menu command limits the estimation to only the current physical property. See Estimate Mixture Properties for documentation.

Note that although state variable values, e.g., temperatures, pressures, and compositions, can be pasted into the estimates table control, estimated values cannot be pasted into the estimates table control. Estimated values must be generated using the Compute Estimates command describe previously.

The values entered into the section's Curve Points Table are displayed as curves in the section's graph. Curves can greatly help visual trends in values and help organize values at different state conditions or from different sources.

You display the Curve Points Table by selecting the "Curve Points" values type in the Properties dialog. (See above.)

The curve points are displayed in the units shown in the units rows near the top of the table.

Clicking the right mouse button on the curve points table control displays the commands menu.

The menu's commands enable you to copy, cut and paste values to and from the curve points table control. See Common Menu Commands for documentation on the commands commonly found on command menus.

The Edit Values menu command activate the Curves Edit dialog. See documentation on the Curves Edit Dialog for details.

1. Open a "working" copy of the MKS Sample Knowledge Base document or create a copy of the document. See here for details on how to create copies of documents.
2. Change to the Mixtures Chapter and navigate to the '2-Butanol + n-Octane' mixture. (See the Navigation Overview documentation for details on navigating chapters and pages.)
3. Scroll down to the Phase Equilibria section and click the left mouse button in the property control. The application activates the Properties - f(T,P,X) dialog.
4. Select 'VLE, Dew Point - f(T,P,X)' from the list of properties and Curve Points from the list of values types. Press the OK button. The application will close the dialog and display the Curve Points table.
5. Click on the table's units controls as needed to select units of 'K' for temperature, 'kPa' for pressure, and 'mol frac' for composition. Click on a units control change units. (See below for details.)
6. Click the left mouse button anywhere in the large values area of the table control. The application activates the Curve Points entry dialog.
7. Click and hold the left mouse button in the first cell in the table shown above. While holding the mouse button down, drag the mouse to the table's lower right corner. Then press the ctrl-c key combination to copy the values to clipboard.
8. Click the left mouse button on the table's first row. Then click the right mouse button. The application will activate the dialog's commands menu.
9. Select the Paste Values command from the menu. The values copied from the table above will be pasted into the dialog's table.
10. Press the dialog's Commands button and select the 'Selcect All' command from the commands menu. The dialog will select all table rows with values.
11. Press the dialog's Set Curve button. The application activates the Set Curve Name dialog. Enter a value and press the dialog's OK button.
12. Press the dialog's Save button to store these values in the document. The section's graph shows the curve formed from the entered curve points.

The data shown in the previous figure are for the dew point at a pressure of 101.3 kPa. The displayed curve makes it easy to follow the trend of the data and 'fill in' those composition regions which are missing data.

Values for dependent properties are often fitted to equations for analysis and dissemination. The section's Equations Table enables you to store one or more equations for each physical property.

Each equation entry displays the equation's name, form and parameters. The dependent variable is not shown and the independent variable is denoted by the character "X".

The section's Equations Table displays the chosen physical property's equation and parameter values. You display the Equations Table by selecting the "Equations" values type in the Properties dialog. (See above.)

Clicking the left mouse button on the Equations Table Control activates the Equations Edit dialog. See documentation on the Equations Edit Dialog for details.

Clicking the right mouse button on the equations control displays the command menu.

The menu's commands enable you to copy, cut and paste values to and from the equations table control. See Common Menu Commands for documentation on the commands commonly found on command menus.

The Edit Equations menu command activate the Equations Edit dialog. See documentation on the Equations Edit Dialog for details.

It is typically better to enter large compilations of equations and/or equation parameters in an estimation technique. See documentation for the Techniques Chapter's Parameters Section for details.

Selecting new units from the list and press the OK button changes the current units in which the property is displayed. (Note that all data are stored in their original units - changing the displayed units does not change any stored data.) The dialog's Std Units button displays the default units used by Cranium and Synapse for the current physical property. All estimated values are generated by Cranium and Synapse in standard units. (See documentation on the Property Units Dialog for additional details on changing property units.)

The units set via the Set Property Units dialog, accessed either from the Options menu's Set Units command or clicking on the Units control in a physical property field, are assigned for all documents in the application. For example, if you have three knowledge base documents open and then change the units of the liquid viscosity, all documents will update their liquid viscosity displays using the newly selected units.

Also note that changing state variable units will change these units for all values throughout the application. Thus, changing the temperature units in this section's table control will also change the temperature units in the Compositon-Temperature-Pressure Dependent Section as well as the temperature dependent sections in the chemicals chapter.

Units are also stored in the application. The next time Cranium or Synapse starts, the set of units used in your last session will be used again.

The Phase Equilibria Section's contains a compound graph control. This control contains two different graphs. You use the right hand side vertical scroll bar to switch between graphs.

1	Use the graph field's scroll bar to quickly switch between the section's two graphs.

The first type of graph in the graphs field is an XY graph. This graph control displays the selected physical property's data values, estimated values, and curve points on a single graph.

1	Data Values: data values are represented by squares, circles, upwards triangles, and downwards triangles. These symbols are always filled with either black, blue, or red color. Each datum reference is associated with a symbol having a different shape or color.
2	Estimated Values: estimated values are represented by diamonds. The diamond's internal color and border color are different for each different technique used to generate the estimated values.
3	Curve Points: curve points are represented by curves drawn through the given points. Curve points are typically assigned a curve name depending upon similar attributes, e.g., data values at two different temperatures. Each named curve is draw in a different color.
4	Units: values are graphed in their current units. These units are also appended to the default x and y axis labels.
5	Axis Limits: the default limits for the x and y axes are determined from the minimum and maximum of the data, estimates, and curve point values. These limits can be changed by using the Graph Attributes dialog (see below).

Clicking the left mouse button on an XY graph control activates the Values Details Dialog.

The Values Details dialog shows the description of each symbol or curve displayed on the graph. For data values, the description is the identifier of the associated reference. For estimated values, the description is the name of the technique used to generate the estimates. For curve points, the description is the name of the curve.

The Values Details dialog provides commands for reporting, transferring values to graph documents, and displaying references. See the documentation for the XY Graph Key Dialog for details.

Clicking the right mouse button on an XY graph control displays the control's commands menu.

• Edit Graph Attributes: activates the XY Graph Attributes dialog.

  The Graph Attributes dialog enables you change the attributes being displayed, transform values, set formats, and set axis limits. See documentation on the XY Graph Attributes Dialog for details.

• Show Reference Key: activates the Values Details dialog which shows the description of each symbol or curve displayed on the graph. See documentation for the XY Graph Key Dialog for details.
• Examine Graph: activates the Graph Examination Dialog which enables you to select and identify each point displayed in the graph, zoom into specific areas of the graph, and fit curves to selected values.
  See documentation on the XY Graph Examination Dialog for details.
• Edit Static Curves: activates the Static Curve Points edit dialog which enables you to add curve points that will appear on every Temperature and Pressure Dependent Property Section's graph in the current document. Static graphs are very powerful tools for comparing the physical property values of different chemicals and mixtures. See documetation on Using Static Graphs for details.
• Copy Graph: copies an image of the graph onto the clipboard for pasting into other applications.

For certain phase equilibrium properties of ternary mixtures, e.g., liquid-liquid equilibrium values, presentation on triangular diagrams is very helpful. The triangular graph control is the second type of graph displayed in this section's compound graph control. Triangular graph controls display the selected physical property's data values, estimated values, and curve points on a single graph.

1	Data Values: data values are represented by squares, circles, upwards triangles, and downwards triangles. These symbols are always filled with either black, blue, or red color. Each datum reference is associated with a symbol having a different shape or color.
2	Estimated Values: estimated values are represented by diamonds. The diamond's internal color and border color are different for each different technique used to generate the estimated values.
3	Curve Points: curve points are represented by curves drawn through the given points. Curve points are typically assigned a curve name depending upon similar attributes, e.g., data values at two different temperatures. Each named curve is draw in a different color. Note that triangular graphs can also automatically display tie lines as curves on the graph. These tie lines will appear in the graph's details dialog.
4	Units: values are graphed in their current composition units. These units are also appended to the default x, y, and z axis labels. Note that all three axes are displayed in the same composition units.
5	Axis Limits: the default limits for all axes are either 1 or 100. The default limits are determined from the minimum and maximum of the data, estimates, and curve point values. These limits can be changed by using the Graph Attributes dialog (see below).

Clicking the left mouse button on a triangular graph control activates the Values Details Dialog.

The Values Details dialog shows the description of each symbol or curve displayed on the graph. For data values, the description is the identifier of the associated reference. For estimated values, the description is the name of the technique used to generate the estimates. For curve points, the description is the name of the curve.

The Values Details dialog provides commands for reporting, transferring values to graph documents, and displaying references. See the documentation for the Triangular Graph Key Dialog for details.

Clicking the right mouse button on a triangular graph control displays the control's commands menu.

• Edit Graph Attributes: activates the Triangular Graph Attributes dialog.

  The Graph Attributes dialog enables you change the order of the axes, set formats, and set axis limits. See documentation on the Triangular Graph Attributes Dialog for details.

• Show Reference Key: activates the Values Details dialog which shows the description of each symbol or curve displayed on the graph. See documentation for the Triangular Graph Key Dialog for details.
• Examine Graph: activates the Graph Examination Dialog which enables you to select and identify each point displayed in the graph.
  See documentation on the Triangular Graph Examination Dialog for details.
• Edit Static Curves: activates the Static Curve Points edit dialog which enables you to add curve points that will appear on every Temperature and Pressure Dependent Property Section's graph in the current document. Static graphs are very powerful tools for comparing the physical property values of different chemicals and mixtures. See documetation on Using Static Graphs for details.
• Copy Graph: copies an image of the graph onto the clipboard for pasting into other applications.

Topic	Description
Estimating Mixture Properties	a short video demonstrating how to estimate physical properties using either Synapse or Cranium.
Getting Started using Cranium	provides a quick tour of Cranium's capabilities including data entry and physical property estimation.
Mixtures Chapter	the mixtures chapter contains numerous sections for entering and displaying data and estimates.