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Introduction to MULTIPHASE



The aim of this page is to provide a guided introduction to each command within the MULTIPHASE module through a series of examples which illustrate not only the function of each command, but how they can be used in combination. Each example consists of text and output, the output being given in a separate table. The commands issued are given in both and are printed in red italics. The text contains appropriate and helpful comments, and should be read in conjunction with the relevant output. 

The emphasis in these examples is mainly on the techniques of using MULTIPHASE to get the results of interest. On the other hand, it should not be forgotten that the user is in control. It is possible to pose problems that have no solution and, in these cases, MULTIPHASE may not be able to give much guidance on where the problem lies. Difficulties are most likely to be experienced with problems in which the activities or equilibrium amounts of substances are constrained. For example, setting the partial pressures of sulphur dioxide and oxygen could result in the impossible conditions of an activity of condensed sulphur being greater than unity or, in a system with hydrogen, pressures of hydrogen sulphide greater than the overall pressure.

The advice is to use MULTIPHASE as a tool, keep an eye on its messages and do not forget to use your own knowledge and experience.


Setting up a system and making a calculation

define system="C,H,O" source=sub_sgte !

DEFINE SYSTEM allows the user to enter the system components into the program as a list separated by commas and within quotes. The parameter SOURCE instructs the program to search the specified database(s) - in this case the SGTE substance database - for data for all compounds which are combinations of the three elements and for all relevant solution phases.

A report of this search is given - there are 12 phases and 84 species. The data for these phases and species are read from the database into the memory and also written to an output file which in this case has a default name, since none was specified by the user.

list system=components !

The command LIST produces a display - in this case of components - in the system, together with useful attributes. In referring to components in later commands, it is important to use the numbers that appear in this list. STATUS=NORMAL means that the component is present and will be considered in the calculations. The status of any component can be altered using the CLASSIFY command. AMOUNT is the number of moles of component in the system; an entry in this column registers any changes in the amount of components brought about by use of the SET command.

list system=phases !

In referring to phases in later commands prior to the calculations it is important to use the numbers and/or the names given in this list. When controlling the graphical output a separate list is used. All condensed substances are assigned to different phases unless their phase names are identical (see Databases, Definitions and Models).

list system=substances !

In referring to substances in later commands it is important to use the numbers and/or names given in this list. Please note that names may be used to identify substances only when the components are elements. When the amount of substance at equilibrium is fixed using the SET command, this constraint also appears under the STATUS heading.

classify absent pha(C1H4O1,H2O1) !
lis sys phases !

It is not necessary to type all keywords in full; any unique abbreviation will do.

We want to do some calculations on the behaviour of this system at high temperatures, so it is not very useful to retain liquid water and methanol. They can be deleted as phases C1H4O1 and H2O1 or phases 7 and 11 or as substances 79 and 83. The phases could be reinstated by using classify normal=phase(C1H4O1,H2O1) !.

Suppose that the aim is to convert coke (nominally pure carbon) to combustible gases by passing over it a mixture of water and air (for simplicity represented here by oxygen). The air is needed to sustain the temperature, as the reactions are otherwise endothermic.

set temperature 1000 pressure 2E6 !

Temperature is in kelvins and pressure in pascals.

set ?
 

 MULTIPHASE OPTION ?  define system="C,H,O" source=sub_sgte !
 SEARCHING FOR SYSTEM C,H,O,/-
 
 SEARCHING DATABASE(S) :

 sub_sgte        - SGTE Substance Database version 12.1 - June 2009
 
 
 SEARCHING FOR SYSTEM C,H,O,/-
 
 SEARCHING DATABASE(S) :

 sub_sgte        - SGTE Substance Database version 12.1 - June 2009
 

 ******                 GOOD DATAFILE CREATED                 ******

 Date and time of run 11-MAR-2011  11:31:17
 * DATAFILE = D:\atd\MTDATA\handbook\multiphase\def.mpi -  CREATED 11:31:17 11-MAR-2011
 * SYSTEM = C,H,O,/-,
 * NUMBER OF PHASES  =   12
 * NUMBER OF SPECIES =   84
 *
 MULTIPHASE OPTION ? list system=components !

 NUMBER    COMPONENT               STATUS      AMOUNT     DELTA    REF.P
    1      C                       NORMAL     undefined            
    2      H                       NORMAL     undefined            
    3      O                       NORMAL     undefined            
 
 MULTIPHASE OPTION ? list system=phases !

 NUMBER    PHASE                   STATUS      MODEL
    1      C                       NORMAL      PURE SUBSTANCE     
    2      DIAMOND                 NORMAL      PURE SUBSTANCE     
    3      GAS                     NORMAL      IDEAL GAS          
    4      C60                     NORMAL      PURE SUBSTANCE     
    5      C6H6_LIQUID             NORMAL      PURE SUBSTANCE     
    6      C1H2O2_LIQUID           NORMAL      PURE SUBSTANCE     
    7      C1H4O1_LIQUID           NORMAL      PURE SUBSTANCE     
    8      C2H4O2_LIQUID           NORMAL      PURE SUBSTANCE     
    9      C2H6O1_LIQUID           NORMAL      PURE SUBSTANCE     
   10      C2H6O2_LIQUID           NORMAL      PURE SUBSTANCE     
   11      H2O1_LIQUID             NORMAL      PURE SUBSTANCE     
   12      H2O2_LIQUID             NORMAL      PURE SUBSTANCE     
 
 MULTIPHASE OPTION ? list system=substances !

 NUMBER    SUBSTANCE               STATUS/CONSTRAINT
    1      C                       NORMAL                       
    2      C<DIAMOND>              NORMAL                       
    3      C<g>                    NORMAL                       
    4      C2<g>                   NORMAL                       
    5      C3<g>                   NORMAL                       
    6      C4<g>                   NORMAL                       
    7      C5<g>                   NORMAL                       
    8      C60<g>                  NORMAL                       
    9      CH<g>                   NORMAL                       
   10      CH2<g>                  NORMAL                       
   11      CH3<g>                  NORMAL                       
   12      CH4<g>                  NORMAL                       
   13      C2H<g>                  NORMAL                       
   14      C2H2<g>                 NORMAL                       
   15      C2H3<g>                 NORMAL                       
   16      C2H4<g>                 NORMAL                       
   17      C2H5<g>                 NORMAL                       
   18      C2H6<g>                 NORMAL                       
   19      C3H<g>                  NORMAL                       
   20      C3H4_1<g>               NORMAL                       
   21      C3H4_2<g>               NORMAL                       
   22      C3H6_1<g>               NORMAL                       
   23      C3H6_2<g>               NORMAL                       
   24      C3H8<g>                 NORMAL                       
   25      C4H<g>                  NORMAL                       
   26      C4H2<g>                 NORMAL                       
   27      C4H4<g>                 NORMAL                       
   28      C4H4_1,3<g>             NORMAL                       
   29      C4H6_1<g>               NORMAL                       
   30      C4H6_2<g>               NORMAL                       
   31      C4H6_3<g>               NORMAL                       
   32      C4H6_4<g>               NORMAL                       
   33      C4H6_5<g>               NORMAL                       
   34      C4H8<g>                 NORMAL                       
   35      C4H8_1<g>               NORMAL                       
   36      C4H8_2<g>               NORMAL                       
   37      C4H8_3<g>               NORMAL                       
   38      C4H8_4<g>               NORMAL                       
   39      C4H8_5<g>               NORMAL                       
   40      C4H10_1<g>              NORMAL                       
   41      C4H10_2<g>              NORMAL                       
   42      C6H6<g>                 NORMAL                       
   43      CHO<g>                  NORMAL                       
   44      CHO2<g>                 NORMAL                       
   45      CH2O<g>                 NORMAL                       
   46      CH2O2_CIS<g>            NORMAL                       
   47      CH2O2_DIOXIRANE<g>      NORMAL                       
   48      CH2O2_TRANS<g>          NORMAL                       
   49      CH3O_CH2OH<g>           NORMAL                       
   50      CH3O_CH3O<g>            NORMAL                       
   51      CH4O<g>                 NORMAL                       
   52      C2H2O<g>                NORMAL                       
   53      C2H4O_ACETALDEHYDE<g    NORMAL                       
   54      C2H4O_OXIRANE<g>        NORMAL                       
   55      C2H4O2_ACETICACID<g>    NORMAL                       
   56      C2H4O2_DIOXETANE<g>     NORMAL                       
   57      C2H4O3_123TRIOXOLANE    NORMAL                       
   58      C2H4O3_124TRIOXOLANE    NORMAL                       
   59      C2H6O<g>                NORMAL                       
   60      C2H6O2<g>               NORMAL                       
   61      C3H6O<g>                NORMAL                       
   62      C6H6O<g>                NORMAL                       
   63      CO<g>                   NORMAL                       
   64      CO2<g>                  NORMAL                       
   65      C2O<g>                  NORMAL                       
   66      C3O2<g>                 NORMAL                       
   67      H<g>                    NORMAL                       
   68      H2<g>                   NORMAL                       
   69      HO<g>                   NORMAL                       
   70      HO2<g>                  NORMAL                       
   71      H2O<g>                  NORMAL                       
   72      H2O2<g>                 NORMAL                       
   73      O<g>                    NORMAL                       
   74      O2<g>                   NORMAL                       
   75      O3<g>                   NORMAL                       
   76      C60                     NORMAL                       
   77      C6H6<C6H6_LIQUID>       NORMAL                       
   78      CH2O2<C1H2O2_LIQUID>    NORMAL                       
   79      CH4O<C1H4O1_LIQUID>     NORMAL                       
   80      C2H4O2<C2H4O2_LIQUID    NORMAL                       
   81      C2H6O<C2H6O1_LIQUID>    NORMAL                       
   82      C2H6O2<C2H6O2_LIQUID    NORMAL                       
   83      H2O<H2O1_LIQUID>        NORMAL                       
   84      H2O2<H2O2_LIQUID>       NORMAL                       
 
 MULTIPHASE OPTION ?
classify absent pha(C1H4O1,H2O1) !
 MULTIPHASE OPTION ? lis sys phases !

 NUMBER    PHASE                   STATUS      MODEL
    1      C                       NORMAL      PURE SUBSTANCE     
    2      DIAMOND                 NORMAL      PURE SUBSTANCE     
    3      GAS                     NORMAL      IDEAL GAS          
    4      C60                     NORMAL      PURE SUBSTANCE     
    5      C6H6_LIQUID             NORMAL      PURE SUBSTANCE     
    6      C1H2O2_LIQUID           NORMAL      PURE SUBSTANCE     
    7      C1H4O1_LIQUID           absent      PURE SUBSTANCE     
    8      C2H4O2_LIQUID           NORMAL      PURE SUBSTANCE     
    9      C2H6O1_LIQUID           NORMAL      PURE SUBSTANCE     
   10      C2H6O2_LIQUID           NORMAL      PURE SUBSTANCE     
   11      H2O1_LIQUID             absent      PURE SUBSTANCE     
   12      H2O2_LIQUID             NORMAL      PURE SUBSTANCE     
 
 MULTIPHASE OPTION ? set temperature 1000 pressure 2E6 !

 MULTIPHASE OPTION ? set ?

 TEMPERATURE
 PRESSURE(*)
 VOLUME
 N(*)
 W(*)
 X(*)
 LGT_P(*)
 MOLALITY(*)
 LGT_M(*)
 CO_MOL_FR(*)
 CO_WT_FR(*)
 USER_VARIABLE(*)
 SYSTEM_ENTHALPY
 MASS_PHASE(*)
 ACTIVITY(*)
 STOP
 <'GROUP NAME'>

 SET WHAT ? n(C) 20 n(H2O) 25 n(O2) 2.5 !

 MULTIPHASE OPTION ? list system settings !

 TEMPERATURE       :   1000.000
 PRESSURE/Pa       :   2000000.
 VOLUME/m3         :    undefined
 SYSTEM AMOUNT/mol :    undefined
 COMP. AMOUNTS/mol :   20.00000       50.00000       30.00000
 SYSTEM MASS/kg    :    undefined
 COMP. MASSES/kg   :  0.2402140      0.5039700E-01  0.4799820
 
 SUBSTANCE            AMOUNT TO BE CONVERTED INTO COMPONENT MOLES
 C                      20.00000   
 H2O<g>                 25.00000   
 O2<g>                  2.500000   
 
 
 MULTIPHASE OPTION ?
compute

 CALCULATION OPTIONS ? ?

 INITIAL_POINT_OPTION
 STAGES_REQUIRED
 PRINT_LEVEL
 MESSAGE_LEVEL
 STOP

 CALCULATION OPTIONS ? stages ?


 BOTH_LARGE
 1_ONLY
 2_ONLY
 BOTH_SMALL
 ROBUST_STAGE_2
 STAGE_1_PLUS
 NONE

 ENTER OPTION FOR STAGE-1/STAGE-2 : both_small !


*** MULTIPHASE - Stage 2 Results ***

Temperature =  1000.0000 K

Fixed pressure =  2.000000E+06 Pa,    1.973847E+01 atm

Calculated gas volume =  1.414264E-01 m3

                           Amount  Partial pressure/atm
                            mole
                                   Notional activity
Stoichiometric phases
 C                     3.431038E+00  1.000000E+00
Phase DIAMOND            
 C<DIAMOND>                          4.935429E-01
Phase GAS                
 C<g>                  8.822097E-30  5.118722E-30
 C2<g>                 8.001167E-34  4.642405E-34
 C3<g>                 9.333069E-33  5.415196E-33
 C4<g>                 3.018642E-42  1.751464E-42
 C5<g>                 3.062722E-42  1.777040E-42
 C60<g>                1.609686-126  9.339654-127
 CH<g>                 1.783895E-25  1.035045E-25
 CH2<g>                2.470795E-17  1.433594E-17
 CH3<g>                7.172294E-08  4.161479E-08
 CH4<g>                3.774212E+00  2.189858E+00
 C2H<g>                6.997788E-23  4.060228E-23
 C2H2<g>               1.035957E-08  6.010789E-09
 C2H3<g>               3.102971E-12  1.800394E-12
 C2H4<g>               2.374375E-05  1.377650E-05
 C2H5<g>               6.738971E-10  3.910058E-10
 C2H6<g>               3.102855E-04  1.800326E-04
 C3H<g>                1.362928E-24  7.907923E-25
 C3H4_1<g>             1.690228E-11  9.806975E-12
 C3H4_2<g>             6.295231E-11  3.652594E-11
 C3H6_1<g>             5.873120E-08  3.407678E-08
 C3H6_2<g>             5.934832E-08  3.443484E-08
 C3H8<g>               8.970655E-08  5.204917E-08
 C4H<g>                9.170252E-32  5.320727E-32
 C4H2<g>               3.867219E-18  2.243822E-18
 C4H4<g>               1.031745E-15  5.986349E-16
 C4H4_1,3<g>           1.460399E-21  8.473467E-22
 C4H6_1<g>             3.804727E-14  2.207563E-14
 C4H6_2<g>             4.314453E-12  2.503314E-12
 C4H6_3<g>             2.163527E-14  1.255313E-14
 C4H6_4<g>             6.374584E-14  3.698635E-14
 C4H6_5<g>             1.090139E-15  6.325163E-16
 C4H8<g>               3.127129E-15  1.814410E-15
 C4H8_1<g>             1.425131E-11  8.268837E-12
 C4H8_2<g>             1.250412E-11  7.255089E-12
 C4H8_3<g>             1.772948E-11  1.028693E-11
 C4H8_4<g>             1.917978E-15  1.112841E-15
 C4H8_5<g>             2.812627E-11  1.631931E-11
 C4H10_1<g>            3.265313E-11  1.894587E-11
 C4H10_2<g>            1.658961E-11  9.625554E-12
 C6H6<g>               5.165497E-12  2.997104E-12
 CHO<g>                7.534675E-10  4.371739E-10
 CHO2<g>               1.731915E-10  1.004885E-10
 CH2O<g>               1.321711E-05  7.668781E-06
 CH2O2_CIS<g>          2.814419E-05  1.632971E-05
 CH2O2_DIOXIRANE<g>    2.775534E-27  1.610409E-27
 CH2O2_TRANS<g>        4.050887E-06  2.350389E-06
 CH3O_CH2OH<g>         6.836357E-12  3.966563E-12
 CH3O_CH3O<g>          1.607101E-14  9.324657E-15
 CH4O<g>               3.339064E-06  1.937378E-06
 C2H2O<g>              8.721568E-19  5.060393E-19
 C2H4O_ACETALDEHYDE<g  4.784526E-07  2.776059E-07
 C2H4O_OXIRANE<g>      3.875527E-14  2.248643E-14
 C2H4O2_ACETICACID<g>  1.939212E-07  1.125162E-07
 C2H4O2_DIOXETANE<g>   7.207551E-32  4.181936E-32
 C2H4O3_123TRIOXOLANE  3.821635E-39  2.217374E-39
 C2H4O3_124TRIOXOLANE  2.062746E-34  1.196838E-34
 C2H6O<g>              5.936796E-09  3.444624E-09
 C2H6O2<g>             1.204372E-13  6.987960E-14
 C3H6O<g>              1.698382E-09  9.854285E-10
 C6H6O<g>              2.001440E-15  1.161267E-15
 CO<g>                 4.869307E+00  2.825249E+00
 CO2<g>                7.924724E+00  4.598052E+00
 C2O<g>                2.598352E-19  1.507606E-19
 C3O2<g>               1.619057E-12  9.394027E-13
 H<g>                  8.467802E-09  4.913154E-09
 H2<g>                 8.169380E+00  4.740005E+00
 HO<g>                 2.119306E-11  1.229655E-11
 HO2<g>                5.266339E-23  3.055614E-23
 H2O<g>                9.281163E+00  5.385079E+00
 H2O2<g>               2.486873E-18  1.442923E-18
 O<g>                  2.645098E-20  1.534728E-20
 O2<g>                 1.663381E-20  9.651204E-21
 O3<g>                 1.634691E-41  9.484741E-42
 Phase total is        3.401917E+01  1.973847E+01
Stoichiometric phases
 C60                                 0.000000E+00
Phase C6H6_LIQUID        
 C6H6<C6H6_LIQUID>                   1.925176E-15
Phase C1H2O2_LIQUID      
 CH2O2<C1H2O2_LIQUID>                2.119187E-08
Phase C2H4O2_LIQUID      
 C2H4O2<C2H4O2_LIQUID                1.585930E-10
Phase C2H6O1_LIQUID      
 C2H6O<C2H6O1_LIQUID>                9.919240E-13
Phase C2H6O2_LIQUID      
 C2H6O2<C2H6O2_LIQUID                3.107214E-17
Phase H2O2_LIQUID        
 H2O2<H2O2_LIQUID>                   2.774765E-21

Component      Ref.Phase     Chem.Pot.    Activity     Amount/mol   Mass/kg
C                           -1.265925E+04 2.181551E-01 2.000000E+01 2.402140E-01
H                           -6.624312E+04 3.466586E-04 5.000000E+01 5.039700E-02
O                           -3.019797E+05 1.684983E-16 3.000000E+01 4.799820E-01
Total                                                  1.000000E+02 7.705930E-01

 Number of Gibbs Energy evaluations in Stage 1 =       266
 Number of Gibbs Energy, compnt residual calculations in Stage 2 = 3,  2

 Estimated maximum relative error on species amounts =  1.0E-06

              Percentage distribution of components between phases
                                  C                H                O              
              C                   1.7155190E+01    0.0000000E+00    0.0000000E+00
              GAS                 8.2844810E+01    1.0000000E+02    1.0000000E+02

Amount        Phase               Mole fraction of component within phase
compnt moles
                                  C                H                O              
 3.431038E+00 C                   1.0000000E+00    0.0000000E+00    0.0000000E+00
 9.656896E+01 GAS                 1.7157647E-01    5.1776470E-01    3.1065882E-01

Mass/kg       Phase               Mass fraction of component within phase
                                  C                H                O              
 4.120917E-02 C                   1.0000000E+00    0.0000000E+00    0.0000000E+00
 7.293838E-01 GAS                 2.7283966E-01    6.9095312E-02    6.5806502E-01

Gibbs Energy = -1.2624732531E+07 J   System Enthalpy = -5.2150799196E+06 J
                      *************************************
                      * WARNING/ERRORS HAVE BEEN DETECTED *
                      *************************************
 
     90 Warnings: Multiphase, temperature range violation -  Unary data
 
 MULTIPHASE OPTION ?



Before it is possible to do a calculation, some quantities are required. The entry of set ? shows what is possible. One way is by specifying the total amount of each component in the system. SET allows overall component and equilibrium substance amounts to be fixed. "n" refers to amount in moles ("w" would indicate mass, and "x" mole fraction at equilibrium), and the number or name in brackets e.g. n(2) specifies the component and n(H2O) specifies the species whose amount is being used as a convenient way to SET the amounts of components H and O.

In the present example it is more convenient to specify the composition in terms of the reactants being fed into the system. Do not mix the entry of input amounts of components and of substances containing those components. Also do not set components by both weight and moles. The entry of n(H2O)=25 means 25 moles of water.  Notice also that the phase label of the H2O is omitted.

n(C) 20 n(H2O) 25 n(O2) 2.5 !
list system settings !

This gives the pressure, volume, temperature, amounts and other constraints on the system. (Notice that the conversion between component amount and component mass is automatically provided). It would also be possible to set an overall system amount and (say) the amounts of components 1 and 2, thus indirectly fixing the amount of component 3.

compute
?
stages ?
both_small !

There are five parameters that can be set within the COMPUTE command: these can be left at their default values simply by completing the command with an exclamation mark. However, we want to look at some of the minor products so we decide to look at the options by entry of a question mark and, after checking the response, to make use of both stages of computation. The difference between both_large and both_small is dealt with here and is not significant in this particular case. Unless a previous calculation has been carried out for similar conditions, it is essential to use STAGE 1 before STAGE 2.

The computer responds by giving the following information:

-    Warnings are printed if the temperature limits of some or all of the data have been exceeded. These warnings should not be ignored. Usually the substances concerned are above their normal stability range. In order to preserve continuity of results, MULTIPHASE automatically extends the temperature range. Therefore always look to see if these substances are becoming dominant at high temperatures.

-    If no solution is found this will be indicated, otherwise the usually very small rounding errors are given

-    The temperature and fixed or calculated volume and pressure are given.

-    There follows a listing of the amounts of products. The amount in moles is self explanatory; the next column lists either the mole fraction, partial pressure or molality of species within a phase, or the notional activity of condensed phases. A value of unity, as for carbon in this table indicates that the phase is present. A value not very much below unity indicates that the phase is on the edge of stability and might appear under slightly different conditions or might tend to dissolve in a phase of similar structure.

-    The remainder of the information is of interest mainly to check the efficiency of the operation of the program. If many calculations were required for a process plant optimisation, it would be useful to explore the effect on the computation time of varying the parameters in the COMPUTE command.

 
Calculating and plotting a graph

The temperature dependence of equilibria in the carbon - hydrogen - oxygen system is of enormous economic importance; this section shows how to set up the calculation and obtain plots that give a graphical representation of the chemistry. The example follows on from that described above.

step temp 700 1500 20 !
compute stages robust init ?

Because the equilibrium at 1000 K has just been calculated, it is possible to undertake related calculations using STAGE 2 only, provided a check is maintained of warning messages. (In graphical output, warnings of failure to reach a solution are printed in the key to the plot. If the temperature limit of the data for individual substances is exceeded the line showing the value for that substance is broken (or in colour on PC implementations). Only if the substance is a very minor carrier of all components can it be safely ignored.)

The ? after init asks for initialisation options. The following sequence of user input chooses initiation by previous solution and selects graphics output. The output to the screen during calculation comprises only the step variable and warning messages.

previous
print ?
graphics !

plot go

A graph showing the major species is given below. Graphite is formed at low temperatures and when it disappears, at temperatures above 1000 K, the proportion of methane declines sharply. Concomitantly carbon monoxide and hydrogen replace water and carbon dioxide as the most abundant gaseous species. The command laser is used to send the plotted diagram to a hard copy device.

ordinate log=y limit  2  -7  ! plot go 

The ORDINATE and ABSCISSA commands may be used to change the function to be plotted, whether it should be displayed with a log scale and to enlarge a certain part of the calculated diagram. The resultant plot is shown below.

 

Calculating and plotting a graph

 MULTIPHASE OPTION ? step temp 700 1500 20 !
 MULTIPHASE OPTION ? compute stages robust init ?
 
 READ_IN_FROM_USER
 AUTOMATIC
 PREVIOUS_SOLUTION
 LOWER_BOUNDS

 ENTER OPTION FOR INITIAL POINT OF CALCULATION : previous

 CALCULATION OPTIONS ? print ?

 GRAPHICS_OUTPUT
 MINIMAL
 BRIEF
 DEFAULT_RESULTS
 EACH_STAGE_RESULTS
 PHASE_TABLES
 MOLE_FRACTION_TABLE
 WEIGHT_FRACTION_TABL
 SPECIATION_AND_BASIC
 SPECIATION_AND_PHASE
 SPECIATION_AND_MOLE_
 SPECIATION_AND_WEIGH
 SPECIATION_AND_NONE

 ENTER OPTION FOR PRINTOUT FROM MULTIPHASE : graphics !

 NUMBER OF STEPS =  41
 
     700.000
     720.000
     .......
     1500.00
 
                      *************************************
                      * WARNING/ERRORS HAVE BEEN DETECTED *
                      *************************************
 
   7490 Warnings: Multiphase, temperature range violation -  Unary data
 
 MULTIPHASE OPTION ? plot go

 MULTIPHASE OPTION ? ordinate log=y limit  2  -7  ! plot go 
 MULTIPHASE OPTION ?

 

Species amounts calculated as described

Species amounts calculated as described

Results from previous figure plotted on log scale with selected ordinate limits

Results from previous figure plotted on log scale with selected ordinate limits

 
Defining a system in which the components are compounds (ie not elements)

define system="H2O,CH4" source=sub_sgte !
list system substances !

This command defines the components as compounds. The database is searched in the same way as in the previous section. However, here, most of the species do not have formulae which can be formed by combining H2O and CH4 and for each of these a warning message is displayed indicating that it is not in the defined system. The list of substances in the system is now very simple. This leads to the next example in which compound components are also used but where the system is rather more complex.

 

Defining a system in which the components are compounds (ie not elements)

 MULTIPHASE OPTION ?  define system="H2O,CH4" source=sub_sgte !

 SEARCHING FOR SYSTEM H2O,CH4,/-
 
 SEARCHING DATABASE(S) :

 sub_sgte        - SGTE Substance Database version 12.1 - June 2009
 
 
 SEARCHING FOR SYSTEM H2O,CH4,O/-2
 
 SEARCHING DATABASE(S) :

 sub_sgte        - SGTE Substance Database version 12.1 - June 2009
 
 C                    WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C<DIAMOND>           WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C<g>                 WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2<g>                WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C3<g>                WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4<g>                WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C5<g>                WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C60                  WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C60<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CH<g>                WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CH2<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CH3<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H2<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H3<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H4<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H5<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H6<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C3H<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C3H4_1<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C3H4_2<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C3H6_1<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C3H6_2<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C3H8<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H2<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H4<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H4_1,3<g>          WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H6_1<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H6_2<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H6_3<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H6_4<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H6_5<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H8<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H8_1<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H8_2<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H8_3<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H8_4<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H8_5<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H10_1<g>           WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C4H10_2<g>           WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C6H6<C6H6_LIQUID>    WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C6H6<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CHO<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CHO2<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CH2O<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CH2O2<C1H2O2_LIQUID> WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CH2O2_CIS<g>         WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CH2O2_DIOXIRANE<g>   WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CH2O2_TRANS<g>       WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CH3O_CH2OH<g>        WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CH3O_CH3O<g>         WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CH4O<C1H4O1_LIQUID>  WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CH4O<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H2O<g>             WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H4O_ACETALDEHYDE<g WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H4O_OXIRANE<g>     WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H4O2<C2H4O2_LIQUID WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H4O2_ACETICACID<g> WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H4O2_DIOXETANE<g>  WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H4O3_123TRIOXOLANE WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H4O3_124TRIOXOLANE WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H6O<C2H6O1_LIQUID> WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H6O<g>             WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H6O2<C2H6O2_LIQUID WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2H6O2<g>            WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C3H6O<g>             WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C6H6O<g>             WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CHO/+<g>             WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CH/+<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CO<g>                WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CO2<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2O<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C3O2<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CO/+<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CO2/+<g>             WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 CO2/-<g>             WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C/+<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C/-<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2/+<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 C2/-<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 H<g>                 WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 H2<g>                WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 HO<g>                WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 HO2<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 H2O2<H2O2_LIQUID>    WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 H2O2<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 HO/+<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 HO2/-<g>             WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 H2O/+<g>             WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 H/-<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 H2/+<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 H2/-<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 H3/+<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 O<g>                 WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 O2<g>                WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 O3<g>                WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 O/+<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 O/-<g>               WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 O2/+<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 O2/-<g>              WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM
 /-<g>                WARNING: SPECIES IS NOT IN THE DEFINED SYSTEM

 ******                 GOOD DATAFILE CREATED                 ******

 Date and time of run 11-MAR-2011  15:01:41
 * DATAFILE = D:\atd\MTDATA\handbook\multiphase\def.mpi -  CREATED 15:01:41 11-MAR-2011
 * SYSTEM = H2O,CH4,O/-2,
 * NUMBER OF PHASES  =    2
 * NUMBER OF SPECIES =    3
 *
 MULTIPHASE OPTION ?
list system substances !

 NUMBER    SUBSTANCE               STATUS/CONSTRAINT
    1      CH4<g>                  NORMAL                       
    2      H2O<g>                  NORMAL                       
    3      H2O<H2O1_LIQUID>        NORMAL                       
 
 MULTIPHASE OPTION ? 


Calculations in a condensed system with solution phases

define system = "KCl,CaCl2,ZnCl2" source=demo_1 !

The CaCl2-KCl-ZnCl2 system is of interest as a molten salt medium for metallurgical processing. Defining the system in terms of the salts restricts the system to the composition plane between them and therefore excludes consideration of, for example, evolution of chlorine. A particular advantage of using the pure salts as components in this case is that their behaviour in the melt can be modelled in the same way as are alloy components in liquid metals.

set temp 800 !
list system components !

Notice that the components are now compounds, but otherwise the format of the table is the same as previously.

list system phases !
set n(1) 0.4  n(2) 0.5 n(3) 0.1 !
list system substances !

Compare the phase and substance lists. Notice that Phase 2 consists of Substances 2, 3 and 4, which have an identical phase label.

co sta 1 ini auto pri default !

The above input commands the computation with STAGE 1 only, automatic initialisation, and default printing (no graph). These are all the default options.

The results show a three phase equilibrium between the stoichiometric compounds CaCl2 and KCaCl3 and a liquid solution with the indicated composition. The amounts of each of the phases are also given.

Calculations in a condensed system with solution phases

 MULTIPHASE OPTION ?  define system = "KCl,CaCl2,ZnCl2" source=demo_1 !

 SEARCHING FOR SYSTEM KCl,CaCl2,ZnCl2,/-
 
 SEARCHING DATABASE(S) :

 demo_1          - Test database - use only with macro 'testmt.mac'
 
 
 SEARCHING FOR SYSTEM KCl,CaCl2,ZnCl2,/-
 
 SEARCHING DATABASE(S) :

 demo_1          - Test database - use only with macro 'testmt.mac'
 

 ******                 GOOD DATAFILE CREATED                 ******

 Date and time of run 11-MAR-2011  15:07:42
 * DATAFILE = D:\atd\MTDATA\handbook\multiphase\def.mpi -  CREATED 15:07:42 11-MAR-2011
 * SYSTEM = KCl,CaCl2,ZnCl2,/-,
 * NUMBER OF PHASES  =    8
 * NUMBER OF SPECIES =   10
 *
 MULTIPHASE OPTION ? set temp 800 !

 MULTIPHASE OPTION ? list system components !

 NUMBER    COMPONENT               STATUS      AMOUNT     DELTA    REF.P
    1      KCl                     NORMAL     undefined            
    2      CaCl2                   NORMAL     undefined            
    3      ZnCl2                   NORMAL     undefined            
 
 MULTIPHASE OPTION ?
list system phases !

 NUMBER    PHASE                   STATUS      MODEL
    1      CaCl2                   NORMAL      PURE SUBSTANCE     
    2      LIQUID                  NORMAL      REDLICH-KISTER     
    3      CaCl3K                  NORMAL      PURE SUBSTANCE     
    4      HALITE                  NORMAL      PURE SUBSTANCE     
    5      Cl4K2Zn                 NORMAL      PURE SUBSTANCE     
    6      Cl5KZn2                 NORMAL      PURE SUBSTANCE     
    7      Cl7K3Zn2                NORMAL      PURE SUBSTANCE     
    8      Cl2Zn                   NORMAL      PURE SUBSTANCE     
 
 MULTIPHASE OPTION ? 
set n(1) 0.4  n(2) 0.5 n(3) 0.1 !
 MULTIPHASE OPTION ? list system substances !

 NUMBER    SUBSTANCE               STATUS/CONSTRAINT
    1      CaCl2                   NORMAL                       
    2      CaCl2<LIQUID>           NORMAL                       
    3      ClK<LIQUID>             NORMAL                       
    4      Cl2Zn<LIQUID>           NORMAL                       
    5      CaCl3K                  NORMAL                       
    6      ClK<HALITE>             NORMAL                       
    7      Cl4K2Zn                 NORMAL                       
    8      Cl5KZn2                 NORMAL                       
    9      Cl7K3Zn2                NORMAL                       
   10      Cl2Zn                   NORMAL                       
 
 MULTIPHASE OPTION ? co sta 1 ini auto pri default !


*** MULTIPHASE - Stage 1* Results ***

Temperature =   800.0000 K

Fixed pressure =  1.013250E+05 Pa,    1.000000E+00 atm

                           Amount         Mole fraction
                            mole
                                        Notional activity
Stoichiometric phases
 CaCl2                     1.32666E-01      1.0000000
Phase LIQUID             
 CaCl2<LIQUID>             1.11429E-01      0.3134214
 ClK<LIQUID>               1.44095E-01      0.4053035
 Cl2Zn<LIQUID>             1.00000E-01      0.2812751
 Phase total is            3.55524E-01      1.0000000
Stoichiometric phases
 CaCl3K                    2.55905E-01      1.0000000
Phase HALITE             
 ClK<HALITE>                              4.622860E-02
Stoichiometric phases
 Cl4K2Zn                                  1.069573E-01
 Cl5KZn2                                  8.378843E-04
 Cl7K3Zn2                                 1.415508E-03
 Cl2Zn                                    1.707058E-02

Component      Ref.Phase     Chem.Pot.    Activity     Amount/mol   Mass/kg
KCl                         -5.384164E+05 7.012953E-36 4.000000E-01 2.982052E-02
CaCl2                       -9.042299E+05 9.148167E-60 5.000000E-01 5.549200E-02
ZnCl2                       -5.508702E+05 1.078387E-36 1.000000E-01 1.363150E-02
Total                                                  1.000000E+00 9.894402E-02

 Number of Gibbs Energy evaluations in Stage 1 =        23

Estimate of Stage 1* calculational inaccuracy in species mole amount ni
 (ignoring inaccuracies in data) = Errabs + Errrel * ni where
 Errabs =  5.0E-06
 Errrel =  2.0E-05

              Percentage distribution of components between phases
                                  KCl             CaCl2           ZnCl2         
              CaCl2              0.00000        26.53325         0.00000
              LIQUID            36.02376        22.28575       100.00000
              CaCl3K            63.97624        51.18099         0.00000

Amount        Phase               Mole fraction of component within phase
compnt moles
                                  KCl             CaCl2           ZnCl2         
 1.326663E-01 CaCl2              0.0000000       1.0000000       0.0000000
 3.555238E-01 LIQUID             0.4053035       0.3134214       0.2812751
 5.118099E-01 CaCl3K             0.5000000       0.5000000       0.0000000

Mass/kg       Phase               Mass fraction of component within phase
                                  KCl             CaCl2           ZnCl2         
 1.472383E-02 CaCl2              0.0000000       1.0000000       0.0000000
 3.674078E-02 LIQUID             0.2923855       0.3365963       0.3710182
 4.747940E-02 CaCl3K             0.4018173       0.5981827       0.0000000

              Percentage distribution of elements between phases
                                  Ca              Cl              K             
              CaCl2             26.53325        16.58328         0.00000
              LIQUID            22.28575        35.43454        36.02376
              CaCl3K            51.18099        47.98218        63.97624
 
                                  Zn            
              CaCl2              0.00000
              LIQUID           100.00000
              CaCl3K             0.00000

Amount        Phase               Mole fraction of element within phase
elemt moles
                                  Ca              Cl              K             
 3.979988E-01 CaCl2              0.3333333       0.6666667       0.0000000
 9.224764E-01 LIQUID             0.1207931       0.6145985       0.1562046
 1.279525E+00 CaCl3K             0.2000000       0.6000000       0.2000000
 
                                  Zn            
 3.979988E-01 CaCl2              0.0000000
 9.224764E-01 LIQUID             0.1084039
 1.279525E+00 CaCl3K             0.0000000

Mass/kg       Phase               Mass fraction of element within phase
                                  Ca              Cl              K             
 1.472383E-02 CaCl2              0.3611151       0.6388849       0.0000000
 3.674078E-02 LIQUID             0.1215500       0.5470806       0.1533411
 4.747940E-02 CaCl3K             0.2160128       0.5732548       0.2107324
 
                                  Zn            
 1.472383E-02 CaCl2              0.0000000
 3.674078E-02 LIQUID             0.1780283
 4.747940E-02 CaCl3K             0.0000000

Gibbs Energy = -7.2256855043E+05 J   System Enthalpy = -5.7894587012E+05 J

 MULTIPHASE OPTION ?


Specifying equilibrium amounts of substances

The purpose of this section is to show how to set up a calculation in which the amount of a product substance is specified as distinct from the amounts of reactants. It is relatively easy in this type of calculation to pose a problem that does not have a solution. The example chosen is deliberately simple to keep the volume of output at a reasonable level.

define system="H, N" source=sub_sgte !

The SGTE substance database is searched for substances which could possibly be present in the N-H system at equilibrium.

list system substances !
classify absent 6 !

CLASSIFY is used to remove or restore substances. In this case one of the N2H2<g> isomers, substance 6, has been removed.

set temp 400 pres 1e5 !
set p(NH3<g>)=0.4 !

When SET is used to specify the amount, pressure, molality or activity of a product at equilibrium, the phase must be specified. In this case the partial pressure of ammonia has been set to 0.4.

The warning in the table below is a reminder that if the equilibrium amount of NH3<g> has been specified, then the total component amounts for N and H cannot both be fixed, since the problem would then be overdetermined. At present both the components N and H are classified as NORMAL.

lis sy co !

Ignoring the warning and getting another one:

set n(2)=1.0 !

This sets the amount of nitrogen to one mol by atoms and results in another warning.

classify free co(1) !

As a consequence of the above warning, it is decided not to fix the amount of H, i.e. component 1: it is therefore classified as FREE. The component amount will therefore be a result of the calculation, not one of its constraints. This is an arbitrary decision which allows a solution to be calculated, although it will in general not be unique.

comp !

Attempting to compute a solution now is feasible in principle but in this case the program needs an initial guess for the amount of hydrogen. This seems a restriction but does allow cases where there are two solutions to be adequately explored - for example, in this case, there are solutions at n(H)=1.483 and 5.193.

set n(1)=4 !
lis sy all !

Setting an initial amount for the remaining component amount provides enough information for a solution to be calculated.

comp stages b_s !

The results reveal a successful computation using STAGES 1 and 2. Only nitrogen, hydrogen and ammonia are significant products. It is of interest to see what happens if STAGE 1 only is used, because, whereas STAGE 2 is able to use the constrained partial pressure directly in the calculation, STAGE 1 works towards a solution by gradually changing the amount of the free component.

It is worth noting the significance in STAGE 1 of the parameter DELTA in the list of components. This is automatically set to one tenth the amount of a free component as specified by the user. DELTA can be changed by the user by means of the classify command but normally a better course, if this seemed necessary, would be to change the component amount itself.

comp sta 1 !

As indicated in the output, the result is identical to that obtained using STAGE 2.

set te 500 ! co !

When the temperature is raised to 500 K, MULTIPHASE cannot find a solution. It would be fairly easy to tackle the problem graphically by hand. If so one would find that as the amount of the free component, hydrogen, was increased from low values, the partial pressure of ammonia would at first increase but, as a consequence of adding the hydrogen, the volume of gas would also increase, so decreasing the partial pressure of nitrogen. This would cause the ammonia partial pressure to pass through a maximum and then to decrease without reaching the specified value.

The error messages given by MULTIPHASE are not given in these chemical terms. If difficulties in interpreting them are experienced, they may be referred to NPL staff.

 MULTIPHASE OPTION ? define system="H, N" source=sub_sgte !

 SEARCHING FOR SYSTEM H, N,/-
 
 SEARCHING DATABASE(S) :

 sub_sgte        - SGTE Substance Database version 12.1 - June 2009
 
  SEARCHING FOR SYSTEM H, N,/-
 
 SEARCHING DATABASE(S) :

 sub_sgte        - SGTE Substance Database version 12.1 - June 2009
 
 ******                 GOOD DATAFILE CREATED                 ******

 Date and time of run 11-MAR-2011  15:15:29
 * DATAFILE = D:\atd\MTDATA\handbook\multiphase\def.mpi -  CREATED 15:15:29 11-MAR-2011
 * SYSTEM = H,N,/-,
 * NUMBER OF PHASES  =    2
 * NUMBER OF SPECIES =   14
 *
 MULTIPHASE OPTION ? list system substances !


 NUMBER    SUBSTANCE               STATUS/CONSTRAINT
    1      H<g>                    NORMAL                       
    2      H2<g>                   NORMAL                       
    3      HN<g>                   NORMAL                       
    4      HN3<g>                  NORMAL                       
    5      H2N<g>                  NORMAL                       
    6      H2N2_1,1N2H2<g>         NORMAL                       
    7      H2N2_CIS<g>             NORMAL                       
    8      H2N2_TRANS<g>           NORMAL                       
    9      H3N<g>                  NORMAL                       
   10      H4N2<g>                 NORMAL                       
   11      N<g>                    NORMAL                       
   12      N2<g>                   NORMAL                       
   13      N3<g>                   NORMAL                       
   14      H4N2<H4N2_LIQUID>       NORMAL                       
 
 MULTIPHASE OPTION ? classify absent 6 !

 MULTIPHASE OPTION ? set temp 400 pres 1e5 !
 MULTIPHASE OPTION ? set p(NH3<g>)=0.4 !

 ***WARNING: AMOUNT/CONSTRAINT CONFLICT FOR SUBSTANCE           9

 MULTIPHASE OPTION ? lis sy co !


 NUMBER    COMPONENT               STATUS      AMOUNT     DELTA    REF.P
    1      H                       NORMAL     undefined            
    2      N                       NORMAL     undefined            
 
 MULTIPHASE OPTION ? set n(2)=1.0 !


 ***WARNING: AMOUNT/CONSTRAINT CONFLICT FOR SUBSTANCE           9

 MULTIPHASE OPTION ? classify free co(1) !

 MULTIPHASE OPTION ? comp !

 ***Error*** Multiphase, problem specification
 Some component amounts undefined

                      *************************************
                      * WARNING/ERRORS HAVE BEEN DETECTED *
                      *************************************
 
      1 Errors  : Problem specification -  Some component amounts undefined
 
 MULTIPHASE OPTION ? set n(1)=4 !

 MULTIPHASE OPTION ? lis sy all !

 SYSTEM ELEMENTS : HN
 
 NUMBER    COMPONENT               STATUS      AMOUNT     DELTA    REF.P
    1      H                       FREE        4.00000             
    2      N                       NORMAL      1.00000             
 
 NUMBER    PHASE                   STATUS      MODEL
    1      GAS                     NORMAL      IDEAL GAS          
    2      H4N2_LIQUID             NORMAL      PURE SUBSTANCE     
 
 NUMBER    SUBSTANCE               STATUS/CONSTRAINT
    1      H<g>                    NORMAL                       
    2      H2<g>                   NORMAL                       
    3      HN<g>                   NORMAL                       
    4      HN3<g>                  NORMAL                       
    5      H2N<g>                  NORMAL                       
    6      H2N2_1,1N2H2<g>         absent                       
    7      H2N2_CIS<g>             NORMAL                       
    8      H2N2_TRANS<g>           NORMAL                       
    9      H3N<g>                  PRESSURE(*) = 0.4            
   10      H4N2<g>                 NORMAL                       
   11      N<g>                    NORMAL                       
   12      N2<g>                   NORMAL                       
   13      N3<g>                   NORMAL                       
   14      H4N2<H4N2_LIQUID>       NORMAL                       
 
 UNARY                             SOURCE             Tmin/K     Tmax/K
 H<g>                              sub_sgte            298.15    6000.00
 H2<g>                             sub_sgte            298.15    6000.00
 HN<g>                             sub_sgte            298.15   20000.00
 HN3<g>                            sub_sgte            298.15    6000.00
 H2N<g>                            sub_sgte            298.15    6000.00
 H2N2_1,1N2H2<g>                   sub_sgte            298.15    6000.00
 H2N2_CIS<g>                       sub_sgte            298.15    6000.00
 H2N2_TRANS<g>                     sub_sgte            298.15    6000.00
 H3N<g>                            sub_sgte            298.15    6000.00
 H4N2<g>                           sub_sgte            298.15    6000.00
 N<g>                              sub_sgte            298.15    6000.00
 N2<g>                             sub_sgte            298.15    6000.00
 N3<g>                             sub_sgte            298.15    6000.00
 H4N2<H4N2_LIQUID>                 sub_sgte            298.15     800.00
 
 TEMPERATURE       :   400.0000
 PRESSURE/Pa       :   100000.0
 VOLUME/m3         :    undefined
 SYSTEM AMOUNT/mol :    undefined
 COMP. AMOUNTS/mol :   4.000000       1.000000
 SYSTEM MASS/kg    :    undefined
 COMP. MASSES/kg   :  0.4031760E-02  0.1400670E-01
  
 CONSTRAINT                        VALUE OF EQUILIBRIUM CONSTRAINT
 PRESSURE(9)                           0.4000000   
 
 MULTIPHASE OPTION ? comp stages b_s !


*** MULTIPHASE - Stage 2 Results ***

Temperature =   400.0000 K

Fixed pressure =  1.000000E+05 Pa,    9.869233E-01 atm

Calculated gas volume =  7.328055E-02 m3

                           Amount  Partial pressure/atm
                            mole
                                   Notional activity
Phase GAS                
 H<g>                  2.219481E-26  9.941289E-27
 H2<g>                 1.256876E+00  5.629680E-01
 HN<g>                 4.543718E-47  2.035179E-47
 HN3<g>                2.870645E-47  1.285792E-47
 H2N<g>                6.555179E-28  2.936134E-28
 H2N2_CIS<g>           4.419404E-40  1.979498E-40
 H2N2_TRANS<g>         2.206605E-35  9.883617E-36
 H3N<g>                8.930354E-01  4.000000E-01
 H4N2<g>               3.422128E-26  1.532807E-26
 N<g>                  6.704452E-60  3.002995E-60
 N2<g>                 5.348228E-02  2.395528E-02
 N3<g>                 4.099525E-63  1.836221E-63
 Phase total is        2.203394E+00  9.869233E-01
Phase H4N2_LIQUID        
 H4N2<H4N2_LIQUID>                   1.010511E-26

Component      Ref.Phase     Chem.Pot.    Activity     Amount/mol   Mass/kg
H                           -2.729690E+04 2.725712E-04 5.192858E+00 5.234090E-03
N                           -4.473412E+04 1.440360E-06 1.000000E+00 1.400670E-02
Total                                                  6.192858E+00 1.924079E-02

 Number of Gibbs Energy evaluations in Stage 1 =        41
 Number of Gibbs Energy, compnt residual calculations in Stage 2 = 3,  5

 Estimated maximum relative error on species amounts =  1.0E-06

              Percentage distribution of components between phases
                                  H                N              
              GAS                 1.0000000E+02    1.0000000E+02

Amount        Phase               Mole fraction of component within phase
compnt moles
                                  H                N              
 6.192858E+00 GAS                 8.3852367E-01    1.6147633E-01

Mass/kg       Phase               Mass fraction of component within phase
                                  H                N              
 1.924079E-02 GAS                 2.7203091E-01    7.2796909E-01

Gibbs Energy = -1.8648306968E+05 J   System Enthalpy = -3.3772747761E+04 J

 MULTIPHASE OPTION ? comp sta 1 !


*** MULTIPHASE - Stage 1* Results ***

Temperature =   400.0000 K

Fixed pressure =  1.000000E+05 Pa,    9.869233E-01 atm

Calculated gas volume =  7.328055E-02 m3

                           Amount       Partial pressure/atm
                            mole
                                        Notional activity
Phase GAS                
 H<g>                      0.00000E+00      0.0000000
 H2<g>                     1.25688E+00      0.5629680
 HN<g>                     0.00000E+00      0.0000000
 HN3<g>                    0.00000E+00      0.0000000
 H2N<g>                    0.00000E+00      0.0000000
 H2N2_CIS<g>               0.00000E+00      0.0000000
 H2N2_TRANS<g>             0.00000E+00      0.0000000
 H3N<g>                    8.93035E-01      0.4000000
 H4N2<g>                   0.00000E+00      0.0000000
 N<g>                      0.00000E+00      0.0000000
 N2<g>                     5.34823E-02      0.0239553
 N3<g>                     0.00000E+00      0.0000000
 Phase total is            2.20339E+00      0.9869233
Phase H4N2_LIQUID        
 H4N2<H4N2_LIQUID>                        1.010508E-26

Component      Ref.Phase     Chem.Pot.    Activity     Amount/mol   Mass/kg
H                           -2.729690E+04 2.725713E-04 5.192858E+00 5.234090E-03
N                           -4.473413E+04 1.440357E-06 1.000000E+00 1.400670E-02
Total                                                  6.192858E+00 1.924079E-02

 Number of Gibbs Energy evaluations in Stage 1 =        91

Estimate of Stage 1* calculational inaccuracy in species mole amount ni
 (ignoring inaccuracies in data) = Errabs + Errrel * ni where
 Errabs =  5.0E-06
 Errrel =  3.7E-05

              Percentage distribution of components between phases
                                  H               N             
              GAS              100.00000       100.00000

Amount        Phase               Mole fraction of component within phase
compnt moles
                                  H               N             
 6.192858E+00 GAS                0.8385237       0.1614763

Mass/kg       Phase               Mass fraction of component within phase
                                  H               N             
 1.924079E-02 GAS                0.2720309       0.7279691

Gibbs Energy = -1.8648306957E+05 J   System Enthalpy = -3.3772747756E+04 J

 MULTIPHASE OPTION ? set te 500 ! co !


                      *************************************

                      * WARNING/ERRORS HAVE BEEN DETECTED *
                      *************************************
 
      1 Errors  : Multiphase, Stage 1 -  too many iterations in interpolation
                  routine
 
 MULTIPHASE OPTION ?

Calculation of Adibatic Temperatures

Another example of calculations with additional constraints is for the determination of the adiabatic temperature for a particular chemical reation ie the temperature reached by the reacting mixtures assuming that no heat is lost to the environment. A very simple example is one where hydrogren and oxygen react together. Initially we should retrieve the data for hydrogen and oxygen from the SGTE Substance database.

def sys 'H2,O2' sou sub !

Then we should set the composition of the mixture and we have chosen the composition of water ie 1 mole of H2 and 0.5 moles of O2. 

set n(1) 1 n(2) .5 !

For this calculation we wish to calculate the temperature where the net enthalpy change is zero. We need to give an initial guess for this temperature and we might guess a value of 2000 K.

set temp 2000 !

We also need to assign a value to the enthalpy of the final state. Because our components are elements in their standard states their enthalpies at 298.15 are zero. Therefore the enthalpy of final state should also be zero. If our components were not elements in their standard states or if the intial temperature is not zero we would have to adjust our system enthalpy accordingly.

set sy_enth 0 !

We also need to indicate that we want the temperature to vary ie by classifying it as free.

cl free temp !

It is always a good idea to check whether you are happy with the way the calculations have been set up.

lis sy set !

Once we are satisfied we can start the calculation off.

comp !

We find that the final temperature is 3079.6 K.

Having sucessfully completed ont calculation it is tempting to see how this adiabatic temperature varies with the amount of oxygen

step n(2) 0 1 .01 !

We are now varying the oxygen amount from 0 to 1 in steps of .01 ie a series of 101 calculations

comp pri gr in las !

and we would like to obatin graphical output of the results of the calculations.

ord temp sys !
pl go

The graph is show below. It is interesting to note that the maximum temperature that can be achieved is slightly oxygen poor of the ideal H2O stoichiometry. This is because in this case there is less material to heat up than at the stoichiometric composition ie there is balance between the maximum enthalpy release and the amount of material in the system.

 MULTIPHASE OPTION ? def sys 'H2,O2' sou sub !

 SEARCHING FOR SYSTEM H2,O2,/-

 SEARCHING DATABASE(S) :

 sub_sgte        - SGTE Substance Database version 12.1 - June 2009


 SEARCHING FOR SYSTEM H2,O2,/-

 SEARCHING DATABASE(S) :

 sub_sgte        - SGTE Substance Database version 12.1 - June 2009


 ******                 GOOD DATAFILE CREATED                 ******

 Date and time of run 17-MAR-2011  15:49:55
 * DATAFILE = D:\MTDATA\handbook\def.mpi -  CREATED 15:49:55 17-MAR-2011
 * SYSTEM = H2,O2,/-,
 * NUMBER OF PHASES  =    3
 * NUMBER OF SPECIES =   11
 *
 MULTIPHASE OPTION ? set n(1) 1
n(2) .5 !
 MULTIPHASE OPTION ? set temp 2000 !
 MULTIPHASE OPTION ? set sy_enth 0 !
 MULTIPHASE OPTION ? cl free temp !
 MULTIPHASE OPTION ? lis sy set !

 TEMPERATURE       :   2000.000    STATUS  FREE
 PRESSURE/Pa       :   101325.0
 VOLUME/m3         :    undefined
 SYSTEM AMOUNT/mol :    undefined
 COMP. AMOUNTS/mol :   1.000000      0.5000000
 SYSTEM MASS/kg    :    undefined
 COMP. MASSES/kg   :  0.2015880E-02  0.1599940E-01


 CONSTRAINT                        VALUE OF EQUILIBRIUM CONSTRAINT
 SYSTEM_ENTHALPY                        0.000000

 MULTIPHASE OPTION ? comp !

 Warning, Stage 1,
 There is a discontinuity in the constraint at this point
 Warning, Stage 1,
 May not be full accuracy in obeying constraint

*** MULTIPHASE - Stage 1* Results ***

Calculated temperature =  3079.6241 K

Fixed pressure =  1.013250E+05 Pa,    1.000000E+00 atm

Calculated gas volume =  3.062630E-01 m3

                           Amount       Partial pressure/atm
                            mole
                                        Notional activity
Phase GAS
 H<g>                      9.32239E-02      0.0769220
 H2<g>                     1.80112E-01      0.1486164
 HO<g>                     1.27861E-01      0.1055021
 HO2<g>                    5.49644E-05      0.0000454
 H2O<g>                    7.09315E-01      0.5852779
 H2O2<g>                   3.05348E-06      0.0000025
 O<g>                      4.00078E-02      0.0330117
 O2<g>                     6.13503E-02      0.0506221
 O3<g>                     0.00000E+00      0.0000000
 Phase total is            1.21193E+00      1.0000000
Phase H2O1_LIQUID
 H2O<H2O1_LIQUID>                         0.000000E+00
Phase H2O2_LIQUID
 H2O2<H2O2_LIQUID>                        0.000000E+00

Component      Ref.Phase     Chem.Pot.    Activity     Amount/mol   Mass/kg
H2                          -5.845654E+05 1.216802E-10 1.000000E+00 2.015880E-03
O2                          -8.541539E+05 3.256468E-15 5.000000E-01 1.599940E-02
Total                                                  1.500000E+00 1.801528E-02

 Norm of projected gradient  2.4821E-06

 Number of Gibbs Energy evaluations in Stage 1 =      1457

Estimate of Stage 1* calculational inaccuracy in species mole amount ni
 (ignoring inaccuracies in data) = Errabs + Errrel * ni where
 Errabs =  5.0E-06
 Errrel =  1.1E-05

              Percentage distribution of components between phases
                                  H2              O2
              GAS              100.00000       100.00000

Amount        Phase               Mole fraction of component within phase
compnt moles                                  H2              O2
 1.500000E+00 GAS                0.6666667       0.3333333

Mass/kg       Phase               Mass fraction of component within phase
                                  H2              O2
 1.801528E-02 GAS                0.1118984       0.8881016

Gibbs Energy = -1.0116423874E+06 J   System Enthalpy =  0.0000000000E+00 J
                      *************************************
                      * WARNING/ERRORS HAVE BEEN DETECTED *
                      *************************************

      1 Warnings: Multiphase, Stage 1 - There is a discontinuity in the constraint at this
                  point

      1 Warnings: Multiphase, Stage 1 - May not be full accuracy in obeying constraint
     24 Warnings: Multiphase, temperature range violation -  Unary data

 MULTIPHASE OPTION ? step n(2) 0 1 .01 !
 MULTIPHASE OPTION ? comp pri gr in las !

 NUMBER OF STEPS = 101

     1.00000E-01
                      *************************************
                      * WARNING/ERRORS HAVE BEEN DETECTED *
                      *************************************

   2820 Warnings: Multiphase, temperature range violation -  Unary data
     94 Warnings: Multiphase, Stage 1 - May not be full accuracy in obeying
                  constraint
     80 Warnings: Multiphase, Stage 1 - There is a discontinuity in the constr
                  aint at this point

 MULTIPHASE OPTION ? ord temp sys !
 MULTIPHASE OPTION ? pl go

Results of adiabatic calculation

Phase equilibria in steels

The structural and high temperature properties of steels are critically dependent on their microstructure, which in turn depends on their composition and heat treatment. The significant components in addition to iron may include nickel, chromium, carbon, silicon, titanium and others. Oxygen, nitrogen, sulphur and phosphorus may also influence processing and properties.

Use of MULTIPHASE enables the equilibrium phase distribution and the individual compositions of the phases to be calculated very efficiently using data from a database for the binary and ternary subsystems. The figures below were obtained from sample calculations on a steel. The plots show the overall phase composition and the distribution of carbon over a wide range of temperature. The table below shows how the problem was set up and the corresponding results of a single calculation.

The function of the various commands used is described below.

define system="C,Cr,Fe,Ni,Si,Ti"  sou  sgsol  !
list sys comp phas subs ! 
cl nor p(fcc_a1,hcp_a3,bcc_a2,m23c6,laves_c14,laves_c15,laves_c15) !

The listings show that the data take account of the formation of many different phases and identify which components are permitted to dissolve in which phases. A search of the database indicates that a number of binary interactions for key phases are missing. These have been omited from the table below. In such cases MTDATA classifies them automatically as being ABSENT. It is therefore important to check through which phases are been automatically included in the calculations and amend as necessary.

set te=800 w=1 !

Setting w=1 means that the total mass is 1 kilogram. This makes it possible to enter the weight fraction of the alloying components, leaving the program to calculate the weight fraction of iron.

set w(1)=0.0008 w(2)=0.18 w(4)=0.1 w(5)=0.01 !
set w(6)=0.004 !

The composition corresponds to a type 321 titanium stabilised stainless steel.

comp !

These few commands are sufficient to calculate the complex equilibrium presented in Table 2.6.

To obtain enough points for plotting, the temperature range must be set.

step te 600 1500 10 !

The efficiency of calculation is improved by using the "last active set" of working variables and the print parameter must be set to graph.

comp ini last print graph !
ord mass phase log y ! plot go
ord component_dist component(C) ! plot go
ord comp_dist mass(fcc_a1) ! pl go

The graphs obtained from the resulting set of calculations are presented below.
 

Phase equilibria in steels

 MULTIPHASE OPTION ? define system="C,Cr,Fe,Ni,Si,Ti"  sou  sgsol  !

 SEARCHING FOR SYSTEM C,Cr,Fe,Ni,Si,Ti,/-
 
 SEARCHING DATABASE(S) :

 sgsol           - SGTE Solution Database v4.31 27/11/2008
 
  SEARCHING FOR SYSTEM C,Cr,Fe,Ni,Si,Ti,/-
 
 SEARCHING DATABASE(S) :

 sgsol           - SGTE Solution Database v4.31 27/11/2008
 
 ******   16 PHASES IDENTIFIED WITH INCORRECT OR MISSING DATA ******
 PHASE: DIAMOND_A4                                       
 ERROR: Missing data for binary interaction(s)
 PHASE: BCC_A2:1:3                                       
 ERROR: Missing data for binary interaction(s)
 PHASE: CBCC_A12:1:1                                     
 ERROR: Missing data for unary(s)
 PHASE: CUB_A13:1:1                                      
 ERROR: Missing data for unary(s)
 PHASE: FCC_A1:1:1                                       
 ERROR: Missing data for binary interaction(s)
 PHASE: HCP_A3:1:.5                                      
 ERROR: Missing data for binary interaction(s)
 PHASE: BCC_B2:.5:.5:3                                   
 ERROR: Missing data for unary(s)
 PHASE: BCC_B2:1:3                                       
 ERROR: Missing data for binary interaction(s)
 PHASE: FCC_L12:.75:.25:1                                
 ERROR: Missing data for unary(s)
 PHASE: FCC_L12:1:1                                      
 ERROR: Missing data for binary interaction(s)
 PHASE: M23C6:20:3:6                                     
 ERROR: Missing data for binary interaction(s)
 PHASE: FE4N:4:1                                         
 ERROR: Missing data for unary(s)
 PHASE: LAVES_C14:2:1                                    
 ERROR: Missing data for unary(s)
 PHASE: LAVES_C15:2:1                                    
 ERROR: Missing data for unary(s)
 PHASE: LAVES_C36:2:1                                    
 ERROR: Missing data for unary(s)
 PHASE: HCP_ZN                                           
 ERROR: Missing data for binary interaction(s)
 ****** GOOD DATAFILE CREATED (but missing/inconsistent data) ******

               ****************************************************
               * FOR MISSING INTERACTION DATA SEE FILE misbin.dbl *
               ****************************************************

 Date and time of run 11-MAR-2011  15:40:43
 * DATAFILE = D:\atd\MTDATA\handbook\multiphase\def.mpi -  CREATED 15:40:43 11-MAR-2011
 * SYSTEM = C,Cr,Fe,Ni,Si,Ti,/-,
 * NUMBER OF PHASES  =   83
 * NUMBER OF SPECIES =  212
 *
                         ********************************
                         * UNASSESSED OR INCORRECT DATA *
                         ********************************
                      *************************************
                      * WARNING/ERRORS HAVE BEEN DETECTED *
                      *************************************
 
      6 Warnings: UNASSESSED DATA -  Missing data for binary(s)
      8 Warnings: UNASSESSED DATA -  Missing data for unary(s)
 
 MULTIPHASE OPTION ? list sys comp phas subs !

 NUMBER    COMPONENT               STATUS      AMOUNT     DELTA    REF.P
    1      C                       NORMAL     undefined            
    2      Cr                      NORMAL     undefined            
    3      Fe                      NORMAL     undefined            
    4      Ni                      NORMAL     undefined            
    5      Si                      NORMAL     undefined            
    6      Ti                      NORMAL     undefined            
 

 NUMBER    PHASE                   STATUS      MODEL
    1      DIAMOND_A4              absent      REDLICH-KISTER     
    2      GRAPHITE                NORMAL      PURE SUBSTANCE     
    3      LIQUID                  NORMAL      REDLICH-KISTER     
    4      BCC_A2                  absent      SUBLATTICE         
    5      CBCC_A12                absent      SUBLATTICE         
    6      CEMENTITE               NORMAL      SUBLATTICE         
    7      CUB_A13                 absent      SUBLATTICE         
    8      FCC_A1                  absent      SUBLATTICE         
    9      HCP_A3                  absent      SUBLATTICE         
   10      KSI_CARBIDE             NORMAL      SUBLATTICE         
   11      M3C2                    NORMAL      SUBLATTICE         
   12      M7C3                    NORMAL      SUBLATTICE         
   13      BCC_B2                  absent      CHEMICAL ORDERING(C)
   14      FCC_L12                 absent      CHEMICAL ORDERING  
   15      M23C6                   absent      SUBLATTICE         
   16      FE4N                    absent      SUBLATTICE         
   17      FECN_CHI                NORMAL      PURE SUBSTANCE     
   18      M5C2                    NORMAL      PURE SUBSTANCE     
   19      V3C2                    NORMAL      PURE SUBSTANCE     
   20      FE8SI2C                 NORMAL      PURE SUBSTANCE     
   21      NITI2                   NORMAL      SUBLATTICE         
   22      AL4C3                   NORMAL      PURE SUBSTANCE     
   23      SIC                     NORMAL      PURE SUBSTANCE     
   24      TI2N                    NORMAL      PURE SUBSTANCE     
   25      CR3SI_A15               NORMAL      SUBLATTICE         
   26      CRSI2                   NORMAL      SUBLATTICE         
   27      LAVES_C14               absent      SUBLATTICE         
   28      LAVES_C15               absent      SUBLATTICE         
   29      LAVES_C36               absent      SUBLATTICE         
   30      CHI_A12                 NORMAL      SUBLATTICE         
   31      HIGH_SIGMA              NORMAL      SUBLATTICE         
   32      SIGMA                   NORMAL      SUBLATTICE         
   33      CR5SI3                  NORMAL      PURE SUBSTANCE     
   34      CRSI                    NORMAL      PURE SUBSTANCE     
   35      HCP_ZN                  absent      REDLICH-KISTER     
   36      AL5FE4                  NORMAL      PURE SUBSTANCE     
   37      ORTHORHOMBIC_A20        NORMAL      PURE SUBSTANCE     
   38      TETRAGONAL_U            NORMAL      PURE SUBSTANCE     
   39      FE2U                    NORMAL      PURE SUBSTANCE     
   40      FESB                    NORMAL      PURE SUBSTANCE     
   41      FEU6                    NORMAL      PURE SUBSTANCE     
   42      FEUZR_DELTA             NORMAL      PURE SUBSTANCE     
   43      FEZN4                   NORMAL      PURE SUBSTANCE     
   44      FEZN_DELTA              NORMAL      PURE SUBSTANCE     
   45      FEZN_GAMMA_D82          NORMAL      PURE SUBSTANCE     
   46      FEZN_ZETA               NORMAL      PURE SUBSTANCE     
   47      FEZR2                   NORMAL      PURE SUBSTANCE     
   48      FEZR3                   NORMAL      PURE SUBSTANCE     
   49      FE2SI                   NORMAL      PURE SUBSTANCE     
   50      FE5SI3                  NORMAL      PURE SUBSTANCE     
   51      FESI2_H                 NORMAL      PURE SUBSTANCE     
   52      FESI2_L                 NORMAL      PURE SUBSTANCE     
   53      FESI                    NORMAL      PURE SUBSTANCE     
   54      M3SI                    NORMAL      PURE SUBSTANCE     
   55      FETI                    NORMAL      PURE SUBSTANCE     
   56      B2_BCC                  NORMAL      REDLICH-KISTER     
   57      NI3MOTA                 NORMAL      PURE SUBSTANCE     
   58      NI3NB                   NORMAL      PURE SUBSTANCE     
   59      NI2SI                   NORMAL      PURE SUBSTANCE     
   60      NI31SI12                NORMAL      PURE SUBSTANCE     
   61      NI3SI2                  NORMAL      PURE SUBSTANCE     
   62      NI3SI_MONOCL            NORMAL      PURE SUBSTANCE     
   63      NI3SI_ORTHO             NORMAL      PURE SUBSTANCE     
   64      NISI2_C1                NORMAL      PURE SUBSTANCE     
   65      NISI_B31                NORMAL      PURE SUBSTANCE     
   66      NI2SI_TETA              NORMAL      REDLICH-KISTER     
   67      NI3TI                   NORMAL      SUBLATTICE         
   68      NI10ZR7                 NORMAL      PURE SUBSTANCE     
   69      NI3ZR                   NORMAL      PURE SUBSTANCE     
   70      NI5ZR                   NORMAL      PURE SUBSTANCE     
   71      SIV3                    NORMAL      PURE SUBSTANCE     
   72      SI2TI                   NORMAL      PURE SUBSTANCE     
   73      SI4TI5                  NORMAL      PURE SUBSTANCE     
   74      SITI3                   NORMAL      PURE SUBSTANCE     
   75      SITI                    NORMAL      PURE SUBSTANCE     
   76      SI3TI5                  NORMAL      SUBLATTICE         
   77      BCT_A5                  NORMAL      PURE SUBSTANCE     
   78      AL3M_D022               NORMAL      PURE SUBSTANCE     
   79      ALM_D019                NORMAL      PURE SUBSTANCE     
   80      ALTI                    NORMAL      PURE SUBSTANCE     
   81      CU4TI                   NORMAL      PURE SUBSTANCE     
   82      CUTI                    NORMAL      PURE SUBSTANCE     
   83      SNTI3                   NORMAL      PURE SUBSTANCE     
 
 NUMBER    SUBSTANCE               STATUS/CONSTRAINT
    1      C<DIAMOND_A4>           NORMAL                       
    2      Si<DIAMOND_A4>          NORMAL                       
    3      Ti<DIAMOND_A4>          NORMAL                       
    4      C<GRAPHITE>             NORMAL                       
    5      C<LIQUID>               NORMAL                       
    6      Cr<LIQUID>              NORMAL                       
    7      Fe<LIQUID>              NORMAL                       
    8      Ni<LIQUID>              NORMAL                       
    9      Si<LIQUID>              NORMAL                       
   10      Ti<LIQUID>              NORMAL                       
   11      Cr:1<BCC_A2>            NORMAL                       
   12      Fe:1<BCC_A2>            NORMAL                       
   13      Ni:1<BCC_A2>            NORMAL                       
   14      Si:1<BCC_A2>            NORMAL                       
   15      Ti:1<BCC_A2>            NORMAL                       
   16      C:2<BCC_A2>             NORMAL                       
   17      Va:2<BCC_A2>            NORMAL                       
   18      Cr:1<CBCC_A12>          NORMAL                       
   19      Fe:1<CBCC_A12>          NORMAL                       
   20      Ni:1<CBCC_A12>          NORMAL                       
   21      Si:1<CBCC_A12>          NORMAL                       
   22      Ti:1<CBCC_A12>          NORMAL                       
   23      C:2<CBCC_A12>           NORMAL                       
   24      Va:2<CBCC_A12>          NORMAL                       
   25      Cr:1<CEMENTITE>         NORMAL                       
   26      Fe:1<CEMENTITE>         NORMAL                       
   27      Ni:1<CEMENTITE>         NORMAL                       
   28      C:2<CEMENTITE>          NORMAL                       
   29      Cr:1<CUB_A13>           NORMAL                       
   30      Fe:1<CUB_A13>           NORMAL                       
   31      Ni:1<CUB_A13>           NORMAL                       
   32      Si:1<CUB_A13>           NORMAL                       
   33      Ti:1<CUB_A13>           NORMAL                       
   34      C:2<CUB_A13>            NORMAL                       
   35      Va:2<CUB_A13>           NORMAL                       
   36      Cr:1<FCC_A1>            NORMAL                       
   37      Fe:1<FCC_A1>            NORMAL                       
   38      Ni:1<FCC_A1>            NORMAL                       
   39      Si:1<FCC_A1>            NORMAL                       
   40      Ti:1<FCC_A1>            NORMAL                       
   41      C:2<FCC_A1>             NORMAL                       
   42      Va:2<FCC_A1>            NORMAL                       
   43      Cr:1<HCP_A3>            NORMAL                       
   44      Fe:1<HCP_A3>            NORMAL                       
   45      Ni:1<HCP_A3>            NORMAL                       
   46      Si:1<HCP_A3>            NORMAL                       
   47      Ti:1<HCP_A3>            NORMAL                       
   48      C:2<HCP_A3>             NORMAL                       
   49      Va:2<HCP_A3>            NORMAL                       
   50      Cr:1<KSI_CARBIDE>       NORMAL                       
   51      Fe:1<KSI_CARBIDE>       NORMAL                       
   52      C:2<KSI_CARBIDE>        NORMAL                       
   53      Cr:1<M3C2>              NORMAL                       
   54      Fe:1<M3C2>              NORMAL                       
   55      C:2<M3C2>               NORMAL                       
   56      Cr:1<M7C3>              NORMAL                       
   57      Fe:1<M7C3>              NORMAL                       
   58      Ni:1<M7C3>              NORMAL                       
   59      C:2<M7C3>               NORMAL                       
   60      Cr:1<BCC_B2>            NORMAL                       
   61      Fe:1<BCC_B2>            NORMAL                       
   62      Ni:1<BCC_B2>            NORMAL                       
   63      Si:1<BCC_B2>            NORMAL                       
   64      Ti:1<BCC_B2>            NORMAL                       
   65      Cr:2<BCC_B2>            NORMAL                       
   66      Fe:2<BCC_B2>            NORMAL                       
   67      Ni:2<BCC_B2>            NORMAL                       
   68      Si:2<BCC_B2>            NORMAL                       
   69      Ti:2<BCC_B2>            NORMAL                       
   70      C:3<BCC_B2>             NORMAL                       
   71      Va:3<BCC_B2>            NORMAL                       
   72      Cr:1<FCC_L12>           NORMAL                       
   73      Fe:1<FCC_L12>           NORMAL                       
   74      Ni:1<FCC_L12>           NORMAL                       
   75      Si:1<FCC_L12>           NORMAL                       
   76      Ti:1<FCC_L12>           NORMAL                       
   77      Cr:2<FCC_L12>           NORMAL                       
   78      Fe:2<FCC_L12>           NORMAL                       
   79      Ni:2<FCC_L12>           NORMAL                       
   80      Si:2<FCC_L12>           NORMAL                       
   81      Ti:2<FCC_L12>           NORMAL                       
   82      C:3<FCC_L12>            NORMAL                       
   83      Va:3<FCC_L12>           NORMAL                       
   84      Cr:1<M23C6>             NORMAL                       
   85      Fe:1<M23C6>             NORMAL                       
   86      Ni:1<M23C6>             NORMAL                       
   87      Cr:2<M23C6>             NORMAL                       
   88      Fe:2<M23C6>             NORMAL                       
   89      Ni:2<M23C6>             NORMAL                       
   90      C:3<M23C6>              NORMAL                       
   91      Fe:1<FE4N>              NORMAL                       
   92      Ni:1<FE4N>              NORMAL                       
   93      C:2<FE4N>               NORMAL                       
   94      Va:2<FE4N>              NORMAL                       
   95      Fe5C2<FECN_CHI>         NORMAL                       
   96      Fe5C2<M5C2>             NORMAL                       
   97      Fe3C2<V3C2>             NORMAL                       
   98      Fe8Si2C<FE8SI2C>        NORMAL                       
   99      Ni:1<NITI2>             NORMAL                       
  100      Ti:2<NITI2>             NORMAL                       
  101      C:3<NITI2>              NORMAL                       
  102      Va:3<NITI2>             NORMAL                       
  103      Si4C3<AL4C3>            NORMAL                       
  104      SiC<SIC>                NORMAL                       
  105      Ti2C<TI2N>              NORMAL                       
  106      Cr:1<CR3SI_A15>         NORMAL                       
  107      Si:1<CR3SI_A15>         NORMAL                       
  108      Cr:2<CR3SI_A15>         NORMAL                       
  109      Si:2<CR3SI_A15>         NORMAL                       
  110      Cr:1<CRSI2>             NORMAL                       
  111      Si:1<CRSI2>             NORMAL                       
  112      Cr:2<CRSI2>             NORMAL                       
  113      Si:2<CRSI2>             NORMAL                       
  114      Cr:1<LAVES_C14>         NORMAL                       
  115      Fe:1<LAVES_C14>         NORMAL                       
  116      Ni:1<LAVES_C14>         NORMAL                       
  117      Ti:1<LAVES_C14>         NORMAL                       
  118      Cr:2<LAVES_C14>         NORMAL                       
  119      Fe:2<LAVES_C14>         NORMAL                       
  120      Ni:2<LAVES_C14>         NORMAL                       
  121      Ti:2<LAVES_C14>         NORMAL                       
  122      Cr:1<LAVES_C15>         NORMAL                       
  123      Fe:1<LAVES_C15>         NORMAL                       
  124      Ni:1<LAVES_C15>         NORMAL                       
  125      Si:1<LAVES_C15>         NORMAL                       
  126      Ti:1<LAVES_C15>         NORMAL                       
  127      Cr:2<LAVES_C15>         NORMAL                       
  128      Fe:2<LAVES_C15>         NORMAL                       
  129      Ni:2<LAVES_C15>         NORMAL                       
  130      Si:2<LAVES_C15>         NORMAL                       
  131      Ti:2<LAVES_C15>         NORMAL                       
  132      Cr:1<LAVES_C36>         NORMAL                       
  133      Ni:1<LAVES_C36>         NORMAL                       
  134      Cr:2<LAVES_C36>         NORMAL                       
  135      Ni:2<LAVES_C36>         NORMAL                       
  136      Cr:1<CHI_A12>           NORMAL                       
  137      Fe:1<CHI_A12>           NORMAL                       
  138      Cr:2<CHI_A12>           NORMAL                       
  139      Cr:3<CHI_A12>           NORMAL                       
  140      Fe:3<CHI_A12>           NORMAL                       
  141      Fe:1<HIGH_SIGMA>        NORMAL                       
  142      Cr:2<HIGH_SIGMA>        NORMAL                       
  143      Cr:3<HIGH_SIGMA>        NORMAL                       
  144      Fe:3<HIGH_SIGMA>        NORMAL                       
  145      Fe:1<SIGMA>             NORMAL                       
  146      Ni:1<SIGMA>             NORMAL                       
  147      Cr:2<SIGMA>             NORMAL                       
  148      Cr:3<SIGMA>             NORMAL                       
  149      Fe:3<SIGMA>             NORMAL                       
  150      Ni:3<SIGMA>             NORMAL                       
  151      Cr5Si3<CR5SI3>          NORMAL                       
  152      CrSi<CRSI>              NORMAL                       
  153      Cr<HCP_ZN>              NORMAL                       
  154      Si<HCP_ZN>              NORMAL                       
  155      Fe<AL5FE4>              NORMAL                       
  156      Fe<ORTHORHOMBIC_A20>    NORMAL                       
  157      Fe<TETRAGONAL_U>        NORMAL                       
  158      Fe2Fe<FE2U>             NORMAL                       
  159      FeFe<FESB>              NORMAL                       
  160      FeFe6<FEU6>             NORMAL                       
  161      FeFe2<FEUZR_DELTA>      NORMAL                       
  162      Fe.25Fe.75<FEZN4>       NORMAL                       
  163      Fe.125Fe.875<FEZN_DE    NORMAL                       
  164      Fe.3Fe.7<FEZN_GAMMA_    NORMAL                       
  165      Fe.072Fe0.928<FEZN_Z    NORMAL                       
  166      FeFe2<FEZR2>            NORMAL                       
  167      FeFe3<FEZR3>            NORMAL                       
  168      Fe2Si<FE2SI>            NORMAL                       
  169      Fe5Si3<FE5SI3>          NORMAL                       
  170      Fe3Si7<FESI2_H>         NORMAL                       
  171      FeSi2<FESI2_L>          NORMAL                       
  172      FeSi<FESI>              NORMAL                       
  173      Fe3Si<M3SI>             NORMAL                       
  174      FeTi<FETI>              NORMAL                       
  175      NiNi<B2_BCC>            NORMAL                       
  176      Ni<B2_BCC>              NORMAL                       
  177      Ni.75Ni.25<NI3MOTA>     NORMAL                       
  178      Ni3Ni<NI3NB>            NORMAL                       
  179      Ni2Si<NI2SI>            NORMAL                       
  180      Ni5Si2<NI31SI12>        NORMAL                       
  181      Ni3Si2<NI3SI2>          NORMAL                       
  182      Ni3Si<NI3SI_MONOCL>     NORMAL                       
  183      Ni3Si<NI3SI_ORTHO>      NORMAL                       
  184      NiSi2<NISI2_C1>         NORMAL                       
  185      NiSi<NISI_B31>          NORMAL                       
  186      NiNiSi<NI2SI_TETA>      NORMAL                       
  187      NiSi<NI2SI_TETA>        NORMAL                       
  188      Ni:1<NI3TI>             NORMAL                       
  189      Ti:1<NI3TI>             NORMAL                       
  190      Ni:2<NI3TI>             NORMAL                       
  191      Ti:2<NI3TI>             NORMAL                       
  192      Va:3<NI3TI>             NORMAL                       
  193      Ni.575<NI10ZR7>         NORMAL                       
  194      Ni.75<NI3ZR>            NORMAL                       
  195      Ni.833<NI5ZR>           NORMAL                       
  196      SiSi3<SIV3>             NORMAL                       
  197      Si2Ti<SI2TI>            NORMAL                       
  198      Si4Ti5<SI4TI5>          NORMAL                       
  199      SiTi3<SITI3>            NORMAL                       
  200      SiTi<SITI>              NORMAL                       
  201      Si:1<SI3TI5>            NORMAL                       
  202      Ti:1<SI3TI5>            NORMAL                       
  203      Si:2<SI3TI5>            NORMAL                       
  204      Ti:2<SI3TI5>            NORMAL                       
  205      Ti:3<SI3TI5>            NORMAL                       
  206      Ti<BCT_A5>              NORMAL                       
  207      Ti3Ti<AL3M_D022>        NORMAL                       
  208      Ti3Ti<ALM_D019>         NORMAL                       
  209      TiTi<ALTI>              NORMAL                       
  210      Ti4Ti<CU4TI>            NORMAL                       
  211      TiTi<CUTI>              NORMAL                       
  212      TiTi3<SNTI3>            NORMAL                       
 
 MULTIPHASE OPTION ? cl nor p(fcc_a1,hcp_a3,bcc_a2,m23c6,laves_c14,laves_c15,laves_c15) !
 MULTIPHASE OPTION ? set te=800 w=1 !
 MULTIPHASE OPTION ? set w(1)=0.0008 w(2)=0.18 w(4)=0.1 w(5)=0.01 !
 MULTIPHASE OPTION ? set w(6)=0.004 !
 MULTIPHASE OPTION ? comp !

*** MULTIPHASE - Stage 1* Results ***

Temperature =   800.0000 K

Fixed pressure =  1.013250E+05 Pa,    1.000000E+00 atm

                           Amount         Mole fraction
                            mole
                                        Notional activity
Phase GRAPHITE           
 C<GRAPHITE>                              4.861322E-05
Phase LIQUID             
 C<LIQUID>          
 Cr<LIQUID>         
 Fe<LIQUID>         
 Ni<LIQUID>         
 Si<LIQUID>         
 Ti<LIQUID>         
 Notional activity                        5.073579E-03
Phase BCC_A2             
 Cr:1<BCC_A2>              2.68832E+00      0.0472502
 Fe:1<BCC_A2>              1.03996E+01      0.1827851
 Ni:1<BCC_A2>              8.36428E-01      0.0147011
 Si:1<BCC_A2>              2.96651E-01      0.0052140
 Ti:1<BCC_A2>              2.82459E-03      0.0000496
 C:2<BCC_A2>               1.79097E-06      0.0000000
 Va:2<BCC_A2>              4.26715E+01      0.7500000
 Phase total is            5.68954E+01      1.0000000
Phase BCC_A2             
 Cr:1<BCC_A2>       
 Fe:1<BCC_A2>       
 Ni:1<BCC_A2>       
 Si:1<BCC_A2>       
 Ti:1<BCC_A2>       
 C:2<BCC_A2>        
 Va:2<BCC_A2>       
 Notional activity                        0.000000E+00
Phase CEMENTITE          
 Cr:1<CEMENTITE>    
 Fe:1<CEMENTITE>    
 Ni:1<CEMENTITE>    
 C:2<CEMENTITE>     
 Notional activity                        1.188048E-04
Phase FCC_A1             
 Cr:1<FCC_A1>              3.01993E-01      0.0505765
 Fe:1<FCC_A1>              1.80870E+00      0.3029135
 Ni:1<FCC_A1>              8.13405E-01      0.1362257
 Si:1<FCC_A1>              5.94047E-02      0.0099489
 Ti:1<FCC_A1>              2.00307E-03      0.0003355
 C:2<FCC_A1>               7.88997E-07      0.0000001
 Va:2<FCC_A1>              2.98550E+00      0.4999999
 Phase total is            5.97101E+00      1.0000000
Phase FCC_A1             
 Cr:1<FCC_A1>              7.37143E-06      0.0000480
 Fe:1<FCC_A1>              0.00000E+00      0.0000000
 Ni:1<FCC_A1>              0.00000E+00      0.0000000
 Si:1<FCC_A1>              0.00000E+00      0.0000000
 Ti:1<FCC_A1>              7.66994E-02      0.4999520
 C:2<FCC_A1>               6.66047E-02      0.4341512
 Va:2<FCC_A1>              1.01021E-02      0.0658488
 Phase total is            1.53414E-01      1.0000000
Phase HCP_A3             
 Cr:1<HCP_A3>       
 Fe:1<HCP_A3>       
 Ni:1<HCP_A3>       
 Si:1<HCP_A3>       
 Ti:1<HCP_A3>       
 C:2<HCP_A3>        
 Va:2<HCP_A3>       
 Notional activity                        8.939529E-16
Phase HCP_A3             
 Cr:1<HCP_A3>       
 Fe:1<HCP_A3>       
 Ni:1<HCP_A3>       
 Si:1<HCP_A3>       
 Ti:1<HCP_A3>       
 C:2<HCP_A3>        
 Va:2<HCP_A3>       
 Notional activity                        0.000000E+00
Phase KSI_CARBIDE        
 Cr:1<KSI_CARBIDE>  
 Fe:1<KSI_CARBIDE>  
 C:2<KSI_CARBIDE>   
 Notional activity                        1.126814E-05
Phase M3C2               
 Cr:1<M3C2>         
 Fe:1<M3C2>         
 C:2<M3C2>          
 Notional activity                        4.564303E-05
Phase M7C3               
 Cr:1<M7C3>         
 Fe:1<M7C3>         
 Ni:1<M7C3>         
 C:2<M7C3>          
 Notional activity                        9.073575E-06
Phase M23C6              
 Cr:1<M23C6>        
 Fe:1<M23C6>        
 Ni:1<M23C6>        
 Cr:2<M23C6>        
 Fe:2<M23C6>        
 Ni:2<M23C6>        
 C:3<M23C6>         
 Notional activity                        3.698981E-06
Phase FECN_CHI           
 Fe5C2<FECN_CHI>                          1.876556E-11
Phase M5C2               
 Fe5C2<M5C2>                              2.205194E-12
Phase V3C2               
 Fe3C2<V3C2>                              5.747631E-12
Phase FE8SI2C            
 Fe8Si2C<FE8SI2C>                         5.347469E-09
Phase NITI2              
 Ni:1<NITI2>        
 Ti:2<NITI2>        
 C:3<NITI2>         
 Va:3<NITI2>        
 Notional activity                        6.739874E-28
Phase AL4C3              
 Si4C3<AL4C3>                             1.954402E-44
Phase SIC                
 SiC<SIC>                                 4.423136E-09
Phase TI2N               
 Ti2C<TI2N>                               6.048365E-06
Phase CR3SI_A15          
 Cr:1<CR3SI_A15>    
 Si:1<CR3SI_A15>    
 Cr:2<CR3SI_A15>    
 Si:2<CR3SI_A15>    
 Notional activity                        4.482326E-12
Phase CRSI2              
 Cr:1<CRSI2>        
 Si:1<CRSI2>        
 Cr:2<CRSI2>        
 Si:2<CRSI2>        
 Notional activity                        1.636673E-22
Phase LAVES_C14          
 Cr:1<LAVES_C14>    
 Fe:1<LAVES_C14>    
 Ni:1<LAVES_C14>    
 Ti:1<LAVES_C14>    
 Cr:2<LAVES_C14>    
 Fe:2<LAVES_C14>    
 Ni:2<LAVES_C14>    
 Ti:2<LAVES_C14>    
 Notional activity                        1.135321E-18
Phase LAVES_C14          
 Cr:1<LAVES_C14>    
 Fe:1<LAVES_C14>    
 Ni:1<LAVES_C14>    
 Ti:1<LAVES_C14>    
 Cr:2<LAVES_C14>    
 Fe:2<LAVES_C14>    
 Ni:2<LAVES_C14>    
 Ti:2<LAVES_C14>    
 Notional activity                        0.000000E+00
Phase LAVES_C15          
 Cr:1<LAVES_C15>    
 Fe:1<LAVES_C15>    
 Ni:1<LAVES_C15>    
 Si:1<LAVES_C15>    
 Ti:1<LAVES_C15>    
 Cr:2<LAVES_C15>    
 Fe:2<LAVES_C15>    
 Ni:2<LAVES_C15>    
 Si:2<LAVES_C15>    
 Ti:2<LAVES_C15>    
 Notional activity                        2.958078E-65
Phase LAVES_C15          
 Cr:1<LAVES_C15>    
 Fe:1<LAVES_C15>    
 Ni:1<LAVES_C15>    
 Si:1<LAVES_C15>    
 Ti:1<LAVES_C15>    
 Cr:2<LAVES_C15>    
 Fe:2<LAVES_C15>    
 Ni:2<LAVES_C15>    
 Si:2<LAVES_C15>    
 Ti:2<LAVES_C15>    
 Notional activity                        0.000000E+00
Phase CHI_A12            
 Cr:1<CHI_A12>      
 Fe:1<CHI_A12>      
 Cr:2<CHI_A12>      
 Cr:3<CHI_A12>      
 Fe:3<CHI_A12>      
 Notional activity                        6.690502E-02
Phase HIGH_SIGMA         
 Fe:1<HIGH_SIGMA>   
 Cr:2<HIGH_SIGMA>   
 Cr:3<HIGH_SIGMA>   
 Fe:3<HIGH_SIGMA>   
 Notional activity                        6.549071E-01
Phase SIGMA              
 Fe:1<SIGMA>               2.18709E-01      0.2329707
 Ni:1<SIGMA>               3.16332E-02      0.0336960
 Cr:2<SIGMA>               1.25171E-01      0.1333333
 Cr:3<SIGMA>               3.46309E-01      0.3688913
 Fe:3<SIGMA>               2.00772E-01      0.2138644
 Ni:3<SIGMA>               1.61887E-02      0.0172443
 Phase total is            9.38783E-01      1.0000000
Phase CR5SI3             
 Cr5Si3<CR5SI3>                           3.308519E-09
Phase CRSI               
 CrSi<CRSI>                               2.912961E-05
Phase AL5FE4             
 Fe<AL5FE4>                               2.695390E-01
Phase ORTHORHOMBIC_A20   
 Fe<ORTHORHOMBIC_A20>                     2.699051E-01
Phase TETRAGONAL_U       
 Fe<TETRAGONAL_U>                         2.699051E-01
Phase FE2U               
 Fe2Fe<FE2U>                              9.185914E-04
Phase FESB               
 FeFe<FESB>                               2.713265E-01
Phase FEU6               
 FeFe6<FEU6>                              8.202612E-08
Phase FEUZR_DELTA        
 FeFe2<FEUZR_DELTA>                       8.841989E-02
Phase FEZN4              
 Fe.25Fe.75<FEZN4>                        1.474540E-10
Phase FEZN_DELTA         
 Fe.125Fe.875<FEZN_DE                     5.140883E-02
Phase FEZN_GAMMA_D82     
 Fe.3Fe.7<FEZN_GAMMA_                     1.218846E-01
Phase FEZN_ZETA          
 Fe.072Fe0.928<FEZN_Z                     4.542034E-02
Phase FEZR2              
 FeFe2<FEZR2>                             1.966226E-02
Phase FEZR3              
 FeFe3<FEZR3>                             5.306945E-03
Phase FE2SI              
 Fe2Si<FE2SI>                             2.066247E-04
Phase FE5SI3             
 Fe5Si3<FE5SI3>                           1.578362E-11
Phase FESI2_H            
 Fe3Si7<FESI2_H>                          5.387188E-47
Phase FESI2_L            
 FeSi2<FESI2_L>                           5.771999E-13
Phase FESI               
 FeSi<FESI>                               7.398043E-05
Phase M3SI               
 Fe3Si<M3SI>                              1.610381E-03
Phase FETI               
 FeTi<FETI>                               6.390248E-04
Phase B2_BCC             
 NiNi<B2_BCC>       
 Ni<B2_BCC>         
 Notional activity                        4.752643E-12
Phase NI3MOTA            
 Ni.75Ni.25<NI3MOTA>                      4.709223E-02
Phase NI3NB              
 Ni3Ni<NI3NB>                             4.918097E-06
Phase NI2SI              
 Ni2Si<NI2SI>                             1.883118E-02
Phase NI31SI12           
 Ni5Si2<NI31SI12>                         8.241096E-03
Phase NI3SI2             
 Ni3Si2<NI3SI2>                           1.749579E-06
Phase NI3SI_MONOCL       
 Ni3Si<NI3SI_MONOCL>                      5.496785E-02
Phase NI3SI_ORTHO        
 Ni3Si<NI3SI_ORTHO>                       5.406305E-02
Phase NISI2_C1           
 NiSi2<NISI2_C1>                          1.138029E-12
Phase NISI_B31           
 NiSi<NISI_B31>                           5.570673E-05
Phase NI2SI_TETA         
 NiNiSi<NI2SI_TETA> 
 NiSi<NI2SI_TETA>   
 Notional activity                        5.342071E-07
Phase NI3TI              
 Ni:1<NI3TI>               6.11419E-03      0.5000000
 Ti:1<NI3TI>               0.00000E+00      0.0000000
 Ni:2<NI3TI>               2.68052E-07      0.0000219
 Ti:2<NI3TI>               2.03779E-03      0.1666447
 Va:3<NI3TI>               4.07613E-03      0.3333333
 Phase total is            1.22284E-02      1.0000000
Phase NI10ZR7            
 Ni.575<NI10ZR7>                          2.626165E-02
Phase NI3ZR              
 Ni.75<NI3ZR>                             7.558418E-03
Phase NI5ZR              
 Ni.833<NI5ZR>                            4.745871E-03
Phase SIV3               
 SiSi3<SIV3>                              9.303778E-44
Phase SI2TI              
 Si2Ti<SI2TI>                             2.848806E-12
Phase SI4TI5             
 Si4Ti5<SI4TI5>                           1.037694E-18
Phase SITI3              
 SiTi3<SITI3>                             5.234834E-14
Phase SITI               
 SiTi<SITI>                               2.491507E-05
Phase SI3TI5             
 Si:1<SI3TI5>       
 Ti:1<SI3TI5>       
 Si:2<SI3TI5>       
 Ti:2<SI3TI5>       
 Ti:3<SI3TI5>       
 Notional activity                        1.160169E-35
Phase BCT_A5             
 Ti<BCT_A5>                               5.995881E-07
Phase AL3M_D022          
 Ti3Ti<AL3M_D022>                         5.851225E-26
Phase ALM_D019           
 Ti3Ti<ALM_D019>                          2.051386E-24
Phase ALTI               
 TiTi<ALTI>                               2.418931E-13
Phase CU4TI              
 Ti4Ti<CU4TI>                             5.746456E-32
Phase CUTI               
 TiTi<CUTI>                               3.189775E-13
Phase SNTI3              
 TiTi3<SNTI3>                             2.054472E-24

Component      Ref.Phase     Chem.Pot.    Activity     Amount/mol   Mass/kg
C                           -7.428306E+04 1.412331E-05 6.660727E-02 8.000000E-04
Cr                          -2.715946E+04 1.685443E-02 3.461798E+00 1.800000E-01
Fe                          -3.167367E+04 8.550154E-03 1.262781E+01 7.052000E-01
Ni                          -4.748152E+04 7.940596E-04 1.703769E+00 1.000000E-01
Si                          -1.502413E+05 1.550580E-10 3.560556E-01 1.000000E-02
Ti                          -1.230845E+05 9.196251E-09 8.356488E-02 4.000000E-03
Total                                                  1.829960E+01 1.000000E+00

 Number of Gibbs Energy evaluations in Stage 1 =      3454

Estimate of Stage 1* calculational inaccuracy in species mole amount ni
 (ignoring inaccuracies in data) = Errabs + Errrel * ni where
 Errabs =  5.0E-06
 Errrel =  8.3E-04

              Percentage distribution of components between phases
                                  C               Cr              Fe            
              BCC_A2             0.00269        77.65670        82.35497
              FCC_A1             0.00118         8.72358        14.32315
              FCC_A1            99.99613         0.00021         0.00000
              SIGMA              0.00000        13.61951         3.32188
              NI3TI              0.00000         0.00000         0.00000
 
                                  Ni              Si              Ti            
              BCC_A2            49.09278        83.31588         3.38012
              FCC_A1            47.74151        16.68412         2.39702
              FCC_A1             0.00000         0.00000        91.78428
              SIGMA              2.80683         0.00000         0.00000
              NI3TI              0.35888         0.00000         2.43858

Amount        Phase               Mole fraction of component within phase
compnt moles
                                  C               Cr              Fe            
 1.422385E+01 BCC_A2             0.0000001       0.1890007       0.7311401
 2.985506E+00 FCC_A1             0.0000003       0.1011530       0.6058268
 1.433115E-01 FCC_A1             0.4647548       0.0000514       0.0000000
 9.387828E-01 SIGMA              0.0000000       0.5022246       0.4468351
 8.152252E-03 NI3TI              0.0000000       0.0000000       0.0000000
 
                                  Ni              Si              Ti            
 1.422385E+01 BCC_A2             0.0588046       0.0208559       0.0001986
 2.985506E+00 FCC_A1             0.2724514       0.0198977       0.0006709
 1.433115E-01 FCC_A1             0.0000000       0.0000000       0.5351938
 9.387828E-01 SIGMA              0.0509403       0.0000000       0.0000000
 8.152252E-03 NI3TI              0.7500329       0.0000000       0.2499671

Mass/kg       Phase               Mass fraction of component within phase
                                  C               Cr              Fe            
 7.781089E-01 BCC_A2             0.0000000       0.1796433       0.7463830
 1.662151E-01 FCC_A1             0.0000001       0.0944707       0.6076874
 4.471723E-03 FCC_A1             0.1788950       0.0000857       0.0000000
 5.074786E-02 SIGMA              0.0000000       0.4830767       0.4616140
 4.564214E-04 NI3TI              0.0000000       0.0000000       0.0000000
 
                                  Ni              Si              Ti            
 7.781089E-01 BCC_A2             0.0630924       0.0107075       0.0001738
 1.662151E-01 FCC_A1             0.2872273       0.0100377       0.0005768
 4.471723E-03 FCC_A1             0.0000000       0.0000000       0.8210193
 5.074786E-02 SIGMA              0.0553093       0.0000000       0.0000000
 4.564214E-04 NI3TI              0.7862871       0.0000000       0.2137129

Gibbs Energy = -6.4361461679E+05 J   System Enthalpy =  2.9624431915E+05 J
                      *************************************
                      * WARNING/ERRORS HAVE BEEN DETECTED *
                      *************************************
 
    312 Warnings: Multiphase, temperature range violation -  Unary data
 
 MULTIPHASE OPTION ? step te 600 1500 10 !
 MULTIPHASE OPTION ? comp ini last print graph !

 NUMBER OF STEPS =  91

 
     600.000
     610.000
     .......
     1500.00

 
                      *************************************
                      * WARNING/ERRORS HAVE BEEN DETECTED *
                      *************************************
 
  35490 Warnings: Multiphase, temperature range violation -  Unary data
      4 Warnings: Multiphase, Stage 1 - Less accuracy than normal
 
 MULTIPHASE OPTION ? ord mass phase log y ! plot go
 MULTIPHASE OPTION ? ord component_dist component(C) ! plot go
 MULTIPHASE OPTION ? ord comp_dist mass(fcc_a1) ! pl go
 MULTIPHASE OPTION ?


Calculated phase distribution

Calculated phase distribution

 

Distribution of carbon between the various phases

Distribution of carbon between the various phases

 Composition of the fcc phase

Composition of the fcc phase

Investigation of the solidification behaviour of an aluminium alloy


The previous example shows how MTDATA can be used to investigate the composition of a particular phase through a stepped set of MULTIPHASE calculations. When studying how a material solidifies it is useful to track the composition of the liquid phase. First we search the SGTE solution data for data for the Al-Si-Mg system

mul def sys 'Al,Si,Mg' sou sgsol !

and check the list of phases for missing interactions for important phases

lis sy p !

The temperature range of interest will be between 750 and 950 K as aluminium melts at 933.47 K. A step size of 2 K will be sufficient to give definition on the graphical output.

ste t 750 950 2 !

We choose to enter the composition in mass terms setting the overall size of the system to be 100 kg.

set w 100 w(1) undef w(2) 7 w(3) .5 !

We ask the computer to start the calculations with the results going to a graphics file.

comp in las pr gr !

To start with we wish to look at the way in the amount of the various phases varies with temperature.

ord mas p !
pl go

We can see that the liquidus temperature, ie where the solid aluminium based solid solution (fcc_a1) starts to form from the melt, is at about 888 K. 

ord comp_dis mass(liq) !
pl go

We can also track the composition of the liquid phase as it solidifies as shown in the following figure.


 WHICH MODULE ? mul def sys 'Al,Si,Mg' sou sgsol !

 SEARCHING FOR SYSTEM Al,Si,Mg,/-

 SEARCHING DATABASE(S) :

 sgsol           - SGTE Solution Database v4.31 27/11/2008

 **** PHASE AL3NI2:3:2:1 INFERRED METASTABLE AND CLASSIFIED ABSENT

 SEARCHING FOR SYSTEM Al,Si,Mg,/-

 SEARCHING DATABASE(S) :

 sgsol           - SGTE Solution Database v4.31 27/11/2008

 
 ******    7 PHASES IDENTIFIED WITH INCORRECT OR MISSING DATA ******
 PHASE: LAVES_C15:2:1
 ERROR: Missing data for unary(s)
 PHASE: ALLI:1:1
 ERROR: Missing data for binary interaction(s)
 PHASE: CBCC_A12
 ERROR: Missing data for binary interaction(s)
 PHASE: CUB_A13
 ERROR: Missing data for binary interaction(s)
 PHASE: HCP_ZN
 ERROR: Missing data for binary interaction(s)
 PHASE: BCC_B2:.5:.5:3
 ERROR: Missing data for binary interaction(s)
 PHASE: FCC_L12:.75:.25:1
 ERROR: Missing data for unary(s)
 ****** GOOD DATAFILE CREATED (but missing/inconsistent data) ******

               ****************************************************
               * FOR MISSING INTERACTION DATA SEE FILE misbin.dbl *
               ****************************************************
 Date and time of run 18-MAR-2011  11:27:20
 * DATAFILE = D:\MTDATA\handbook\def.mpi -  CREATED 11:27:20 18-MAR-20
 * SYSTEM = Al,Si,Mg,/-,
 * NUMBER OF PHASES  =   37
 * NUMBER OF SPECIES =   87
 *
                         ********************************
                         * UNASSESSED OR INCORRECT DATA *
                         ********************************
                      *************************************
                      * WARNING/ERRORS HAVE BEEN DETECTED *
                      *************************************

      2 Warnings: UNASSESSED DATA -  Missing data for unary(s)
      5 Warnings: UNASSESSED DATA -  Missing data for binary(s)

 MULTIPHASE OPTION ? lis sy p !

 NUMBER    PHASE                   STATUS      MODEL
    1      AL5FE4                  NORMAL      PURE SUBSTANCE
    2      ALCE_AMORPHOUS          NORMAL      PURE SUBSTANCE
    3      BCT_A5                  NORMAL      PURE SUBSTANCE
    4      DIAMOND_A4              1  M-G      REDLICH-KISTER
    5      LIQUID                  NORMAL      REDLICH-KISTER
    6      AL3NB                   NORMAL      PURE SUBSTANCE
    7      ALCU_THETA              NORMAL      PURE SUBSTANCE
    8      ALM_D019                NORMAL      PURE SUBSTANCE
    9      ALNB3                   NORMAL      PURE SUBSTANCE
   10      ALTI                    NORMAL      PURE SUBSTANCE
   11      LAVES_C14               NORMAL      SUBLATTICE
   12      LAVES_C15               absent      SUBLATTICE
   13      LAVES_C36               NORMAL      SUBLATTICE
   14      ALMGZN_PHI              NORMAL      PURE SUBSTANCE
   15      ALMG_BETA               NORMAL      PURE SUBSTANCE
   16      ALMG_EPSILON            NORMAL      PURE SUBSTANCE
   17      MG2ZN3                  NORMAL      PURE SUBSTANCE
   18      MGZN                    NORMAL      PURE SUBSTANCE
   19      ALLI                    absent      SUBLATTICE
   20      ALMG_DZETA              NORMAL      PURE SUBSTANCE
   21      ALMG_GAMMA              NORMAL      SUBLATTICE
   22      ALMGZN_TAU              NORMAL      SUBLATTICE
   23      BCC_A2                  NORMAL      REDLICH-KISTER
   24      CBCC_A12                absent      REDLICH-KISTER
   25      CUB_A13                 absent      REDLICH-KISTER
   26      FCC_A1                  NORMAL      REDLICH-KISTER
   27      HCP_A3                  NORMAL      REDLICH-KISTER
   28      HCP_ZN                  absent      REDLICH-KISTER
   29      BCC_B2                  absent      CHEMICAL ORDERING(C)
   30      ALCUZN_T                NORMAL      PURE SUBSTANCE
   31      B2_BCC                  NORMAL      PURE SUBSTANCE
   32      FCC_L12                 absent      CHEMICAL ORDERING
   33      MG2Y                    NORMAL      PURE SUBSTANCE
   34      MG2SI                   NORMAL      PURE SUBSTANCE
   35      CR3SI_A15               NORMAL      PURE SUBSTANCE
   36      CRSI2                   NORMAL      PURE SUBSTANCE
   37      SIV3                    NORMAL      PURE SUBSTANCE

 MULTIPHASE OPTION ? ste t 750 950 2 !
 MULTIPHASE OPTION ? set w 100 w(1) undef w(2) 7 w(3) .5 !
 MULTIPHASE OPTION ? comp in las pr gr !
 NUMBER OF STEPS = 101

     950.000
                      *************************************
                      * WARNING/ERRORS HAVE BEEN DETECTED *
                      *************************************

      1 Warnings: Multiphase, Stage 1 - Less accuracy than normal

 MULTIPHASE OPTION ? ord mas p !
 MULTIPHASE OPTION ? pl go

 MULTIPHASE OPTION ? ord comp_dis mass(liq) !
 MULTIPHASE OPTION ? pl go

Mass phase plot lm25

LM25 liquid composition

The liquid phase composition can be tracked without using the graphical output. An easy way to do this is using the list property command. We set the temperature initially to be 1 K below the liquid temperature calculated in the previous section and computer the equilibrium. The list property command allows you to view all sorts of results from the previous calculation. In this we want to examine the weight fraction of components in the phases predicted to be in equilibrium.

set t 887 !
comp !
lis prop w !

We can do this for a number of different temperatures.


set t 880 ! comp ! lis prop w !

In this way we can view the composition of the liquid phase for each temperature assuming that the alloy maintained thermodynamic equilibrium at each step ie the diffusion of the atoms in each phase is fast compared with the solidification time. This is sometimes called the "lever rule" model for solidification and would be expected to be followed if the alloy was allowed to cool very slowly.

An alternative simple model for cooling of an alloy, a so-called Scheil solidification scheme assumes that diffusion in the liquid is fast compared to the solidification time, while diffusion in the solid phase is zero. This can be simulated within MULTIPHASE by setting the composition of the liquid phase from one equilibrium calculations to be the overall composition for the next calculation. This can be demonstrated below using a combination of SET commands.

set t 887 ! comp !

The composition of Al in the liquid is transferred into a user variable which is then in turn compied into the overall Al amount for the next calculation. The same process is repeated for each of the components.

set u(al) w(Al<LIQUID>) !
set w(1) u(al) !
set u(si) w(Si<LIQUID>) !
set w(2) u(si) !
set u(mg) w(Mg<LIQUID>) !
set w(3) u(mg) !
set t 886 ! comp !

Finally the results are tabulated. The same procedure can be then repeated at lower temperatures.

lis prop w !

set u(al) w(Al<LIQUID>) !
set w(1) u(al) !
set u(si) w(Si<LIQUID>) !
set w(2) u(si) !
set u(mg) w(Mg<LIQUID>) !
set w(3) u(mg) !
set t 885 ! comp !
lis prop w !

set u(al) w(Al<LIQUID>) !
set w(1) u(al) !
set u(si) w(Si<LIQUID>) !
set w(2) u(si) !
set u(mg) w(Mg<LIQUID>) !
set w(3) u(mg) !
set t 884 ! comp !
lis prop w !

 MULTIPHASE OPTION ? set t 887 !
 MULTIPHASE OPTION ? comp !
 MULTIPHASE OPTION ? lis prop w !

 LIQUID

 Al                  Si                  Mg
  0.923763051941898       7.116375428448210E-002  5.073193773620270E-003

 FCC_A1

 Al                  Si                  Mg
  0.991141402317922       7.772374669644612E-003  1.086223012433319E-003

 Property = undefined

 MULTIPHASE OPTION ? set t 880 ! comp ! lis prop w !

 LIQUID

 Al                  Si                  Mg
  0.913072252280840       8.121904553478844E-002  5.708702184371688E-003

 FCC_A1

 Al                  Si                  Mg
  0.989857343368602       8.996238164460128E-003  1.146418466938333E-003

 Property = undefined

 MULTIPHASE OPTION ? set t 887 ! comp !
 MULTIPHASE OPTION ? lis prop w !

 LIQUID

 Al                  Si                  Mg
  0.923763051941898       7.116375428448210E-002  5.073193773620270E-003

 FCC_A1

 Al                  Si                  Mg
  0.991141402317922       7.772374669644612E-003  1.086223012433319E-003

 Property = undefined

 MULTIPHASE OPTION ? set u(al) w(Al<LIQUID>) !
 MULTIPHASE OPTION ? set w(1) u(al) !
 MULTIPHASE OPTION ? set u(si) w(Si<LIQUID>) !
 MULTIPHASE OPTION ? set w(2) u(si) !
 MULTIPHASE OPTION ? set u(mg) w(Mg<LIQUID>) !
 MULTIPHASE OPTION ? set w(3) u(mg) !
 MULTIPHASE OPTION ? set t 886 ! comp !
 MULTIPHASE OPTION ? lis prop w !

 LIQUID

 Al                  Si                  Mg
  0.922223502806219       7.261217203237874E-002  5.164325161401805E-003

 FCC_A1

 Al                  Si                  Mg
  0.990957982132608       7.946337102191243E-003  1.095680765201115E-003

 Property = undefined

 MULTIPHASE OPTION ? set u(al) w(Al<LIQUID>) !
 MULTIPHASE OPTION ? set w(1) u(al) !
 MULTIPHASE OPTION ? set u(si) w(Si<LIQUID>) !
 MULTIPHASE OPTION ? set w(2) u(si) !
 MULTIPHASE OPTION ? set u(mg) w(Mg<LIQUID>) !
 MULTIPHASE OPTION ? set w(3) u(mg) !
 MULTIPHASE OPTION ? set t 885 ! comp !
 MULTIPHASE OPTION ? lis prop w !

 LIQUID

 Al                  Si                  Mg
  0.920688115496832       7.405663582769868E-002  5.255248675469761E-003

 FCC_A1

 Al                  Si                  Mg
  0.990774579595744       8.120595250913720E-003  1.104825153341785E-003

 Property = undefined

 MULTIPHASE OPTION ? set u(al) w(Al<LIQUID>) !
 MULTIPHASE OPTION ? set w(1) u(al) !
 MULTIPHASE OPTION ? set u(si) w(Si<LIQUID>) !
 MULTIPHASE OPTION ? set w(2) u(si) !
 MULTIPHASE OPTION ? set u(mg) w(Mg<LIQUID>) !
 MULTIPHASE OPTION ? set w(3) u(mg) !
 MULTIPHASE OPTION ? set t 884 ! comp !
 MULTIPHASE OPTION ? lis prop w !

 LIQUID

 Al                  Si                  Mg
  0.919156878119897       7.549715116633254E-002  5.345970713770816E-003

 FCC_A1

 Al                  Si                  Mg
  0.990591182737286       8.295152918312594E-003  1.113664344401326E-003

 Property = undefined
 
MULTIPHASE OPTION ?




Updated 18 March 2011