« Zen+k » A computer code for phase diagram prediction User's guide
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1. Zen k A computer code for phase diagram prediction User s guide Bernard GUY and Jean Marie PLA Ecole Nationale Sup rieure des Mines de Saint Etienne 158 Cours Fauriel 42023 Saint Etienne C dex 2 France e mail Guy emse fr Pla emse fr Version 3 0 June 1999 Contents Foreword notations Data input and display File and Display Correction of data Edit Calculation Run Output Display Printing Options Examples References Zen k A computer code for phase diagram prediction Version 3 0 User s guide The computer code was written in Pascal by J M Pla on the basis of a collaborative work with B Guy Guy and Pla 1997a and b The present non commercial version of the code is given free of charge People should refer to Guy and Pla 1997a and b in any publication using the code The authors are not responsible for problems that may arise from the use of the program They will be pleased to receive any questions appearing from this version of the code Next version of the program may be sent upon request The current user s guide gives a brief account of the main capacities of the program version 3 0 1 Foreword notations Zen k constructs linear approximations of several types of phase diagrams for pure compounds such as T p u u X T diagrams and so on and needs a limited amount of thermodynamic data It fully exploits the al2. affigraphy is generated by the n k row vectors of a chemical reaction matrix of the system where reactions are written in columns they construct a generalized diagram in duality with chemography Chemography is the representation of the phases in the n dimensional composition space units numbers of moles of the phases in the system vector xi in the affigraphy the standard chemical affinities of the dissociation of the phases into elementary compounds are represented as A AG p7 9i pi where gi P T is Gibbs molar free energy of phase i and u chemical potential of phase i At equilibrium so called complementarity relation A x 0 holds with x gt 0 Ai 0 gi ui for the present phases Xi 0 A gt 0 ui lt gi for the absent phases Affigraphy is thus a space of absent phases and affigraphy vectors are absent phase vectors According to a fundamental theorem exposed in Guy and Pla 1997a the phase diagrams are obtained by intersecting by appropriate two dimensional planes the n k absent phase vectors inside the k dimensional affigraphy Invariant points resp univariant lines are the traces on the planes of the k 2 resp k 1 dimensional subspaces spanned by these vectors The coordinates of the representative point of the system in the k dimensional space provides information on the nature and stability of the phase associations Notation of stability indices Different associations o
3. the order of metastable phases is changed first case H stab index 1 lt M 2 lt W 3 lt P 4 lt T 5 lt I 6 second case P stab index 1 lt T 2 lt H 3 lt M 4 lt W 5 lt I 6 There is a change in scale and origin with InP u u RT For instance in order to have InPO one must subtract U o2 Qoz from u and divide by RT 19 Stability of six calcium potassium aluminum silicium magnesium phases in space HCAO LK 0 Problem Youcef1 simulates the transformation of schists by exchange of calcium and potassium with an external medium Bouftouha Y thesis in progress Table 10 gives the composition matrix and chemography of the system data at 298 15 K 1b Chemography is represented for the three inert components SiOz s Al2O3 a and MgO m that will be conserved during the solid transformations Target shows default composition of the system in the inert component chemical space Mobile components are CaO c and K2O k System phases are Biotite B KAISisMg3Oo OH 5 actually this is magnesium biotite named phlogopite K Feldspar K KAISi3Og Quartz Q SiOz Andalusite A SiAl2Os Anorthite O CaAl2Si20g and Diopside D CaMgSi 0 Following calculations are done at 750 K and 1 kb Tables 11 12 and 13 give the tables for Reaction matrix Chemography Affigraphy Invariant points Univariant lines Univariant segments and Univariant half lines Table 14 giv
4. unit J mol K equivalent to kJ mol k K and molar volume v unit J mol bar equivalent to kJ mol kb Note that molar entropy is manipulated with a sign added by the program A prefix i is assigned by default to each component in the matrix i means inert as explained above the status of components may be changed to m menu Edit Mobility All the foregoing permanent composition and thermodynamic information are called the data to be modified in the Edit menu see Sect 3 Data need be implemented whatever type of diagram will be constructed Admissible values of n and k Although the structure of the program is valid for any value of n and k these parameters are limited to n k lt 13 in the present version of the program For higher values the number of phases is too great for convenient display Display of composition matrix As is shown in the display of the composition matrix Display Matrices Composition all session parameters may be subject to modification in the commands Run Parameters see Sect 4 If some elements have been chosen as mobile Edit Mobility a prefix m is added to the corresponding label in the table At last a line labeled g is added to composition matrix it corresponds to the g of the phase for current pressure and temperature values that may differ from reference values g line also takes into acco
5. choice of 18 temperature and pressure in the system 1000 K 1b in the corresponding domain of the diagram see next Table 5 the two stable associations stab index 0 are SQ Sillimanite and Quartz and CS Sillimanite and Corundum Association Sillimanite Corundum indicated by is obtained for the current default chemical content of the system which is richer in Aluminum than in Silicium By varying pressure and temperature the different domains of the diagram may be explored and phase association information similar to that given in Table 4 may be obtained Table 5 gives the complete T p diagram there are three stable invariant points Q C and A and two metastable invariant points D and S System is degenerate and invariant points Q and C coincide stable phase associations obtained are indicated by chemographic bar inside each domain of the diagram bulk composition of the system is indicated by a point in the chemographic bar Below restricted diagram is given for the specific system content of previous table Corundum is always present for this aluminum rich system and invariant point C disappears quartz is absent in all domains Stability of iron oxides sulfides and sulfate in the space pO US Table 6 gives composition matrix of the Fe S O 1 system data for solids at 800 K 1b The basis of independent chemical components comprises f Fe s S2 and o Os These last two components are
6. invariant point D is split into DG DA and DQ A becomes AO In Table 21 restricted diagram is given for default composition of the system Acknowledgments the authors thank the people with whom they have discussed the concepts or examples for application of the program MM Garcia Gruy Lecoze Thomas The axes are dependent on the chosen reference compounds used as a basis to compute phase formation Gibbs free energies Elements not oxides are taken so that the current axes are HCAO uCaO and uKO uK20 21 9 References Guy B and Pla J M 1997a Structure of phase diagrams for n component n k phase chemical systems the concept of affigraphy C R Acad Sc Paris 324 Il a 1 7 Guy B and Pla J M 1997b Zen k a computer code for phase diagram prediction based on a new multi dimensional approach Int Confer Calphad XXVI University of Florida May 11 16 1997 T Anderson editor p D5 Pla J M 1996 Cours de Programmation lin aire Ecole des Mines de Saint Etienne Robie R A Hemingway B S and Fisher J R 1979 Thermodynamic properties of minerals and related substances at 298 15 K and 1 bar 10 Pascal pressure and at higher temperatures Geological Survey Bulletin 1452 456 p Zen E An 1966a Construction of pressure temperature diagrams for multicomponent systems after the method of Schreinemakers a geometric approach Geological Survey Bulletin n 1225 56 p Zen E An 1966b
7. the phases note that changing the composition of the system will change its content see previous section dX quantity that can be added 3 Thermodynamic parameters Tr r f rence temperature cannot be changed T current temperature Pr r f rence temperature cannot be changed vi value along the first vector v2 value along the second vector By activating Reset starting default values are restored default composition value one mole of each phase in the system default temperature and pressure reference values default potentials zero L and C transformations refer to Section 7 10 5 Output Display Matrices C and R already discussed in Section 2 above Chemography graphically or with a table restricted Affigraphy graphically or with a table The tables for chemography and affigraphy give the co ordinates of phase or absent phase vectors in the current basis or co basis The graphics give projections of the corresponding vectors the chemography is projected onto an affine three dimensional triangle the affigraphy is projected onto a two dimensional vectorial diagram When n gt 3 and k gt 2 the axes of the three dimensional chemography or the two dimensional affigraphy may be changed by use of the tabulation key three or two chemical components are alternatively taken in the whole set Chemography is computed for inert components dimension i conversely the dimens
8. Some topological relationships in multisystems of n 3 phases General theory unary and binary systems American Journal of Science 264 401 427 22
9. ata have been taken in Robie et al 1979 T p diagram for a one component three phase system aluminum silicates polymorphs DisthenO system comprises phases Andalusite A Kyanite D in French Disth ne and Sillimanite S with same composition SiAl O5 Table 1 gives composition matrix data at 600 K 1b reaction matrix tables for chemography affigraphy invariant points one invariant point here univariant lines and univariant half lines In Table 2 the computed T p diagram is given There is one invariant point and three univariant lines Line A Andalusite is absent represents reaction S D Line A is metastable portion of line A Below the table of bases and cobases for the position of the target in the diagram The stable phase is Andalusite stab index 0 then by increasing stability order Sillimanite stab index 1 and Kyanite stab index 2 In Table 3 another position of the target is chosen in the diagram in that case the order of metastable phases Kyanite and Sillimanite is exchanged T p diagram for a 2 3 system system AlO SiO Metam01 Two phases are added to preceding system Quartz SiO2 and Corundum Al20 3 and number of independent components is raised to two system composition may now be variable between SiO and Al20 Table 4 gives composition matrix data at 600 K 1b displayed g line calculated at 1000 K 1b chemography and table of bases and cobases for one specific
10. bases restricted chemography r affigraphy r phase diagram Bases co bases A basis is an association of n independent phases no chemical reaction and a co basis is the complementary set of k phases with respect to the whole set of n k phases absent phases By commanding Bases cobases one displays a table containing a reminder of the current values of the parameters and the corresponding table of bases and co bases Phase associations in the different domains may be determined by use of the table of bases and co bases that provide information on the nature and stability of phase associations depending on the value of the control parameters P T ps on the content of the system in independent chemical components and on the possible modification of the reference gj s of the phases in the case these are unknown these parameters may be modified by the command Run Parameters before each table is computed 14 The table displays the column of the bases that of the co bases the negativity index and the stability index In the list of the co basis the number of phases with negative sign is the stability index of the corresponding basis Reciprocally in the list of the basis the number of phases with negative sign gives the negativity or co stability index of the co basis A negative phase in a basis corresponds to a negative quantity of this phase in the assemblage It is not p
11. chosen as mobile and prefixed by m Seven phases may exist native Iron Fe VV Wustite FeO H Hematite Fe O3 M Magnetite Fe3sOa T Troilite FeS P Pyrite FeS and S sulfate Fes SO 3 Below the matrix the uO US diagram is given Stable phases observed in the different domains are indicated Computed diagram is similar to standard diagrams with INPO and InPS axes Table 7 gives the complete diagram with all invariant points and univariant lines with all stability levels as computed by the program scale is automatically chosen so that all points are visible In subsequent diagram below labels are omitted In Table 7bis a magnification of a part of previous diagram is shown invariant points IWTS and IWMT are stable IWT H IWM P IWS P singly metastable IW HP and IT HM doubly metastable and I HMP triply metastable line segments connecting these points have according stability levels Below another part of Table 7 diagram has been magnified most stable line portions have been omitted as an option for display In Table 8 scale is changed and only stable invariant points with their labels are represented Below another diagram where stab index 1 lines and points are also represented with no label In Table 9 bases and cobases are given for two different choices of the values of chemical potential of oxygen and sulfur in the diagram 1 0 0 2 100 200 stable phase is sulfate in both cases but
12. ers dashboard The parameters defining the diagram axes P T ui etc may be changed directly by moving a target on the screen as explained below section display so as to see the effect of the variation upon the phase assemblages All the parameters including composition content of the system control parameters P T u may be changed on the dashboard Three groups of parameters are defined 1 Parameters relevant to independent chemical components cr0 for memory cannot be changed content in independent chemical component given at the beginning calculated from the defautit composition value for the phases one mole of each phase cr current content in chemical component may be changed number of moles c cannot be changed result of the modification of crO by the action of 5X see below V1 definition of a first vector in n dimensional composition space that may be used to define a composition type diagram V2 definition of a second vector in composition space u current values of the chemical potentials of the chemical components 2 Parameters relevant to phases gr0 for memory cannot be changed values of Gibbs Free Energies given at the start is changed if the data are modified through edit gr current value of Gibbs Free Energy at r f rence state can be changed g current value of Gibbs Free Energy for current values of P and T XO initial composition can be changed number of moles of
13. es such as File refer to commands in the menus The user may select the command by typing active yellow letter or by selecting the item by use of keyboard arrows and pressing Return A systematic inventory of the commands is not presented here but rather those most useful in the natural order of a session Examples are discussed in Sect 8 2 Data input and display Menu File and Display To begin a new problem command File must be chosen in the main menu then New to enter the data A name is given to the problem The data may be defined within a Composition or Reaction matrix Composition matrix C Values of n and k must be given so as reference temperature and pressure T and P for thermodynamic data default values 298 15 K and 1 bar units 1 K K 1000 K and ikb Names of independent chemical components and names and compositions of the phases are indicated For convenience in the diagram display only one letter is chosen for each phase or component label the program keeps in memory the whole name of the phases and components The list of the correspondences between one letter symbols and item names is displayed by pressing S In the composition matrix phases are written in columns three thermodynamic data are needed for each phase reference molar Gibbs free energy gr g T P at chosen reference temperature and pressure unit kJ mol molar entropy s at T
14. es the pCAO HK2O diagram of the system It has three stable D A and K and three metastable Q O and B invariant points Because of the system degeneracy invariant points D and B coincide Below the composition matrix is given again with g line calculated for 750 K and 1kb A specific point is indicated in the diagram by a target for potential values uCa0 650 kJ and uK20 1000 kJ On next table Table 15 bases and cobases are indicated for the position of the target Restricted chemography for above values of potentials is indicated Current composition of the system is indicated by a target in the chemography same composition as in Table 10 Stable bases are BQO DBQ and BAO for current composition of the system observed realizable basis is BQO In Table 16 another choice is made for the chemical potentials of calcium and potassium oxides 800 0 while keeping the same chemical composition of the system Table of bases and cobases is indicated for that case so as the restricted corresponding chemography observable phase association is now BKA and stable bases are BKQ BDQ and BKA whose union makes the displayed restricted chemography Table 17 shows the complete uCaO uK O diagram with indication of all restricted chemographies for each domain of the diagram Current chemical composition of the system is indicated by a point inside the chemography In Table 18 restricted diagram for current composition of t
15. f not visible it may be displayed by pressing X by pressing again it disappears Target Y makes appear the target at point 0 0 in that case scale of diagram is modified or disappear Exploration of diagram By typing E the diagram is fixed in its present display scale labels symbols stability levels cannot be modified but the target may be moved in order the different phase associations in the diagram domain are known Movement of target is operated by use of keyboard arrows by pressing P steP the movement of the target is done by smaller steps so that position is more accurately adjusted by pressing P again the initial speed of target movement is restored by pressing the target is displayed at the center of the screen this may be useful if the starting position is outside the visible part of the diagram By pressing X the target is displayed wiped Once a domain has been chosen in the diagram one may press B to shift to the table of bases for that given point in the diagram see below by pressing C cHemography the restricted chemography for the current position in the diagram is displayed by pressing A the 13 affigraphy by pressing R the table of reactions is displayed by pressing M Composition the list of stable phase association is displayed onto the diagram itself in the form of the one letter phase symbols If the metastable lines a
16. f phases co exist at invariant points along univariant lines or inside divariant domains of the diagrams In the affigraphy approach the stability of an association of phases such as A B C D or ABCD is obtained by the properties of the set of absent phases EFGH with respect to the whole set This last set is written between brackets as EFGH in the affigraphy approach each of the lacking phases is given a positive or negative sign in the k dimensional space in relation to the sign of the corresponding affinity For example if phase F is taken as F this means that Ar lt 0 and F should be present The complete set of absent phases may be noted as for example E F G H The three negative signs of the last association indicate that ABCD is triply metastable By convenience the foregoing group of absent phases will be labeled G EFH where symbol separates the group of positive phases from that of the negative ones If all the absent phases are positive the labeling is EFGH and if all are negative it is EFGH The lowest stability level corresponds to the most stable association all absent phases positive stability index 0 and the highest stability level to the least stable or most metastable association all absent phases negative stability index k 1 In the diagrams generated by Zen k the invariant points are labeled by the names of the absent phases in the corresponding associations The knowledge of the phase
17. gebraic properties of the equations ruling thermodynamic equilibrium and treats the diagram as a unique object in multidimensional space and not as the addition of independent lines it thus avoids algebraic redundancy obtained by computing each reaction separately The positioning with respect to the multidimensional object gives all stability information in the same time Zen k allows to discuss many qualitative aspects of phase diagrams including the organization of reactions around invariant points the organization of invariant points in the diagram the nature and stability metastability of phase associations as a function of control parameters the influence of data on diagram topology and so on It gives a quick overview of the structure or topology of the diagrams In the case of chemical potential predominance diagrams the program gives the exact solution Zen k program is based on an original thermodynamic concept exposed in Guy and Pla 1997a namely the affigraphy concept Systems will be considered with n independent Name of the program was chosen as a tribute to E A Zen this author discussed methods to predict phase diagram structure mostly for n 2 and n 3 phase systems e g Zen 1966a and b our method may deal with n k phase systems with k arbitrary chemical components and n k phases in total in the present approach these have fixed composition pure compounds one species per phase Basically
18. he system is given as a direct output of the program For the current composition all the reactions are not visible restricted diagram thus shows less invariant points and univariant reactions than the complete one Phase associations in the different domains are written one per domain For chosen composition two reactions are not seen by the system B Q D K vertical line emanating from A and K Q O emanating from the same point Diagram of Table 18 may be recovered from the preceding one Tab 17 20 Below a non physical diagram is shown The signs of free energies have been changed in the starting matrix The obtained diagram is in duality with that computed in Table 14 stable and metastable points are exchanged same affigraphy is cut with a plane of similar orientation but symmetric to the first with respect to the origin of co ordinates in affigraphy space Stability of seven calcium potassium aluminum silicium magnesium phases in the space CaO HK20 In Youcef2 one phase is added to the preceding system grossular garnet G CaAloSi3O49 New chemography is represented in Table 19 so as new chemical composition matrix 298 15 K 1b calculations at 750 K 1kb In Table 20 complete diagram is shown so as a magnification of a part below Compared to the diagram of the system without garnet invariant points have now two phase labels Invariant point K of Table 14 is split into KA KG and KQ and
19. he system is shown These operations are not connected to the rest of the program Help command The Help command is not available in the present version of Zen k By pressing Time the current time is displayed 17 8 Examples mettre des gA gB des x des X T etc Following examples illustrate outputs of program commands for several model systems Note that due to linearization method thermodynamic co ordinates of invariant points may be not be exact depending on the change between starting data and those for which diagrams are computed or depending on distance in T p diagram from reference values The discrepancy may be important when using the program with condensable compounds especially gases whose molar volume greatly changes with pressure When gases are put in the external medium and treated by their chemical potentials the computation does not suffer these limitations Examples have been chosen in geology petrology and materials sciences the actual use of diagrams for solving problems computing stability of phase associations drawing diffusion paths for corrosion or metasomatism and so on is not discussed in detail In the following tables and figures are associated and all named tables Some information has been added by hand or type to raw program outputs such as reference T and p names of phases in diagram domains and so on The difference of font makes the distinction clear Thermodynamic d
20. hysically permitted A negative phase in the co basis means that the affinity of dissociation of the corresponding phase is negative the phase is absent but would be stable in the system so that the corresponding phase association or paragenesis is metastable Symbol indicates that corresponding phase association with both stability and negativity indices at value 0 is observed for the current composition of the system and for the current value of control parameters All phase associations with O stability index are stable only one is observed for a given composition their union defines the restricted chemography of the system for the current control parameter position of the target in the phase diagram Reciprocally all absent phase associations with negativity index at 0 are co stable their association in the affigraphy space defines a restricted affigraphy its intersection by two dimensional plane provides restricted phase diagram for composition of the system indicated by the target in the chemography Table of bases also indicates all possible metastable associations that may occur for current values of control parameters Their stability index is given so that phase associations may be ordered by increasing metastability It may happen that several associations have the same index In that case the present combinatorial approach is not enough to obtain the full ordering and one should compare the different free energy values
21. ion of affigraphy is m k i and m stand for inert and mobile component numbers respectively Target for system bulk composition may or may not be displayed in chemography restricted Diagrams x Display Diagram Graph gt Computed diagrams may be displayed independently of their being displayed in the Run commands A diagram will be composed of several invariant points connected by univariant line portions points and line portions have different stability levels A scale and an area of display are automatically chosen by the program in such manner as all the invariant points whatever stable or metastable are visible within the screen Scale area of display and stability levels may be modified according to the following commands Choice of scale is made by use of arrows page up U page down T 4 gt with the following effects T homogeneous dilation of the diagram U homogeneous contraction T vertical dilation 4 vertical contraction horizontal dilation lt horizontal contraction home or depending on the keyboards Fn lt goes back to the default representation as given at the start 11 Choice of region to display translation is made by use of function keys F1 to F5 with the following effects F1 moves the drawing to the right the window is moved to the left F2 moves the drawing to the left F3 moves the drawing up F4 moves the drawing down F5 back to the starting posi
22. of phase associations for a given composition of the system this procedure is lacking in the present version of the program By pressing T sorT the ordered table may be displayed Ordered table The phase associations are listed in decreasing order of Gibbs Free energies Reactions List of chemical reactions with the coefficients of the phases in the reactions the coefficients ar chosen as the list of smallest integers by pressing the tabulation key Tab the variations in free energy volume and entropy of the reactions are displayed In case some chemical components are chosen as mobile second table of reactions indicates the variation of chemical potential involved in the reactions Restricted phase diagrams are called pseudosections in petrological literature 15 Parameters This option goes to the dashboard cf above but in the present case parameters cannot be modified 6 Printing There is no special menu for printing Printing options are found within the different tables displayed by the program The command is I The printer is chosen in the first menu Tables may be printed in a file Frames for tables are chosen in the option menu below When in Windows system the printing of a specific phase diagram must follow two steps first the screen is saved by command alt print screen and put into the buffer then use may be made of a drawing code such as MSPaint before printing 7 Op
23. on of data Edit Commands in Edit menu allow permanent modification of the basic data of a problem phase composition and thermodynamic data all other modifications of parameters allowing exploration of the diagrams are done in the Run Parameters menu Following commands are possible Data name and coefficients of the chemical components and phases thermodynamic data Reference reference temperature and pressure Columns adding deleting or moving the column of a phase in the composition matrix Rows adding deleting or moving the row of a chemical component in the composition matrix Mobility choosing some chemical components as mobile m by default the components are inert i Name changing the name of the problem This name appears in the tables and graphics generated by the program Note that this name may be different from the file name stored in the hard disk 4 Calculation Menu Run The option of calculation allows a display of the graphs and so on that are calculated These may also be displayed in the separate option display Some items cannot be displayed if they have not been previously calculated in appropriate Run command if the data or parameters have been changed by action of Edit or Run Parameters they may have not been taken into account unless a new Diagram Run has been ordered Three possible
24. or reaction In the display Display Matrices Reaction a line g is also added to reaction matrix it gives the free energy variation of the reactions for current values of temperature pressure and chemical potential of mobile elements In the case when some components are mobile problem defined by composition matrix lines are added to reaction matrix for coefficients of mobile components in chemical reactions Current axes of phase diagram are indicated by x and y as prefix before corresponding names of lines of reaction matrix for instance x before the s entropy line indicates that temperature is chosen as x axis Other commands of File Saving of input data may be done by command Save a name is asked if a name has already been given it will be proposed again by the program A specific directory may be chosen to save or load the data Directory When a file defining a specific chemical system already exists it may be loaded by the command Open The name of the file is chosen by moving the spot and selecting it by pressing Return Suppressing files may be done by Delete The choice of the printer to print the tables not the graphs is done by choosing Printer Three possibilities are offered local printer network printer path must be indicated for printers or file default name Zenpk txt To exit the program select Exit in the File menu 3 Correcti
25. re displayed the list of metastable bases will also be displayed in the diagram the number of base degrees is in accordance with the number of line degrees The labels of phases are followed by a point and a number for the stability degree The last phase association may be wiped by typing lt By pressing Q Quit the diagram is recovered in its initial configuration that may be subject to modification except for target movement Tables of points lines and segments Display 7 Diagram Points Lines Segments Halflines vertical lines horizontal lines After calculation of a diagram has been commanded Run several kinds of tables may be displayed labeling and stability of points and lines by means of positive or negative phase indices is made according to rules indicated in Section 1 Points name co ordinates in current axes P T Us and stability of invariant points Points located at infinity are not registered Lines name and slope in current axes Slope is given by dx and dy for axes x and y T and dp for instance when T and pare current axes Segment name origin extremity slope by means of x and dy stability of univariant segments Half lines name origin slope and stability of the semi infinite lines Vertical lines in case of a mixed composition potential diagram Horizontal lines in case of a mixed diagram Table of bases and co
26. rial effect this number greatly increases with n and k and may be impossible to handle by the program If the program is unable to handle the total as given by the problem the indication is given that only the user may then choose a lower value Note that this maximum number does not alter the computation of all possible phase associations in bases and co bases see below Composition diagram Similarly to the preceding case the axes of such diagram may be chosen In the present case these are GA 5B for the phase da db for the elements provided the corresponding elements have not been chosen as mobile otherwise they appear as in the list and also 11 and T2 two arbitrary vectors that may be defined in the Parameters menu Similarly the maximum negativity number may be chosen Mixed diagram The first horizontal axis is taken in the list of the composition type variables oA 6B Ti T2 da db Note that T2 is not the molar fraction between 0 and 1 The second vertical axis is taken in the list of the thermodynamic type variables The maximum number of metastability index refers to the thermodynamic variables in agreement with the choice made on the mixed type diagrams see above After the axes of the diagram have been chosen diagram is computed and displayed Comments about diagram display and all possible operations on diagrams are given in Sect 5 Other commands in Run Paramet
27. s present is obtained by complementation to the absent phases In the program outputs only the invariant points are labeled except in the case when k 2 where univariant lines are labeled The word stability is a characteristic of the absent phases of one given association they would like to enter the basis they are stable or not By duality the word negativity is a characteristic of a present phase association in composition type diagram This lies on a generalization since sme of the phases may be in negative quantity Status of compounds Following the terminology used in Petrology inert i elements will be those for which a conservation constraint holds closed system behavior mobile m those for which no conservation constraint hold and whose chemical potential or partial pressure for gases or activity for solutes etc controls the spatial variation of the phases of the system open system behavior and perfectly mobile om those abundant elements whose potential has the same value everywhere Practically these last components may not be written in the composition matrix Choices made in the representation of stabilities of phase associations in mixed type diagrams In order to start the program user must select file Zen k exe and activate it Other files stored are useful for running main program examples bear suffix psy for physical system In the following the names written in italics and in quot
28. tion By simultaneous use of the Ctrl key the movements produced by the preceding functions are made greater 12 Choice of stability levels for the univariant lines and invariant points is done by means of keys F6 to F10 with the following effects see definitions of stability levels in Sect 1 F6 one stability level is wiped beginning with lower most stable level F7 one stability level is drawn again beginning with lower level F8 one stability level is drawn again beginning with higher less stable or most metastable level F9 one metastability level is wiped beginning with higher level F10 back to the starting display with all stability levels displayed By use of F6 to F9 any level or interval of stability levels may be displayed Style Univariant reactions of different stability levels may be drawn either with different types of dotted lines or with different colors If the dotted line option is chosen only two types of invariant points are distinguished black stable white metastable whatever metastability level in the colored line option points are displayed with different colors Restriction R Labels of invariant points may be displayed canceled by pressing N List of symbols for phases and compounds may be displayed canceled by pressing S Target showing current value of the intensive parameters corresponding to the axes of the diagram e g p T U is always present i
29. tions Option for display Option I Graphs Zoom gt 1 the default zoom step factor is 1 2 it may be changed The default maximum magnification or zoom with respect to the starting display is 20 It may be increased until 200 Half lines default length for semi infinite univariant lines is 100 pixels It may be modified up to 400 pixels Style the different types of univariant line portions stable singly metastable and so on may be represented either with different kinds of dotted lines or with different colors Digits number of digits displayed in the composition matrices and so on Frames choice of type of frames for the tables Computation frequency high low Orthogonalization procedure automatic or by hand 16 Elementary operations on matrices Run L transformation C transformation It is possible to transform the composition and reaction matrices by means of elementary operations on lines s L transformation operates on C matrix or on columns C transformation operates on R matrix By choosing the appropriate coefficient of the matrix as a pivot one can change the representation basis of the matrix This may be useful to change the phases that serve as a basis for the composition of the system or conversely to change the nature of the basic reaction and thereby calculating coefficients involved in another reaction The effect of these operations on the phase composition of t
30. types of diagrams may be generated Thermodynamic diagram The axes may be p and T chemical potential u and u2 of elements 1 and 2 or any two variable combination between p T and Ms In the case one or two potentials are chosen corresponding elements must first have been defined as mobile among independent chemical component list given at the start Menu Edit Mobility otherwise they will not appear in the menu or just by the symbol in the corresponding place of the list If the number of components chosen as mobile in the Edit menu is larger than the actual number of mobile components chosen for the diagram one or two other components remain perfectly mobile in the system if one wants corresponding components be inert in the system they must be re defined as such by Edit Mobility Among the possible axes axes of a new type may be chosen these are the Gibbs free energies of the phases ga gg and so on If they are unknown they are taken as parameters and the diagram shows the phase associations that obtain when they are varied Examples are given in Section 8 The maximum level of stability negativity is chosen by the user stability is used for the thermodynamic and negativity for the composition type diagrams Maximum stability index rules the maximum number of types for the univariant lines and invariant points that will be computed and displayed by the program Because of combinato
31. unt the chemical potentials of the mobile elements thus for phase j gj Qjr T Tr Sjr P PV Hi Hir Cj Where cij is number of moles of component i in one mole of phase j Reference and parameter default value for chemical potential of component i is zero Linearization procedure vvill be done from this reference data i Although not needed to construct chemical potential diagrams molar entropies and volumes must be indicated If some data are lacking e g some of the g s or s s or v s tentative values may be assigned The influence of the data on diagram topology may be explored by using the program Reaction matrix R Although the case is less frequent the system may similarly be defined by its reaction matrix File New Reaction gt Phases are written in lines reactions in columns Coefficients of reactions are written so as their Ag s As s and Av s at reference temperature and pressure named grs s s and v s respectively If the problem is defined by its composition matrix the program will automatically propose a corresponding reaction matrix after a basis has been selected in the composition matrix The different reactions are named a b c and so on Conversely if the problem is defined by a reaction matrix the program will propose a composition matrix The correction of data see Sect 3 is possible only for those data in the matrix defined at the start either composition
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