$ $ mc_sma_v1.000.tdb $ $*********RELEASE CANDIDATE - in publications refer to this version*********** $ $ MatCalc shape memory alloys (SMA) database, version 1.000, created 2012-11-27 $ $ This database contains a selection of assessed thermodynamic data for Ti-Ni shape memory alloys. $ Thermodynamic parameters of version 1.000 have been assessed in 2012 at TU Wien $ by Povoden-Karadeniz Erwin. $ Extensions to multi-component SMA is under construction. $ $ ############################################################################ $ $ Use with the most actual MatCalc version 5.51 release 0019 $ $ ############################################################################ $ $ Copyright and editor: Erwin Povoden-Karadeniz (erwin.povoden-karadeniz@tuwien.ac.at) $ You are not eligible for publishing this database or parts of it. $ $ ########################################################################### $ $ The following assessments are in parts incorporated in this database: $ $ ... see list of publications in the reference section at the end of this file ... $ $ The following elements are included in this database (to be extended soon): $ $ Ti, Ni $ $ This database is especially adapted to the demands of thermo-kinetic precipitation simulations in shape memory alloys. $ The reduced low-temperature limit of 250K, compared to SGTE, also meets sma simulation demands (calculations of T0 of martensite formation). $ Test calculations show that reproduction of experimental heat capacities is still satisfying at the low-temperature limit of 250K. $ $ The following phases are included in this database: $ They are listed in the order of their appearance in part D) Thermodynamic model parameters for phases $ For their documentation see part D). $ Documentation and priority rankings suggested by the editor are visible after reading the database and marking the phase of interest. $ $ LIQUID $ $ FCC_A1 $ BCC_A2 $ HCP_A3 $ Intermetallic equilibrium phases $ BCC_B2 (TiNi, split model used) $ TINI3 $ TI2NI $ Intermetallic metastable precipitates $ TI2NI3 $ TI3NI4 $ Martensite phases $ B19_PRIME $ B19 $ R_PHASE $************************************************************************ $ $ A) Definition of elements $ From A. T. Dinsdale, SGTE data for pure elements (REF 0) $ $************************************************************************ $ $Element Standard state mass [g/mol] enthalpy_298 entropy_298 ELEMENT VA VACUUM 0.0 0.0 0.00 ! ELEMENT NI FCC_A1 58.69 4787.0 29.7955 ! ELEMENT TI HCP_A3 47.88 4824.0 30.72 ! $************************************************************************ $ B) MatCalc commands $ $ Defines Ti as reference element REFERENCE_ELEMENT Ti ! $ Defines ordered B2-phase ATTACH_CONTRIBUTION BCC_B2 BCC_A2 ORDER_DISORDER ! $************************************************************************ $ $ C) Gibbs energy functions of elements $ $************************************************************************ $ $ ########################################################### $ SER (Standard elements references) $ ########################################################### $ FUNCTION GHSERNI 250.00 -5179.159+117.854*T-22.096*T*LN(T)-4.8407E-3*T**2; 1728.00 Y -27840.655+279.135*T-43.10*T*LN(T)+1.12754E+31*T**(-9); 6000.00 N REF:0 ! FUNCTION GHSERTI 250.00 -8059.921+133.615208*T-23.9933*T*LN(T) -4.777975E-3*T**2+1.06716E-07*T**3+72636*T**(-1); 900.00 Y -7811.815+132.988068*T-23.9887*T*LN(T) -4.2033E-3*T**2-9.0876E-08*T**3+42680*T**(-1); 1155.00 Y +908.837+66.976538*T-14.9466*T*LN(T) -8.1465E-3*T**2+2.02715E-07*T**3-1477660*T**(-1); 1941.00 Y -124526.786+638.806871*T-87.2182461*T*LN(T) +8.204849E-3*T**2-3.04747E-07*T**3+36699805*T**(-1); 6000.00 N REF:0 ! $ $ ########################################################### $ Gibbs energy functions other than SER $ ########################################################### $ FUNCTION GHSERNIA 250.00 -5179.159+117.854*T-22.096*T*LN(T)-4.8407E-3*T**2; 6000.00 N REF:pov12 ! FUNCTION GHSERTIA 250.00 -8059.921+133.615208*T-23.9933*T*LN(T) -4.777975E-3*T**2+1.06716E-07*T**3+72636*T**(-1); 6000.00 N REF:pov12 ! $ FUNCTION GNIBCC 250.00 +8715.084-3.556*T+GHSERNI#; 6000.00 N REF:0 ! FUNCTION GTIBCC 250.00 +6787.856+1.098972*T-1.5835*T*LN(T) +4.11413E-3*T**2-0.385519E-6*T**3-65428*T**(-1)+GHSERTI#; 900.00 Y +6539.750+1.726111*T-1.5881*T*LN(T) +3.539455E-3*T**2-0.187927E-6*T**3-35472*T**(-1)+GHSERTI#; 1155.00 Y +5758.548+38.389841*T-7.4305*T*LN(T) +9.363570E-3*T**2-1.048055E-6*T**3-525090*T**(-1)+GHSERTI#; 1941.00 Y +151010.046-821.233343*T+106.3083366*T*LN(T) -30.213169E-3*T**2+1.533611E-6*T**3-35299304*T**(-1)+GHSERTI#; 6000.00 N REF:0 ! FUNCTION GTIFCC 250.00 +6000-0.1*T+GHSERTI#; 6000.00 N REF:0 ! FUNCTION GTIFCCA 250.00 +6000-0.1*T+GHSERTIA#; 6000.00 N REF:pov12 ! FUNCTION GNIHCP 250.00 +1046+1.2552*T+GHSERNI#; 6000.00 N REF:0 ! FUNCTION GNIHCPA 250.00 +1046+1.2552*T+GHSERNIA#; 6000.00 N REF:pov12 ! $ FUNCTION GDHCNI 250.00 +0.5*GNIHCP#+0.5*GHSERNI#; 6000.00 N REF:152 ! FUNCTION GDHCTI 250.00 +0.5*GHSERTI#+0.5*GTIFCC#; 6000.00 N REF:152 ! FUNCTION GDHCNIA 250.00 +0.5*GNIHCPA#+0.5*GHSERNIA#; 6000.00 N REF:pov12 ! FUNCTION GDHCTIA 250.00 +0.5*GHSERTIA#+0.5*GTIFCCA#; 6000.00 N REF:pov12 ! FUNCTION GTI2NI 250.00 +0.33333*GHSERNIA#+0.66666667*GHSERTIA#-27514.218 +2.85345219*T; 6000.00 N REF:152 ! FUNCTION DGLAV 250.00 +5000; 6000.00 N REF:152 ! FUNCTION GLAVNI 250.00 +GHSERNI#+DGLAV#; 6000.00 N REF:152 ! FUNCTION GLAVTI 250.00 +GHSERTI#+DGLAV#; 6000.00 N REF:152 ! $************************************************************************ $ $ D) Thermodynamic model parameters $ $************************************************************************ $ $############################################################### $ THERMODYNAMIC PARAMETERS: LIQUID $############################################################## $ PHASE LIQUID % 1 1.0 > >> 6 ! CONSTITUENT LIQUID :NI,TI : ! $------------------------------------------------------------------- $ liquid pure elements $------------------------------------------------------------------- PARAMETER G(LIQUID,NI;0) 250.00 +16414.686-9.397*T-3.82318E-21*T**7+GHSERNI#; 1728.00 Y +18290.88-10.537*T-1.12754E+31*T**(-9)+GHSERNI#; 6000.00 N REF:0 ! PARAMETER G(LIQUID,TI;0) 250.00 +12194.415-6.980938*T+GHSERTI#; 1300.00 Y +368610.36-2620.9995038*T+357.005867*T*LN(T) -155.262855E-3*T**2+12.254402E-6*T**3-65556856*T**(-1)+GHSERTI#; 1941.00 Y +104639.72-340.070171*T+40.9282461*T*LN(T) -0.01*T**2+0.304747E-6*T**3-36699805*T**(-1)+GHSERTI#; 6000.00 N REF:pov12 ! $------------------------------------------------------------------- $ liquid binary interactions $------------------------------------------------------------------- PARAMETER L(LIQUID,NI,TI;0) 250.00 -160000+38*T; 6000.00 N REF:pov12 ! PARAMETER L(LIQUID,NI,TI;1) 250.00 -80000+18*T; 6000.00 N REF:pov12 ! PARAMETER L(LIQUID,NI,TI;2) 250.00 -5000-8*T; 6000.00 N REF:pov12 ! PARAMETER L(LIQUID,NI,TI;3) 250.00 +3000; 6000.00 N REF:pov12 ! $ $######################################################################## $ THERMODYNAMIC PARAMETERS: FCC_A1 $######################################################################## $ TYPE_DEFINITION ' GES A_P_D FCC_A1 MAGNETIC -3.0 0.28 ! PHASE FCC_A1 %' 2 1 1 > >> 1 ! CONSTITUENT FCC_A1 : NI%,TI : VA : ! $------------------------------------------------------------------- $ FCC_A1 endmember compounds $------------------------------------------------------------------- PARAMETER G(FCC_A1,NI:VA;0) 250.00 +GHSERNI#; 3000.00 N REF:0 ! PARAMETER G(FCC_A1,TI:VA;0) 250.00 +6000-0.1*T+GHSERTI#; 3000.00 N REF:0 ! $------------------------------------------------------------------- $ FCC_A1 interaction parameters $------------------------------------------------------------------- PARAMETER L(FCC_A1,NI,TI:VA;0) 250.00 -111400+5.66*T; 6000.00 N REF:pov12 ! PARAMETER L(FCC_A1,NI,TI:VA;1) 250.00 -52046; 6000.00 N REF:pov12 ! PARAMETER L(FCC_A1,NI,TI:VA;2) 250.00 0; 6000.00 N REF:pov12 ! $------------------------------------------------------------------- $ FCC_A1 magnetic contribution $------------------------------------------------------------------- PARAMETER TC(FCC_A1,NI:VA;0) 250.00 +633; 6000.00 N REF:0 ! PARAMETER BMAGN(FCC_A1,NI:VA;0) 250.00 +0.52; 6000.00 N REF:0 ! PARAMETER TC(FCC_A1,NI,TI:VA;0) 250.00 -2500; 6000.00 N REF:152 ! PARAMETER TC(FCC_A1,NI,TI:VA;1) 250.00 -3000; 6000.00 N REF:152 ! PARAMETER TC(FCC_A1,NI,TI:VA;2) 250.00 +1300; 6000.00 N REF:152 ! $ $######################################################################### $ THERMODYNAMIC PARAMETERS: BCC_A2 $######################################################################### $ TYPE_DEFINITION & GES A_P_D BCC_A2 MAGNETIC -1.0 0.4 ! PHASE BCC_A2 %& 2 1 3 > >> 1 ! CONSTITUENT BCC_A2 :NI,TI : VA% : ! $------------------------------------------------------------------- $ BCC_A2 endmember compounds $------------------------------------------------------------------- PARAMETER G(BCC_A2,NI:VA;0) 50.00 +8715.084-3.556*T+GHSERNI#; 3000.00 N REF:0 ! PARAMETER G(BCC_A2,TI:VA;0) 50.00 +GTIBCC#; 6000.00 N REF:0 ! $------------------------------------------------------------------- $ BCC_A2 interaction parameters $------------------------------------------------------------------- PARAMETER L(BCC_A2,NI,TI:VA;0) 50.00 -97427+12.112*T; 6000.00 N REF:152 ! PARAMETER L(BCC_A2,NI,TI:VA;1) 50.00 -32315; 6000.00 N REF:152 ! $------------------------------------------------------------------- $ BCC_A2 magnetic contribution $------------------------------------------------------------------- PARAMETER TC(BCC_A2,NI:VA;0) 50.00 +575; 6000.00 N REF:0 ! PARAMETER BMAGN(BCC_A2,NI:VA;0) 50.00 +0.85; 6000.00 N REF:0 ! PARAMETER TC(BCC_A2,NI,TI:VA;0) 50.00 -575; 6000.00 N REF:152 ! PARAMETER BMAGN(BCC_A2,NI,TI:VA;0) 50.00 -0.85; 6000.00 N REF:152 ! $ $######################################################################### $ THERMODYNAMIC PARAMETERS: HCP_A3 $######################################################################### $ TYPE_DEFINITION ) GES A_P_D HCP_A3 MAGNETIC -3.0 0.28 ! PHASE HCP_A3 %) 2 1 0.5 > >> 1 ! CONSTITUENT HCP_A3 :NI,TI% : VA% : ! $------------------------------------------------------------------- $ HCP_A3 endmember compounds $------------------------------------------------------------------- PARAMETER G(HCP_A3,NI:VA;0) 250.00 +1046+1.255*T+GHSERNI#; 3000.00 N REF:0 ! PARAMETER G(HCP_A3,TI:VA;0) 250.00 +GHSERTI#; 4000.00 N REF:0 ! $------------------------------------------------------------------- $ HCP_A3 interaction parameters $------------------------------------------------------------------- PARAMETER L(HCP_A3,NI,TI:VA;0) 250.00 -20000; 6000.00 N REF:152 ! PARAMETER TC(HCP_A3,NI:VA;0) 250.00 +633; 6000.00 N REF:0 ! PARAMETER BMAGN(HCP_A3,NI:VA;0) 250.00 +0.52; 6000.00 N REF:0 ! $ $###################################################################### $ THERMODYNAMIC DATA: BCC_B2 $###################################################################### $ PHASE BCC_B2 % 3 0.5 0.5 3 > essential cubic NiTi matrix-phase in sma. 2-substitutional sublattices split model used to describe ordering >> 5 ! CONSTITUENT BCC_B2 : NI,TI% :NI%,TI : VA : ! PARAMETER G(BCC_B2,NI:TI:VA;0) 250.00 -31000+11*T; 6000.00 N REF:pov12 ! PARAMETER G(BCC_B2,TI:NI:VA;0) 250.00 -31000+11*T; 6000.00 N REF:pov12 ! $----------------------Interaction parameters---------------------- PARAMETER L(BCC_B2,TI:NI,TI:VA;0) 250.00 +70000-13*T; 6000.00 N REF:pov12 ! PARAMETER L(BCC_B2,NI,TI:TI:VA;0) 250.00 +70000-13*T; 6000.00 N REF:pov12 ! PARAMETER L(BCC_B2,TI:NI,TI:VA;1) 250.00 -10000+8*T; 6000.00 N REF:pov12 ! PARAMETER L(BCC_B2,NI,TI:TI:VA;1) 250.00 -10000+8*T; 6000.00 N REF:pov12 ! PARAMETER L(BCC_B2,NI:NI,TI:VA;0) 250.00 -56500+23*T; 6000.00 N REF:pov12 ! PARAMETER L(BCC_B2,NI,TI:NI:VA;0) 250.00 -56500+23*T; 6000.00 N REF:pov12 ! PARAMETER L(BCC_B2,NI:NI,TI:VA;1) 250.00 +13500-8*T; 6000.00 N REF:pov12 ! PARAMETER L(BCC_B2,NI,TI:NI:VA;1) 250.00 +13500-8*T; 6000.00 N REF:pov12 ! PARAMETER L(BCC_B2,NI:NI,TI:VA;2) 250.00 +37000-14*T; 6000.00 N REF:pov12 ! PARAMETER L(BCC_B2,NI,TI:NI:VA;2) 250.00 +37000-14*T; 6000.00 N REF:pov12 ! $ $######################################################################## $ THERMODYNAMIC PARAMETERS: TINI3 $######################################################################## $ PHASE TINI3 % 2 3 1 > hexagonal equilibrium eta-phase, precipitate in sma >> 3 ! CONSTITUENT TINI3 : NI%,TI : NI,TI% : ! $------------------------------------------------------------------- $ TINI3 endmember compounds $------------------------------------------------------------------- PARAMETER G(TINI3,NI:NI;0) 250.00 +2*GNIHCP#+2*GHSERNI#; 6000.00 N REF:152 ! PARAMETER G(TINI3,NI:TI;0) 250.00 -181000+19*T +0.0072*T**2-5e-8*T**3+450525*T**(-1)+3*GDHCNIA#+GDHCTIA#; 6000.00 N REF:pov12 ! PARAMETER G(TINI3,TI:NI;0) 250.00 +181000-19*T +0.0072*T**2-5e-8*T**3+450525*T**(-1)+GDHCNIA#+3*GDHCTIA#; 6000.00 N REF:pov12 ! PARAMETER G(TINI3,TI:TI;0) 250.00 +2*GHSERTI#+2*GTIFCC#; 6000.00 N REF:152 ! $------------------------------------------------------------------- $ TINI3 interaction parameters $------------------------------------------------------------------- PARAMETER L(TINI3,NI:NI,TI;0) 250.00 +143216-101.776*T; 6000.00 N REF:pov12 ! PARAMETER L(TINI3,NI:NI,TI;1) 250.00 +109156-66.448*T; 6000.00 N REF:152 ! PARAMETER L(TINI3,TI:NI,TI;0) 250.00 +50000; 6000.00 N REF:pov12 ! PARAMETER L(TINI3,NI,TI:TI;0) 250.00 +50000; 6000.00 N REF:pov12 ! $ $######################################################################### $ THERMODYNAMIC PARAMETERS: TI2NI $######################################################################## $ PHASE TI2NI % 2 2 1 ! > cubic equilibrium phase >> 2 ! CONSTITUENT TI2NI : NI,TI% : NI%,TI : ! $------------------------------------------------------------------- $ TI2NI endmember compounds $------------------------------------------------------------------- PARAMETER G(TI2NI,TI:NI;0) 250.00 +3*GTI2NI#+14*T-800 +5.5e-3*T**2-2.78*T*LN(T)-1.87e-7*T**3 +33285*T**(-1); 6000.00 N REF:pov12 ! PARAMETER G(TI2NI,NI:TI;0) 250.00 +2*GLAVNI#+GLAVTI# +30000-3*GTI2NI#; 6000.00 N REF:152 ! $------------------------------------------------------------------- $ TI2NI interaction parameters $------------------------------------------------------------------- PARAMETER L(TI2NI,NI,TI:NI;0) 250.00 +60000; 6000.00 N REF:152 ! PARAMETER L(TI2NI,NI:NI,TI;0) 250.00 +60000; 6000.00 N REF:152 ! PARAMETER L(TI2NI,TI:NI,TI;0) 250.00 +60000; 6000.00 N REF:152 ! PARAMETER L(TI2NI,NI,TI:TI;0) 250.00 +60000; 6000.00 N REF:152 ! $###################################################################### $ THERMODYNAMIC PARAMETERS: TI2NI3 $###################################################################### $ PHASE TI2NI3 % 2 3 2 > tetragonal metastable precipitate >> 4 ! CONSTITUENT TI2NI3 : NI : TI : ! PARAMETER G(TI2NI3,NI:TI;0) 250.00 +3*GDHCNIA#+2*GDHCTIA# -200000+11.5*T+0.0086*T**2-2e-7*T**3+589836*T**(-1); 6000.00 N REF:pov12 ! $ $########################################################################## $ THERMODYNAMIC PARAMETERS: TI3NI4 $######################################################################### $ PHASE TI3NI4 % 2 4 3 > rhombohedral metastable precipitate >> 5 ! CONSTITUENT TI3NI4 : NI% : TI% : ! PARAMETER G(TI3NI4,NI:TI;0) 250.00 +4*GDHCNIA#+3*GDHCTIA# -264000-5*T+0.0175*T**2-3e-7*T**3+609713*T**(-1); 6000.00 N REF:pov12 ! $ $##################################################################### $ THERMODYNAMIC PARAMETERS: B19_PRIME $#################################################################### $ PHASE B19_PRIME % 2 0.5 0.5 > monoclinic martensite essential for shape memory effect >> 5 ! CONSTITUENT B19_PRIME : NI,TI% : NI%,VA : ! $------------------------------------------------------------------- $ B19_PRIME endmember compounds $------------------------------------------------------------------- PARAMETER G(B19_PRIME,NI:NI;0) 250.00 +GNIBCC#; 6000.00 N REF:166 ! PARAMETER G(B19_PRIME,TI:NI;0) 250.00 -46750+16.3*T+0.5*GNIBCC# +0.5*GTIBCC#-0.002*T**2+50000*T**(-1); 6000.00 N REF:pov12 ! PARAMETER G(B19_PRIME,NI:VA;0) 250.00 +50000+0.5*GNIBCC#; 6000.00 N REF:166 ! PARAMETER G(B19_PRIME,TI:VA;0) 250.00 +22500+0.5*GTIBCC#; 6000.00 N REF:166 ! $------------------------------------------------------------------- $ B19_PRIME interaction parameters $------------------------------------------------------------------- PARAMETER L(B19_PRIME,NI,TI:NI;0) 250.00 +8000; 6000.00 N REF:pov12 ! PARAMETER L(B19_PRIME,TI:NI,VA;0) 250.00 -18000+8*T; 6000.00 N REF:pov12 ! $ $##################################################################### $ THERMODYNAMIC PARAMETERS: B19_ORTHO $#################################################################### $ PHASE B19_ORTHO % 2 0.5 0.5 > orthorhombic intermediate martensite >> 3 ! CONSTITUENT B19_ORTHO : NI,TI% : NI%,VA : ! $------------------------------------------------------------------- $ B19_ORTHO endmember compounds $------------------------------------------------------------------- PARAMETER G(B19_ORTHO,NI:NI;0) 250.00 +GNIBCC#; 6000.00 N REF:pov12 ! PARAMETER G(B19_ORTHO,TI:NI;0) 250.00 -45314+16.3*T+0.5*GNIBCC# +0.5*GTIBCC#-0.002*T**2+50000*T**(-1); 6000.00 N REF:pov12 ! PARAMETER G(B19_ORTHO,NI:VA;0) 250.00 +50000+0.5*GNIBCC#; 6000.00 N REF:pov12 ! PARAMETER G(B19_ORTHO,TI:VA;0) 250.00 +22500+0.5*GTIBCC#; 6000.00 N REF:pov12 ! $------------------------------------------------------------------- $ B19_ORTHO interaction parameters $------------------------------------------------------------------- PARAMETER L(B19_ORTHO,NI,TI:NI;0) 250.00 +8000; 6000.00 N REF:pov12 ! PARAMETER L(B19_ORTHO,TI:NI,VA;0) 250.00 -18000+8*T; 6000.00 N REF:pov12 ! $ $##################################################################### $ THERMODYNAMIC PARAMETERS: R_PHASE $#################################################################### $ PHASE R_PHASE % 2 0.5 0.5 > rhombohedral intermediate martensite >> 4 ! CONSTITUENT R_PHASE : NI,TI% : NI%,VA : ! $------------------------------------------------------------------- $ R_PHASE endmember compounds $------------------------------------------------------------------- PARAMETER G(R_PHASE,NI:NI;0) 250.00 +GNIBCC#; 6000.00 N REF:pov12 ! PARAMETER G(R_PHASE,TI:NI;0) 250.00 -44678+10.75*T+0.5*GNIBCC# +0.5*GTIBCC#-0.002*T**2+50000*T**(-1); 6000.00 N REF:pov12 ! PARAMETER G(R_PHASE,NI:VA;0) 250.00 +50000+0.5*GNIBCC#; 6000.00 N REF:pov12 ! PARAMETER G(R_PHASE,TI:VA;0) 250.00 +22500+0.5*GTIBCC#; 6000.00 N REF:pov12 ! $------------------------------------------------------------------- $ R_PHASE interaction parameters $------------------------------------------------------------------- PARAMETER L(R_PHASE,NI,TI:NI;0) 250.00 +8000; 6000.00 N REF:pov12 ! PARAMETER L(R_PHASE,TI:NI,VA;0) 250.00 -18000+8*T; 6000.00 N REF:pov12 ! $***************************************************************************** $ $ E) List of references $ $***************************************************************************** $ A00201-0 unary A.T. Dinsdale, SGTE Data of pure elements, CALPHAD, Vol. 15, No. 4, pp 317-425, 1991. A00229-152 Fe-Ni-Ti J. De Keyzer, G. Cacciamani, N. Dupin, P. Wollants, Thermodynamic modeling and optimization of the Fe-Ni-Ti system, CALPHAD, Vol. 33, pp 109-123, 2009. A00250-166 Ni-Ti W. Tang, B. Sundman, R. Sandström, C. Qiu, New modelling of the B2 phase and its associated martensitic transformation in the Ti-Ni system, Acta Mater., Vol. 47, No. 12, pp. 3457-3468, 1999. pov12 E. Povoden-Karadeniz, unpublished 2012.