Thermodynamics: ThermoCalc Console

The following is an excerpt from Dewar - Characterization and Evaluation of Aged 20Cr32Ni1Nb Stainless Steels, and references a stainless steel used in this thesis. The content of this article can also be applied to a general case, and should not be limited to to the presented example.

1. ThermoCalc Introduction

Potential and molar phase diagrams are the centerpiece of materials science, and are used as a visual representation of a materials system, providing critical information on how the system reacts to changes in composition, temperature, pressure, or volume. Phase diagrams also give insight into the stability of a phase, and transformation reactions that occur from crossing monovariant, or invariant phase boundaries. Although phase diagrams are a useful tool for visualizing binary, or ternary systems, there is no real method of visualization of a multicomponent system other than to reduce the dimensionality of the system to a pseudo-binary, or isoplethal diagram. While isopleths are a useful representation of multicomponent system, unless the specific alloy composition has previously been calculated, the researcher will have to do the thermodynamic calculations on their own. For large systems this can become very tedious trying to provide interaction parameters for each constituent interaction in each sublattice of each phase of the system. Thankfully a lot of work in the past two decades has gone into building large databases to compile such data. CALPHAD and ThermoCalc are the forerunners in compiling thermodynamic data, and providing computational tools to simply, and efficiently be able to analyze predicted equilibria for specific material systems.

ThermoCalc is a tremendously powerful tool for metallurgists, and materials scientists, as its simplicity does not require the user to have much understanding of material thermodynamics, but can provide a vast amount of information, and insight into the alloy the user is dealing with. Whether there is sparse literature on the alloy, or the user is looking to tweak certain variables to modify the the microstructure, ThermoCalc can vastly reduce the time and money needed for experimentation, and may altogether eliminate the trail by error approach utilized in the past.

In the present work, ThermoCalc was used to analyze how additions of both nitrogen, and titanium can affect the equilibrium microstructure of a 2032Nb alloy, and which chemistry provides the most optimal microstructure. With isoplethal sectioning only one component can be an independent variable while the others remain constant. In a proper design matrix all possible permutations and combinations must be encompassed. In a system with seven elements (chromium, nickel, niobium, silicon, carbon, manganese, and nitrogen/titanium), hundreds of phase diagrams would need to be analyzed in order to determine the effects each element, and their interactions have on phase stability, phase solubility, and the driving force of a phase. In the following sections a method for analyzing, and optimizing the composition of a multicomponent system is proposed with the use of ThermoCalc as a subroutine. The next section will discuss a proposed Gibbs energy model for calculating equilibrium for a 2032Nb alloy, and a basic outline of how to use the ThermoCalc console program will be provided. Afterwords, a proposed methodology for compiling the data output by ThermoCalc will be presented, as well as ways of representing the data, to ultimately draw conclusions on how composition of the alloy affects the systems equilibrium microstructure.


2. ThermoCalc Scripts

ThermoCalc software contains both a windows version which is a typical user interface, and a classical console version which requires input of subsequent command-line inputs. The console version will be primarily discussed in this document as it will be used later as a subroutine in the executable module to output the equilbrium of the compositional matrix array used for chemistry optimization. The console version is separated into multiple modules for first initializing the system, setting conditions for the equilibrium, running either a stepping routine (1-dimenional) for computing property diagrams or mapping routines (2-4 dimensional) for computing phase diagrams, and finally a graphing module. A flow chart of each of the modules along with their associated commands is outlined in Figure 1.



Fig. 1: Flow chart of the set of the modules for calculating phase diagrams with the console version of ThermoCalc. The bolded text in each box are the associated commandeds to enter into each module


Typically you will want to create a new file in the computers directory for every equilibrium calculation you are going to run. Inside this folder copy a shortcut to the ThermoCalc classic executable. When you enter the shortcut any files that will be saved will be saved in that directory. Upon entering the console version the first step is to save every command you input in the console into a log file. The command s-l-f, or set-log-file will create a .log file in directory that the ThermoCalc shortcut is with the filename specified in the following argument. The next line is the heading information to describe what the following file will do.

s-l-f filename  @@set log file 
Calculate isopleth of 2032Nb system @@heading for the .log file
					

The next step is to go into the appropriate initialization module. For equilibrium calculations most of the time you will use the data module to first initialize the system. The data module gives the most amount of freedom to set the specific criteria on the system, however there is a simplified module that will ask the user questions to specify the parameters for the system. The simplified module is accessed by first going into the poly-3 module by typing the command “go p-3”, and then typing “def-mat”. For the purposes of this script we will need to suspend certain constituents in the G-phase sublattice module so the data module should be used. The last thing to note is that if the user wants to perform Scheil calculations, the module command is simply “go scheil” it is set up the same way as the “def-mat” module where it will ask you a series up questions to set up the parameters.

The default database ThermoCalc will draw from is the TCFE* database, TCS Steels/Fe-alloys database. The version used in this document is version 6, and does not contain G-phase; however version 7 has recently been released and does now contain G-phase. The TTNI8 database, TT Ni-based superalloys database, was appended to the system to include G-phase in the system. It should be noted that the TT databases do not contain volumetic data whereas, the TC databases do. Therefore volumetric parameters will have to be calculated in a post process if the data is imported from a TT database.

The first step is to specify the components in the system and then import the appropriate phases for both the TCFE6 database, and the TTNI8 database. The rej P * command on line 5 rejects all the phases in the database, where the * is a wild card term meaning all. If the user does not know what phases should be present in the system, the lines 5 and 6 can be omitted an a generic run can be performed. It is necessary to specify the phases in the system, as sometimes phases that are not present in any literature on the alloy will be stable in the equilibrium calculation, which then cannot be verified. In the TCFE6 database every phase specified for the system should be restored in line 6. Be sure to input the get command after to pull the relevant information from the database. To reject certain constituents of a phase the command rej c < phase > < sublattice > can be input, where the user will then be prompted for which element they would like to reject. This operation can also be done in the windows version of ThermoCalc.

go data
def-ele Fe Cr Ni Si Nb C Mn N Mo
rej P *
res P FCC_A1 M7C3 M23C6 M6C MC Liq Z-Phase
get
app TTNI8
def-ele Fe Cr Ni Si Nb C Mn Ti Mo
rej P *
res P G_Phase
rej c g-phase 1
fe

rej c g-phase 3
Cr

rej c g-phase 3
Mn

get

After the system has been initialized it is time to set up the conditions for equilibrium. The command s-c is short for set-condition, where the intensive properties such as temperature, and pressure, and extensive properties such as the size of the system (e.g. n = 1mol), and the composition (xi) need to be defined. Temperature is in kelvin, and composition is defined as weight fraction w(element), or mole fraction x(element). Weight fractions should be input for all but one of the components, which will be the dependent variables. This will make sure that the sum of the weight fractions is equal to unity. The command c-e calculates the equilibrium, while l-e lists the equilibrium either on screen or in this case to a file eq.txt. The conditions set will be the initial equilibrium calculated, and does not hold any relevance over the subsequent mapping or stepping functions. Next, is to map the phase diagram over the set axis variable limits. s-a-v 1 t sets the y-axis to temperature with a range between 400-1800K, and s-a-v 2 w(N) sets the x-axis to the weight fraction of nitrogen. The map command will initiate the mapping procedure.

go p-3
s-c t=1089 n=1 p=101325
s-c w(Cr)=0.19 w(Ni)=0.31 w(Si)=0.005
c-e
l-e
eq.txt
VWCS
s-a-v 1 t 410 1800 27.8
s-a-v 2 w(N) 0 0.3 0.001
map

Alternatively, to produce property diagrams (dependent vs. independent variables) only the first axis will need to be specified, followed by the step command. ThermoCalc will initiate its global minimization procedure, and incrementally step along the axis between the set boundaries. Stepping is a much faster operation than mapping and should be considered depending on what type of information needs to be analyzed. There are numerous options for the stepping function, but in this case the default NORMAL command was chosen. More information about these options can be read in the ThermoCalc TCC user manual supplied with the software package.

s-a-v 1 t 410 1800 27.8
step @@ an alternative to the mapping procedure
NORMAL

After the mapping or stepping functions have completed, the user should proceed to the post module for producing phase, and property diagrams. For the mapping command the default diagram contains both of the variable axis set prior to mapping. For stepping the default property diagram sets the y-axis to the molar phase fraction of each stable phase in the system over variable axis set above. The s-d-a command stands for ‘set-diagram-axis’ where in the case of line 35, the x-axis is being changed to display the temperature in Celsius. The s-s command stand for ‘set-scaling-status’, and can be used to set the axis maximum and minimum values. The plot will show the resulting diagram in a separate window. It is important to know the composition of each of the phases after stepping or mapping procedures, where the constituents that occupy each sublattice, and their site fractions can be determined. The composition of a phase can be determined by changing the y-axis to represent the mole fraction of a phase, where the wild card represents every component in the phase. Lastly, to export the data of a property diagram, the l-d-t command will export the data either to text or to excel. Note that the extension on the excel output is .xls, and not .xlsx.

post
s-d-a x t-c
s-s y n 0 0.1
plot
s-d-a y x(FCC_A1#1,*)
*
plot
FCC_A1#1.ps
l-d-t
FCC_A1#1.xls

After the program is exited, the .log file can be accessed, and will contain all of the commands inpute during the ThermoCalc session. To run the .log file through ThermoCalc, change the extension on the file from .log to .tcm.

3. References

[1]    Shi, S., Lippold, J.. Microstructure evolution during service exposure of two cast, heat-resisting stainless steels – hp-nb modified and 20-32nb. Mater Charact 2008;59(8):1029–1040.

[2]    Berghof-Hasselbcher, E., Gawenda, P., Schorr, M., Schtze, M., Hoffman, J.. Atlas of Microstructures. Materials Technology Institute; 2008.

[3]    Nishimoto, K., Saida, K., Inui, M., Takahashi, M.. Changes in microstructure of hp-modified heat-resisting cast alloys with long term aging. repair weld cracking of long term exposed hp-modified heat-resisting cast alloys. (report 2). Quarterly Journal of the Japan Welding Society 2000;18(3):449–458.

[4]    Nishimoto, K., Saida, K., Inui, M., Takahashi, M.. Mechanism of hot cracking in haz of repair weldments. repair weld cracking of long term exposed hp-modified heat-resisting cast alloys. (report 3). Quarterly Journal of the Japan Welding Society 2000;18(4):590–599.

[5]    Powell, D.J., Pilkington, R., Miller, D.A.. The precipitation characteristics of 20% cr/25% ni—nb stabilised stainless steel. Acta Metall 1988;36(3):713–724.

[6]    Chen, Q.Z., Thomas, C.W., Knowles, D.M.. Characterisation of 20cr32ni1nb alloys in as-cast and ex-service conditions by sem, tem and edx. Mater Sci Eng, A 2004;374(1-2):398–408.

[7]    Danielsen, H.K., Hald, J.. On the nucleation and dissolution process of z-phase cr(v,nb)n in martensitic 12%cr steels. Mater Sci Eng, A 2009;505(1-2):169–177.

[8]    Danielsen, H., Hald, J.. Influence of z-phase on long-term creep stability of martensitic 9-12%cr steels. In: 9th Liege Conference on Materials for Advanced Power Engineering. 2010, p. 310.

[9]    Sourmail, T., Bhadeshia, H.. Microstructural evolution in two variants of nf709 at 1023 and 1073 k. Metall Mater Trans A 2005;36(1):23–34.

[10]    Erneman, J., Schwind, M., Liu, P., Nilsson, J.O., Andrén, H.O., Ågren, J.. Precipitation reactions caused by nitrogen uptake during service at high temperatures of a niobium stabilised austenitic stainless steel. Acta Mater 2004;52(14):4337–4350.

[11]    Pickering, F.B., Keown, S.. Niobium in stainless steels. In: Stuart, H., editor. Niobium, Proceedings of the International Symposium. Warrendale, PA: Met. Soc. AIME; 1981, p. 1113–1142.

[12]    Sourmail, T.. Literature review precipitation in creep resistant austenitic stainless steels. Mater Sci Technol 2001;17(January):1–14. URL http://www.thomas-sourmail.org/papers_html/precipitation_review/precipitation_review.pdf.

[13]    Xiao, B., Xing, J.D., Feng, J., Zhou, C.T., Li, Y.F., Su, W., et al. A comparative study of cr 7 c 3 , fe 3 c and fe 2 b in cast iron both from ab initio calculations and experiments. Journal of Physics D: Applied Physics 2009;42(11):115415.

[14]    Jo, T.S., Lim, J.H., Kim, Y.D.. Dissociation of cr-rich m23c6 carbide in alloy 617 by severe plastic deformation. J Nucl Mater 2010;406(3):360–364.

[15]    Holman, K.L., Morosan, E., Casey, P.A., Li, L., Ong, N.P., Klimczuk, T., et al. Crystal structure and physical properties of mg6cu16si7-type m6ni16si7, for m = mg, sc, ti, nb, and ta. Mater Res Bull 2008;43(1):9–15.

[16]    Hans Lukas, S.G.F., Sundman, B.. Computational Thermodynamics. Cambridge University Press; 2007.

[17]    Hillert, M.. Phase Equilibria, Phase Diagrams and Phase Transformations: Their Thermodynamic Basis. Cambridge University Press; 2007.

[18]    Liu, Z.K.. Computational thermodynamics using thermo-calc; 2010. ThemoCalc & Dictra Training Course.

[19]    Song, Y.Y.. Thermodynamic study on b and fe substituted cr23c6 using first-principles calculations. Ph.D. thesis; Pohang University of Science and Technology; 2010.

[20]    Hoffman, J., Magnan, J.. Cast 20cr32ni1nb alloy aged mechanical property improvements via chemistry modifications. In: Corrosion 2003. no. 3469; NACE International; 2003,.

[21]    Vitek, J.. G-phase formation in aged type 308 stainless steel. Metallurgical and Materials Transactions A 1987;18(1):154–156.

[22]    Danielsen, H.K., Hald, J.. A thermodynamic model of the z-phase cr(v, nb)n. Calphad 2007;31(4):505–514.

[23]    Shi, S., Lippold, J., Ramirez, J.. Hot ductility behavior and repair weldability of service-aged, heat-resistant stainless steel castings. Weld J 2010;89(10):210–217.

[24]    Shibasaki, T., Mohri, T., Takemura, K.. Experience with cast material for steam reformer furnaces. Ammonia Plant Saf Relat Facil 1994;34:166–176.

[25]    Hoffman, J.. High temperature aging characteristics of 20cr32ni1nb castings. In: Corrosion 2000. no. 512; NACE International; 2000,.

[26]    Montgomery, D., Runger, G.. Applied Statistics and Probability for Engineers, 4th Edition. John Wiley & Sons; 2006.

[27]    Spliid, H.. Design and analysis af experiments with k factors having p levels; 2002.

[28]    Minitab, . Technical support document rank deficiency; 2010. http://www.minitab.com/support/documentation/Answers /RankDeficiency.pdf.

 

4.Glossary *

constituent
Element, or species, that occupies a specific sublattice of a specific phase. A phase can also be considered as a constituent of the total system.. 5, 14

 

end-member
The final chemical formula of a stable or metastable phase whose sublattice(s) are occupied by single constituents. For example M23C6 is an end member of (Cr,Ni,Fe,Nb)23C6.. 8

 

factor
The independent variable of a factorial design. 23

 

main effect
How much the change in an individual factor effects the change in the response variable of a factorial design.. 24

 

replicate
Independent repetition of a treatment in a factorial experiment. 26
response variable
The dependent variable of a factorial experiment, or a regression model.. 24

 

ThermoCalc
A computational thermodynamics program that can calculate equilibrium phase diagrams for multicomponent systems, as well as Scheil simulations, and various thermodynamic properties (Cp, ΔHm, ΔGm etc...). 3
treatment
A specific level of a factor in a factorial design.. 24

5. Acronyms *

ANOVA
Analysis of variance. 24, 25

 

CEF
Compound-energy formalism. 8

 

LRO
Long Range Ordering. 8

 

6. Nomenclature *

βj
the effect of the ith level of factor ‘B’
ϵijk
random error component
for all instances of ...
in a set ...
μ
Overall mean effect
μi
Chemical potential of component or end-member i
ψk
the effect of the ith level of factor ‘C’
τi
the effect of the ith level of factor ‘A’
G
total Gibbs energy; G = αmα ·Gmα
Giα
partial Gibbs energy of component i in phase α; Giα = (  α)
 ∂∂GNi-T,P,Nj
Gmα
integral molar Gibbs energy of a phase
Ii
constituent array of order i
LI
interaction parameter of compound I
mα
fraction of a phase
Ni
moles of component i
R
gas constant, 8.314Jmol-1K-1
R2
coefficient of multiple determination
Smα
molar entropy of a phase
T
Temperature (K)
xi
total mol fraction of component i; xi = αmα · xiα
xiα
mole fraction of component i in phase α

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