computational thermodynamics and kinetics in materials ...€¦ · traditionally, pourbaix...

Applications in Materials Corrosion

www.thermocalc.com

Computational Thermodynamics and Kinetics

in Materials Modeling and Simulations

Materials Corrosion Applications

with Thermo-Calc Software


Materials Corrosion Applications with Thermo-Calc Software

A. Introduction

B. Thermo-Calc Software:

B1. Thermodynamic Models and Databases

B2. Calculations of Pourbaix Diagrams and Other Diagrams

C. Applications in Aqueous Corrosion of Stainless Steels

D. Applications in Aqueous Corrosion of Carbon Steels in Seawater

E. Applications in Aqueous Corrosion of HPCRM Alloys in Groundwater

F. Applications in High-Temperature Gaseous Corrosion

G. Applications in Molten-Salt Corrosion

H. References

A. INTRODUCTION

Materials corrosion almost occurs everywhere, which may appear as serious material damages, lead to

unexpected application failures, cause tremendous economic costs, bring environmental degradations, provoke

natural disasters, and so forth. Therefore, scientists and engineers often have to conduct many expansive and

time-consuming corrosion experiments in the processes of failure analysis, risk evaluations, quality

improvements and application enhancements.

Thermodynamic investigation of materials corrosion under various environments are extremely important for

efficient design and production of high-quality materials, for advanced processing of corrosion-resistant

coatings, for optimal performances of commercial materials in industrial, environmental, medical and military

applications, and for environmental protections and safety assessments.

Traditionally, Pourbaix diagrams, Latimer diagrams, Frost diagrams, Ellingham diagrams, potential diagrams,

predominance diagrams, and other types of phase diagrams and property diagrams were often used as some

sort of basic thermodynamic guidance for studies of materials corrosion behaviours under some selected

environments (Pourbaix, 1973, 1974; Cramer and Covino, 2003; Verink, 2011; Thompson et al., 2011; Revie,

2011); however, the usage of such tools were rather limited, due to the facts that thermodynamic models were

inadequate, used data were inconsistent and incomplete, calculation routines were somewhat amateurish,

considered interactions were over-simplified, and system-reality relevancies might be inappropriate.

In order to provide powerful academic and engineering tools for studying thermodynamics of complex corrosion

phenomena, within the Thermo-Calc software/database/programming-interface package which is well-known

worldwide in the field of Computational Thermodynamics, some sophisticated models, critically-assessed and

internally-consistent databases, comprehensive calculation techniques and advanced simulation modules have

been successfully developed over the past 15 years (Sundman and Shi, 1997; Shi, 2013; Shi et al., 2011a,

2011b). With such comprehensive contributions, better understandings of corrosion schemes and corrosion

mechanisms of a wide range of materials, under various corrosive environments (such as aqueous solutions,

non-aqueous solutions, molten salts, high-temperature gases, low-temperature atmospheres, etc.) during

materials application/service processes, can be effectively achieved, even although corrosion kinetics is not

considered in the current approach.

This extensive technical document gives some general descriptions about thermodynamic model, databases

and modules which are currently available within the Thermo-Calc software, and illustrates some specific

application examples of thermodynamic investigations on several types of materials corrosion phenomena in

some industrial and environmental processes.


B. Thermo-Calc Software

The Thermo-Calc software (Sundman et al., 1985; Sundman and Shi, 1997; Andersson et al., 2002; Shi, 2013;

Shi et al., 2005, 2007, 2011a, 2011b; TCSAB, 2013) can precisely calculate various thermodynamic properties,

complicated heterogeneous phase equilibria and multi-component phase/ property diagrams, which are ensured

by many comprehensive thermodynamic models for complex solution/compound phases (in

stable/metastable/amorphous forms, and in solid/liquid/gaseous states) over a wide T-P-X range and by an

extensive spectrum of critically-assessed, internally-consistent and high-quality thermodynamic databases for

many different types of materials (such as various steels/Fe-alloys, Ni-/NiFe-/Co-based superalloys, Ti-/Al-/Mg-

/Zr-based alloys, slag, Au-/Ag-/Cu-/Sn-based solder alloys, metal powders, noble metals, semi-/super-

conductors, fuel-cell materials, ceramics, automotive and aerospace materials, heavy/precision instrument

materials, medical materials, nuclear materials, molten salts, aqueous solution, minerals, organic materials,

polymers, inorganic/organic gases, and so forth).

Thermo-Calc is also served as the thermodynamic calculation engine, not only within the DICTRA software

which can effectively simulate diffusion-controlled phase transformations in multicomponent metallic systems,

but also within the TC-PI application programming interfaces (i.e., TQ, TCAPI, and TC-Toolbox in MATLAB)

which are flexible and easy-to-use for secondary developments of programs and tools for calculating material

properties and simulating material structures. All such software are most renowned worldwide for their powerful

functionality, unique facilities, user-friendliness and wide applications.

Currently, Pourbaix diagrams (Eh-pH), Ellingham diagrams (o

fG -T), potential diagrams (e.g. 2Op -

2SOp ),

Psychrometric charts (dew-point vs air temperature), and other types of phase diagrams and property diagrams

for various types of materials corrosion (such as aqueous corrosion, molten salt corrosion, high-temperature

oxidation/sulfidation, low-temperature atmospheric corrosion, etc.) can be thermodynamically calculated by the

Thermo-Calc software, as illustrated in the following sections. Moreover, the DICTRA software can also be used

for kinetic simulations of e.g. (diffusion-controlled) formations of oxides on alloy surfaces.

B1. Thermodynamic Models and Databases

For various solid solution phases, many different sophisticated thermodynamic models have been applied; for

instance, the General CEF (Compound-Energy Formalism) can have ionic constraints, chemical-/magnetic-

ordering contributions and other physical and mechanic contributions. For various liquid solution phases, one

can choose to use e.g. the General CEF Model, Two-Sublattice Ionic Solution Model, Quasi-Chemical Models,

or Associate Model. The gaseous mixture phase is normally handled by the Ideal EOS (Equation of State) and

Ideal Mixing Model, while other models (such as SUPERFLUID Model) can also be applied. There is a wide

spectrum of general and/or specialized thermodynamic databases available for various phases and systems

which are treated by their most appropriate thermodynamic models. All kinds of details on models and

databases can be found in (Shi, 2013; TCSAB, 2013).

Particularly for aqueous solutions, several models for describing thermodynamic and transport properties over a

wide T-P-X range (including the critical region of water) have been developed and implemented within the

Thermo-Calc software system; namely, they are the DHLL (Debye-Hückel Limiting Law) Term, SIT Model (the

Specific Ion Interaction Theory), HKF Model (the Complete Revised Helgeson-Kirkham-Flowers Model) and

PITZ Model (the Generalized Pitzer Formalism) (Shi, 2013).

Take the HKF Model (which bears the most appropriate and complete thermodynamic descriptions for complex

aqueous solutions) as an example, the following three parts have been implemented into GES (Gibbs Energy

System) of the Thermo-Calc software:

For solvent (H2O): PVT EOS, standard thermodynamic, electrostatic, and transport properties, over a

very wide range of P-T conditions (including within its critical P-T region);


For solute species (cations/anions, and inorganic/organic metal complexes): PVT EOS and standard

thermodynamic properties, over a rather wide range of P-T conditions in aqueous solution;

For aqueous solution: non-ideal mixing properties (DHLL terms, ionic solvation, binary/ternary/...

interactions), over a wide P-T-X conditions.

Being connected with these models, two thermodynamic databases have been created through critical

assessment and data evaluations (against available experimental results, empirical correlations and theoretical

equations), namely the TCAQ2 and AQS2 databases (Shi, 2013).

Different thermodynamic models (and thus their corresponding aqueous solution databases) are capable for

applications in different P-T-X ranges, as illustrated in Figure 1 and Table 1.

Figure 1. Schematic P-T relations for available thermodynamic models for H2O and aqueous solution.

Table 1. Applicable P-T-X ranges of different available thermodynamic models for aqueous solution.

Thermodynamic Model Pressure Temperature Concentration

DHLL (Debye-Hückel Limiting Law) 1 atm 0 -- ~100oC Dilute

PITZ (Generalized Pitzer Formalism) 1 atm 0 -- ~100oC up to saturation

SIT (Specific Ionic Interaction Theory) 1 -- ~200 atm 0 -- ~350oC ~3 Eq. m NaCl

HKF (Complete Revised Helgeson-Kirkham-Flowers Model) 0 – 5 kbar 0 -- 1000oC up to saturation

B2. Calculations of Pourbaix Diagrams and Other Diagrams

When a metal or alloy is exposed to an aqueous solution of a specific inorganic-/organic-mixture concentration

under a given temperature-pressure condition for a defined time-period and over a certain spatial-configuration

(in terms of e.g. surface shape/size, fracture structure/depth, welding-soldering position, flow path/direction,

etc.), corrosion phenomena may occur at a corresponding degree, with some metallic phases being dissolved,

the metal/alloy surface being damaged, and some secondary solid phases (such as oxides, hydroxides,

silicates, sulfides, sulphates, carbonates, nitrates, phosphates, borates, halides, etc.) being formed at the solid-

liquid interfaces. From the thermodynamic point of view, such corrosive chemical/electrochemical reactions (if

reaching their equilibrium states) can be studies by means of the widely-applied Eh-pH, or the so-called

Pourbaix diagrams (Pourbaix, 1973, 1974; Cramer and Covino, 2003; Verink, 2011; Thompson et al., 2011).

PVT EOS: H2O

Pre

ssu

re

Temperature

CP

ICE

BP

TP

( 5 kbar)

(100

oC

)

(217.7 atm)

(0.00607 atm)

(373

.95o

C)

(100

0oC

)

(0.0

1oC

)

(1 atm)

GASEOUS PHASE

HKF

SIT

PITZ

DHLL

COMPRESSIBLE

AQUEOUS PHASE

PVT EOS: Aqueous Solution


Scientists and engineers in the materials

corrosion field are rather familiar with the text

book of “Atlas of Electrochemical Equilibria in

Aqueous Solutions, 2nd

Ed” (Pourbaix, 1974)

and other similar publications, where the

plotted Pourbaix diagrams are often for pure

metals in pure water (or extremely-simple

dilute aqueous solutions) under room

pressure and room temperature. Although

there are many other limitations (as briefly

listed here), Pourbaix diagrams can provide

some basic and useful information about

aqueous corrosion behaviours of various

materials.

With the Thermo-Calc software and associated databases, Pourbaix diagrams and other diagrams can be

efficiently calculated and easily generated, for much more complex heterogeneous interactions between

multicomponent primary alloy solution/compound phases, concentrated aqueous solutions (with dissolved

inorganic and organic substances), complicated secondary solids (oxides, hydroxides, silicates, sulfides,

sulphates, carbonates, nitrates, phosphates, borates, halides, …) and oxidizing/reducing gaseous mixtures,

over a wide range of P-T-X conditions. Beside a concentrated aqueous solution phase handled by the SIT, HKF

or PITZ model, it is also possible to consider extraordinarily-complicated alloy solution/compound phases, as

well as so-called secondary solid phases and gaseous mixtures that are treated by specific solution models.

Empowered by the Gibbs energy minimization technique, the Thermo-Calc software maps out possible stable

(equilibrium) phases of an aqueous-bearing heterogeneous electrochemical interaction system over an

electronic potential vs acidity space, therefore such a Pourbaix diagram shall be read much like a standard

phase diagram with a different set of axes; actually, beyond the Eh (standard hydrogen electronic potential) vs

pH (acidity) plots, other aqueous properties [such as Ah (electronic affinity), pe (electronic activity log10ACRe),

IS (ionic strength), TM (total aqueous concentration, in molality), OC (Osmotic coefficient), activity or activity

coefficient of solvent H2O, activities or activity coefficients or concentrations in m (molality) of charged or neutral

solute species [e.g., Fe+2

, Fe+3

; FeO, FeO+1

, FeO2-1

; Fe(OH)+1

, Fe(OH)+2

, Fe2(OH)2+4

; FeO(OH), FeO(OH)-1

;

FeCl+1

, FeCl2, FeCl+2

, FeCl2+1

, FeCl3, FeCl4-1

; Fe(Formate)+1

, Fe(Formate)2, Fe(Acetate)+1

, Fe(Acetate)2,

Fe(Propanoate)+1

, Fe(Propanoate)2, Fe(Butanoate)+1

, Fe(Butanoate)2, Fe(Pentanoate)+1

, Fe(Pentanoate)2,

Fe(Galycolate)+1

, Fe(Galycolate)2, Fe(Galycinate)+1

, Fe(Galycinate)2, Fe(Lactate)+1

, Fe(Lactate)2, Fe(Alanate)+1

,

Fe(Alanate)2,; …], and so forth, can also be set as axis variables.

A Pourbaix diagram indicates regions of “immunity”, “corrosion” and “passivity” which thus give a guide to the

stability of a particular metal/alloy in a specific aqueous electrochemical environment under a certain pH-Eh and

P-T condition, as illustrated in Fig. 2 as an example: immunity means that the metal/alloy is not attacked,

corrosion shows that general attack will occur and thus the damaged metal/alloy is dissolved into the aqueous

solution, and passivation occurs when the metal/alloy forms a relatively-stable coating of an oxide or another

protective solid on its surface.

Routines for Pourbaix Diagram Calculations: The advanced and easy-to-use POURBAIX Module in the

Console Mode of the Thermo-Calc 3.0 software-version (and its previous Thermo-Calc Classic version e.g.

TCCS) has been developed, for the calculations of Pourbaix diagram and other types of phase diagrams and

property diagrams resulted from complex aqueous-bearing heterogeneous interactions in multicomponent

systems involving metals/alloys, aqueous solutions, gaseous mixture and various secondary solid phases (Shi,

2013; Shi et al., 2007, 2011b). The other way is to go through the ordinary TDB-GES-POLY-POST module-

routine; in the same spirit, this also makes it possible to perform such calculations within the Graphical Mode of

the Thermo-Calc 3.0 software-version.


As shown in Fig. 3, a calculation is always conducted for a multicomponent multi-phase system with 1 kg of

water as the basis, and the other additional settings for equilibrium conditions should be appropriately made, on

the initial amount and composition of the investigated alloy [or alloyed phase(s) of interest], on the initial

concentration of aqueous solution (in terms of dissolved NaCl, for instance), and on the P-T conditions. Most

frequently, a Poubaix diagram is calculated for a specific alloyed phase with the initial alloying composition (e.g.

the FCC solution phase in an austenite steel); however, one can also calculate a Pourbaix diagram for two

coexisting phases (e.g. the FCC+BCC solution phases in a duplex steel) or even for more coexisting phases. In

the decision on appropriately selecting the initial alloyed phase(s), one has to take into account of many details

on how the applied alloy material has been originally produced and processed (in terms of e.g. its matrix phases

and structures, costing/rolling parameters, aging temperature, joining/forging/welding/…, heat-treatment,

surface treatment, and so forth). After a single mapping calculation over a defined “lnACR(H+1) – MUR(ZE)”

space, a Pourbaix diagram and many other associated phase diagrams can be plotted for the same system.

Figure 2. Pourbaix diagram (pH-Eh plot) and “Fe+2

-molality vs pH” graph for the heterogeneous interaction

between 0.001 mole of austenite steel [Fe-19Cr-9Ni (at%)] and 1 kg of water (with 3 m NaCl), at

200oC and 100 bar.

Figure 3. Various routines and important aspects for calculating aqueous-bearing heterogeneous systems.

10-12

10-10

10-8

10-6

10-4

.01

1

Mol

ality

of

FE

+2

0 1 2 3 4 5 6 7 8 9 10

pH

200 C 100 bar 3mNaCl 1.9002E-04mCR 7.2003E-04mFE 9E-05mNI

THERMO-CALC (2013.03.13:11.58) :Property Diagram

1

1:*HALITE

2

2:*NIFE2O4

2

2

2

3

3:*FECR2O4

333

3

4

4:*CR2O3

44

4

5

5:*HEMATITE

5

6

6:*GAS

6

566

1 14

4

4

4

5 5

5

2

2

7

7:*FCC_A1

7

7

7

1 1

1

8 8:*MAGNETITE

86

6

8

68

7

2

856

1

344 621

1

5

5

2013-03-13 12:02:50.63 output by user pingfang from AETHER

10-12

10-10

10-8

10-6

10-4

.01

1

Mol

ality

of

FE

+2

0 1 2 3 4 5 6 7 8 9 10

pH



1

1:*HALITE

2

2:*NIFE2O4

2

2

2

3

3:*FECR2O4

333

3

4

4:*CR2O3

44

4

5

5:*HEMATITE

5

6

6:*GAS

6

566

1 14

4

4

4

5 5

5

2

2

7

7:*FCC_A1

7

7

7

1 1

1

8 8:*MAGNETITE

86

6

8

68

7

2

856

1

344 621

1

5

5


10-12

10-10

10-8

10-6

10-4

.01

1

Mol

ality

of

FE

+2

0 1 2 3 4 5 6 7 8 9 10

pH



1

1:*HALITE

2

2:*NIFE2O4

2

2

2

3

3:*FECR2O4

333

3

4

4:*CR2O3

44

4

5

5:*HEMATITE

5

6

6:*GAS

6

566

1 14

4

4

4

5 5

5

2

2

7

7:*FCC_A1

7

7

7

1 1

1

8 8:*MAGNETITE

86

6

8

68

7

2

856

1

344 621

1

5

5



One important concept used in defining an aqueous-bearing heterogeneous interaction system is the so-called

“Effective Interaction Ratio” between the initial alloy (or alloyed phases) and initial aqueous solution; as the

initial aqueous solution is always based on 1 kg of water, this is why a calculated Pourbaix diagram is usually

presented for an initial amount of the interacting metal (or alloy) at a certain level, e.g., 10-6

, 1E-3, 0.1 or 1 mole

of metal/alloy. The importance of this concept is double-fold:

It has the implications of kinetic/dynamic effects (from e.g. chemical reaction mechanism and kinetics,

fluid flow dynamics, surface area, interaction time, and other factors);

When it is stated as at 10-6

mole of metal (or alloy), it is not a completely-arbitrary choice for a “common

standard”, thanks to that it has been regarded (by the materials corrosion society) as the “detectable”

solubility limit for cathodic corrosion protection by immunity.

For these obvious reasons, one may need to consider on making a series of calculations designed for some

different levels of initial amount of the interacting metal/alloy (whilst the other settings for initial aqueous

concentration, P-T and pH-Eh conditions are fixed).

Data Requirements for Pourbaix Diagram Calculations: For the purpose of calculating a Pourbaix diagram

and/or other diagram for an aqueous-bearing heterogeneous interaction system, there should be sufficient

thermodynamic data available for at least four different types of phases:

1) AQUEOUS solution phase which applies a certain aqueous solution model [retrieved from e.g. TCAQ2 or

AQS2 database; either of them also includes data for the REF_ELECTRODE phase that is used for

properly setting the reference state of the standard hydrogen electrode];

2) ALLOY solution and/or compound phases selected for the primary matrix (and maybe also precipitated)

phases (such as FCC_A1, BCC_A2, HCP_A3, SIGMA, CEMENTITE, etc.) in the considered alloy

[retrieved from e.g. TCFE7 database for steels/Fe-alloys, TCNI6 for Ni-based superalloys, TCAL2 for

Al-based alloys, TCMG2 for Mg-based alloys, TCSLD1 for Au-/Ag-/Cu-/Sn-based solder alloys,

SSOL5 for general alloys, etc.];

3) secondary SOLID phases (such as oxides, hydroxides, silicates, sulfides, sulphates, carbonates, nitrates,

phosphates, borates, halides, and other solids) that would form as stable phases as a result of the

heterogeneous chemical/electrochemical reactions [retrieved from e.g. SSUB5 database for pure solid

compounds, and/or TCOX5 for complex oxide solids];

4) GAS (gaseous mixture) phase [retrieved from e.g. SSUB5 database].

It is important that all the thermodynamic data used for such an aqueous-bearing heterogeneous interaction

system must be critically-assessed and internally-consistent, and that when data are retrieved from several

databases they must also be externally consistent among other each, at a degree as high as possible.

Practically, in order to calculate Pourbaix diagrams and other diagrams of steel corrosion processes, for

instance, it is usually recommended using either the TCAQ2+TCFE7+SSUB5+TCOX5 or AQS2+

TCFE7+SSUB5+TCOX5 database-combination. It is good to remember that the public PAQ2 or PAQS2

database (which contains thermodynamic data for all four types of phases and is thus capable of conducting

Pourbaix diagram alone) is designed solely for demonstrating the functionality of the POURBAIX Module, and

therefore any such testing calculations are only valid for some simple cases where some major phases within a

small chemical framework of a few elements are considered.

Electrochemical Reactions of Water: From a full thermodynamics point of view, the GAS (gaseous mixture)

phase must be considered in calculating a Pourbaix diagram, this is because of that, under a defined P-T

condition, the solvent water has its thermodynamic stability limits that are governed by the electrochemical

reactions H2O + 2e = H2 + 2OH

-1 (forming H2-dominated gaseous mixture, under reducing conditions) and

2H2O = O2 + 4H+1

+ 4e (forming O2-dominated gaseous mixture, under oxidizing conditions). However, one

may also choose to ignore the GAS phase in the calculation (as the aforementioned two major electrochemical

reactions concerning H2O (forming H2- or O2-dominated gases) have rather high kinetic barriers and are slower


than other electrochemical and chemical reactions in the interaction systems), and thus the generated Pourbaix

diagram will not show the H2O-stability limiting lines.

Regarding Predominance Diagrams: The predominant ion boundaries may also be represented by dashed

and straight lines imposed on a traditional Pourbaix diagram for a simple interaction system (Pourbaix, 1973,

1974; Cramer and Covino, 2003; Verink, 2011; Thompson et al., 2011). However, such a predominance

boundary is normally an equal-molality (or equal-activity) line for a pair of two most-concentrated aqueous

solute species (charged or neutral) involving a common metal [for instance, Fe+2

/Fe+3

or Fe+2

/Fe(OH)2+1

or

Fe+3

/Fe(OH)3], which is determined simply by the reaction constant of its corresponding electrochemical

reaction in the homogeneous aqueous solution phase [Fe+2

= Fe+3

+ e , or Fe

+2 + 2H2O = Fe(OH)2

+1 + 2H

+1 +

e , or Fe+3

+ 3H2O = Fe(OH)3 + 3H

+1]; as a result, its position on a plotted Eh-pH diagram really has nothing to

do with any equilibrium state with a minimum total Gibbs energy in the defined interaction system. On the

contrary, as a special type of phase diagram, each point on the lines/curves on an Eh-pH diagram represents a

certain minimum state of Gibbs energy where a phase transformation should occur when crossing the line/curve

from one side to the other. Therefore, in the Gibbs energy minimization approach implemented inside the

Thermo-Calc software, a mapped and plotted Pourbaix diagram does not bear any predominant ion boundary.

Restrictively speaking, the relative importance of different aqueous solute species (especially those major ones)

can only be precisely calculated using the Gibbs energy minimization approach; after a proper mapping or

stepping calculation, one can easily set the equilibrated concentrations (in molality or alike) or activities of a

defined group of charged/neutral solute species as one axis variable in a plotted phase diagram or property

diagram.

Other types of phase diagrams and property diagrams: For an aqueous-bearing heterogeneous interaction

system, Pourbaix diagram [that is mapped over a “lnACR(H+1) – MUR(ZE)” space, and is presented on the

“Eh–pH” plot) represents only one type of important graphs that provide useful thermodynamic information

about an aqueous corrosion process, while there are many other types of phase diagrams and property

diagrams that can be calculated and generated inside the Thermo-Calc software. One may choose other

equilibrium conditions or condition-combinations as the (at least two) independent variables for another

MAPPING calculation, and then generate other types of phase diagrams for the interaction system. However, a

Pourbaix diagram or another type of phase diagram only shows the stability relationships (over a space

constructed by two or more intensive state variables) among various stable phases, whilst it does not tell the

equilibrium amounts (and other extensive properties) of stable phases, as well as some other thermodynamic

properties of various phases and their phase constituents in the system. Compared with the Pourbaix diagram

and other types of phase diagrams, property diagrams (resulted from a STEPPING calculation that uses one of

the controlling condition as the independent variable) are often calculated and generated, for the purposes of

reach a better and clearer understanding of how significant are various formed phases, how much the original

alloy phases are damaged or transformed to other solid phases, what are the concentrations and activities of

various dissolved aqueous solute species, and so forth, under different values of the defined controlling

condition.

C. Applications in Aqueous Corrosion of Stainless Steels

Steels/Fe-alloys are used always everywhere nowadays. All steels/Fe-alloys (even stainless steels) are subject

to aqueous corrosion under a wide range of application circumstances and service conditions. Using the

available databases for steels/Fe-alloys, aqueous solution and various secondary solids and gaseous mixture,

one can effectively conduct calculations of Pourbaix diagrams and many other types of phase diagrams or

property diagrams that are relevant to various industrial, environmental, medical and military environments.

Such calculated diagrams can gain some insights into that how the investigated steels/Fe-alloys would be

preserved or corroded, depending upon the formations of various simple and complex oxides, sulfides (and/or

other secondary solid phases) under different pH-Eh-T-P conditions.


Graphically illustrated in Figs. 4 and 5 are two examples of such calculations/simulations for complex aqueous

corrosion cases (one applied for nuclear power plants, and the other for chemical engineering pipelines),

inflecting their corrosion behaviors under different environments and conditions.

Figure 4. Pourbaix diagram (pH-Eh) for the heterogeneous interaction between 0.001 mole of steel [Fe-

7.676Cr-5.0Ni-2.1887Mn-1.0Cu (at%)] and 1 kg of water (and with 1.2 m H3BO3, 0.022 m Li and

0.001 m NH3), at 25oC and 1 bar. This application is particular useful for safety assessments of

nuclear reactors and nuclear waste repositories.

Figure 5. Property diagrams (stable phase amount and major aqueous speciation, varied along with the Eh

condition) for the heterogeneous interaction system between 0.1 g of stainless steel [Fe-17Cr-

12Ni-2.5Mo (wt%)] and 1 kg of water (and with 0.537 m H2SO4), at 85oC and 1 bar. This

application is particular useful for risk evaluation of chemical engineering pipelines.

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

FU

NC

TIO

N E

H

0 5 10 15

FUNCTION PH

1

1:*MN1O2_S

2:*FE2NI1O4_S

3:*H1MN1O2_S

3

3

3

4

4:*CU2FE2O4_S

5

5:*CR2O3_S

5

4

6:*CU1O1_S

6

1

1

1

1

6

6

4

7:*CR2FE1O4_S

7

2

7

7

2

2

5

8

8:*GAS

5

9:*FCC_A1

9

10:*FE2O3_HEMATITE

14

10

10

11

11:*FE2MN1O4_S

112

2

12:*BCC_A2

12

12

13

13:*H2MN1O2_S

13

10

14:*MAGNETITE

9

15:*B1H1O2_S

15

8

5

14

12

10

5 10

8

15

87

Eh

(V

)

pH

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

FU

NC

TIO

N E

H

0 5 10 15

FUNCTION PH

1

1:*MN1O2_S

2:*FE2NI1O4_S

3:*H1MN1O2_S

3

3

3

4

4:*CU2FE2O4_S

5

5:*CR2O3_S

5

4

6:*CU1O1_S

6

1

1

1

1

6

6

4

7:*CR2FE1O4_S

7

2

7

7

2

2

5

8

8:*GAS

5

9:*FCC_A1

9

10:*FE2O3_HEMATITE

14

10

10

11

11:*FE2MN1O4_S

112

2

12:*BCC_A2

12

12

13

13:*H2MN1O2_S

13

10

14:*MAGNETITE

9

15:*B1H1O2_S

15

8

5

14

12

10

5 10

8

15

87

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

FU

NC

TIO

N E

H

0 5 10 15

FUNCTION PH

1

1:*MN1O2_S

2:*FE2NI1O4_S

3:*H1MN1O2_S

3

3

3

4

4:*CU2FE2O4_S

5

5:*CR2O3_S

5

4

6:*CU1O1_S

6

1

1

1

1

6

6

4

7:*CR2FE1O4_S

7

2

7

7

2

2

5

8

8:*GAS

5

9:*FCC_A1

9

10:*FE2O3_HEMATITE

14

10

10

11

11:*FE2MN1O4_S

112

2

12:*BCC_A2

12

12

13

13:*H2MN1O2_S

13

10

14:*MAGNETITE

9

15:*B1H1O2_S

15

8

5

14

12

10

5 10

8

15

87

Eh

(V

)

pH

Gas(H2 )+BO(OH)

Gas(H2)

Aqs+Hm+Cr2O

3

Aqs+FCC+Mt+Cr2FeO

4+MnO(OH)

Aqs+CuO

Aqs+Hm

Aqs+Cr2O3

Aqs+Cr2FeO4

Gas(H2)+BCC+BO(OH)

Aqs+FCC+Cr2FeO4

Aqs+Hm+Cr2O

3+Fe2NiO

4

Aqs

Aqs+FCC+Cr2O3

Aqs+Hm+Cr2 FeO

4

Aqs+FCC+Hm+Cr2FeO

4+Fe2MnO

4+Fe2NiO

4Aqs+FCC+Mt+Cr2FeO4

Aqs+Mt+Cr2FeO

4

Aqs+Hm+Cr2O3+Cu2Fe2O4 +Fe2NiO4+MnO(OH)

Aqs+Hm+MnO(OH)

Aqs+BCC+Mt+Cr2FeO4

Aqs+Hm+MnO2

Aqs+Hm+Cr2O

3+MnO(OH)+Fe2NiO

4

Aqs+Hm+Cr2O3+Cu2Fe2O4

+Fe2MnO4 +Fe2NiO4

Aqs+Hm+Cr2FeO

4+Fe2MnO

4+Fe2NiO

4

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

Eh

(V

)

0 2 4 6 8 10 12 14

pH

THERMO-CALC (2003.11.26): Pourbaix Diagram Calculation

T=358.15 K, P=1 bar, B(H2O)=1000 g, N(H2SO4)=0.537 m

N(Fe)=1.2266E-3, N(Cr)=3.2695E-4, N(Mo)=2.6058E-5, N(Ni)=2.0446E-4

1:*CR2O3

2:*HEMATITE

3:*MOO2

4:*FECR2O4

5:*MOS2

5

3

2

51

6:*MAGNETITE

6

2

7

7:*PYRITE

4

8:*NIS2

8

8

71

9:*GAS

4

4

9

10:*AQUEOUS

11:*PYRRHOTITE_FE_877S

11

1110

12:*NI3S2

12

7

13:*NIS

1211

1112

13

1

8

8

8

71

9

9

8

3

1

7

6

22

6

5

5

9

1

3

314

14:*MOO2_75

15:*MOO2_8751516

16:*MOO2_889

17:*MOO3

17

17

2

9

91

4

13 9

13

1

4

1

2003-11-26 12:29:31.64 output by user pingfang from PIFF

Steel: Fe- 17.00Cr-12.00Ni-2.5Mo (wt%)Aqueous Solution: 1 kg of water with 0.537 m H2SO4T=85oC, P=1 bar

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

Eh

(V

)

0 2 4 6 8 10 12 14

pH




1:*CR2O3

2:*HEMATITE

3:*MOO2

4:*FECR2O4

5:*MOS2

5

3

2

51

6:*MAGNETITE

6

2

7

7:*PYRITE

4

8:*NIS2

8

8

71

9:*GAS

4

4

9

10:*AQUEOUS


11

1110

12:*NI3S2

12

7

13:*NIS

1211

1112

13

1

8

8

8

71

9

9

8

3

1

7

6

22

6

5

5

9

1

3

314

14:*MOO2_75

15:*MOO2_8751516

16:*MOO2_889

17:*MOO3

17

17

2

9

91

4

13 9

13

1

4

1


Steel: Fe- 17.00Cr-12.00Ni-2.5Mo (wt%)Aqueous Solution: 1 kg of water with 0.537 m H2SO4T=85oC, P=1 bar-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

FU

NC

TIO

N E

H

0 5 10 15

FUNCTION PH

1

1:*MN1O2_S

2:*FE2NI1O4_S

3:*H1MN1O2_S

3

3

3

4

4:*CU2FE2O4_S

5

5:*CR2O3_S

5

4

6:*CU1O1_S

6

1

1

1

1

6

6

4

7:*CR2FE1O4_S

7

2

7

7

2

2

5

8

8:*GAS

5

9:*FCC_A1

9

10:*FE2O3_HEMATITE

14

10

10

11

11:*FE2MN1O4_S

112

2

12:*BCC_A2

12

12

13

13:*H2MN1O2_S

13

10

14:*MAGNETITE

9

15:*B1H1O2_S

15

8

5

14

12

10

5 10

8

15

87

Eh

(V

)

pH

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

FU

NC

TIO

N E

H

0 5 10 15

FUNCTION PH

1

1:*MN1O2_S

2:*FE2NI1O4_S

3:*H1MN1O2_S

3

3

3

4

4:*CU2FE2O4_S

5

5:*CR2O3_S

5

4

6:*CU1O1_S

6

1

1

1

1

6

6

4

7:*CR2FE1O4_S

7

2

7

7

2

2

5

8

8:*GAS

5

9:*FCC_A1

9

10:*FE2O3_HEMATITE

14

10

10

11

11:*FE2MN1O4_S

112

2

12:*BCC_A2

12

12

13

13:*H2MN1O2_S

13

10

14:*MAGNETITE

9

15:*B1H1O2_S

15

8

5

14

12

10

5 10

8

15

87

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

FU

NC

TIO

N E

H

0 5 10 15

FUNCTION PH

1

1:*MN1O2_S

2:*FE2NI1O4_S

3:*H1MN1O2_S

3

3

3

4

4:*CU2FE2O4_S

5

5:*CR2O3_S

5

4

6:*CU1O1_S

6

1

1

1

1

6

6

4

7:*CR2FE1O4_S

7

2

7

7

2

2

5

8

8:*GAS

5

9:*FCC_A1

9

10:*FE2O3_HEMATITE

14

10

10

11

11:*FE2MN1O4_S

112

2

12:*BCC_A2

12

12

13

13:*H2MN1O2_S

13

10

14:*MAGNETITE

9

15:*B1H1O2_S

15

8

5

14

12

10

5 10

8

15

87

Eh

(V

)

pH

Gas(H2 )+BO(OH)

Gas(H2)

Aqs+Hm+Cr2O

3

Aqs+FCC+Mt+Cr2FeO

4+MnO(OH)

Aqs+CuO

Aqs+Hm

Aqs+Cr2O3

Aqs+Cr2FeO4

Gas(H2)+BCC+BO(OH)

Aqs+FCC+Cr2FeO4

Aqs+Hm+Cr2O

3+Fe2NiO

4

Aqs

Aqs+FCC+Cr2O3

Aqs+Hm+Cr2 FeO

4

Aqs+FCC+Hm+Cr2FeO

4+Fe2MnO

4+Fe2NiO

4Aqs+FCC+Mt+Cr2FeO4

Aqs+Mt+Cr2FeO

4

Aqs+Hm+Cr2O3+Cu2Fe2O4 +Fe2NiO4+MnO(OH)

Aqs+Hm+MnO(OH)

Aqs+BCC+Mt+Cr2FeO4

Aqs+Hm+MnO2

Aqs+Hm+Cr2O

3+MnO(OH)+Fe2NiO

4

Aqs+Hm+Cr2O3+Cu2Fe2O4

+Fe2MnO4 +Fe2NiO4

Aqs+Hm+Cr2FeO

4+Fe2MnO

4+Fe2NiO

4

-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

Eh

(V

)

0 2 4 6 8 10 12 14

pH




1:*CR2O3

2:*HEMATITE

3:*MOO2

4:*FECR2O4

5:*MOS2

5

3

2

51

6:*MAGNETITE

6

2

7

7:*PYRITE

4

8:*NIS2

8

8

71

9:*GAS

4

4

9

10:*AQUEOUS


11

1110

12:*NI3S2

12

7

13:*NIS

1211

1112

13

1

8

8

8

71

9

9

8

3

1

7

6

22

6

5

5

9

1

3

314

14:*MOO2_75

15:*MOO2_8751516

16:*MOO2_889

17:*MOO3

17

17

2

9

91

4

13 9

13

1

4

1



-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

Eh

(V

)

0 2 4 6 8 10 12 14

pH




1:*CR2O3

2:*HEMATITE

3:*MOO2

4:*FECR2O4

5:*MOS2

5

3

2

51

6:*MAGNETITE

6

2

7

7:*PYRITE

4

8:*NIS2

8

8

71

9:*GAS

4

4

9

10:*AQUEOUS


11

1110

12:*NI3S2

12

7

13:*NIS

1211

1112

13

1

8

8

8

71

9

9

8

3

1

7

6

22

6

5

5

9

1

3

314

14:*MOO2_75

15:*MOO2_8751516

16:*MOO2_889

17:*MOO3

17

17

2

9

91

4

13 9

13

1

4

1



.001

.01

.1

1

10

100

1000

10000

Sta

ble

Ph

ases /

gra

ms

-1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0

Eh (V)

THERMO-CALC (2003.11.26): Property Diagram Calculation



Gaseous Mixture

Aqueous Solution

MoO2

MoO2.75

Ga

se

ou

s M

ixtu

re

MoO2.889

Cr2O3

MoS2

NiS2

Pyrite

Ma

gn

eti

te

Fe

Cr2

O4

Au

ste

nit

e

(O2

-do

min

an

t)(H2O-dominant)

Ga

se

ou

s M

ixtu

re(H

2-d

om

ina

nt)


Steel: 0.1 g [Fe-17.00Cr-12.00Ni-2.5Mo (wt%)]Aqueous Solution: 1 kg of water with 0.537 m H2SO4T=85oC, P=1 bar

Aqueous Solution

.001

.01

.1

1

10

100

1000

10000

Sta

ble

Ph

ases /

gra

ms

-1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0

Eh (V)




Gaseous Mixture

Aqueous Solution

MoO2

MoO2.75

Ga

se

ou

s M

ixtu

re

MoO2.889

Cr2O3

MoS2

NiS2

Pyrite

Ma

gn

eti

te

Fe

Cr2

O4

Au

ste

nit

e

(O2

-do

min

an

t)(H2O-dominant)

Ga

se

ou

s M

ixtu

re(H

2-d

om

ina

nt)


Steel: 0.1 g [Fe-17.00Cr-12.00Ni-2.5Mo (wt%)]Aqueous Solution: 1 kg of water with 0.537 m H2SO4T=85oC, P=1 bar

Aqueous Solution


D. Applications in Aqueous Corrosion of Carbon Steels in Seawater

Carbon steels are applied widely in various industries; as high tensile carbon steels AISI-4140 and AISI-4340

offer a good balance of strength, toughness and shock/wear-resistance, excellent impact properties, good

machinability and reasonable weldability, they are suitable for a variety of applications in petroleum and

petrochemical sectors, chemical engineering, power plants, boilers and other industries for the production of

reactors, heat exchangers, separators, tank, gas cans, liquid gas storage tank, nuclear reactor pressure vessel,

boiler drum, liquefied petroleum gas cylinders, high-pressure water station, scroll wheel and other equipment

and components.

During employments for services in petroleum industry, they are often exposed to seawaters and other

corrosive aquatic systems. As experienced and commented by researchers at Petrobras, through an extensive

thermodynamic investigation on Pourbaix diagrams and other types of phase diagrams and property diagrams

for the complex heterogeneous interaction systems between the AISI-4140 or AISI-4340 and seawaters under

various P-T conditions, petroleum industries would benefit significantly. Figs. 6 and 7 give two examples of

calculated Pourbaix diagrams for such application cases.

Figure 6. Pourbaix diagrams for the heterogeneous interaction systems between 0.1 mole of AISI4340

stainless steel [Fe-0.80Cr-1.85Ni-0.70Mn-0.25Mo-0.25Si-0.40C wt%] and 1 kg of sea-water

(with equivalent 0.6054 m NaCl), at 25oC and 1 bar. This application is particular useful for

failure analysis of petroleum exploitation industry.


Figure 7. Pourbaix diagrams for the heterogeneous interaction systems between 0.1 mole of AISI4340

stainless steel [Fe-0.80Cr-1.85Ni-0.70Mn-0.25Mo-0.25Si-0.40C wt%] and 1 kg of sea-water

(with equivalent 0.6054 m NaCl), at 25oC and 1 bar; note that in this particular calculation the

gaseous mixture is not considered, i.e. ignoring the two major electrochemical reactions

concerning H2O (forming H2- or O2-dominated gases). This application is particular useful for

failure analysis of petroleum exploitation industry.

E. Applications in Aqueous Corrosion of HPCRM Alloys in Groundwater

Of particular importance to environmental safety assessments of the nuclear-waste repository in nature, the

corrosion resistances of amorphous iron coatings offer substantial performance and cost saving as compared

with other high-performance corrosion-resistant materials (e.g., C-22 superalloy, and amorphous steels SAM40,

SAM7 & SAM2X5). In the course of experimental observations and calculations of corrosion behaviours of

SAM40, SAM7, SAM2X5, C-22 and other HPCRM alloys, within the US-DOE Yucca Mountain Project for

Nuclear Waste Repository, Kaufman and co-workers (Kaufman, 2002, 2009; Kaufman et al., 2009) performed

many series of thermodynamic calculations on Pourbaix diagrams and other phase diagrams and property

diagrams for the complex heterogeneous interaction processes between such alloys and different types of

natural groundwater and simulated waters, and made some comprehensive investigations by extensively

comparing experimentally-measured corrosion data with the calculated results.

Demonstrated in Fig. 8 is the corrosion studies of the SAM40 steel [which is an amorphous Fe-19Cr-2.5Mo-

1.7W-16B-4C (at%) alloy] that is exposed to a specific seawater at 90oC, and the calculation results fairly agree

with experimental observations. Fig. 9 presents the corrosion case of the C-22 superalloy [58.1Ni-21.3Cr-

13.6Mo-4.0Fe-3.0W wt%] in two different specific groundwater (BSW and BAW) under two different

temperatures (30 and 90oC) and 1 bar.


Figure 8. Thermodynamic calculations and experimental measurements conducted for aqueous corrosion

processes of SAM40 steel under various conditions (Kaufman, 2009; Kaufman et al., 2009).

8a) Pourbaix diagram (pH-Eh) for the heterogeneous interaction between 0.001 mole of SAM40 alloy and 1 kg of

seawater (with 0.68 Eq. m NaCl), at 90oC and 1 bar.

8b) Property diagram (stable phase amount versus varied Eh condition) for the heterogeneous interaction system

between 0.001 mole of SAM40 alloy and 1 kg of seawater (with 0.68 Eq. m NaCl), under a constant

pH=6.4, at 90oC and 1 bar. Note that converted voltages related to the Ag/AgCl reference electrode are

also displayed.

8c) Cyclic polarization measurements (using the Ag/AgCl reference electrode) at 90oC for an amorphous melt

spun ribbon (MSR) sample of SAM40 alloy that had been annealed at 600oC for 5 min. The pre-test

measured pH was 7.4, while post-test value was 6.4. The specific features of measured voltages are to be

compared with the calculated values shown in Fig. 8b.


Figure 9. Pourbaix diagrams for 1 gram of C-22 superalloy (58.1Ni-21.3Cr-13.6Mo-4.0Fe-3.0W wt%) in two

different specific groundwater under two different temperatures and 1 bar (Kaufman, 2002):

9a) In Basic Simulated Groundwater (BSW) at 30oC. The BSW contains 1 kg of H2O, 141.7 gram of NO3

-1, 186.6

gram of Na+1

, 166.0 gram of Cl-1

and 70.1 gram of K+1

. The following components of BSW were not

included in calculations: 6.1 gram of SiO2, 1.51 gram of F-1

, 64.2 gram of CO3-2

and 15.8 gram of SO4-2

.

The entire stable Aqueous Solution Range also contains N2-rich GAS except for the small sliver near the

O2 GAS boundary that contains solid KNO3.

9b) In Basic Acidic Groundwater (BAW) at 90oC. The BAW contains 1 kg of H2O, 23.0 gram of NO3

-1, 137.6 gram

of Na+1

, 24.25 gram of Cl-1

and 38.6 gram of SO4-2

. The following components of SAW were not included in

calculations: 1.0 gram of Ca+2

, 3.4 gram of K+1

, 0.058 gram of SiO2, and 1.0 gram of Mg+2

. The entire

space is covered by an aqueous solution and a GAS phase whose composition varies except for the

regions noted with asterisks(*) in which there is no GAS phase.

F. Applications in High-Temperature Gaseous Corrosion

During materials applications in various service environments and during materials processing (e.g., heat

treatments, surface engineering), complex interactions between material surfaces and surrounding

inorganic/organic gases may play significant roles, resulting in certain degrees of gaseous corrosions

(especially at high-temperature conditions), can be investigated through the uses of Thermo-Calc software and

available databases. Such thermodynamic calculations can effectively provide different types of phase diagrams

and property diagrams for heterogeneous interaction processes involving certain alloy solution/compound

phases, gaseous mixtures and various formed solid/liquid phases. For instance, Ellingham diagrams (o

fG -T),

potential diagrams (e.g. 2Op -

2SOp ), and many more types of diagrams (as presented below), can be easily

calculated and generated for high-temperature gaseous corrosion processes, and Psychrometric charts (dew-

point vs air temperature) can be plotted for studying low-temperature atmospheric corrosion.

High-temperature gaseous corrosion processes normally involve many different types of redox reactions:

oxidation (formation of oxides) and reductions (formations of sulphides, or sulfidations). Thermodynamic phase

relations and equilibrium properties in such interaction systems often depend upon chemical potential of O2

component (2Ou ) [in other words, oxygen activity

2Oa , oxygen fugacity 2Of or oxygen partial-pressure

2Op ]

and sometimes chemical potential or composition of another component (e.g., H2, CH4, CO, CO2, S2, H2S, SO2)

or a certain ratio of properties for two components (e.g., CO2/CO, H2/CO2, H2S/SO2), beside the P-T conditions.


As an example, Fig. 10 plots the calculated property diagrams of the heterogeneous interaction between 100 g

of Incoloy 801 steel (wrought Fe-based superalloy with a composition of 44.5Fe-32Ni-20.5Cr-1.1Ti-0.8Mn-0.5Si-

0.05C wt%) and a gaseous mixture (of 1 g H2O, 0.001 mole HCl, 0.0001 mole HF and 0.001 mole H2SO4). The

gaseous mixture will dissolve the steel components (especially with increasing temperatures); meanwhile

LIQUID or SLAG+Ti2O3 phases may form during the interaction over certain temperature ranges.

Figure 10. Property diagrams of the heterogeneous interaction between 100 g of Incoloy 801 steel and

a gaseous mixture (of 1 g H2O, 0.001 mole HCl, 0.0001 mole HF and 0.001 mole H2SO4).

Figure 11. Graphite stability in certain H2-N2-Ar-CH4-O2 gaseous mixtures. The initial compositional rates of

hydrogen, methane and oxygen in the gaseous mixtures determine the graphite-gas boundary.

Graphite-bearing furnace and refractory are widely used in heat treatments, steel-making and metallurgical

processes, and many other industrial and engineering systems; the stability of graphite in various atmospheres

and temperature-pressure settings is an extremely important subject in many scientific and technological fields.

One example is given in Fig. 11 as the calculated graphite-gas phase boundary in a specific gaseous mixture of

H2-N2-Ar-CH4-O2. Such graphs (and many other related property diagrams from the same calculations) can tell

10-4

.001

.01

.1

1

10

100

1000

Sta

ble

Ph

ases (

Weig

ht_

Perc

en

t)

500 1000 1500 2000 2500

Temperature_Celsius

THERMO-CALC (2005.09.26:17.10) :

DATABASE: TCMP2

GAS

1:T-273.15,BP(GAS)

2:T-273.15,BP(LIQUID)

3:T-273.15,BP(BCC_A2)

LIQUID

BCC 4:T-273.15,BP(FCC_A1#1)

5:T-273.15,BP(SLAG)FCC 6:T-273.15,BP(TI2O3)

SLAG

Ti2O3

M23C6

7:T-273.15,BP(M23C6)

Cr5Si3

8:T-273.15,BP(CR5SI3)

9:T-273.15,BP(CR3SI)Cr3Si

BCC

MnCl2

10:T-273.15,BP(MNCL2)

TiF3

100 g of Incoloy801 Steel in interaction with a gaseous mixture

(initial gas:1g H2O, 0.001m HCl, 0.0001HF and 0.001m H2SO4)


10-4

.001

.01

.1

1

10

100

1000

Sta

ble

Ph

ases (

Weig

ht_

Perc

en

t)

500 1000 1500 2000 2500

Temperature_Celsius

THERMO-CALC (2005.09.26:17.10) :

DATABASE: TCMP2

GAS

1:T-273.15,BP(GAS)

2:T-273.15,BP(LIQUID)

3:T-273.15,BP(BCC_A2)

LIQUID

BCC 4:T-273.15,BP(FCC_A1#1)

5:T-273.15,BP(SLAG)FCC 6:T-273.15,BP(TI2O3)

SLAG

Ti2O3

M23C6

7:T-273.15,BP(M23C6)

Cr5Si3

8:T-273.15,BP(CR5SI3)

9:T-273.15,BP(CR3SI)Cr3Si

BCC

MnCl2

10:T-273.15,BP(MNCL2)

TiF3


(initial gas:1g H2O, 0.001m HCl, 0.0001HF and 0.001m H2SO4)


10-12

10-10

10-8

10-6

10-4

.01

1

100

Ma

ss

of

co

mp

on

en

ts in

GA

S p

ha

se

(g

ram

)

500 1000 1500 2000 2500

Temperature_Celsius

THERMO-CALC (2005.09.26:17.28) :

DATABASE: TCMP2

1:T-273.15,B(GAS,C)

2:T-273.15,B(GAS,CL)

3:T-273.15,B(GAS,CR)

4:T-273.15,B(GAS,F)

5:T-273.15,B(GAS,FE)

6:T-273.15,B(GAS,H)

7:T-273.15,B(GAS,MN)

8:T-273.15,B(GAS,NI)

9:T-273.15,B(GAS,O)

10:T-273.15,B(GAS,S)

11:T-273.15,B(GAS,SI)

12:T-273.15,B(GAS,TI)

Cl

Mn

S

C

Ti

F

Ni

O

S

Cl

H

Cr

Si

Fe

GAS


(initial gas:1g H2O, 0.001m HCl, 0.0001m HF and 0.001m H2SO4)


0

200

400

600

800

1000

1200

1400

T

em

pera

ture

(C

)

.1 1 10 100

Initial H2 Amount (Mole_Percent)

THERMO-CALC (2009.02.23:12.14) :

Graphite-Gas phase boundary: in H2-N2-Ar-CH4-O2 gaseous mixture

Graphite Stable with respect to gaseous mixture

[fixed conditions: x(Ar)=50 mole%, n(O2)=1 ppm ]

x(CH4) = 0

x(CH4) =

0.001 mole%

0.01

0.1

x(CH4) = 1 m

ole%

Graphite Unstable with

respect to

gaseous mixture

(Graphite decomposition is negligible)

(Graphite will b

e decomposited, and then

establish equilibriu

m with gaseous mixture)

2009-02-23 12:33:56.87 output by user pingfang from BLYGER


that in some T-P-X conditions graphite in furnace/refractory may be corroded by atmospheres and that in other

conditions active-carbon may be formed in reaction chambers. Based on this type of calculation, one can find

the optimal gaseous mixture settings and operation conditions.

Figure 12. Stable phases and element distribution of remaining austenite during the surface oxidation of the

Fe-16Cr-0.3Mn-0.3Si-0.01V-1C (wt%) steel at 800oC, as a function of oxygen activity in the

atmosphere.

Figure 13. Emergence conditions with respect to the Fe3O4 and Cr2O3 oxides during oxidation of the H13

Hot Work Steel [Fe-5.14Cr-0.41Mn-1.02Si-0.40C-0.93V-1.46Mo-0.001S-0.009P (wt%)], at

different temperatures (between 400 and 800oC) and 1 bar.

Investigations of redox reactions and oxidation sequences are essential not only for empowering fundamental

guidance on effective formations of protective oxide layers on steels and alloys, but also for providing useful

information about potential corrosion scenarios in materials applications and engineering. During the surface

treatment of a steel or alloy under specific oxygen fugacity conditions, various oxides (simple or multiple) may

form or disappear. Fig. 12 illustrates the calculated results of complex oxidation sequences for an Fe-16Cr-

0.3Mn-0.3Si-0.01V-1C (wt%) steel, under 800℃ and varied oxygen activity, as well as the element distributions

in the remaining austenite phase.

10-4

.001

.01

.1

1

Mass F

racti

on

of

Sta

ble

Ph

ases

10-28

10-27

10-26

10-25

10-24

10-23

10-22

10-21

10-20

10-19

10-18

Oxygen Activity in Gaseous Mixture

THERMO-CALC (2008.05.22:17.49) :

DATABASE: TCFE6

P=100000, T=1073, B=100, B(Cr)=16., B(V)=1E-1, B(C)=1., B(Mn)=3E-1, B(Si)=3E-1

1:ACR(O2,GAS),BPW(BETA_QUARTZ)

2:ACR(O2,GAS),BPW(CR2O3_S)

3:ACR(O2,GAS),BPW(FCC_A1#1)

4:ACR(O2,GAS),BPW(M7C3)

5:ACR(O2,GAS),BPW(TEPHROITE)

6

6:ACR(O2,GAS),BPW(FCC_A1#2)

47

7:ACR(O2,GAS),BPW(CEMENTITE)

6

2

5

2

8:ACR(O2,GAS),BPW(C_S)

6

3

8

1

9:ACR(O2,GAS),BPW(O3V2_S)

10:ACR(O2,GAS),BPW(CR2FE1O4_S)

8

9

10

5

3

1

11

11:ACR(O2,GAS),BPW(FE1O4V2_S)

12 12:ACR(O2,GAS),BPW(GAS)13

13:ACR(O2,GAS),BPW(FAYALITE)

12

10

13

14

14:ACR(O2,GAS),BPW(FE1O1_S)

11

51 15:ACR(O2,GAS),BPW(BCC_A2)

51

2

5

15

4

9

Formation of Oxide Layer on Steel Surface


10-12

10-10

10-8

10-6

10-4

.01

1

M

ass F

racti

on

of

Ele

men

ts i

n A

uste

nit

e

10-28

10-27

10-26

10-25

10-24

10-23

10-22

10-21

10-20

10-19

10-18

Oxygen Activity in Gaseous Mixture

THERMO-CALC (2008.05.23:10.36) : Formation of Oxide Layer on Steel Surface

DATABASE:TCFE5

C

Cr

Si

V

Mn

Fe


0

20

40

60

80

100

120

140

M

ag

neti

te (

g);

fo

rmed

fro

m 1

00g

H13 s

teel

su

rface

10-32

10-28

10-24

10-20

10-16

10-12

10-8

10-4

1

Oxygen Partial Pressure [p(O2) in Pa]

THERMO-CALC (2008.05.22:14.41) :

600

650

700

750

800

Databases: SSOL4+SSUB4400 4

50

500

550

600 6

50

700

750

800

400

450

500

550

H13 Hot Work Steels: Emergence Condition with respect to Magnetite Phase


H13 Hot Work Steel:

Emergence condition with respect to Fe3O4 phase

0

20

40

60

80

100

120

140

M

ag

neti

te (

g);

fo

rmed

fro

m 1

00g

H13 s

teel

su

rface

10-32

10-28

10-24

10-20

10-16

10-12

10-8

10-4

1


THERMO-CALC (2008.05.22:14.41) :

600

650

700

750

800

Databases: SSOL4+SSUB4400 4

50

500

550

600 6

50

700

750

800

400

450

500

550

H13 Hot Work Steels: Emergence Condition with respect to Magnetite Phase


H13 Hot Work Steel:

Emergence condition with respect to Fe3O4 phase

0

1

2

3

4

5

6

7

8

9

10

C

r2O

3 (

g);

fo

rmed

fro

m 1

00g

H13 s

teel

su

rface

10-36

10-32

10-28

10-24

10-20

10-16

10-12

10-8

10-4

1


THERMO-CALC (2008.05.22:10.52) :

400

450

500

550

600

650

700

750

800

H13 Hot Work Steels: Emergence Condition with respect to Cr2O3 Phase

800

750

700

650

600

550

500

450

Databases: SSOL4+SSUB4


H13 Hot Work Steel:

Emergence condition with respect to Cr2O3 phase

0

1

2

3

4

5

6

7

8

9

10

C

r2O

3 (

g);

fo

rmed

fro

m 1

00g

H13 s

teel

su

rface

10-36

10-32

10-28

10-24

10-20

10-16

10-12

10-8

10-4

1


THERMO-CALC (2008.05.22:10.52) :

400

450

500

550

600

650

700

750

800

H13 Hot Work Steels: Emergence Condition with respect to Cr2O3 Phase

800

750

700

650

600

550

500

450

Databases: SSOL4+SSUB4


H13 Hot Work Steel:

Emergence condition with respect to Cr2O3 phase


When a steel or alloy is used in a certain environment, its alloying elements may be extracted from material

surface by some corrosive chemical agents (such as O2, H2, H2S, SO2, H2SO4, CO2, HCl, NaCl, among others)

in the surroundings. It is good to know what the so-called Emergence Conditions are for formations of some

specific oxides/silicates/carbonates/ sulphates/phosphates/borates/…, which are critical for judging the safe

performance or damage occurrence. A calculated Emergence Condition diagram (normally plotted as stable

oxide phase amount vs O2 partial pressure, under several different service temperature conditions and a fixed

total pressure) provides corrosion-tendency information similar as an Ellingham diagram, but gives more details

on the redox states. As an example, Fig. 13 shows the emergence conditions with respect to the Fe3O4 and

Cr2O3 phases, during the oxidation processes of H13 Hot Work Steel [Fe-5.14Cr-0.41Mn-1.46Mo-1.02Si-0.93V-

0.40C-0.001S-0.009P (wt%)] under several different temperatures (between 400 and 800oC) and 1 bar (Min et

al., 2006). Note that many more similar plots can also be generated (from the same ) as the emergence

conditions for formations of other concerned oxides/silicates/carbonates/…, e.g.,FeO, Fe2O3, FeCr2O4, V2O3,

VO2, FeV2O4, FeV2O6, SiO2, FeSiO4, MnSiO4, FeCO3 and MnCO3 in this defined system.

Often, potential diagrams (e.g., 2Op -

2SOp ) and other types of diagrams with one or two axis variables set as

controlling redox conditions (e.g., 2Op ,

2Of , 2Sa ,

2COu , 2COp / COp ,

2Hp /2COp ) are calculated and plotted for

investigating heat-treatment and gaseous corrosion processes. Fig. 14 shows the calculation results on various

oxide scale formations (halite, spinel and corundum) in an austenitic Fe-Mn-Cr stainless steel [Fe-17.8Mn-

9.5Cr-1.0Ni-0.27C in wt%], which is widely applied in fusion reactors, under various oxygen partial-pressures

during a heat treatment at constant 900oC: a Fe-Mn rich spinel phase is formed below the outer scale (that is

stabilized as corundum phase), and a layer with halite phase and a Cr-Mn rich spinel phase are formed next to

the substrate; these results are verified with available experimental information of Douglas et al. (1986).

Figure 14. Thermo-Calc calculation of oxide scale formations in a Fe-17.8Mn-9.5Cr-1.0Ni-0.27C (wt%)

steel under various oxygen partial pressures and a constant 900oC, verified with available

experimental data of Douglas et al. (1986).


Figure 15. DICTRA kinetic simulation of oxide layer formations (wüstite, magnetite and hematite) on pure

iron surface at 600oC, compared with available experimental data (Hallström et al., 2011).

The DICTRA software and kinetic/mobility databases, coupled with the Thermo-Calc software and

thermodynamic databases, can also be applied to perform kinetic simulations of certain types of material

corrosion processes. Fig. 15 illustrates the simulation results on formations of various oxide layers (wüstite,

magnetite and hematite) on steel surface (as a simplified calculation, pure Fe was considered in this case) after

24 hours of surface-oxidation treatments under the conditions of 600oC and dry oxygen atmosphere, that

compare fairly-well with available experimental data of Hallström et al. (2011).

Pure Fe, 600oC, dry O2, 24h; Total oxide thickness is 34 μm.

(the hematite, magnetite and wustite layers as 2, 11 and 21 μm, respectively)

10 μmFe

Hematite

Magnetite

Wüstite

Magnetite HematiteWustite

Calculated: 45 µm 10 µm 2 µm

Experimental: 21 µm 11 µm 2 µm



10 μmFe

Hematite

Magnetite

Wüstite



10 μmFe

Hematite

Magnetite

Wüstite

Magnetite HematiteWustite

Calculated: 45 µm 10 µm 2 µm

Experimental: 21 µm 11 µm 2 µm


G. Applications in Molten-Salt Corrosion

Molten salt corrosions of alloys often cause destructions of coating layers (by decomposing or transforming

corrosion-protection and thermal-barrier layers) and even alloy matrixes.

A coated Cr2O3 layer is the typical protective layer on the surfaces of stainless steels, Ni-based superalloys or

other alloys, under normal circumstances. However, such a layer, if exposed to molten salts at elevated

temperature conditions under some specific salty environments (such as marine, salt lake, and salty rock bed

environments), may be damaged by aggressive molten salty agents, resulting in that the alloy materials may be

exposed to further corrosion attacks by other oxidizing or reducing substances in their application life-cycles.

Thermodynamic calculations can effectively help predicting dissolution of a Cr2O3 layer caused by molten salt

corrosion. The amount of stable phases (Fig. 16a) and Cr partitions in various stable phases (Fig. 16b) as a

function of temperature are shown. The calculation was done for the heterogeneous equilibrium state in a

multicomponent Cr-C-H-O-S-N-Na-Cl system which originally consists of 0.05 mole of Cr2O3 solid, a salt mixture

(0.01 mole of NaCl, 0.46247 mole of Na2SO4 and 0.03253 mole of Na2CO3) and 431.16 g of C-H-O-N gaseous

mixture (note that all such settings are actual data on chemical compositions of the interacting NaCl-Na2SO4-

Na2CO3) salt mixture and C-H-O-N gas mixture inside a specific gas turbine severing in an chemical

engineering process). The calculation results show that at an operation temperature of 750oC, the Cr2O3 layer

dissolves (with a remaining amount of 0.031756 mole), forming a crystalline Na2CrO4-Na2SO4 solid solution

(Hexagonal) and a liquid mixture (Ionic_Liquid) that are stable with an equilibrated gaseous mixture. As

temperature increases, the molten salt corrosion becomes more serious; and when 1200oC is reached, the

entire Cr2O3 layer on the alloy surface may be completely destroyed if exposed for a long period under such a

corrosive environment.

Figure 16. Stable phases remaining/formed (16a) and Cr-partition in various phases (16b) as a function of

operation temperature condition, during the molten salt corrosion of the Cr2O3 layer (on surfaces of stainless steels,

superalloys or other alloys) when it is attacked by a NaCl-Na2SO4-Na2CO3 salt mixture and a C-H-O-N gaseous

mixture, simultaneously.


H. References

Andersson J-O, Helander T, Höglund L, Shi Pingfang, and Sundman B (2002): Thermo-Calc and DICTRA, Computational

tools for materials science. Calphad, 26: 273-312.

Ciavatta L (1990): The specific interaction theory in equilibrium analysis. Some empirical rules for estimating interaction

coefficients of metal ion complexes. Ann Chim. (Rome), 80: 255-263.

Cramer SD and Covino BS Jr. (2003): Corrosion: Fundamentals, Testing, and Protection. ASM Handbook, Volume 13A.

Douglas DL, Gesmundo F, and De Asmundis C (1986): The Air Oxidation of an austenitic Fe-Mn-Cr stainless steel for

fusion-reactor applications. Oxidation of Metals, 25: 235-268.

Hallström S, Höglund L, and Ågren J (2011): Modeling of iron diffusion in the iron oxides magnetite and hematite with

variable stoichiometry. Acta Materialia, 59: 53-60.

Helgeson HC, Kirkham DH, and Flowers GC (1981): Theoretical prediction of the thermodynamic behavior of aqueous

electrolytes at high pressures and temperatures: IV. Calculation of activity coefficients, osmotic coefficients, and

apparent molal and standard and relative partial molal properties to 600oC and 5 kb. Am. J. Sci., 281: 1249- 1516.

Johnson JM and Norton D (1991): Critical phenomena in hydrothermal system: State, thermodynamic, electrostatic, and

transport properties of H2O in the critical region. Am. J. Sci., 291: 541-648.

Kaufman L (2002) Calculation of Pourbaix diagrams for C22 in various well water chemistries. In: Proceedings for the 5th

Nickel Development Institute Workshop on Fabrication of Welding of Nickel Alloys (R. Moeller, ed.), Nickel Development

Institute, Las Vegas, Nevada, 16-17 Oct., 2002.

Kaufman L (2009): Computation materials design. J. Phase Equilibria and Diffusion, 30: 418-428.

Kaufman L, Perepezko JH, Hildal K, Farmer J, Day D, Yang N, and Branagan D (2009): Transformation, stability and

Pourbaix diagrams of high performance corrosion resistant (HPCRM) alloys. Calphad, 33: 89-99.

Min YA, Wu XC, Wang R, Li L, Xu LP (2006): Prediction and analysis of the oxidation on H13 hot work steel. J. Iron & Steel

Res. Intl., 13: 44-49.

Pourbaix M (1973): Lectures on Electrochemical Corrosion. Plenum Press, New York.

Pourbaix M (1974): Atlas of Electrochemical Equilibria in Aqueous Solutions, 2nd

Ed, Houston, Tex., National Association of

Corrosion Engineers.

Revie RW (2011, Ed.): Uhlig’s Corrosion Handbook, 3rd

Edition. The Electrochemical Society and John Wiley & Sons, New

Jersey.

Shi Pingfang (2013): Thermo-Calc 3.0 (Console Mode) Manual (including TC3-CM User’s Guide, TC3-CM Examples Book,

Thermo-Calc Software System, and Thermo-Calc Database Manager’s Guide), Thermo-Calc Software, Stockholm,

Sweden.

Shi Pingfang, Engström A, Höglund L, Sundman B, and Ågren J (2005): Thermo-Calc and DICTRA enhance materials

design and processing. Materials Science Forum, 475-479: 3339-3346.

Shi Pingfang, Engström A, Höglund L, Chen Q, Sundman B, Ågren J, and Hillert M (2007): Computational thermodynamics

and kinetics in materials modelling and simulations. J. Iron & Steel Res. Intl., 14: 210-215.

Shi Pingfang, Engström A, Sundman B, and Ågren J (2011a): Thermodynamic calculations and kinetic simulations of some

advanced materials. Materials Science Forum, 675-677: 961-974.

Shi Pingfang, Engström A, and Sundman B (2011b): Thermodynamic investigations on materials corrosion in some

industrial and environmental processes. Journal of Environmental Sciences, 23 (Supplement): S1-S7.

Shock EL, Oelkers EH, Johnson JW, Sverjensky DA, and Helgeson HC (1992: Calculation of the thermodynamic properties

of aqueous species at high pressures and temperatures. Effective electrostatic radii, dissociation constants and standard

partial molal properties to 1000oC and 5 kbar. J. Chem. Soc. Faraday Trans., 88(6): 803-826.

Sundman B, Jansson B, and Andersson J-O (1985): The Thermo-Calc databank system. Calphad, 9: 153-199.

Sundman B and Shi Pingfang (1997): Applications of Thermo-Calc in high-temperature materials chemistry. Electrochemical

Society Proceedings, 97-39: 52-59.

TCSAB (Thermo-Calc Software AB, 2013): Thermo-Calc, DICTRA and TC-PRISMA: software, databases, programming-

interfaces and applications. Stockholm, Sweden. http://www.thermocalc.com.

Thompson WT, Kaye MH, Bale CW, and Pelton AD (2011): Pourbaix diagrams for multielement systems. In: Uhlig's

Corrosion Handbook, 3rd

Edition (Revie RW, Ed.), The Electrochemical Society and Jon Wiley & Sons, New Jersey.

Verink ED, 2011. Simplified procedure for constructing Pourbaix diagrams. In: Uhlig's Corrosion Handbook, 3rd

Edition

(Revie RW, Ed.), The Electrochemical Society and Jon Wiley & Sons, New Jersey.

http://www.thermocalc.com/


Thermo-Calc Software is capable for effectively performing many different types of advanced thermodynamic calculations on materials corrosion.

Thermo-Calc Software AB USA, Canada and Mexico Norra Stationsgatan 93 4160 Washington Road SE-113 64 Stockholm McMurry, PA 15317 SWEDEN USA E-mail: [email protected] E-mail: [email protected] Phone: +46-8-545 959 30 Phone: (724) 731 0074 Fax: +46-8-673 37 15 Fax: (724) 731 0078

.001

.01

.1

1

10

100

1000

10000

Sta

ble

Ph

ases /

gra

ms

-1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0

Eh (V)




Gaseous Mixture

Aqueous Solution

MoO2

MoO2.75

Ga

se

ou

s M

ixtu

re

MoO2.889

Cr2O3

MoS2

NiS2

Pyrite

Ma

gn

eti

te

Fe

Cr2

O4

Au

ste

nit

e

(O2

-do

min

an

t)(H2O-dominant)

Ga

se

ou

s M

ixtu

re(H

2-d

om

ina

nt)


10-4

.001

.01

.1

1

Sta

ble

ph

ases (

weig

ht_

fracti

on

)

200 400 600 800 1000 1200 1400

TEMPERATURE_CELSIUS

THERMO-CALC (2004.11.02:07.13):Databases: SLAT1 + SSUB

Corrosion of Cr2O3 in C-H-O-S-N-Na-Cl environment

Gaseous Mixture 1:T-273.15,BPW(GAS) 2:T-273.15,BPW(IONIC_LIQ) 3:T-273.15,BPW(CR2O3_S) 4:T-273.15,BPW(HEX)

Cr2O3

Ionic_Liquid

5:T-273.15,BPW(HALITE)

Hexagonal

Halite

Ort

ho

rho

mb

ic

6:T-273.15,BPW(ORTHO_NA2SO4)

2004-11-02 07:19:49.28 output by user Pingfang from NEMO

mailto:[email protected]

computational thermodynamics and kinetics in materials ...€¦ · traditionally, pourbaix...

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