THERMODYNAMICS OF PHASE TRANSFORMATIONS IN STEELS AND ALLOYS

Prévia do material em texto

IN A ID OF ENGINEERS AND PRODUCTION PERSONNEL 
THERMODYNAMICS OF PHASE TRANSFORMATIONS 
STEELS AND ALLOYS 
B. M. Mogutnov , I . A . Tomi l in , 
and L . A . Shvar tsman 
IN 
UDC 669.018:621.1.016.7 
The processes that occur in meta ls and a l loys dur ing var ious types of heat t reatment a re main ly chemi - 
ca l react ions or phase t rans format ions . Consequent ly , the d i rec t ion and completeness of these processes can 
be determined f rom the taws of chemica l thermodynamics . In conformi ty with these laws, the d i rect ion of the 
react ion at constant temperature and pressure depends on the sign of the change in f ree energy AG, and the 
completeness on the condit ions of equ i l ib r ium, at which AG = 0. 
For react ions in so lut ions , which are phases const i tut ing meta l l i c a l loys , the equ i l ib r ium condit ions can 
be expressed as the value of K, the so -ca l led equ i l ib r ium constant . For example , for the prec ip i ta t ion of ex - 
cess phase MXn (carb ide, n l t r ide , in termeta l l i c compound, etc.) 
+ nX = ,~tx~ (~) (1) 
the equ i l ib r ium constant takes the form 
1 
K- - 
aM ate ' (2) 
where a M and a x a re the act iv i t ies of components in the so lut ion. 
The value of K var ies l inear ly with the f ree energy dur ing format ion of phase MX n f rom its e lements 
(AG~) by the equat ion 
~6~. = -Rr tn K. (3) 
Consequent ly , the prec ip i ta t ion of excess phases is poss ib le on condit ion that 
a o0 
L = %, a~¢ >~ e ,~r (4) 
The value of L = 1/K is ca l led the act iv i ty product . 
Another equ i l ib r ium equat ion is more su i tab le for cons ider ing the equ i l ib r ium between so lut ions . It is 
based on the equal i ty of chemica l potent ia ls ~i of the components in the coex is t ing phases . The value of ta i is 
re la ted to the act iv i ty component a i by the equat ion 
ei = o + RT lnai, (5) 
where t~ is the chemica l potent ia l of the component in the s tandard s ta te . This is e i ther a pure substance or 
an inf in i te ly d i luted so lut ion. Thus, to ca lcu la te the equ i l ib r ium react ions occur r ing dur ing heat t reatment of 
a l loys we need data on the act iv i ty of the components in meta l l i c so lut ions as a function of the i r concentrat ion 
and the f ree energy of fo rmat ion of the phase . These data can be obtained exper imenta l ly . Cons iderab le data 
have a l ready been accumulated , which are cont inuous ly being broadened and ana lyzed in handbooks - [1, 2], for 
example . 
In this a r t i c le we sha l l give severa l examples to ind icate the poss ib i l i ty of us ing the laws of thermo- 
dynamics in meta l sc ience . 
P rec ip i ta t ion of Carb ides . Chromium carb ide is often observed in the gra in boundar ies of austen i t i c 
Cr -N i s tee ls . This reduces the loca l concent rat ion of chromium and cor respond ing ly towers the cor ros ion 
I. P. Bard in Cent ra l Sc ient i f i c -Research Inst i tute of Fer rous Meta l lu rgy . T rans la ted f rom Meta l love- 
denie i Termlcheskaya Obrabotka Meta l lov , No. 1, pp. 68-72, January , 1977. 
This material is protected by copy~ght registered in the name o f Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. I0011. No part [ 
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74 
resistance of the grain boundaries. Because of the low diffusion mobility of chromium, the transfer of this 
element from the bulk of the grains does not compensate the increase in its concentration in the boundaries. 
The high diffusion mobility of carbon leads to the fact that all the carbon in the bulk of the grains participates 
in carbide formation. Thus, local equilibrium in the grain boundaries can be described by the equation 
acr a~ = LCrC a, 
where a C is the activity of carbon in steel; aCr is the activity of chromium in the grain boundary. From the 
value of LCrCn and the activity of carbon, the value to which the activity of chromium decreases and the con- 
eentration of chromium in the grain boundaries when carbide phase is precipitated can be calculated. The 
maximum permissible concentration of carbon in the steel at which impoverishment of the grain boundaries in 
chromium does not reach the crit ical level (~ 12"/0), and thus the corrosion resistance does not decrease, was 
calculated by this method. 
At any carbon concentration the activity of carbon varies with additional alloying. Detailed calculations 
were given in [3] for more complex alloys to determine the effect of alloying elements on the activity of car - 
bon. A functional relationship between the conditions of carbide precipitation and the character ist ics of inter- 
crystal l ine corrosion was found. 
Carbide phases are often precipitated from dilute solutions during heat treatment. In this case the 
activity of the components is proportional to the concentration, and Eq. (4) is simplified: 
L' = [M] [X]". (6) 
For example, precipitation of chromium carbide CrC n from austenite should occur when the product of 
the actual concentrations of chromium and carbon exceeds L~rCn. 
Let us demonstrate the use of this equation to calculate the quantity of carbide phase precipitated (out- 
come of the reaction) and the residual concentrations of the components in the solid solution. We shall desig- 
nate as ~ the reduction of the chromium concentration in the solution after equilibrium is reached. Obviously, 
the reduction of the carbon concentration is determined by the stoichiometric coefficient n, and amounts to 
(12/52)/3n, where 12 and 52 are the atomic weights of carbon and chromium, respectively. With equilibrium 
{[Crl -- p}/[Cl -- 
12 
5~ -~ n 1" = £crcn" (7) 
/ 
t 
The solution of this equation gives the value of/3, and consequently all the values sought. 
Phase Diagrams. Phase diagrams are one of the basic theoretical tools of metal science. Plotting 
phase diagrams is very time consuming. The use of thermodynamics makes it possible to reduce experimen- 
tal work considerably, and also obtain lines of phase equilibrium at low temperatures, where ordinary methods 
of investigation are ineffective due to the impossibility of reaching equilibrium. 
Two methods of thermodynamic calculation of phase diagrams are used. The first is to solve a system 
of equations expressing the equality of chemical potentials of all components in all phases. The second is 
based on comparison of the equations of free energy of the system with subsequent determination of the mini- 
mum. 
For binary systems the variation of the free energy of each phase with temperature and composition 
can be expressed graphically - by plotting a curve on a plane. The conditions of phase equilibrium are deter- 
mined from the position of the common tangent. Phase diagrams are practically impossible to construct for 
three-component and more complex systems. For such systems we use the analytical method, which is pos- 
sible due to the widespread use of computers. The difficulty of using this method is due to the limited number 
of experimental thermodynamic data for multicomponent systems. These data usually pertain only to binary 
systems, rarely to ternary systems. For this reason, it is impossible to predict the thermodynamic proper- 
ties of complex systems from the properties of their components. 
In general form this problem is unresolved, and therefore we must use empirical laws in combinationwith general thermodynamic relationships and various models of statistical concepts. Methods of predicting 
the thermodynamic properties are described in [4, 5]. 
As an example, let us consider the Fe- Ni -A l system, for which the solubility of two intermetallic 
compounds, NiAl and Ni3Al, has been calculated on the basis of data concerning the thermodynamic proper- 
ties of three binary systems - Ni- AI, Fe- Al, and Ni- Fe. The problem of determining the composition of 
75 
o.,\ 
o o, o5 o,1o 4¢~ a, eo t¢ .~ 
Fig. I 
AG 
I I ~ , . . I t 1 
i I "-.! ~+1 
i i l "u 
I¢cl M, ,¢ Nz t¢8- I 
Fig. 2 
Fig. 1. Results of calculating equilibrium in Fe -N i -A t system at 
500°C. 1) Solubility of NiAI; 2) solubility of Ni3Al. a) Perfect solu- 
tion of Fe -N i ; b) regular solution of Fe -N i . 
Fig. 2. Formation of metastable precipitates during aging of alloys. 
1) Free energy of solid solution; 2, 3, 4) free energies of formation 
of phases. 
the equilibrium solid solution and the composition of the excess phases precipitated, with a wide region of 
homogeneity, was posed. 
Let us f irst select the composition of the alloy and the temperature. Let us assume that the composi- 
tion of the precipitating phase is NinAl. This phase begins to precipitate when the sum of the chemical poten- 
tials of nickel and aluminum in the solution is larger than the free energy of its formation, i .e., when 
/~ht + n FNt > A G~ (Ni, hl), (8) 
and the calculation is based on the following stoichiometric equation: 
(N m , N^,) orig.d.s. "* "" N,. Al + (I -- =) (N~,, N~,) equi.d.s. (9) 
The change in the free energy during such a reaction is expressed by the equation 
AG==. A ~(NInAI)-t- (1--=)h O~ equi.d.s 0 • - - a Ol orig.d.s. (10) 
where 1'; are atomic percents; ~ is the number of gram-atoms of precipitating phase from one gram-atom of 
the original solution, determined from the balance of mass. Then we select the value of n at which the drop 
of the free energy AG is maximum. The results of these calculations, by means of the computer, are shown 
in Fig. 1. It is assumed In the calculations that the solution of Fe - Ni is perfect or regular. 
The results of calculating several phase diagrams of alloys of refractory metals based on the simple 
model of regular solutions are given in [6]. 
An example of quantitative calculation of binary diagrams, Fe -Cr in particular, can be found in [7]. 
It should be noted that calculations of phase diagrams are widely used in studying phase equilibrium at 
high pressure [8]. 
Decomposition of Supersaturated Solid Solutions. The relationships used in plotting phase diagrams are 
also used to analyze the possible processes of decomposition of supersaturated solid solutions. This is shown 
schematical ly in Fig. 2. Curve 1 expresses the free energy of the solid solution in relation to the composition. 
Curves 2, 3, and 4 are the free energies of the possible compounds in the system. As can be seen from Fig. 2, 
an alloy of composition N is a supersaturated solid solution. Four decomposition reactions are thermodynami- 
cally possible: dissociation into two coupled solutions of composition Nt and N~; precipitation of compounds 
2, 3, or 4. Obviously, the most resistant decomposition product is compound 4, formation of which is accom- 
panied by the largest drop of free energy. However, any of these transformations may occur, depending on 
the temperature - kinetic conditions. 
Let us take a specific example - the decomposition of austenite at a temperature below the eutectoid 
(Fig. 3). In this case the mixture of ferrite and cementite is the most resistant. However, metastable 
equilibrium can also exist: austen i te - cementite and austen i te - ferr ite. 
Of major practical importance are the alloys with compositions between points b and c in Fig. 3. In 
these alloys the austenlte may decompose by the three processes indicated above. 
'/6 
AG, ca I/g-atom 
7o ~ 
so i ~/ 
7O 
0 
-,o [ iil 
~ ~ ~ olo o,,rs q2o Ne 
AG, calf g-atom 
2oO 
goo 
16o 
Izg 
80 
~0 
I 
f // 
li i~ I I 
; o, o5 o)'a o,z~- 
F ig . 3 F ig . 4 
h 
/ 
t 
/ 
Fig. 3. Free energies of formation of ferrite, austenite, and cemen- 
rite from graphite and ~ iron in relation to carbon concentration at 
980~. 
F ig , 4. Change in thermodynamic s t imulus of decompos i t ion of 
austen i te at 9802£. 
Let us introduce the concept of the driving force of decomposition. This value, causing the process, i~ 
associated with the reduction of the free energy during decomposition and is determined by the location of the 
tangent to the free energy curve of austenite at the point corresponding to the composition of the alloy (Fig. 4). 
For example, at 980°Kthe driving force of decomposition of austenite with N C = 0.045 to cementite and austenite 
of another composition is characterized by line Ig (point I corresponds to the free energy of formation of 
Fe~C), while the driving force of decomposition of austenite with N C = 0.025 to ferrite and austenite of another 
composition is segment kin. 
Let us consider the decomposition of the alloy with N C ~ 0.035. Its free energy may decrease both with 
formation of cementite nuclei and formation of ferrite, since the respective thermodynamic stimuli are not 
equal to zero. Let us assume, e.g., that decomposition begins with formation of cementite nuclei. Growth of 
these nuclei will lead to diffusion of carbon from austenite to cementite and, consequently, to reduction of the 
carbon concentration in the solid solution bordering the cementite nucleus. In this case the thermodynamic 
stimulus of cementite precipitation will decrease and the thermodynamic stimulus of ferrite formation will 
increase (Fig. 4). 
When the carbon concentration in the original solid solution at the boundary with cementite reaches a 
value N C = 0.032 (point b) the precipitation of cementite ceases, since the driving force of this process be- 
comes equal to zero. However, decomposition can continue with formation of ferrite nuclei. With formation 
and growth of ferrite nuclei the mother phase will be enriched in carbon at the boundary with the nuclei. In 
this case, as follows from Fig. 4, the thermodynamic stimulus of ferrite precipitation will increase and the 
stimulus of cementite precipitation will increase. When the carbon content of austenite reaches 0.041 (point c) 
the formation of ferrite ceases and formation of cementite nuclei for continuation of the process becomes im- 
possible. Thus, with decomposition of austenite whose composition lies between prolongations of lines GS and 
ES of the Fe - C phase diagram it is possible for ferrite and cementite to be formed alternately. It is assumed 
that precisely this characteristic of eutectoid decomposition leads to the alternation of plates of ferrite and 
cementite in pearlite [9]. 
Decomposition of supersaturated solid solutions often occurs by the scheme shown in Fig. 2. In par- 
ticular, the existence of metastable regions of phase separation is the reason for the formation of concentra- 
tion heterogeneities in aluminum alloys during the early stages of aging - Guinier - Preston zones (GP) [10, 
11]. Precipitation of metastable intermetallic phases also occurs in these alloys [12]. 
The thermodynamic methods discussed above make it possible to predict metastable equilibrium dia- 
grams. These diagrams make it possible to find the temperature and concentration at which already existing 
77 
12 
/ 
8 
Ct) i/ g " 
o,7 
OJ 
1 
\ 
380 ~20 ~60 500 °C 
u 
A' 
/ / 
i j .f 
I 
?00 300 400 500 GO0 700~'C 
Fig. 5. Change in electrical 
resist ivity with recovery [1] 
and apparent specific heat of 
Fe - Ni - Co - Mo annealed at 
420°C [2]. 
GP zones and metastable phaseswill form or go into solution. It should be noted that solution of such phases 
is the reason for the recovery of the properties of aged alloys at elevated temperatures. 
Thermodynamic methods can be extended also to aging processes in multicomponent alloys. Let us 
take maraging steel as an example. It is known that cobalt substantially improves the strength of Fe - Ni - Mo 
alloys [13]. Thermodynamic studies show that aging of maraging steels with cobalt begins with short-range 
order character ist ic of the Fe - N i - Co system [14-16]. The character ist ic feature is the formation of con- 
centration heterogeneities - the nearest sections surrounding iron atoms consist of cobalt atoms, and the other 
section of nickel atoms. Regions of phase separation exist between these ordered regions. This leads to an 
increase in the thermodynamic activity of nickel and decrease in the activity of iron. 
The reduction of the activity of irion reinforces the thermodynamic stimulus of precipitation of meta- 
stable compounds of nickel with molybdenum, which is also observed in the early stages of aging. The forma- 
tion of metastable compounds is explained in particular by the characterist ics of aging of Fe - Ni - Co - Mo 
alloys by recovery and by the sharp difference in the kinetics of aging [17] at high and low temperatures 
(Fig. 5). Curve 1 in Fig. 5 shows the recovery of the properties (electrical resistivity), and curve 2 the 
change in the specific heat of the previously aged alloy. It can be seen that the maximum recovery corre- 
sponds to the specific heat due to the endotherma[ effect of the solution of the metastable intermetallic com- 
pound of nickel and molybdenum. 
Ordering also affects the precipitation of equilibrium phase Fe2Mo. This is explained by the fact that 
cobalt increases the thermodynamic activity of molybdenum and, in conformity with the rule of the activity 
product, reduces the solubility of Fe2Mo, increasing the number of sections of this phase precipitated. 
The examples given, i l lustrating only a few possibilities of using the laws of thermodynamics in metal 
science, make it possible to understand the reasons for the accelerated research on the thermodynamics of 
alloys in recent years. 
1. 
2. 
3. 
4o 
5. 
6. 
7. 
L ITERATURE C ITED 
R. Hultgren et al., Selected Values of Thermodynamic Propert ies of Binary Alloys, ASM, Metal Park, 
Ohio (1973). 
V. P. Glushko (editor), Thermal Constants of Substances [in Russian], Vols. 1-7, Izd. VINITI, Moscow 
(1965-1974). 
S. D. Bogolyubskii et al., "Thermodynamic analysis of the effect of alloying elements, carbon, and 
nitrogen on susceptibility of stainless steels to intercrystal l ine corrosion," in: Development of Methods 
of Protecting Metals Against Corrosion [in Russian], Prague (1975), p. 86. 
L Ansara, Int. Symp. on Metallurgical Chemistry, Fund. and Appl., Brunel Univ. (1971), 
P. Spencer, F. Hayes, and O. Kubaschewski, Revue Chimie Minerale, 9, 13 (1972}. 
L. Kaufman and H. Bernstein, Plotting Phase Diagrams by Means of Computer [Russian translation], 
Mir, Moscow (1972). 
O. Kubaschewski and T. Chart, J . Inst. Metals, 9_.~3, 329 (1964-65). 
78 
8. I . L . Aptekar', "Plotting and analysis of phase diagrams with use of the computer. Basic principles 
and prospects," in: Imperfection of Crystal Structure and Martensitic Transformations [in Russian], 
Nauka, Moscow (1972), p. 101. 
9. J. Hobstetter, Decomposition of Austenite by Diffusional Processes, New York - London (1962), p. 1. 
10. R. Baur and \;. Gerold, Acta Met., 19.0, 637 (1962). 
11. M. Hil lert, J. Physique et Radium, 2__~3, 835 (1962). 
12. A. Guinier, Heterogeneous Metallic Solid Solutions ~ussian translation], IL, Moscow (1962). 
13. M.D. Perkas and V. M. Kardonskii, High-Strength Maraging Steels [in Russian], Metallurgiya, 
IVloscow (1970). 
14. M.A. Kablukovskaya and B. M. Mogutnov, "Effect of cobalt on mechanism of aging of maraging 
steels," Fiz. Met. Metallovedo, 3_.55, No. 4, 791 (1973). 
15. B.M. Mogutnov, "Short-range order in maraging alloys and its effect on precipitation of intermetallic 
compounds," Fiz. Met. MetaIloved., 3__88, No. 2, 260 (1974). 
16. M.D. Perkas et al., "Effect of cobalt on aging of martensite in Fe -N i -Mo alloys," Metalloved. Term. 
Obrab. Met., No. 10, 2 (1972). 
17. M.A. Kablukovskaya and B. M. Mogutnov, "Role of ordering in aging of martensite in Fe-Ni - Co- Mo 
alloys," Dokl. Akad. Nauk SSSR, 220, No. 1, 71 (1975). 
79