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Chemical compatibility between zirconia dispersion and gamma titanium aluminide matrix
CALPHAD Vol. 17, No. 2, pp. f33-140, Printed in the USA.
0364~5916l93 $6.00 + .OO (c) 1993 Pe~amon Press Ltd.
1993
ChemicaI Compatibility between Zirconia Dispersion and Gamma ~~niurn Aluminide Matrix
M. Grujicic and S. Arokiaraj Center for Advanced Mmufacturing. Department of Mechanical Engineering Clemson University, Clemson, S.C. 29634-092 1
ABSTRACT: Deformation-induced marten&c transformation in a ZrOz-base dispersion can be utilized as a toughening mechanism in gamma-TiAl at lower temperatures. However, chemical reactions between zirconia and gamma-TiAl at higher temperatures can lead to a serious degradation of the material’s properties. In the present paper a thermodynamics-based analysis was carried out to determine the chemical compositions of the two phases which will minimize the extent of chemical reactions at high temperatures. 1. Introduction Gamma titanium aluminide (y-TiAl) possesses good high-temperature properties such as creep strength, oxidation resistance, etc. which make it a viable candidate material in advanced gas turbine applications. However, the lack of tensile ductility and fracture toughness at temperatures below approximately 6GO°C limits presently the use of this material. Grujicic and Narayan [ 1,2] showed that significant enhancement in ductility and toughness of y-TiAl can be achieved by the in~~uction of a metastable dispersion of the Ti-base b.c.c. phase which undergoes defolmation-induced martensitic transformation. However, due to metallic character of the b.c.c. phase high temperature creep properties are compromised. It was suggested [3] that the introduction of a ceramictype me&stable dispersion (such as partially stabilized zirconia) can give rise to similar ~~fo~ation-~ughe~ng effects without the attend~t loss of ~gh-~rn~ra~e creep strength. The work presented here deals with the thermodynamics-based design of such a metastable, yitria-stabilized zirconia (and the corresponding gamma TiAl phase) which could be used as a lowtemperature toughening agent in the gamma TiAl without sacrificing its creep resistance. In order to increase the reduction resistance of zirconia with respect to the Ti- and Al-base oxides, zirconia is alloyed with isomorphous hafnia. To achieve the necessary thermodynamic stability of the tetragonal ZrO2 phase with respect to its low-temperature monoclinic modification, zirconia is alloyed with 5 mole percent of yitria (Y2O3). 2. Thermodynamic Analysis In order for the y-TiAl + (Zr,Hf,Y)Oz two phase system to meet the above mentioned functional requirements the following thermodynamic conditions should be fulfilled: a) The tetragonal (Zr,Hf,Y)O;! phase should have the necessary the~~ynamic stability so that it can be maintained as metastable phase on cooling to room temperature; and b) The (Zr,Hf,Y)Oz phase should be sufficiently stable against reduction by Ti and Al in the --__~_~_~_-_~_______________c~~_________ Received 14 September 1%
133
M. GRUJlClCand S. AROKIARAJ
134
g~ma-Tin matrix. According to the phase diagram for ZrG2-Y203 [4], the condition (a) can be fulfilled by alloying zirconia with 5 mole% of Y203. The condition (b) could be restated as following: When the (Zr,Hf,Y)Oz phase is in equilibrium with the gamma matrix the oxygen content in the matrix should not exceed the solubility limit with respect to the formation of either Ti- or Al-base oxides. This requirement can be thermodynamically stated by the following equations:
Hf - + 2Q = HE2
AGffP, = 0 = AG&,,
2y -I- 30
AG YP? = 0 = AGFzQ3 + RT ln[ur,,/(u~
mm
qo.905-x)9
= r,o,
~0.0951%95
+
E
=
f RT lnb&(a,
TiO, + x.2.2 f
(090.5 -
- ni)l a:)]
(2) (31
x)Ef f 0.095y
3/2[Zrx, ~~~~~~~~~~Y,.~~ ]O,.9, + 2AA= Al,O, + 3,B.r~ + 3/2(0.905 - x)Hf + 3/2(0.095)_Y
where R is the gas constant, T the temperature, AGO’sthe standard Gibbs free energies for oxide formation, AG’s the Gibbs free energies of the reactions and a’s the activities. The underscores indicate that the elements and the oxides are dissolved in y--TN and (Zr,Hf,Y)Oz respectively. 2.1 Calculation of S&.n&rd Gibbs Free Energy for Oxide Formation Gamma TiAl has a tetragonaliy distorted f.c.c. structure. The proceeding thermodynamic analysis, will hence entail the knowledge of the standard Gibbs free energies for formation of the oxides from the constituent elements in the f.c.c. structure. With the exception of aluminium ah the other metallic elements present in the system are more stable in the h.c.p. structure in the temperature range of interest (R.T. to SSOOC).Oxygen is most stable as gas in this temperature range, at latm pressure. To obtain the necessary standard Gibbs free energies of reactions invoking elements in f.c.c. structure, the corresponding standard Gibbs free energies, based on the constituent elements in their most stable structure have to be modified, to account for the change of the elements into the f.c.c. structure. For example, the necessary standard Gibbs free energy for the formation of A1203 form the constituent elements in f.c.c. structure can be obtained by adding the free energies of the following reactions:
30(fcc)
= 3/20,(g)
(7)
ZIRCONIA DISPERSION IN GAMMA TITANIUM ALUMINIDE
135
Addition of eons. (6) and (7) gives the reaction of formation of A@& from the constituent elements in the f.c.c structure, as following: 2AK.W + 30@c)
= Al@,(s)
(81
Likewrse, the necessary reaction for the formation of Zr-02 is:
can be obtained by adding the following three equations:
Zr@c) = 2rfAcp)
IllI
The remaining reactions and theirrespective Gibbs free energies can be obtained in the similar way. The results for the standard Gibbs free energies for oxides formation from the constituent elements in the f.c.c. structure are shown in Table 1. The data listed in Table 1. pertain to one gram atom, and are obtained by dividing the corresponding Gibbs free energy of the respective chemical reaction by the number of atoms involved in the reaction. The standard Gibbs free energy data for oxides formation from the elements in their stable states were taken from reference [5]. The Gibbs free energy for the formation of oxygen gas from the f.c.c. oxygen was taken as -25,GCOcal/g.at. Tabk 1. Gibbs Free Energies for Formation of Oxides from the Elements in the f.c.c. structure.
Compound
Gibbs Free Energy (caYg.at.)
m2
-97228
HfO2
-98677
u2Q3
-95420
A1203
-88407
TiO2
-85O61
Ti302
-81941
a3y4012
45980
2.2 Themmdynamic M&.&s The molar Gibbs free energy of gammaTiA1 (approximated as the f.c.c. structure) was modelled using the Kohler model [o] given as:
136
M. GRUJICICand S. AROKIARAJ
where Gp is the molar Gibbs free energy of pure component i in the f.c.c. structure. Since we adopted f.cc. as the standard state for all the elements in the system, Cl*= 0. Xiis the mole fraction of the element i, gu and hji the binary interaction parameters between elements i andj. The ternary interaction parameters lgk are not considered in the present analysis due to lack of experimental data. The partial molar Gibbs free energy for the component i is given according to the Kohler model as:
di = cfi”” + RT +
hlX1 + ZXi Xj/(Xi + Xj) [l - Xi f Xj/(Xi + Xj)]gq
{fxj/(Xi
zxj
ij
ij
+
Xj)]'- Xi Xj/(Xi+
Xj)Jhg
where i f j, i f k, j z k. Since Ci = Gifcc+ RT In ai, the following expression can be written for the activity of the element i; RT 1nUi = RT lnXi + Fi
+
-
xj/(xi + xj) [xj/(xi + xj) + 1 - xi]gu
zxj (lIxj/(Xi + Xj)]'ij
Z[g&XT
y
XJCxj
+
Xi
X&l +
Xj/(Xi+
8yIf3:
Xj)thQ
xj/(xj
+
xk)l)
(15)
To evaluate the activities of the elements in y-T&l of a given composition, one must know the Kohler binary interaction parameters, gu and hji.Determination of these parameter are given in the next section. Due to lack of experimental data it was assumed that gg = hji throughout this work. Under this assumption the Kohler model reduces to the regular solution model with a temperature dependent inter~tion parameters, ge. 2 3 Determmanon of Binarv_ -actron
Par-
Two methods have been used to determine the binary interaction parameters in y-T&l, alloyed with Zr, Hf. Y and 0. The first method was originally developed by Kaufman and Bernstein [7] and was used to determine binary interaction parameters for the constituent metallic elements Ti, Al, Zr, Hf and Y present in the system. The second method was based on the use of the meti-oxygen phase diagrams [8,9] to determine the respective binary metal-oxygeninteraction parameters. According to the Kaufman-Bernstein method the binary i-j interaction parameter in the liquid phase, L can be defined as: Lij = ec + ep where Q is defined as:
06)
137
ZIRCONIA DISPERSION IN GAMMA TITANIUM ALUMINIDE
e0
=
2
I
AHfii+~>121
-
OSAHf - 0.5AHi)
callg.at (17)
AHLi is the average enthalpy of vaporization for the transition elements belonging to the group i and is obtained by averaging the corresponding entha.lpies of the transition elements in the second and third row of the periodic table. AHLi and AHLc(i+j)n] values can be obtained from a curve showing the variation of the average enthalpy of vaporization between second and third row elements. er, in eqn. (16) is the internal pressure parameter given by:
eP
=
0.3 (Vi + Vj) [(-
Hi/Vi) ‘I2 - (-
HjlVj)1/2]2
callg.at
(18)
where Hi and Vi are the enthalpy of vaporization and the atomic volume of the pure element i per gram atom at 298K. Hi and Vi values for the elements under consideration were taken from reference [7] and shown in Table 2. Table 2. Enthalpies of Vaporization and Atomic Volumes of Elements at 298% Entbalpy, H (cal/g.at)
Metal
Atomic Volume, V (cm3/g.at)
Zr
-146000
14.04
Hf
-15OOoO
13.5
Ti
-113000
10.72
Al
-77000
10.0
Y
140000
20.38
Once the i-j interaction parameters in the liquid are defined, the corresponding parameters in the f.c.c. structure, gij, can be calculated as follows:
gii = Lij + e, + e2
interaction
(19)
where et is the strain energy parameter and is defined as: e,
=
- 0.5 (Hi + H,) (Vi - Vj)’ (Vi + Vj)-’
cal/g.at
(20)
and parameter e2 is given as:
e2
= 2
AHL?’
rcl+n/=l
-
0 5AHf.
- O.SAHf-
cal/g.at I
(21)
where AHiL*u represents the average enthalpy difference between liquid and f.c.c. phases of the transition elements belonging to the group i and is obtained by averaging the corresponding enthalpy differences of the transition elements in the second and the third row of the periodic table. The calculated values of the parameters eg, er,, et and e2 for atomic pairs comprised of the elements Zr, Ti, Al, Hf and Y are shown in Table 3.. while their respective interaction parameters are given in Table 4.
M. GRUJICIC and S. AROKIARAJ
Table 3. Calculated Values of Parameters eo, ep, er and ez used for the evaluation of Interaction Parameters (cal/g.at.). System
eo
%
el
e2
-1300
I
3
I
2328
II
1060
II
1459
I I
3148
I
-2860
I
97
I
57
I
0
I
Zr-Ti I
t
Zr-Al
t
Zr-Hf
-10500
I
0
I
I
I
I
I
Zr-Y
0
4044
4885
0
Ti-Al
-10500
1384
115
-200
Ti-Hf
1300
55
1732
1060
Ti-Y
0
3653
12204
0
AI-Hf
-10500
2198
2517
-2870
Hf-Y
0
4972
5938
0
The phase diagram method uses oxygen solubility limit (X0) with respect to a given oxide (say Z3-02) in the respective binary (Zr-0) phase diagram and standard relations for regular solution:
RT In (~z,/~z,) = gz,-o
RT ln (a,/~,) =
gZr-O
Xi
(22)
X$,
(23)
to determine the binary interaction parameter (g,_,) as following. Equations (22) and (23) are solved for activities aa and a~, and the latter substituted in the equation for the standard Gibbs free energy of formation of the oxide at equilibrium given as:
AGgd2
= -
RTln{ l/(uz, ai)]
The resulting equation is then solved for the interaction parameter, gz,_o, gzr-0
=
- RTln(X,, [AGO2
Equation (25) can be generalized
g&f-o =
W;xoy -
(24) to get
XfJl/[X~ + 2x&l
(25)
for any binary M,O, compound as follows
RTln (XL XV,)] / [.xX: + yX’$
(26)
Interaction parameters between elements involving oxygen were determined using this method and the results are shown in Table 4. The same method was also used to determine the Z~G~-Y~GJ interaction parameter in the yitria stabilized zirconia. In the calculation, the standard Gibbs free energy for the fOrmatiOn Of the Complex oxide ZrjY4012 from the COnSthent ekmentS in the f.c.c. state was taken as 45.9 kcal/mole [3]. Due to similarity between ZrG2 and HfO2, the interaction parameter between these two oxides is taken as zero (ideal solution, ref. [lo]) and the Hf02-Y2& interaction parameter equal to the ZrQ-Y& interaction parameter which was calculated to be 44295.
ZIRCONIA DISPERSION IN GAMMA TITANIUM ALUMINIDE
Table 4. Binary Interaction Parameters. Interaction parameters
System
2091
Zr-Ti ZT-Al
ZT-Hf
t
-875 1
I
I
154
ZT-Y
8930
ZT-0
-261537
Ti-Al
I
-9201
Ti-Y
I
15857 -330418
Ti-0
-8643
Al-Hf Al-Y
-1c000
Al-o
-132881
Hf-Y
10910
Hf-0
-209334
Y-O
-180481
Zflz-YzQJ
44295 3. Computational Procedure
and Results
As mentioned earlier, to achieve the necessary stability of the tetragonal zirconia with respect to monoclinic zirconia at room temperature, the mole fraction of yitria (Y2G3) in it was set to 0.05. Therefore, the chemical formula of the yitria-stabilized zirconia can be written as (ZT,,Hf(.905_x),Y.095)Ol .g5. The chemical composition of this phase is hence completely determined by a single parameter x=X7-,-02. Due to the dissolution of the zirconia-based dispersion, the gamma matrix contains not only Ti and Al but also Zr, Hf, Y and 0. The ratios of mole fractions of Zr, Hf, Y and 0 in the gamma matrix are thus governed by the corresponding ratios in the oxide phase, that is, the following relations hold: XHf = X~J(0.905-x)/x], Xy = X~,[O.095/x], & = [2/x]X~,, Since the sum of the mole fractions is one, the y-TiAl + (Zr,,Hf (.905-x),Y.095)%95 system is compleW defined by three compositional variables: x, X2 and XTi = l-X~t-Xo-Xa-Xnf-Xy. Activities of the constituent oxides in the dipersed phase (Zr,,Hf(.~5-x),Y,~5)O~.g5 can thus be expressed in terms of a single concentration variable, x=Xza2, while the activities of the constituent elements in the gamma matrix can be expressed in terms of two mole fractions, Xa and Xa. To solve the system of eqns. ( 1) through (3), a computer program was written and implemented into the TK Solver Plus Mathematical package [ 1 l] and executed on a Sun Spark 2 computer workstation. All the calculations were carried out at 850%. The results showed that a solution to the system of equations (1) through (3) exists. The solution also satisfies inequalities given in eqns. (4) and (5). The optimum composition of the zirconia-based phase is associated with x=0.3, that is, (Zro,3.Hfo.sa5,Yo.os5)01.95. The dissolution of this oxide in the gamma TiAl matrix will proceed until the chemical composition of the matrix becomes approximately XrizO.36, X~r=O.38, X~,=O.028, XHfo.06, x,=0.009 and X0=0.16. During the oxide dissolution process, the Gibbs free energies for formation of Al203 and
139
140
M.
GRUJICICand S. AROKIARAJ
TiO2 remain positive that is: AGAtm3 = 20,856 Cal/mole and AGTlO2= 7 1,85 1 Cal/mole respectively. This means that oxygen has not exceeded the solubility limit with respect to the formation of the two oxides. While the result presented above might be encouraging, it must be noted that if the initial volume fraction of the zirconia-based phase is lo%, the equilibrium condition between the oxide dispersion and the TiAl-base matrix is not met until the oxide is almost completely dissolved. Furthermore, when the equilibrium between the zirconia oxide and y-TiAl is established, the mole fractions of Hf and Zr will most likely exceed the solubility limit with respect to the formation of Al$!,r,Hf). Formation of the latter compound can then lead to further dissolution of the oxide phase in the matrix. Fortunately, since the formation of Al#r,Hf’) relies on the diffusion of substitutional species alone, it is, from the kinetics point of view, less critical than the formation of Al203 and TiO2
4. Conclusions Alloying zimonia with hafniacan be beneficial in preventing complete dissolution of the zirconia-base dispersion in the y-TiAl matrix. However, substantial amount of the dispersed phase is dissolved before the equilibrium between the two phases is established. When the equilibrium between the dispersion and the matrix is established, formation of Al- and Ti- base oxides is not thermodynamically feasible. However, formation of Al&Zr,Hf) is feasible and might lead to the further dissolution of the dispersed oxide phase. The latter process, however, is kinetically less critical than the formation of the two oxides. 5. Acknowledgements This work has been supported by the National Science Foundation, #DMR-9017214 and by the Center for Advanced Manufacturing, Clemson University. The authors would like to thank Dr. Bruce A. MacDonald of NSF for encouragement and continuing interest in this work.
6. References 1. M. Grujicic, Mater. Sci. Eng. A, 154 (1992) 75-78. 2. C. P. Narayan, Dispersed-phase Transformation Toughening of Titanium Aluminide, M.S. Thesis, Clemson University, 199 1. 3. S. Arokiaraj, Zirconia Dispersed-phase Transformation Toughening of Mechanically Alloyed Gamma Titanium-Aluminide, M.S. Thesis in progress, Clemson University, 1992. 4. E. M. Levin, H.F. McMurdie and F.P. Hall, Phase Diagrams for Ceramists, The American Ceranic Society, Inc., Vol. 1, (1956) 65. 5. I. Barin and 0. Knacke, Thermochemical Properties of Inorganic Substances, Berlin, New York, Springer-Verlag, 1973. 6. EKohler, Monatsh. Chem., 91 (1960). 738. 7. L. Kaufman and H. Bernstein, ” Computer Calculation of Phase Diagram”, Academic Press, New York, 1970. 8. J. L. Murray, “Phase Diagrams of Binary Titanium Alloys”, ed. J. L. Murray, ASM, Metals Park, Ohio, 1987. 9. J. L. Murray, “Binary Alloy Phase Diagrams”, ed. T. B. Massalski, ASM, Metals Park, Ohio, 1990. 10. L. Kaufman, User Applications of Alloy Phase Diagrams, (conference proceedings) ed. L. Kauf man, ASM, (1987) 145. 11. TK Solver Plus Computer Program, Universal Technical Systems, Rockfort, IL, 1989.
0364~5916l93 $6.00 + .OO (c) 1993 Pe~amon Press Ltd.
1993
ChemicaI Compatibility between Zirconia Dispersion and Gamma ~~niurn Aluminide Matrix
M. Grujicic and S. Arokiaraj Center for Advanced Mmufacturing. Department of Mechanical Engineering Clemson University, Clemson, S.C. 29634-092 1
ABSTRACT: Deformation-induced marten&c transformation in a ZrOz-base dispersion can be utilized as a toughening mechanism in gamma-TiAl at lower temperatures. However, chemical reactions between zirconia and gamma-TiAl at higher temperatures can lead to a serious degradation of the material’s properties. In the present paper a thermodynamics-based analysis was carried out to determine the chemical compositions of the two phases which will minimize the extent of chemical reactions at high temperatures. 1. Introduction Gamma titanium aluminide (y-TiAl) possesses good high-temperature properties such as creep strength, oxidation resistance, etc. which make it a viable candidate material in advanced gas turbine applications. However, the lack of tensile ductility and fracture toughness at temperatures below approximately 6GO°C limits presently the use of this material. Grujicic and Narayan [ 1,2] showed that significant enhancement in ductility and toughness of y-TiAl can be achieved by the in~~uction of a metastable dispersion of the Ti-base b.c.c. phase which undergoes defolmation-induced martensitic transformation. However, due to metallic character of the b.c.c. phase high temperature creep properties are compromised. It was suggested [3] that the introduction of a ceramictype me&stable dispersion (such as partially stabilized zirconia) can give rise to similar ~~fo~ation-~ughe~ng effects without the attend~t loss of ~gh-~rn~ra~e creep strength. The work presented here deals with the thermodynamics-based design of such a metastable, yitria-stabilized zirconia (and the corresponding gamma TiAl phase) which could be used as a lowtemperature toughening agent in the gamma TiAl without sacrificing its creep resistance. In order to increase the reduction resistance of zirconia with respect to the Ti- and Al-base oxides, zirconia is alloyed with isomorphous hafnia. To achieve the necessary thermodynamic stability of the tetragonal ZrO2 phase with respect to its low-temperature monoclinic modification, zirconia is alloyed with 5 mole percent of yitria (Y2O3). 2. Thermodynamic Analysis In order for the y-TiAl + (Zr,Hf,Y)Oz two phase system to meet the above mentioned functional requirements the following thermodynamic conditions should be fulfilled: a) The tetragonal (Zr,Hf,Y)O;! phase should have the necessary the~~ynamic stability so that it can be maintained as metastable phase on cooling to room temperature; and b) The (Zr,Hf,Y)Oz phase should be sufficiently stable against reduction by Ti and Al in the --__~_~_~_-_~_______________c~~_________ Received 14 September 1%
133
M. GRUJlClCand S. AROKIARAJ
134
g~ma-Tin matrix. According to the phase diagram for ZrG2-Y203 [4], the condition (a) can be fulfilled by alloying zirconia with 5 mole% of Y203. The condition (b) could be restated as following: When the (Zr,Hf,Y)Oz phase is in equilibrium with the gamma matrix the oxygen content in the matrix should not exceed the solubility limit with respect to the formation of either Ti- or Al-base oxides. This requirement can be thermodynamically stated by the following equations:
Hf - + 2Q = HE2
AGffP, = 0 = AG&,,
2y -I- 30
AG YP? = 0 = AGFzQ3 + RT ln[ur,,/(u~
mm
qo.905-x)9
= r,o,
~0.0951%95
+
E
=
f RT lnb&(a,
TiO, + x.2.2 f
(090.5 -
- ni)l a:)]
(2) (31
x)Ef f 0.095y
3/2[Zrx, ~~~~~~~~~~Y,.~~ ]O,.9, + 2AA= Al,O, + 3,B.r~ + 3/2(0.905 - x)Hf + 3/2(0.095)_Y
where R is the gas constant, T the temperature, AGO’sthe standard Gibbs free energies for oxide formation, AG’s the Gibbs free energies of the reactions and a’s the activities. The underscores indicate that the elements and the oxides are dissolved in y--TN and (Zr,Hf,Y)Oz respectively. 2.1 Calculation of S&.n&rd Gibbs Free Energy for Oxide Formation Gamma TiAl has a tetragonaliy distorted f.c.c. structure. The proceeding thermodynamic analysis, will hence entail the knowledge of the standard Gibbs free energies for formation of the oxides from the constituent elements in the f.c.c. structure. With the exception of aluminium ah the other metallic elements present in the system are more stable in the h.c.p. structure in the temperature range of interest (R.T. to SSOOC).Oxygen is most stable as gas in this temperature range, at latm pressure. To obtain the necessary standard Gibbs free energies of reactions invoking elements in f.c.c. structure, the corresponding standard Gibbs free energies, based on the constituent elements in their most stable structure have to be modified, to account for the change of the elements into the f.c.c. structure. For example, the necessary standard Gibbs free energy for the formation of A1203 form the constituent elements in f.c.c. structure can be obtained by adding the free energies of the following reactions:
30(fcc)
= 3/20,(g)
(7)
ZIRCONIA DISPERSION IN GAMMA TITANIUM ALUMINIDE
135
Addition of eons. (6) and (7) gives the reaction of formation of A@& from the constituent elements in the f.c.c structure, as following: 2AK.W + 30@c)
= Al@,(s)
(81
Likewrse, the necessary reaction for the formation of Zr-02 is:
can be obtained by adding the following three equations:
Zr@c) = 2rfAcp)
IllI
The remaining reactions and theirrespective Gibbs free energies can be obtained in the similar way. The results for the standard Gibbs free energies for oxides formation from the constituent elements in the f.c.c. structure are shown in Table 1. The data listed in Table 1. pertain to one gram atom, and are obtained by dividing the corresponding Gibbs free energy of the respective chemical reaction by the number of atoms involved in the reaction. The standard Gibbs free energy data for oxides formation from the elements in their stable states were taken from reference [5]. The Gibbs free energy for the formation of oxygen gas from the f.c.c. oxygen was taken as -25,GCOcal/g.at. Tabk 1. Gibbs Free Energies for Formation of Oxides from the Elements in the f.c.c. structure.
Compound
Gibbs Free Energy (caYg.at.)
m2
-97228
HfO2
-98677
u2Q3
-95420
A1203
-88407
TiO2
-85O61
Ti302
-81941
a3y4012
45980
2.2 Themmdynamic M&.&s The molar Gibbs free energy of gammaTiA1 (approximated as the f.c.c. structure) was modelled using the Kohler model [o] given as:
136
M. GRUJICICand S. AROKIARAJ
where Gp is the molar Gibbs free energy of pure component i in the f.c.c. structure. Since we adopted f.cc. as the standard state for all the elements in the system, Cl*= 0. Xiis the mole fraction of the element i, gu and hji the binary interaction parameters between elements i andj. The ternary interaction parameters lgk are not considered in the present analysis due to lack of experimental data. The partial molar Gibbs free energy for the component i is given according to the Kohler model as:
di = cfi”” + RT +
hlX1 + ZXi Xj/(Xi + Xj) [l - Xi f Xj/(Xi + Xj)]gq
{fxj/(Xi
zxj
ij
ij
+
Xj)]'- Xi Xj/(Xi+
Xj)Jhg
where i f j, i f k, j z k. Since Ci = Gifcc+ RT In ai, the following expression can be written for the activity of the element i; RT 1nUi = RT lnXi + Fi
+
-
xj/(xi + xj) [xj/(xi + xj) + 1 - xi]gu
zxj (lIxj/(Xi + Xj)]'ij
Z[g&XT
y
XJCxj
+
Xi
X&l +
Xj/(Xi+
8yIf3:
Xj)thQ
xj/(xj
+
xk)l)
(15)
To evaluate the activities of the elements in y-T&l of a given composition, one must know the Kohler binary interaction parameters, gu and hji.Determination of these parameter are given in the next section. Due to lack of experimental data it was assumed that gg = hji throughout this work. Under this assumption the Kohler model reduces to the regular solution model with a temperature dependent inter~tion parameters, ge. 2 3 Determmanon of Binarv_ -actron
Par-
Two methods have been used to determine the binary interaction parameters in y-T&l, alloyed with Zr, Hf. Y and 0. The first method was originally developed by Kaufman and Bernstein [7] and was used to determine binary interaction parameters for the constituent metallic elements Ti, Al, Zr, Hf and Y present in the system. The second method was based on the use of the meti-oxygen phase diagrams [8,9] to determine the respective binary metal-oxygeninteraction parameters. According to the Kaufman-Bernstein method the binary i-j interaction parameter in the liquid phase, L can be defined as: Lij = ec + ep where Q is defined as:
06)
137
ZIRCONIA DISPERSION IN GAMMA TITANIUM ALUMINIDE
e0
=
2
I
AHfii+~>121
-
OSAHf - 0.5AHi)
callg.at (17)
AHLi is the average enthalpy of vaporization for the transition elements belonging to the group i and is obtained by averaging the corresponding entha.lpies of the transition elements in the second and third row of the periodic table. AHLi and AHLc(i+j)n] values can be obtained from a curve showing the variation of the average enthalpy of vaporization between second and third row elements. er, in eqn. (16) is the internal pressure parameter given by:
eP
=
0.3 (Vi + Vj) [(-
Hi/Vi) ‘I2 - (-
HjlVj)1/2]2
callg.at
(18)
where Hi and Vi are the enthalpy of vaporization and the atomic volume of the pure element i per gram atom at 298K. Hi and Vi values for the elements under consideration were taken from reference [7] and shown in Table 2. Table 2. Enthalpies of Vaporization and Atomic Volumes of Elements at 298% Entbalpy, H (cal/g.at)
Metal
Atomic Volume, V (cm3/g.at)
Zr
-146000
14.04
Hf
-15OOoO
13.5
Ti
-113000
10.72
Al
-77000
10.0
Y
140000
20.38
Once the i-j interaction parameters in the liquid are defined, the corresponding parameters in the f.c.c. structure, gij, can be calculated as follows:
gii = Lij + e, + e2
interaction
(19)
where et is the strain energy parameter and is defined as: e,
=
- 0.5 (Hi + H,) (Vi - Vj)’ (Vi + Vj)-’
cal/g.at
(20)
and parameter e2 is given as:
e2
= 2
AHL?’
rcl+n/=l
-
0 5AHf.
- O.SAHf-
cal/g.at I
(21)
where AHiL*u represents the average enthalpy difference between liquid and f.c.c. phases of the transition elements belonging to the group i and is obtained by averaging the corresponding enthalpy differences of the transition elements in the second and the third row of the periodic table. The calculated values of the parameters eg, er,, et and e2 for atomic pairs comprised of the elements Zr, Ti, Al, Hf and Y are shown in Table 3.. while their respective interaction parameters are given in Table 4.
M. GRUJICIC and S. AROKIARAJ
Table 3. Calculated Values of Parameters eo, ep, er and ez used for the evaluation of Interaction Parameters (cal/g.at.). System
eo
%
el
e2
-1300
I
3
I
2328
II
1060
II
1459
I I
3148
I
-2860
I
97
I
57
I
0
I
Zr-Ti I
t
Zr-Al
t
Zr-Hf
-10500
I
0
I
I
I
I
I
Zr-Y
0
4044
4885
0
Ti-Al
-10500
1384
115
-200
Ti-Hf
1300
55
1732
1060
Ti-Y
0
3653
12204
0
AI-Hf
-10500
2198
2517
-2870
Hf-Y
0
4972
5938
0
The phase diagram method uses oxygen solubility limit (X0) with respect to a given oxide (say Z3-02) in the respective binary (Zr-0) phase diagram and standard relations for regular solution:
RT In (~z,/~z,) = gz,-o
RT ln (a,/~,) =
gZr-O
Xi
(22)
X$,
(23)
to determine the binary interaction parameter (g,_,) as following. Equations (22) and (23) are solved for activities aa and a~, and the latter substituted in the equation for the standard Gibbs free energy of formation of the oxide at equilibrium given as:
AGgd2
= -
RTln{ l/(uz, ai)]
The resulting equation is then solved for the interaction parameter, gz,_o, gzr-0
=
- RTln(X,, [AGO2
Equation (25) can be generalized
g&f-o =
W;xoy -
(24) to get
XfJl/[X~ + 2x&l
(25)
for any binary M,O, compound as follows
RTln (XL XV,)] / [.xX: + yX’$
(26)
Interaction parameters between elements involving oxygen were determined using this method and the results are shown in Table 4. The same method was also used to determine the Z~G~-Y~GJ interaction parameter in the yitria stabilized zirconia. In the calculation, the standard Gibbs free energy for the fOrmatiOn Of the Complex oxide ZrjY4012 from the COnSthent ekmentS in the f.c.c. state was taken as 45.9 kcal/mole [3]. Due to similarity between ZrG2 and HfO2, the interaction parameter between these two oxides is taken as zero (ideal solution, ref. [lo]) and the Hf02-Y2& interaction parameter equal to the ZrQ-Y& interaction parameter which was calculated to be 44295.
ZIRCONIA DISPERSION IN GAMMA TITANIUM ALUMINIDE
Table 4. Binary Interaction Parameters. Interaction parameters
System
2091
Zr-Ti ZT-Al
ZT-Hf
t
-875 1
I
I
154
ZT-Y
8930
ZT-0
-261537
Ti-Al
I
-9201
Ti-Y
I
15857 -330418
Ti-0
-8643
Al-Hf Al-Y
-1c000
Al-o
-132881
Hf-Y
10910
Hf-0
-209334
Y-O
-180481
Zflz-YzQJ
44295 3. Computational Procedure
and Results
As mentioned earlier, to achieve the necessary stability of the tetragonal zirconia with respect to monoclinic zirconia at room temperature, the mole fraction of yitria (Y2G3) in it was set to 0.05. Therefore, the chemical formula of the yitria-stabilized zirconia can be written as (ZT,,Hf(.905_x),Y.095)Ol .g5. The chemical composition of this phase is hence completely determined by a single parameter x=X7-,-02. Due to the dissolution of the zirconia-based dispersion, the gamma matrix contains not only Ti and Al but also Zr, Hf, Y and 0. The ratios of mole fractions of Zr, Hf, Y and 0 in the gamma matrix are thus governed by the corresponding ratios in the oxide phase, that is, the following relations hold: XHf = X~J(0.905-x)/x], Xy = X~,[O.095/x], & = [2/x]X~,, Since the sum of the mole fractions is one, the y-TiAl + (Zr,,Hf (.905-x),Y.095)%95 system is compleW defined by three compositional variables: x, X2 and XTi = l-X~t-Xo-Xa-Xnf-Xy. Activities of the constituent oxides in the dipersed phase (Zr,,Hf(.~5-x),Y,~5)O~.g5 can thus be expressed in terms of a single concentration variable, x=Xza2, while the activities of the constituent elements in the gamma matrix can be expressed in terms of two mole fractions, Xa and Xa. To solve the system of eqns. ( 1) through (3), a computer program was written and implemented into the TK Solver Plus Mathematical package [ 1 l] and executed on a Sun Spark 2 computer workstation. All the calculations were carried out at 850%. The results showed that a solution to the system of equations (1) through (3) exists. The solution also satisfies inequalities given in eqns. (4) and (5). The optimum composition of the zirconia-based phase is associated with x=0.3, that is, (Zro,3.Hfo.sa5,Yo.os5)01.95. The dissolution of this oxide in the gamma TiAl matrix will proceed until the chemical composition of the matrix becomes approximately XrizO.36, X~r=O.38, X~,=O.028, XHfo.06, x,=0.009 and X0=0.16. During the oxide dissolution process, the Gibbs free energies for formation of Al203 and
139
140
M.
GRUJICICand S. AROKIARAJ
TiO2 remain positive that is: AGAtm3 = 20,856 Cal/mole and AGTlO2= 7 1,85 1 Cal/mole respectively. This means that oxygen has not exceeded the solubility limit with respect to the formation of the two oxides. While the result presented above might be encouraging, it must be noted that if the initial volume fraction of the zirconia-based phase is lo%, the equilibrium condition between the oxide dispersion and the TiAl-base matrix is not met until the oxide is almost completely dissolved. Furthermore, when the equilibrium between the zirconia oxide and y-TiAl is established, the mole fractions of Hf and Zr will most likely exceed the solubility limit with respect to the formation of Al$!,r,Hf). Formation of the latter compound can then lead to further dissolution of the oxide phase in the matrix. Fortunately, since the formation of Al#r,Hf’) relies on the diffusion of substitutional species alone, it is, from the kinetics point of view, less critical than the formation of Al203 and TiO2
4. Conclusions Alloying zimonia with hafniacan be beneficial in preventing complete dissolution of the zirconia-base dispersion in the y-TiAl matrix. However, substantial amount of the dispersed phase is dissolved before the equilibrium between the two phases is established. When the equilibrium between the dispersion and the matrix is established, formation of Al- and Ti- base oxides is not thermodynamically feasible. However, formation of Al&Zr,Hf) is feasible and might lead to the further dissolution of the dispersed oxide phase. The latter process, however, is kinetically less critical than the formation of the two oxides. 5. Acknowledgements This work has been supported by the National Science Foundation, #DMR-9017214 and by the Center for Advanced Manufacturing, Clemson University. The authors would like to thank Dr. Bruce A. MacDonald of NSF for encouragement and continuing interest in this work.
6. References 1. M. Grujicic, Mater. Sci. Eng. A, 154 (1992) 75-78. 2. C. P. Narayan, Dispersed-phase Transformation Toughening of Titanium Aluminide, M.S. Thesis, Clemson University, 199 1. 3. S. Arokiaraj, Zirconia Dispersed-phase Transformation Toughening of Mechanically Alloyed Gamma Titanium-Aluminide, M.S. Thesis in progress, Clemson University, 1992. 4. E. M. Levin, H.F. McMurdie and F.P. Hall, Phase Diagrams for Ceramists, The American Ceranic Society, Inc., Vol. 1, (1956) 65. 5. I. Barin and 0. Knacke, Thermochemical Properties of Inorganic Substances, Berlin, New York, Springer-Verlag, 1973. 6. EKohler, Monatsh. Chem., 91 (1960). 738. 7. L. Kaufman and H. Bernstein, ” Computer Calculation of Phase Diagram”, Academic Press, New York, 1970. 8. J. L. Murray, “Phase Diagrams of Binary Titanium Alloys”, ed. J. L. Murray, ASM, Metals Park, Ohio, 1987. 9. J. L. Murray, “Binary Alloy Phase Diagrams”, ed. T. B. Massalski, ASM, Metals Park, Ohio, 1990. 10. L. Kaufman, User Applications of Alloy Phase Diagrams, (conference proceedings) ed. L. Kauf man, ASM, (1987) 145. 11. TK Solver Plus Computer Program, Universal Technical Systems, Rockfort, IL, 1989.