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Hydrogen solubility in molten TiAl alloys
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 8 0 0 8 e8 0 1 3
Available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Hydrogen solubility in molten TiAl alloys Yanqing Su*, Xinwang Liu, Liangshun Luo, Long Zhao, Jingjie Guo, Hengzhi Fu National Key Laboratory of Science and Technology on Precision Heat Processing of Metals, Harbin Institute of Technology, Harbin 150001, PR China
article info
abstract
Article history:
In this work, the hydrogen solubility in a titaniumealuminium (TiAl) binary alloy melt was
Received 16 March 2010
investigated through a theoretical analysis and the results compared subsequently with
Received in revised form
values determined experimentally. Determination of the theoretical values of hydrogen
26 April 2010
solubility is based on a modified version of Sievert’s law, in which hydrogen solubility is
Accepted 8 May 2010
related to the activity coefficient of the alloy melt and the hydrogen solubility in pure liquid
Available online 11 June 2010
metals. The activity coefficient is obtained in terms of the free volume theory, in which excess entropy is sufficiently taken into account. The experimental values of the hydrogen
Keywords:
solubility in the two alloy melts, Ti45Al and Ti47Al, were determined to validate the
Hydrogen
calculated values. This was performed using hydrogen charging apparatus. The experi-
Solubility
mental values obtained were in good agreement with the calculated values.
TiAl alloy
ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
Melt Activity coefficient
1.
Introduction
Titaniumealuminium (TiAl)-based alloys have been considered to have potential applications in aircraft or automotive engines because they display good mechanical properties over a wide range of temperatures [1e3]. When used correctly, hydrogen may improve the processing of TiAl alloys, including sintering, compacting, machining, and hot working [4,5]. The solubility of hydrogen in TiAl alloys has been studied for many years. Initially, hydrogenation treatments were performed by cathodic charging or gas-phase permeation at different temperatures [6e9]. However, these methods are time-consuming. In a recent development, hydrogen was introduced directly into the TiAl melt, resulting in better efficiency because the diffusion rate of hydrogen is much larger in the alloy melt compared to the solid [10]. To ensure that this hydrogenation method for alloys melts is applied properly, the actual values of the hydrogen solubility in TiAl alloy melts have to be obtained.
According to Sievert’s law, the hydrogen solubility in a TiAl alloy melt is dependent on the melt temperature and the partial pressure of hydrogen [11,12]. In other words, the hydrogen solubility changes with the temperature and partial pressure of hydrogen. However, obtaining the actual values of hydrogen solubility through experimentation over a wide range of temperatures and partial pressure variations is both difficult and costly. Instead, calculating the hydrogen solubility based on thermodynamic data is a more efficient means of determining the required information. The activity of TiAl alloy melts has been investigated for several decades now, and therefore the corresponding thermodynamic properties database available is currently comprehensive. Thus, calculating the hydrogen solubility in TiAl alloy melts has become feasible. There are many solution models for this, including the regular solution model, subregular solution model, and quasi-regular solution model [13]. However, these methods do not consider excess entropy or
* Corresponding author. Tel.: þ86 451 86417395; fax: þ86 451 86415776. E-mail address: [email protected] (Y. Su). 0360-3199/$ e see front matter ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.05.054
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 8 0 0 8 e8 0 1 3
Table 1 e Thermodynamic data used for the determination of the activity coefficient. Metal Ti Al
1=3
V (v)
nws ((d.u)1/3)
V2=3 (cm2)
r/p
m
Tm(K)
3.65 4.20
1.47 1.39
4.8 4.6
1.0 1.9
0.04 0.07
1941 933
only address it approximately in calculations. Tanaka et al. then developed the free volume theory, which incorporated an accurate consideration of excess entropy, including excess configuration and vibration entropy [14]. In this theory, a detailed description of excess entropy makes it more suitable for true determinations of hydrogen solubility, especially in cases where the component characteristics of TiAl melts, such as melting point and molar volume, are significantly different. Activity coefficients can also be obtained based on this theory. In this study, we calculate the hydrogen solubility in TiAl alloy melts using a model based on a modified version of Sievert’s law and the free volume theory. Experimental values are then obtained with hydrogen charging apparatus to validate the theoretical values.
2. Model for calculating the hydrogen solubility in TiAl binary alloy melts Hydrogen can decompose on the melt surface of alloys at high temperatures and diffuse into the melt. When the hydrogen dissolution is equal to the terminal solubility of the alloy melt, a dynamic equilibrium is attained between the hydrogen atoms dissolved in the alloy melt and the hydrogen atoms in the melting chamber, which is described as ½ H2(g) ¼ H (dissolved in melt). This equilibrium yields the following equation: CH KP ¼ pffiffiffiffiffiffiffiffi (1) PH2 This equation is also called Sievert’s law, which describes the relationship between hydrogen solubility (CH) and the partial pressure of hydrogen ðPH2 Þ [11]. According to the van’t Hoff relationship, the equilibrium constant (KP) is related to standard free energy of hydrogen dissolved in the alloy melt ðDGqm Þ, which can be expressed as: DGqm ¼ RTlnKP
(2)
8009
where R is the gas constant, and T is the temperature of the alloy melt. Thus, combining Equations (1) with (2), the hydrogen solubility in an alloy melt can be written as: CH ¼
pffiffiffiffiffiffiffiffi PH2 exp DGqm =RT
(3)
For non-ideal solutions, DGqm can be obtained using the following equation: X DGqm ¼ xi DGqi þ DGEX (4) m where xi is molar fraction of i, and DGEX m is the excess free energy of the alloy melt, which can be expressed as: DGEX m ¼ RT
X
xi lngi
(5)
where gi is the activity coefficient of i. According to the above equations, a model of hydrogen solubility in the alloy melts can be written as follows: lnCH ¼
X
Ci xi ln H gi
(6)
where CiH is the hydrogen solubility in a pure Ti or Al melt. The hydrogen solubilities in pure melts have an empirical formula, which can be easily obtained by experiments. Equation (6) thus demonstrates that, when determining the hydrogen solubility in an alloy melt, only the activity coefficients of the components of the melt need to be determined.
3.
Calculation of the activity coefficient
The free volume theory developed by Tanaka is used to determine the activity coefficient of TiAl binary alloy melts [15]. According to Tanaka’s model, a restrictive region, called the atom cell, exists around each atom in the alloy melt, and atoms move towards the nearest restrictive region. This theory is based on a real solution and has been acknowledged extensively [15]. The partition function of a melt can be written as: 8 9 Z =N E0 < JðrÞJð0Þ E0 (7) exp dv ¼vNf exp Q ¼exp ; kT : kT kT cell
where vf ¼ðpL2kT=vÞ3=2 is the free volume; E0 is the alloy potential energy in equilibrium; J(r) is the potential energy of atom i, which is at a distance of r from the atom cell; k is the
Fig. 1 e Dependence of the activity coefficient on the temperature in (a) Ti45Al and (b) Ti47Al alloy melts.
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 8 0 0 8 e8 0 1 3
Fig. 2 e Schematic diagram of the hydrogen charging apparatus.
Boltzmann constant; T is the temperature; N is the number of atoms; and v is the volume of the cell. The following equations can be derived from Equation (7): DHi ¼ Nij Uij =z
(8)
DSEC ¼ x2i x2j U2ij = 2RT2
(9)
(
DSEV
2 Lii Ljj ¼ ð3=2ÞRxi xj Lii Ljj " 2 #) 4Uii Ujj 2Uij Uii þ Ujj Uii þ Ujj þ 2Uii Ujj
For a binary system, there are some basic thermodynamic equations: GEij ¼ DHij TSEij
(16)
SEij ¼ DSEC þ DSEV
(17)
vGEij E Gi ¼ GEij þ ð1 xi Þ vxi
(18)
E
(10)
E
GEij ¼ xi Gi þ xj Gj
(19)
E
where DHij is the heat of formation; Uij is the energy of exchange; DSEC is the excess configuration entropy; DSEV is the excess vibration entropy; z is coordination number; Lii and Ljj are the distances of potential energy for atoms of i and j to expand, respectively; and Uii and Ujj are the potential energies of the atom i and j in the atom cell. The terms Nij, Lii, and Uii can be obtained from the following equations.
(11) Nij ¼ N0 zxi xj 1 xi xj Uij =ðRTÞ pffiffiffi 1=3 Lii ¼ ð1=2Þ 2Vi =N0
(12)
Uii ¼ 685b2i Tm;i
(13)
In the above equations, N0 is Avogadro’s number, Vi is the molar volume of i, bi is the frequency factor of the change of i from solid to liquid at the melting point (generally assigned a value of 0.5), and Tm,i is the melting point of i. The heat of formation (DHij) of a binary alloy melt can be obtained from the Miedema model [16]: h i h i xi 1 þ mi xj fi fj xj 1 þ mj xi fj fi h i h i (14) DHij ¼ fij xi Vi2=3 1 þ mi xj fi fj þ xj Vj2=3 1 þ mj xi fj fi
fij ¼
2PVi2=3 Vj2=3
o n h i2 2 1=3 1=3 q nws fj fi aðr=pÞ nws p j i 1 1 1=3 1=3 nws þ nws i
(15)
j
In Equations (14) and (15), xi and xj are the molar fractions of components i and j, and Vi and Vj are the molars volume of the same. The term nws is the electron density, f is the electronegativity, and the values for m, p, q, r, and a are empirical constants. For a TiAl alloy melt, a ¼ 0.73, p ¼ 12.3, and q ¼ 115.62. Other thermodynamic data are shown in Table 1 as provided by Gocken [17].
Gi ¼ RTlngi
(20)
In the above equations, GEij is the excess free energy of a melt, E SEij is the excess entropy, and Gi is the partial molar excess free energy. The activity coefficient can be obtained from Equations (7)e(20), and can be written as: ( DHij 1=2 . gi ¼exp DHij =ð2RTÞ Aij 1 4 RT R ð3=2ÞBij ð1 xi Þ2 þAij =R þ ð1 xi Þ " # ) 4DHij 1=2 . 1 vHij 0:5 þ 2Aij 1 R $ RT RT vxi
ð21Þ
h . i gj ¼ exp GEij xi RTlngi xj RT
(22)
Table 2 e Hydrogen absorption data of a Ti melt. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Partial pressure Temperature Hydrogen of hydrogen P/Pa T/K solubility CH/wppm 5261 9015 3665 9684 4159 8857 2546 5369 4861 9147 3128 6254 4218 8952
1801 1786 1896 1875 1946 1951 2013 2021 2065 2057 2102 2115 2213 2208
5503 7619 3741 6338 3618 5104 2403 3532 3026 4326 2342 3157 2187 3279
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 8 0 0 8 e8 0 1 3
8011
Fig. 3 e Dependence of the hydrogen solubility in (a) a Ti melt and (b) an Al melt on the partial pressure of hydrogen at different temperatures.
The activity coefficient of the components of a TiAl melt with different compositions can be determined from the above equations. Fig. 1 shows the dependence of the activity coefficients of Ti and Al on temperature for Ti45Al and Ti47Al alloy melts. The activity coefficient increases with the temperature, and the activity coefficient of Al is higher than that of Ti.
4.
Experimental
The experiments for determining hydrogen solubility are operated in hydrogen charging apparatus. The experiments include two steps: ingot preparation and the hydrogen absorption process. TiAl and pure Ti ingots, in button form, were prepared using a non-consumable electrode arc furnace under an argon atmosphere. Ti and Al with purity >99.9 wt.% were used as the starting materials. Alloy buttons weighing about 25e30 g were melted 4e5 times to improve the chemical homogeneity. Two groups of TiAl alloys were prepared and the chemical analyses indicate that the compositions of the ingots are Ti-45Al and Ti-47Al. The process of hydrogen charging was performed in a nonconsumable electrode arc melting furnace, fitted with a water-
cooled copper crucible and a hydrogen analyzer. A schematic diagram of the set-up is shown in Fig. 2. The hydrogen analyzer can detect the volume fraction of hydrogen and the pressure in the melting chamber. The ingots were melted under a gaseous mixture of hydrogen and argon, with the partial pressure of hydrogen being controlled by the hydrogen analyzer. The hydrogen molecules decompose to atoms on the surface of arc and melt and diffuse into the melt. After the hydrogen becomes steady indicated by the hydrogen analyzer, the alloys is allowed to cool in the furnace. Then the sample is turned over and remelted again. This process has been repeated for four times until the hydrogen is saturated in the alloy melt. The hydrogen remains in the alloy during the cooling process because the hydrogen in the melt is also in dynamical equilibrium with the hydrogen in the chamber. During the whole process, the hydrogen fraction in the gaseous mixture and total pressure are monitored by the hydrogen analyzer. The experimental values of the hydrogen solubility in the alloy melt can be determined from a decrease of the partial pressure of hydrogen in the melting chamber based on the Clapeyron equation: PV ¼ nRT. The experimental values of the hydrogen solubility in an alloy melt are obtained from the following equation:
Fig. 4 e Dependence of the hydrogen solubility in (a) Ti45Al and (b) Ti47Al alloy melts on the partial pressure of hydrogen at different temperatures.
8012
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 8 0 0 8 e8 0 1 3
Fig. 5 e Dependence of the hydrogen solubility in (a) Ti45Al and (b) Ti47Al alloy melts on the temperature at different hydrogen partial pressures.
CH ¼
2Pð1 c1 ÞV c1 c2 1 c1 1 c2 mRT
(23)
where P is the total pressure of the gaseous mixture of argon and hydrogen before melting, V is the volume of the melting chamber and hydrogen analyzer (30 L), m is the weight of the alloy melt, R is the gas constant [8.314 J/(molK)], T is the temperature monitored by an infrared thermoscope, and c1 and c2 are the volume fractions of hydrogen before and after the hydrogen absorption process, respectively.
5.
Hydrogen solubilities in Al and Ti melts
The hydrogen solubility in pure metal melts has been studied for many years [18,19]. According to the Arrhenius equation and Sievert’s law, the hydrogen solubility in a liquid melt can be described uniformly by the following equation [20]: ! CH A 1 PH2 (24) þ B þ ln ln 0 ¼ P0 T=T0 2 CH where A and B are constants, and A is affected by the heat of solution for hydrogen in the liquid melt; T is the temperature; T0 is the standard temperature (T0 ¼ 1 K); CH is the hydrogen
solubility; C0H is the standard solubility in hydrogen in a liquid metal ðC0H ¼ 1 wppmÞ; PH2 is the partial pressure of hydrogen; and P0 is the standard pressure (P0 ¼ 101 325 Pa). As such, Equation (24) can be written as: A 1 PH2 lnCH ¼ þ B þ ln (25) 101325 T 2 A comprehensive study of foamed Al has allowed the collection of integrated experimental data about hydrogen solubility in Al melts [21]. Different sources have listed different data for various experimental conditions, so the average values of A and B are used for the hydrogen solubility in an Al melt [22]. This can be computed from: 6159 1 PH2 (26) þ 6:247 þ ln lnCAl H ¼ 101325 T 2 There are few reports about the solubility of hydrogen in a titanium melt. So the solubility of hydrogen in titanium melt was obtained by experiment, using the hydrogen charging equipment (Fig. 2). The solubility of hydrogen in a Ti melt is based on Equation (25). The data collected from measurements taken during hydrogen absorption by a Ti melt are listed in Table 2. The hydrogen solubility in the Ti melt can be obtained from the equation:
Fig. 6 e Comparison of calculated and experimental values of hydrogen solubility at 1900 K at different hydrogen partial pressures. (a)Ti45Al; (b) Ti47Al.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 8 0 0 8 e8 0 1 3
lnCTi H ¼
7783 1 PH2 þ 5:779 þ ln 101325 T 2
(27)
The hydrogen solubility in the Ti melt is similar to Ref. [20]. Fig. 3 shows a graph of the hydrogen solubilities for both the Ti and Al melts according to the above equations. The hydrogen solubilities in the Ti melt decrease with increasing temperature, while the inverse is true of the Al melt.
6.
Results and discussion
6.1.
Hydrogen solubility in TiAl binary alloy melts
The activity coefficients can be calculated from Equations (21) to (22), while the hydrogen solubilities in Ti and Al melts are expressed by Equations (26)e(27). Thus, the hydrogen solubility in a TiAl alloy melt composed of different amounts of Ti and Al can be obtained from Equation (6). The dependence of the hydrogen solubility in the Ti45Al and Ti47Al alloy melts on the partial pressure of hydrogen at different temperatures is shown in Fig. 4. The dependence of the hydrogen solubility in the Ti45Al and Ti47Al alloy melts on temperature is shown in Fig. 5. The hydrogen solubility increases with increasing hydrogen partial pressure and decreases with increasing temperature. At constant temperature and partial pressure of hydrogen, the hydrogen solubilities in TiAl melts decrease with increasing Al content.
6.2. Comparison of experimental and calculated values of hydrogen solubility The experimental (dot) and calculated values (solid line) of hydrogen solubilities in the Ti45Al and Ti47Al alloy melts at 1900 K under different hydrogen partial pressures are compared in Fig. 6. The figure shows that the experimental values closely match the calculated values.
7.
Conclusion
The theoretical hydrogen solubilities in TiAl alloy melts are obtained based on a modified version of Sievert’s law, which relates the thermodynamic properties of a TiAlH alloy melt, including the activity coefficient and hydrogen solubility, with that of pure liquid metals. The activity coefficient is calculated in terms of an improved free volume model. The hydrogen solubility in a pure Ti melt was determined experimentally. The hydrogen solubility in a TiAl melt increases with increasing hydrogen partial pressure and decreases with increasing temperature. At constant temperature and hydrogen partial pressure, the hydrogen solubility in the TiAl alloy melts decreases with increasing Al content. Experimental values were obtained from a hydrogen charging apparatus, and these are consistent with the calculated theoretical values.
Acknowledgements The authors would like to thank the National Natural Science Foundation of China (50975060) and the Foundation of State
8013
Key Lab of Advanced Welding Production Technology of China for the financial support.
references
[1] Goral M, Moskal G, Swadzba L. Gas phase aluminizing of TiAl intermetallics. Intermetallics 2009;17:669e71. [2] Haidar J, Gnanarajan S, Dunlop JB. Direct production of alloys based on titanium aluminides. Intermetallics 2009;17: 651e6. [3] Kartavykh AV, Tcherdyntsev VV, Zollinger J. TiAleNb melt interaction with AlN refractory crucibles. Mater Chem Phys 2009;116:300e4. [4] Senkov ON, Froes FH. Thermohydrogen processing of titanium alloys. Int J Hydrogen Energy 1999;24:565e76. [5] Sun ZG, Zhou WL, Hou HL. Strengthening of Tie6Ale4V alloys by thermohydrogen processing. Int J Hydrogen Energy 2009;34:1971e6. [6] Morasch KR, Bahr DF. The effects of hydrogen on deformation and cross slip in a BCC titanium alloy. Scripta Mater 2001;45:839e45. [7] Liu HJ, Zhou L, Liu P, Liu QW. Microstructural evolution and hydride precipitation mechanism in hydrogenated Tie6Ale4V alloy. Int J Hydrogen Energy 2009;34(23): 9596e602. [8] Iino Y, Gao KW, Okamura K, Qiao LJ, Chu WY. Effects of hightemperature hydrogen exposure on room temperature tensile properties and fatigue crack growth behaviour of TiAl base alloy. Mater Sci Eng 2002;A338:54e9. [9] Lo´pez-Sua´rez A, Rickards J, Trejo-Luna R. Analysis of hydrogen absorption by Ti and Tie6Ale4V using the ERDA technique. Int J Hydrogen Energy 2003;28(10):1107e13. [10] Su YQ, Wang L, Luo LS, Jiang XH, Guo JJ, Fu HZ. Deoxidation of titanium alloy using hydrogen. Int J Hydrogen Energy 2009; 34(21):8958e63. [11] Sieverts A. Absorption of gases by metals. Zeitschrift fur Metallkunde 1929;21:37e46. [12] Wang WE. Thermodynamic evaluation of the titaniumehydrogen system. J Alloys Compd 1996;238:6e12. [13] Hildebrand JH. A quantitative treatment of deviations from Raoult’s law. Proc Natl Acad Sci U S A 1927;13(5):267e72. [14] Tanaka T, Gocken NA, Morita Z. Relationship between enthalpy of mixing and excess entropy in liquid binary alloys. Z Metallkun 1990;81:349e53. [15] Jiang GR, Liu Y, Li YX, Su YQ, Guo JJ. Improvement of calculation method for the activity coefficient of multicomponent alloys. Acta Metal Sinica 2007;5:503e8. [16] Miedema AR, De Chatel PF, De Boer FR. Cohesion in alloysfundamentals of a semi-empirical model. Physica 1980;100B: 1e28. [17] Gocken NA. Thermodynamics. New York: Plenum Press; 1986. 255. [18] Sokolov VM, Fedorenko IV. Estimation of hydrogen solubility in liquid alloys of iron, nickel and copper. Int J Hydrogen Energy 1996;21(11e12):931e4. [19] Yamamura S, Shiota H, Murakami K, Nakajima H. Evaluation of porosity in porous copper fabricated by unidirectional solidification under pressurized hydrogen. Mater Sci Eng 2001;A318(1e2):137e43. [20] Zhang HW, Li YX, Liu Y. Hydrogen solubility in pure metals for GASAR process. Acta Metal Sinica 2007;43:113e8. [21] Anyalebechi PN. Analysis of the effects of alloying elements on hydrogen solubility in liquid aluminium alloys. Scripta Metal Mater 1995;33(8):1209e16. [22] Lakomsky VL, Kalinyuk NN. Solubility of hydrogen in liquid titanium and nickel. Russ Metall 1966;2:80e5.
Available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Hydrogen solubility in molten TiAl alloys Yanqing Su*, Xinwang Liu, Liangshun Luo, Long Zhao, Jingjie Guo, Hengzhi Fu National Key Laboratory of Science and Technology on Precision Heat Processing of Metals, Harbin Institute of Technology, Harbin 150001, PR China
article info
abstract
Article history:
In this work, the hydrogen solubility in a titaniumealuminium (TiAl) binary alloy melt was
Received 16 March 2010
investigated through a theoretical analysis and the results compared subsequently with
Received in revised form
values determined experimentally. Determination of the theoretical values of hydrogen
26 April 2010
solubility is based on a modified version of Sievert’s law, in which hydrogen solubility is
Accepted 8 May 2010
related to the activity coefficient of the alloy melt and the hydrogen solubility in pure liquid
Available online 11 June 2010
metals. The activity coefficient is obtained in terms of the free volume theory, in which excess entropy is sufficiently taken into account. The experimental values of the hydrogen
Keywords:
solubility in the two alloy melts, Ti45Al and Ti47Al, were determined to validate the
Hydrogen
calculated values. This was performed using hydrogen charging apparatus. The experi-
Solubility
mental values obtained were in good agreement with the calculated values.
TiAl alloy
ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
Melt Activity coefficient
1.
Introduction
Titaniumealuminium (TiAl)-based alloys have been considered to have potential applications in aircraft or automotive engines because they display good mechanical properties over a wide range of temperatures [1e3]. When used correctly, hydrogen may improve the processing of TiAl alloys, including sintering, compacting, machining, and hot working [4,5]. The solubility of hydrogen in TiAl alloys has been studied for many years. Initially, hydrogenation treatments were performed by cathodic charging or gas-phase permeation at different temperatures [6e9]. However, these methods are time-consuming. In a recent development, hydrogen was introduced directly into the TiAl melt, resulting in better efficiency because the diffusion rate of hydrogen is much larger in the alloy melt compared to the solid [10]. To ensure that this hydrogenation method for alloys melts is applied properly, the actual values of the hydrogen solubility in TiAl alloy melts have to be obtained.
According to Sievert’s law, the hydrogen solubility in a TiAl alloy melt is dependent on the melt temperature and the partial pressure of hydrogen [11,12]. In other words, the hydrogen solubility changes with the temperature and partial pressure of hydrogen. However, obtaining the actual values of hydrogen solubility through experimentation over a wide range of temperatures and partial pressure variations is both difficult and costly. Instead, calculating the hydrogen solubility based on thermodynamic data is a more efficient means of determining the required information. The activity of TiAl alloy melts has been investigated for several decades now, and therefore the corresponding thermodynamic properties database available is currently comprehensive. Thus, calculating the hydrogen solubility in TiAl alloy melts has become feasible. There are many solution models for this, including the regular solution model, subregular solution model, and quasi-regular solution model [13]. However, these methods do not consider excess entropy or
* Corresponding author. Tel.: þ86 451 86417395; fax: þ86 451 86415776. E-mail address: [email protected] (Y. Su). 0360-3199/$ e see front matter ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.05.054
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 8 0 0 8 e8 0 1 3
Table 1 e Thermodynamic data used for the determination of the activity coefficient. Metal Ti Al
1=3
V (v)
nws ((d.u)1/3)
V2=3 (cm2)
r/p
m
Tm(K)
3.65 4.20
1.47 1.39
4.8 4.6
1.0 1.9
0.04 0.07
1941 933
only address it approximately in calculations. Tanaka et al. then developed the free volume theory, which incorporated an accurate consideration of excess entropy, including excess configuration and vibration entropy [14]. In this theory, a detailed description of excess entropy makes it more suitable for true determinations of hydrogen solubility, especially in cases where the component characteristics of TiAl melts, such as melting point and molar volume, are significantly different. Activity coefficients can also be obtained based on this theory. In this study, we calculate the hydrogen solubility in TiAl alloy melts using a model based on a modified version of Sievert’s law and the free volume theory. Experimental values are then obtained with hydrogen charging apparatus to validate the theoretical values.
2. Model for calculating the hydrogen solubility in TiAl binary alloy melts Hydrogen can decompose on the melt surface of alloys at high temperatures and diffuse into the melt. When the hydrogen dissolution is equal to the terminal solubility of the alloy melt, a dynamic equilibrium is attained between the hydrogen atoms dissolved in the alloy melt and the hydrogen atoms in the melting chamber, which is described as ½ H2(g) ¼ H (dissolved in melt). This equilibrium yields the following equation: CH KP ¼ pffiffiffiffiffiffiffiffi (1) PH2 This equation is also called Sievert’s law, which describes the relationship between hydrogen solubility (CH) and the partial pressure of hydrogen ðPH2 Þ [11]. According to the van’t Hoff relationship, the equilibrium constant (KP) is related to standard free energy of hydrogen dissolved in the alloy melt ðDGqm Þ, which can be expressed as: DGqm ¼ RTlnKP
(2)
8009
where R is the gas constant, and T is the temperature of the alloy melt. Thus, combining Equations (1) with (2), the hydrogen solubility in an alloy melt can be written as: CH ¼
pffiffiffiffiffiffiffiffi PH2 exp DGqm =RT
(3)
For non-ideal solutions, DGqm can be obtained using the following equation: X DGqm ¼ xi DGqi þ DGEX (4) m where xi is molar fraction of i, and DGEX m is the excess free energy of the alloy melt, which can be expressed as: DGEX m ¼ RT
X
xi lngi
(5)
where gi is the activity coefficient of i. According to the above equations, a model of hydrogen solubility in the alloy melts can be written as follows: lnCH ¼
X
Ci xi ln H gi
(6)
where CiH is the hydrogen solubility in a pure Ti or Al melt. The hydrogen solubilities in pure melts have an empirical formula, which can be easily obtained by experiments. Equation (6) thus demonstrates that, when determining the hydrogen solubility in an alloy melt, only the activity coefficients of the components of the melt need to be determined.
3.
Calculation of the activity coefficient
The free volume theory developed by Tanaka is used to determine the activity coefficient of TiAl binary alloy melts [15]. According to Tanaka’s model, a restrictive region, called the atom cell, exists around each atom in the alloy melt, and atoms move towards the nearest restrictive region. This theory is based on a real solution and has been acknowledged extensively [15]. The partition function of a melt can be written as: 8 9 Z =N E0 < JðrÞJð0Þ E0 (7) exp dv ¼vNf exp Q ¼exp ; kT : kT kT cell
where vf ¼ðpL2kT=vÞ3=2 is the free volume; E0 is the alloy potential energy in equilibrium; J(r) is the potential energy of atom i, which is at a distance of r from the atom cell; k is the
Fig. 1 e Dependence of the activity coefficient on the temperature in (a) Ti45Al and (b) Ti47Al alloy melts.
8010
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 8 0 0 8 e8 0 1 3
Fig. 2 e Schematic diagram of the hydrogen charging apparatus.
Boltzmann constant; T is the temperature; N is the number of atoms; and v is the volume of the cell. The following equations can be derived from Equation (7): DHi ¼ Nij Uij =z
(8)
DSEC ¼ x2i x2j U2ij = 2RT2
(9)
(
DSEV
2 Lii Ljj ¼ ð3=2ÞRxi xj Lii Ljj " 2 #) 4Uii Ujj 2Uij Uii þ Ujj Uii þ Ujj þ 2Uii Ujj
For a binary system, there are some basic thermodynamic equations: GEij ¼ DHij TSEij
(16)
SEij ¼ DSEC þ DSEV
(17)
vGEij E Gi ¼ GEij þ ð1 xi Þ vxi
(18)
E
(10)
E
GEij ¼ xi Gi þ xj Gj
(19)
E
where DHij is the heat of formation; Uij is the energy of exchange; DSEC is the excess configuration entropy; DSEV is the excess vibration entropy; z is coordination number; Lii and Ljj are the distances of potential energy for atoms of i and j to expand, respectively; and Uii and Ujj are the potential energies of the atom i and j in the atom cell. The terms Nij, Lii, and Uii can be obtained from the following equations.
(11) Nij ¼ N0 zxi xj 1 xi xj Uij =ðRTÞ pffiffiffi 1=3 Lii ¼ ð1=2Þ 2Vi =N0
(12)
Uii ¼ 685b2i Tm;i
(13)
In the above equations, N0 is Avogadro’s number, Vi is the molar volume of i, bi is the frequency factor of the change of i from solid to liquid at the melting point (generally assigned a value of 0.5), and Tm,i is the melting point of i. The heat of formation (DHij) of a binary alloy melt can be obtained from the Miedema model [16]: h i h i xi 1 þ mi xj fi fj xj 1 þ mj xi fj fi h i h i (14) DHij ¼ fij xi Vi2=3 1 þ mi xj fi fj þ xj Vj2=3 1 þ mj xi fj fi
fij ¼
2PVi2=3 Vj2=3
o n h i2 2 1=3 1=3 q nws fj fi aðr=pÞ nws p j i 1 1 1=3 1=3 nws þ nws i
(15)
j
In Equations (14) and (15), xi and xj are the molar fractions of components i and j, and Vi and Vj are the molars volume of the same. The term nws is the electron density, f is the electronegativity, and the values for m, p, q, r, and a are empirical constants. For a TiAl alloy melt, a ¼ 0.73, p ¼ 12.3, and q ¼ 115.62. Other thermodynamic data are shown in Table 1 as provided by Gocken [17].
Gi ¼ RTlngi
(20)
In the above equations, GEij is the excess free energy of a melt, E SEij is the excess entropy, and Gi is the partial molar excess free energy. The activity coefficient can be obtained from Equations (7)e(20), and can be written as: ( DHij 1=2 . gi ¼exp DHij =ð2RTÞ Aij 1 4 RT R ð3=2ÞBij ð1 xi Þ2 þAij =R þ ð1 xi Þ " # ) 4DHij 1=2 . 1 vHij 0:5 þ 2Aij 1 R $ RT RT vxi
ð21Þ
h . i gj ¼ exp GEij xi RTlngi xj RT
(22)
Table 2 e Hydrogen absorption data of a Ti melt. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Partial pressure Temperature Hydrogen of hydrogen P/Pa T/K solubility CH/wppm 5261 9015 3665 9684 4159 8857 2546 5369 4861 9147 3128 6254 4218 8952
1801 1786 1896 1875 1946 1951 2013 2021 2065 2057 2102 2115 2213 2208
5503 7619 3741 6338 3618 5104 2403 3532 3026 4326 2342 3157 2187 3279
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 8 0 0 8 e8 0 1 3
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Fig. 3 e Dependence of the hydrogen solubility in (a) a Ti melt and (b) an Al melt on the partial pressure of hydrogen at different temperatures.
The activity coefficient of the components of a TiAl melt with different compositions can be determined from the above equations. Fig. 1 shows the dependence of the activity coefficients of Ti and Al on temperature for Ti45Al and Ti47Al alloy melts. The activity coefficient increases with the temperature, and the activity coefficient of Al is higher than that of Ti.
4.
Experimental
The experiments for determining hydrogen solubility are operated in hydrogen charging apparatus. The experiments include two steps: ingot preparation and the hydrogen absorption process. TiAl and pure Ti ingots, in button form, were prepared using a non-consumable electrode arc furnace under an argon atmosphere. Ti and Al with purity >99.9 wt.% were used as the starting materials. Alloy buttons weighing about 25e30 g were melted 4e5 times to improve the chemical homogeneity. Two groups of TiAl alloys were prepared and the chemical analyses indicate that the compositions of the ingots are Ti-45Al and Ti-47Al. The process of hydrogen charging was performed in a nonconsumable electrode arc melting furnace, fitted with a water-
cooled copper crucible and a hydrogen analyzer. A schematic diagram of the set-up is shown in Fig. 2. The hydrogen analyzer can detect the volume fraction of hydrogen and the pressure in the melting chamber. The ingots were melted under a gaseous mixture of hydrogen and argon, with the partial pressure of hydrogen being controlled by the hydrogen analyzer. The hydrogen molecules decompose to atoms on the surface of arc and melt and diffuse into the melt. After the hydrogen becomes steady indicated by the hydrogen analyzer, the alloys is allowed to cool in the furnace. Then the sample is turned over and remelted again. This process has been repeated for four times until the hydrogen is saturated in the alloy melt. The hydrogen remains in the alloy during the cooling process because the hydrogen in the melt is also in dynamical equilibrium with the hydrogen in the chamber. During the whole process, the hydrogen fraction in the gaseous mixture and total pressure are monitored by the hydrogen analyzer. The experimental values of the hydrogen solubility in the alloy melt can be determined from a decrease of the partial pressure of hydrogen in the melting chamber based on the Clapeyron equation: PV ¼ nRT. The experimental values of the hydrogen solubility in an alloy melt are obtained from the following equation:
Fig. 4 e Dependence of the hydrogen solubility in (a) Ti45Al and (b) Ti47Al alloy melts on the partial pressure of hydrogen at different temperatures.
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 8 0 0 8 e8 0 1 3
Fig. 5 e Dependence of the hydrogen solubility in (a) Ti45Al and (b) Ti47Al alloy melts on the temperature at different hydrogen partial pressures.
CH ¼
2Pð1 c1 ÞV c1 c2 1 c1 1 c2 mRT
(23)
where P is the total pressure of the gaseous mixture of argon and hydrogen before melting, V is the volume of the melting chamber and hydrogen analyzer (30 L), m is the weight of the alloy melt, R is the gas constant [8.314 J/(molK)], T is the temperature monitored by an infrared thermoscope, and c1 and c2 are the volume fractions of hydrogen before and after the hydrogen absorption process, respectively.
5.
Hydrogen solubilities in Al and Ti melts
The hydrogen solubility in pure metal melts has been studied for many years [18,19]. According to the Arrhenius equation and Sievert’s law, the hydrogen solubility in a liquid melt can be described uniformly by the following equation [20]: ! CH A 1 PH2 (24) þ B þ ln ln 0 ¼ P0 T=T0 2 CH where A and B are constants, and A is affected by the heat of solution for hydrogen in the liquid melt; T is the temperature; T0 is the standard temperature (T0 ¼ 1 K); CH is the hydrogen
solubility; C0H is the standard solubility in hydrogen in a liquid metal ðC0H ¼ 1 wppmÞ; PH2 is the partial pressure of hydrogen; and P0 is the standard pressure (P0 ¼ 101 325 Pa). As such, Equation (24) can be written as: A 1 PH2 lnCH ¼ þ B þ ln (25) 101325 T 2 A comprehensive study of foamed Al has allowed the collection of integrated experimental data about hydrogen solubility in Al melts [21]. Different sources have listed different data for various experimental conditions, so the average values of A and B are used for the hydrogen solubility in an Al melt [22]. This can be computed from: 6159 1 PH2 (26) þ 6:247 þ ln lnCAl H ¼ 101325 T 2 There are few reports about the solubility of hydrogen in a titanium melt. So the solubility of hydrogen in titanium melt was obtained by experiment, using the hydrogen charging equipment (Fig. 2). The solubility of hydrogen in a Ti melt is based on Equation (25). The data collected from measurements taken during hydrogen absorption by a Ti melt are listed in Table 2. The hydrogen solubility in the Ti melt can be obtained from the equation:
Fig. 6 e Comparison of calculated and experimental values of hydrogen solubility at 1900 K at different hydrogen partial pressures. (a)Ti45Al; (b) Ti47Al.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 8 0 0 8 e8 0 1 3
lnCTi H ¼
7783 1 PH2 þ 5:779 þ ln 101325 T 2
(27)
The hydrogen solubility in the Ti melt is similar to Ref. [20]. Fig. 3 shows a graph of the hydrogen solubilities for both the Ti and Al melts according to the above equations. The hydrogen solubilities in the Ti melt decrease with increasing temperature, while the inverse is true of the Al melt.
6.
Results and discussion
6.1.
Hydrogen solubility in TiAl binary alloy melts
The activity coefficients can be calculated from Equations (21) to (22), while the hydrogen solubilities in Ti and Al melts are expressed by Equations (26)e(27). Thus, the hydrogen solubility in a TiAl alloy melt composed of different amounts of Ti and Al can be obtained from Equation (6). The dependence of the hydrogen solubility in the Ti45Al and Ti47Al alloy melts on the partial pressure of hydrogen at different temperatures is shown in Fig. 4. The dependence of the hydrogen solubility in the Ti45Al and Ti47Al alloy melts on temperature is shown in Fig. 5. The hydrogen solubility increases with increasing hydrogen partial pressure and decreases with increasing temperature. At constant temperature and partial pressure of hydrogen, the hydrogen solubilities in TiAl melts decrease with increasing Al content.
6.2. Comparison of experimental and calculated values of hydrogen solubility The experimental (dot) and calculated values (solid line) of hydrogen solubilities in the Ti45Al and Ti47Al alloy melts at 1900 K under different hydrogen partial pressures are compared in Fig. 6. The figure shows that the experimental values closely match the calculated values.
7.
Conclusion
The theoretical hydrogen solubilities in TiAl alloy melts are obtained based on a modified version of Sievert’s law, which relates the thermodynamic properties of a TiAlH alloy melt, including the activity coefficient and hydrogen solubility, with that of pure liquid metals. The activity coefficient is calculated in terms of an improved free volume model. The hydrogen solubility in a pure Ti melt was determined experimentally. The hydrogen solubility in a TiAl melt increases with increasing hydrogen partial pressure and decreases with increasing temperature. At constant temperature and hydrogen partial pressure, the hydrogen solubility in the TiAl alloy melts decreases with increasing Al content. Experimental values were obtained from a hydrogen charging apparatus, and these are consistent with the calculated theoretical values.
Acknowledgements The authors would like to thank the National Natural Science Foundation of China (50975060) and the Foundation of State
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Key Lab of Advanced Welding Production Technology of China for the financial support.
references
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