Calculation of the Thermodynamic Properties in the Ir-B System Based on the Known Phase Diagram Dragana Zivkovic1, Leonida Stuparevic 1 Technical Faculty VJ 19210 Bor, Serbia and Montenegro; Phone/Fax: ++381 30 424 547; E-mail: dzivkovic@tf.bor.ac.yu Abstract: The results of the thermodynamic properties calculation in the binary Ir-B system is presented in this paper. Based on the known liquidus and solidus lines from the phase diagram, specific calculation procedure according to Rao and Belton was done, so activities and activity coefficients for iridium and boron were determined at the temperatures of 2800, 2900 and 3000K. Keywords: alloy thermodynamics, phase diagram, Ir-B system Received: December 14, 2004 Accepted: September IS, 2005 Introduction Several investigations on the iridium borides have been reported in literature by Arronson et al. in 1962 [1] and 1963 [2], Lundstram in 1967 [3], Rogl et al. in 1971 [4], as well as the liquidus and solidus-liquidus data according to Ipser and Rogl in 1981 [5] and metalo-graphical investigation of Ir-B system by Stuparevic in 1986 [6]. 220C- 20M- at% B Figure I. Phase diagram of the Ir-B system [5]. Table I. Characteristic reactions in the Ir-B system according to Ipser and Rogl [5]. Temperature, °C Reaction B-content (at%) Type of reaction 1259 ± 4 L—>Ir + IrBo.7 37.5 eutectic 1287 ± 4 L IrBo.7 38.5 congr. melt. 1258 ± 4 L —»IrBo.7 + IrBo.9 40.0 eutectic 1333 ±4 L —»IrBo.9 46.5 congr. melt. 1274 ± 0 L + IrBo.s ->IrB 50.0 peritectic 1209 ± 3 IrB —> IrBo.9 + IrBi.35 50.0 eutectoid 1248 ± 3 L —»IrB + IrBi.35 54.0 eutectic 1287 ± 5 L IrBi.35 57.5 congr. melt. 1255 ± 0 L IrBi.35 + B 60.0 eutectic Phase diagram of the Ir-B binary system is given in Fig.l, while the characteristic reactions and their type at the certain compositions and temperatures are presented in Table l. Concerning the thermodynamic data for this binary system, there are no adequate references in literature. The main reason for this is the high investigating temperature, which causes many difficulties in the experimental work. So, as a contribution to the better thermo-dynamic knowledge of the Ir-B binary system, an analytical approach to this subject is presented in this paper. Based on the known liquidus and solidus lines from the phase diagram, specific calculation procedure according to Rao and Belton [7,8] was performed, which enabled the determination of the activities, activity coefficients and other partial molar quantities at the temperature of 2500 K. Theoretical fundamentals In some binary systems it is possible to calculate the activity coefficients of components in liquid solutions from the locations of the liquidus and solidus lines on the phase diagrams. For systems of simple eutectic type, with little or no terminal solid solubility, this method offers a means of obtaining the activity coefficients with acceptable accuracy [7,8]. For illustration of this method, two examples of calculation will be given for the imaginary binary eutectic Mej-Me2 system (where Mej and Me2 are different metals): • first, if there are no terminal solid solubility, and • second, if there is little solid solubility in the investigated system. First case: Assume that on the Me2-rich side of the phase diagram the liquidus descends sharply with increasing Me: content and terminates at the eutectic point (T2, xMe2). Because solid Me2 dissolves no Mep then, at any point on the liquidus curve, a liquid Me^ Me2 solution of composition xMe2 is in equilibrium with pure solid Me2, at temperature T. In other words, MerMe2 (liquid alloy) = Me2 (pure, solid) at T (I) The partial molar free energy of Me2 in the liquid alloy, GMe2, is equal to the molar free energy of the pure solid Me2, G°Me2(s). Thus Gm , = G°m + RT lna.. 2 = G°M 2( A (2) Me2 Me2(l) TMe2 Me2(s) V ' where aMe2 is the activity of Me2 in the liquid alloy with respect to the pure liquid Me2 standard state. Rearranging the terms, RTlnaMe2 = G°Me2(S) - G°Me2(l) = - AG°^l(Me2) (Q) where AG°s^l(Me2) is the standard free energy of fusion for Me2 at temperature T (this quantity should be expressed as a function of temperature using data on heat of fusion and heat capacity). Second case: In the case of eutectic systems, with little terminal solid solubility of Me2 in Mep following equilibrium reaction could be written: MerMe2 (liquid, x^J = Me^ (solid, x^J (4) which means that activity of Me^component is less then I. Further, this can be expressed as Gm _ = G° + RT lna = G1() = G°1() + RT lna1() (5) Me(l) 1(l) 1(l) 1(s) 1(s) 1(s) v ' where aMe1(l) and aMe1(S) are activities of Me1-component in liquid (related to pure liquid Me1 in the standard state) and solid phase (related to pure solid Me1 in the standard state), respectively. When solubility of Me2 in the Me1 is not too high, it can be assumed that the solid phase is amenable to Raoult law, so awe1(S) — x Me1" Rearranging the Eq. (5) one obtains log awe1(l) = log xSMe1 - AG°s^l(Me1) G 2-303R^ (6) which is the basic equation for the calculation of aMe1(l) at different liquidus temperatures T. When values for activities of Me2 - component in liquid alloys of different compositions - at the liquidus temperature are calculated, the activity coefficients at the investigated temperature T' can be calculated assuming regular solution behavior for the melts as follows [8] Y = y (T/TO (U) Systems that are amenable to this type of analysis include, for example, lead-silver, iron-silicon, magnesium-silicon, iron-copper, etc. Often, in this type of system, experimental data on activities are available for only a limited range of compositions, and these data can be combined with activity data deduced from the phase diagram [8]. For some systems, Ir-B for example, where no data are available, this method could be very useful in the thermodynamic analysis and obtaining the activity-composition relation for the investigated composition range. Results and discussion The Ir-B phase diagram belongs to the group of systems for which the described calculation method [78] could be applied. But, the characteristics of this system make it differ from the original look of the simple eutectic type diagrams: numerous iridium borides occurs in the middle region of the phase diagram [5], so concentration range with iridium molar content 0.35-0.65 was not considered. Regions in the concentration range that were investigated are alloys with xIr = 0-0.35 and 0.6-1, respectively. For the first interval, iridium-rich side was treated and thermo-dynamic properties for iridium were determined, and in the second interval, boron-rich side of the phase diagram was investigated and thermodynamic properties for boron were determined. Values of chosen alloy compositions and adequate liquidus temperatures read from the Ir-B phase diagram are shown in Table 2. Table 2. Chosen compositions and adequate liquidus temperatures. xlr xB Tliq, K 0.05 0.95 2503 0.10 0.90 2414 0.15 0.85 2310 0.20 0.80 2184 0.25 0.75 2058 0.30 0.70 1895 0.35 0.65 1732 0.65 0.35 1651 0.70 0.30 1866 0.75 0.25 2058 0.80 0.20 2236 0.85 0.15 2932 0.90 0.10 2532 0.95 0.05 2629 In further analysis, thermodynamic properties for the adequate component were calculated considering the calculation procedure given by Eq. (6). Results of this calculation, which include the value for AG° , for boron and irridium at the corresponding liquidus temperature, the activities and activity coefficients for both components in the liquid phase at the liquidus temperature are presented in Table 3. Table 3. Results of the thermodynamic calculation at the liquidus temperature. xlr logaB aB Yb 0.05 0 -0.04576 0.900 0.947 0.10 331 -0.07774 0.836 0.929 0.15 1289 -0.12605 0.748 0.880 0.20 2448 -0.18348 0.655 0.819 0.25 3605 -0.24639 0.567 0.756 0.30 5095 -0.32751 0.470 0.672 0.35 6570 -0.41996 0.380 0.585 xlr AG°s_>i (Ir) logair air Ylr 0.65 9608 -0.49102 0.323 0.497 0.70 7877 -0.37537 0.421 0.602 0.75 6201 -0.28231 0.522 0.696 0.80 4573 -0.20372 0.626 0.782 0.85 3106 -0.12591 0.748 0.880 0.90 1770 -0.08227 0.827 0.919 0.95 838 -0.03892 0.914 0.962 The calculation of activities and activity coefficients at the investigated temperatures of 2800, 2900 and 3000K, was done according to Eq. (7), assuming regular solution behavior for the melts. As for the illustration, dependencies of iridium and boron activities on composition at the temperature of 3000K are shown in Fig. 2. Negative deviation from the Raoult law in the investigated composition ranges could be noticed for both components (yIr