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The phase diagram of the RbBr–NaBr system
Computer Coupling of Phase Diagrams and Thermochemistry 28 (2004) 9–14 www.elsevier.com/locate/calphad
The phase diagram of the RbBr–NaBr system Jianhui Fanga,b,∗, Weizhong Dingb, Xia Shena, Liyi Shia, Nianyi Chena a College of Science, Shanghai University, Shanghai 200436, China b College of Material Science and Engineering, Shanghai University, Shanghai 200072, China
Received 30 December 2003; accepted 5 March 2004 Available online 9 April 2004
Abstract In this paper, the data from 75 known phase diagrams of MX–M X systems (X = F, Cl, Br, I; M and M are monovalent metals) are processed by an atomic parameter-pattern recognition method (employing the Fisher method). It is pointed out that the solid solution formers and solid solution nonformers are distributed in different regions in a hyperspace spanned by Pauling’s ionic radii and Batsanov’s electronegativities of the constituent elements. On the basis of a criterion found in the paper, the formation of a solid solution of NaBr in RbBr in the RbBr–NaBr system is suggested. The phase diagram of the RbBr–NaBr system is determined by differential thermal analysis. It is suggested that there is a eutectic at 786 K and 55 mol%RbBr in the phase diagram of RbBr–NaBr, with a solubility of NaBr in RbBr of about 8 mol% at the eutectic temperature, and negligible solid solubility on the NaBr side of the diagram. © 2004 Published by Elsevier Ltd Keywords: Phase diagram; Rubidium bromide; Sodium bromide; Atomic parameter-pattern recognition method; DTA
1. Introduction Molten salt phase diagrams are commonly utilized in metallurgy and materials sciences. Due to the interesting thermodynamic properties, the phase diagram of the alkali halides has been investigated comprehensively. A large number of measurements on binary alkali halide systems have been performed in earlier investigations. However, in some systems, there were significant discrepancies [1]. In this paper, the atomic parameter-pattern recognition method is utilized to find the regularity of the solid solution formability of MX–M X (M and M are monovalent metals; X = F, Cl, Br, I) systems. Thus the formability of solid solutions of new systems can be predicted. In the case of the RbBr–NaBr system, only a few studies have been reported. Samuseva and Plyushchev [2] reported a eutectic reaction at a temperature of 768 K with 55 mol%RbBr. The appreciable solid solubility was not unambiguous determined. However, Tovmas’yan et al. [3] determined a eutectic at 767 K and 50 mol%RbBr, but they did not mention the presence of solid solutions. In order to resolve the uncertainties in this binary system, the atomic ∗ Corresponding address: College of Science, Shanghai University, Shanghai 200436, China. E-mail address: [email protected] (J. Fang).
0364-5916/$ - see front matter © 2004 Published by Elsevier Ltd doi:10.1016/j.calphad.2004.03.002
parameter-pattern recognition method has been applied to predict the formability of solid solution and a detailed experimental investigation has been undertaken employing differential thermal analysis (DTA). 2. Computation Chen and co-workers made successful predictions on compound formation of alloy systems and molten salt systems by using the atomic parameter-pattern recognition method [4]. The Fisher method was utilized to find the regularity of the solid solution formability of binary monovalent metal halide MX–M X systems. 2.1. The Fisher recognition method The original data were standardized to scalar quantities and composed the sample set. The hyperspace was spread out using the characteristic parameters as coordinate axes. The sample points x igk are the hyperspace points. Here, the serial number of parameters i = 1, 2, . . . , m, the type g = 1, 2, the serial number of samples k = 1, 2, . . . , n g , the total number of samples N = 2g=1 n g . The parameter pattern of the samples distributed in hyperspace was projected onto a two-dimensional plane.
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J. Fang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 28 (2004) 9–14
The direction of projection was chosen to best distinguish the two types of sample. The projection was a linear transformation of the coordinate axes. The coordinate axis m transform is given by Z gk = i=1 vi x igk , where v = (v1 , v2 , . . . , vm ) . The dispersions of the sample points within the same type and between the two types after projection, w(Z ) and b(Z ), are given respectively by w(Z ) =
ng 2
(Z gk − Z g ) , 2
b(Z ) =
g=1 k=1
2
n g (Z g − Z )2 .
g=1
This may be proved as follows: w(Z ) =
m m
wi j vi v j ,
i=1 i=1
here wi j =
ng 2
(x igk − x ig )(x j gk − x j g ).
g=1 k=1 m m
b(Z ) =
bi j vi v j ,
i=1 j =1
here bi j =
2
n g (x ig − x i )(x j g − x j ).
g=1
The ratio of the dispersions of the sample points within the same type and between the two types, r , is given by r = b(Z )/w(Z ). In order for r to attained the extremum, the necessary condition is ∂r/∂vi = 0: ∂w(Z ) ∂b(Z ) 1 = 0. − b(Z ) w(Z ) ∂vi ∂vi w2 (Z ) Rearranging gives ∂b(Z ) ∂w(Z ) −r = 0. ∂vi ∂vi Hence, ng j =1
bi j v j − r
ng
wi j v j = 0.
j =1
Or, using vector notation: (B − r W )v = 0. Thus, the problem of seeking the direction of projection became that of determining the eigenvector v. The best two directions of projection v1 and v2 were obtained by resolving the matrix equation. The two-dimensional plane spread obtained with v1 and v2 was the best recognition pattern.
XX are the Batsanov electronegativities of M, M and X respectively. Here the element with the larger cation was always defined as M and the smaller one as M in each system. The data from 75 known phase diagrams were used as a training set for the projection map [5, 6]. The sample parameter data are given in Table 1. The solid solutions of M X in MX were investigated. The systems with solid solutions of M X in MX were defined as type “1” samples; there were 37 systems: AgBr–CuBr, AgBr–LiBr, AgBr–NaBr, AgCl–CuCl, AgCl–LiCl, AgCl–NaCl, AgI–LiI, CsBr–KBr, CsBr–RbBr, CsBr–TlBr, CsCl–KCl, CsCl–RbCl, CsCl–TlCl, CsF–KF, CsF–RbF, CsI–KI, CsI–RbI, CuCl–LiCl, CuCl–NaCl, KBr–NaBr, KCl–NaCl, KF–NaF, KI–NaI, NaBr–LiBr, NaCl–LiCl, NaF–LiF, NaI–LiI, RbBr–KBr, RbCl–KCl, RbCl–NaCl, RbCl–TlCl, RbF–KF, RbI–KI, RbI–NaI, TlCl–KCl, TlCl–NaCl, TlI–KI. On the other hand, systems without solid solutions of M X in MX were defined as type “2” samples; there are 38 systems: CsBr–LiBr, CsBr–NaBr, CsCl–AgCl, CsCl–CuCl, CsCl–LiCl, CsCl–NaCl, CsF–LiF, CsF–NaF, CsI–LiI, CsI–NaI, HgCl–CuCl, KBr–AgBr, KBr–CuBr, KBr–LiBr, KCl–AgCl, KCl–CuCl, KCl–LiCl, KF–LiF, KI–AgI, KI–LiI, NH4 Cl–AgCl, NH4 Cl–CuCl, NH4 Cl–HgCl, NH4 Cl–LiCl, RbBr–AgBr, RbBr–LiBr, RbCl–AgCl, RbCl–CuCl, RbCl–LiCl, RbF–LiF, RbF–NaF, RbI–AgI, RbI–LiI, TlBr–AgBr, TlCl–AgCl, TlCl–CuCl, TlCl–LiCl, TlI–AgI. The systems for which predictions had not been made, RbBr–NaBr, CsBr–CuBr and RbBr–CuBr, were defined as type “0” samples. By the Fisher method, a rather good projection map could be obtained, as shown in Fig. 1. The solid solution formers for M X in MX and nonformers could be separated into different regions. The coordinate axes were given by v1 = −0.8901RX − 2.324RM + 2.387RM − 0.5769X X − 1.267E–2X M − 1.094X M + 5.609 v2 = 2.869RX − 0.7562RM + 0.8654RM + 1.561X X + 0.1114X M − 0.3474X M − 9.452. The criterion of formation for a solid solution of M X in MX for MX–M X systems can be roughly expressed as follows: 0.0763 ≤ v1 ≤ 1.2955,
and −0.0965 ≤ v2 ≤ 0.5642.
According to this criterion, the RbBr–NaBr system has a solid solution of NaBr in RbBr, and for the CsBr–CuBr, RbBr–CuBr systems there is negligible solid solubility. The latter result was confirmed by Wojakowska [7, 8]. It was reasonable to infer that the Fisher method was able to recognize whether a binary univalent metal halide system was one with solid solutions.
2.2. The solid solution prediction of M X in MX
2.3. The solid solution prediction for MX in M X
In addition to the atomic parameters, Pauling’s ionic radii and Batsanov’s electronegativities were also used in this work. RM , RM , RX are the ionic radii and XM , XM ,
The solid solution of MX in M X was investigated. The 32 systems with solid solutions of MX in M X were defined as type “1” samples and the other 43 systems were defined
J. Fang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 28 (2004) 9–14
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Table 1 The sample parameter data No
Name
Class
RX
RM
RM
XX
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
RbBr–NaBr AgBr–CuBr AgBr–LiBr AgBr–NaBr AgCl–CuCl AgCl–LiCl AgCl–NaCl AgI–LiI CsBr–KBr CsBr–RbBr CsBr–TlBr CsCl–KCl CsCl–RbCl CsCl–TlCl CsF–KF CsF–RbF CsI–KI CsI–RbI CuCl–LiCl CuCl–NaCl KBr–NaBr KCl–NaCl KF–NaF KI–NaI NaBr–LiBr NaCl–LiCl NaF–LiF NaI–LiI RbBr–KBr RbCl–KCl RbCl–NaCl RbCl–TlCl RbF–KF RbI–KI RbI–NaI TlCl–KCl TlCl–NaCl TlI–KI CsBr–CuBr CsBr–LiBr CsBr–NaBr CsCl–AgCl CsCl–CuCl CsCl–LiCl CsCl–NaCl CsF–LiF CsF–NaF CsI–LiI CsI–NaI HgCl–CuCl KBr–AgBr KBr–CuBr KBr–LiBr KCl–AgCl KCl–CuCl KCl–LiCl KF–LiF KI–AgI
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1.95 1.95 1.95 1.95 1.81 1.81 1.81 2.16 1.95 1.95 1.95 1.81 1.81 1.81 1.36 1.36 2.16 2.16 1.81 1.81 1.95 1.81 1.36 2.16 1.95 1.81 1.36 2.16 1.95 1.81 1.81 1.81 1.36 2.16 2.16 1.81 1.81 2.16 1.95 1.95 1.95 1.81 1.81 1.81 1.81 1.36 1.36 2.16 2.16 1.81 1.95 1.95 1.95 1.81 1.81 1.81 1.36 2.16
1.48 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 0.96 0.96 1.33 1.33 1.33 1.33 0.95 0.95 0.95 0.95 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.44 1.44 1.44 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.26 1.33 1.33 1.33 1.33 1.33 1.33 1.33 1.33
0.95 0.96 0.68 0.95 0.96 0.68 0.95 0.68 1.33 1.48 1.44 1.33 1.48 1.44 1.33 1.48 1.33 1.48 0.68 0.95 0.95 0.95 0.95 0.95 0.68 0.68 0.68 0.68 1.33 1.33 0.95 1.44 1.33 1.33 0.95 1.33 0.95 1.33 0.96 0.68 0.95 1.00 0.96 0.68 0.95 0.68 0.95 0.68 0.95 0.96 1.00 0.96 0.68 1.00 0.96 0.68 0.68 1.00
2.8 2.8 2.8 2.8 3.0 3.0 3.0 2.5 2.8 2.8 2.8 3.0 3.0 3.0 3.95 3.95 2.5 2.5 3.0 3.0 2.8 3.0 3.95 2.5 2.8 3.0 3.95 2.5 2.8 3.0 3.0 3.0 3.95 2.5 2.5 3.0 3.0 2.5 2.8 2.8 2.8 3.0 3.0 3.0 3.0 3.95 3.95 2.5 2.5 3.0 2.8 2.8 2.8 3.0 3.0 3.0 3.95 2.5
XM
XM
0.8 0.9 1.8 1.8 1.8 0.95 1.8 0.9 1.8 1.8 1.8 0.95 1.8 0.9 1.8 0.95 0.75 0.8 0.75 0.8 0.75 1.5 0.75 0.8 0.75 0.8 0.75 1.5 0.75 0.8 0.75 0.8 0.75 0.8 0.75 0.8 1.8 0.95 1.8 0.9 0.8 0.9 0.8 0.9 0.8 0.9 0.8 0.9 0.9 0.95 0.9 0.95 0.9 0.95 0.9 0.95 0.8 0.8 0.8 0.8 0.8 0.9 0.8 1.5 0.8 0.8 0.8 0.8 0.8 0.9 1.5 0.8 1.5 0.9 1.5 0.9 0.75 1.8 0.75 0.95 0.75 0.9 0.75 1.8 0.75 1.8 0.75 0.95 0.75 0.9 0.75 0.95 0.75 0.9 0.75 0.95 0.75 0.9 2.0 1.8 0.8 1.8 0.8 1.8 0.8 0.95 0.8 1.8 0.8 1.8 0.8 0.95 0.8 0.95 0.8 1.8 (continued on next page)
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J. Fang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 28 (2004) 9–14
Table 1 (continued) No
Name
Class
RX
RM
RM
XX
XM
XM
58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77
KI–LiI NH4 Cl–AgCl NH4 Cl–CuCl NH4 Cl–HgCl N4 Cl–LiCl RbBr–AgBr RbBr–CuBr RbBr–LiBr RbCl–AgCl RbCl–CuCl RbCl–LiCl RbF–LiF RbF–NaF RbI–AgI RbI–LiI TlBr–AgBr TlCl–AgCl TlCl–CuCl TlCl–LiCl TlI–AgI
2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2
2.16 1.81 1.81 1.81 1.81 1.95 1.95 1.95 1.81 1.81 1.81 1.36 1.36 2.16 2.16 1.95 1.81 1.81 1.81 2.16
1.33 1.43 1.43 1.43 1.43 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.44 1.44 1.44 1.44 1.44
0.68 1.00 0.96 1.26 0.68 1.00 0.96 0.68 1.00 0.96 0.68 0.68 0.95 1.00 0.68 1.00 1.00 0.96 0.68 1.00
2.5 3.0 3.0 3.0 3.0 2.8 2.8 2.8 3.0 3.0 3.0 3.95 3.95 2.5 2.5 2.8 3.0 3.0 3.0 2.5
0.8 0.96 0.96 0.96 0.96 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 1.5 1.5 1.5 1.5 1.5
0.95 1.8 1.8 2.0 0.95 1.8 1.8 0.95 1.8 1.8 0.95 0.95 0.9 1.8 0.95 1.8 1.8 1.8 0.95 1.8
Fig. 1. The projection map of the pattern recognition for the MX–M X system on the MX side.
J. Fang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 28 (2004) 9–14
13
Fig. 2. The projection map of pattern recognition for the MX–M X system on the M X side.
as type “2” samples. The systems for which predictions had not been made, RbBr–NaBr, CsBr–CuBr and RbBr–CuBr, were defined as type “0” samples. Fig. 2 also shows a rather good projection map with a different set of coordinates. The solid solution formers for MX in M X and nonformers could be separated into different regions. The coordinate axes were given by v1 = −1.341RX − 1.958RM + 2.141RM − 1.135X X + 2.406E–2X M − 0.9083X M + 7.575 v2 = 2.734RX − 1.322RM + 1.522RM + 1.233X X + 0.1233X M − 0.5719X M − 7.818. The criterion for formation of a solid solution of MX in M X for MX–M X systems can be expressed as follows: 0.1729 ≤ v1 ≤ 1.1231,
and 0.0227 ≤ v2 ≤ 0.9619.
The prediction results indicate that there is no solid solubility of RbBr in NaBr and that there are also no solid solutions for the CsBr–CuBr and RbBr–CuBr systems.
3. Experiments Fig. 3. Some DTA traces for the system.
Sample preparation was performed in an argon-filled dry box. The samples of RbBr and NaBr were first dried at 773 K in vacuum, and then the salts of desired composition were mixed and homogenized in an agate mortar. About 20 mg of each mixture was packed into a platinum crucible and hermetically covered by a crucible cap for the DTA measurements. DTA measurements were performed with a DTA-TGtype thermal analyser (WCT-1A Model, Beijing-Ricoh Corp.) under an argon atmosphere. The heating rate was 5 K min−1 . Initially a temperature calibration was performed with Al, Sn, Pb and Zn at the same heating rates. Alumina powder was used as the reference material. The melting points of RbBr and NaBr measured under the same conditions were 965 K and 1020 K, coinciding with the
thermochemical data for the pure substances reported by Barin [9]. TG analysis showed that it was reasonable to neglect the mass change for all samples. Due to the large degree of undercooling of the system, the transition and liquidus temperatures were taken only from the heating curves. The transition temperatures were derived from extrapolated peak onsets for the eutectic reactions and offsets for the liquidus. Typical DTA heating curves are shown in Fig. 3. In the range of 2 mol%–90 mol%RbBr (excluding the component of 55 mol%RbBr), there were apparently two exothermic peaks for each composition of the sample in the heating curve. The first sharp exothermic peak corresponds to the eutectic
14
J. Fang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 28 (2004) 9–14
and Tsusba [3]. The eutectic composition at 55 mol%RbBr agreed with that reported by Samuseva and Plyushchev [2]. 4. Conclusion
Fig. 4. The phase diagram of the RbBr–NaBr system.
reaction at about 786 K, and the second tailed exothermic peak corresponds to the liquidus which varies with the RbBr content of the samples. The two exothermic peaks for 50 mol%RbBr composition nearly completely overlapped. The only peak of the 55 mol%RbBr sample indicated the eutectic point, as was confirmed by extrapolation of liquidus curves and Tamman triangle methods. The first endothermic peak of the 95 mol%RbBr corresponds to the solidus temperature. The results indicated the extent of solid solution as about 8 mol%NaBr in RbBr at the eutectic temperature, but negligible solid solubility on the NaBr side of the diagram. On the basis of the data from the DTA analysis, the phase diagram of the RbBr–NaBr system was plotted; see Fig. 4. The eutectic temperature of 786 K was higher than those reported by Samuseva and Plyushchev [2] and Tovmas’yan
In this paper, the atomic parameter-pattern recognition Fisher method was applied for the first time to estimate the formation of solid solutions in the MX–M X systems (X = F, Cl, Br, I; M and M are monovalent metals). The chosen atomic parameters, Pauling’s ionic radii and Batsanov’s electronegativities, had the advantages of simplicity and credibility. On the basis of a criterion found in the paper, it was predicted successfully that a solid solution of NaBr would form in RbBr in the RbBr–NaBr system. The solubility of NaBr in RbBr at the eutectic temperature (786 K) was confirmed as about 8 mol% by DTA measurements. References [1] J. Sangster, A.D. Pelton, J. Phys. Chem. Ref. Data 16 (1987) 509. [2] R.G. Samuseva, V.E. Plyushchev, Zh. Neorg. Khim 9 (1964) 2436. [3] I.K. Tovmas’yan, T.M. Tsusba, V.P. Radina, Zh. Neorg. Khim 15 (1970) 2535. [4] Nianyi Chen, Wencong Lu, Ruiliang Chen, Pei Qin, P. Villars, J. Alloy Comp. 289 (1999) 120. [5] N.K. Voskresinskaya, Handbook for Fusibility of Anhydrous Inorganic Salt Systems, Publisher of Academy of Sciences of Soviet Union, Moscow, 1961. [6] F.E. Pasipaiko, E.A. Alexivoi, Phase Diagrams of Salt Systems, Metallurgy, Moscow, 1977. [7] A. Wojakowska, E. Krzyzak, A. Wojakowski, Thermochim. Acta 344 (2000) 55. [8] A. Wojakowska, E. Krzyzak, A. Wojakowski, J. Thermal Anal. Calorimetry 65 (2001) 491. [9] I. Barin, Thermochemical Data of Pure Substances, 2nd edition, VCH, 1993.
The phase diagram of the RbBr–NaBr system Jianhui Fanga,b,∗, Weizhong Dingb, Xia Shena, Liyi Shia, Nianyi Chena a College of Science, Shanghai University, Shanghai 200436, China b College of Material Science and Engineering, Shanghai University, Shanghai 200072, China
Received 30 December 2003; accepted 5 March 2004 Available online 9 April 2004
Abstract In this paper, the data from 75 known phase diagrams of MX–M X systems (X = F, Cl, Br, I; M and M are monovalent metals) are processed by an atomic parameter-pattern recognition method (employing the Fisher method). It is pointed out that the solid solution formers and solid solution nonformers are distributed in different regions in a hyperspace spanned by Pauling’s ionic radii and Batsanov’s electronegativities of the constituent elements. On the basis of a criterion found in the paper, the formation of a solid solution of NaBr in RbBr in the RbBr–NaBr system is suggested. The phase diagram of the RbBr–NaBr system is determined by differential thermal analysis. It is suggested that there is a eutectic at 786 K and 55 mol%RbBr in the phase diagram of RbBr–NaBr, with a solubility of NaBr in RbBr of about 8 mol% at the eutectic temperature, and negligible solid solubility on the NaBr side of the diagram. © 2004 Published by Elsevier Ltd Keywords: Phase diagram; Rubidium bromide; Sodium bromide; Atomic parameter-pattern recognition method; DTA
1. Introduction Molten salt phase diagrams are commonly utilized in metallurgy and materials sciences. Due to the interesting thermodynamic properties, the phase diagram of the alkali halides has been investigated comprehensively. A large number of measurements on binary alkali halide systems have been performed in earlier investigations. However, in some systems, there were significant discrepancies [1]. In this paper, the atomic parameter-pattern recognition method is utilized to find the regularity of the solid solution formability of MX–M X (M and M are monovalent metals; X = F, Cl, Br, I) systems. Thus the formability of solid solutions of new systems can be predicted. In the case of the RbBr–NaBr system, only a few studies have been reported. Samuseva and Plyushchev [2] reported a eutectic reaction at a temperature of 768 K with 55 mol%RbBr. The appreciable solid solubility was not unambiguous determined. However, Tovmas’yan et al. [3] determined a eutectic at 767 K and 50 mol%RbBr, but they did not mention the presence of solid solutions. In order to resolve the uncertainties in this binary system, the atomic ∗ Corresponding address: College of Science, Shanghai University, Shanghai 200436, China. E-mail address: [email protected] (J. Fang).
0364-5916/$ - see front matter © 2004 Published by Elsevier Ltd doi:10.1016/j.calphad.2004.03.002
parameter-pattern recognition method has been applied to predict the formability of solid solution and a detailed experimental investigation has been undertaken employing differential thermal analysis (DTA). 2. Computation Chen and co-workers made successful predictions on compound formation of alloy systems and molten salt systems by using the atomic parameter-pattern recognition method [4]. The Fisher method was utilized to find the regularity of the solid solution formability of binary monovalent metal halide MX–M X systems. 2.1. The Fisher recognition method The original data were standardized to scalar quantities and composed the sample set. The hyperspace was spread out using the characteristic parameters as coordinate axes. The sample points x igk are the hyperspace points. Here, the serial number of parameters i = 1, 2, . . . , m, the type g = 1, 2, the serial number of samples k = 1, 2, . . . , n g , the total number of samples N = 2g=1 n g . The parameter pattern of the samples distributed in hyperspace was projected onto a two-dimensional plane.
10
J. Fang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 28 (2004) 9–14
The direction of projection was chosen to best distinguish the two types of sample. The projection was a linear transformation of the coordinate axes. The coordinate axis m transform is given by Z gk = i=1 vi x igk , where v = (v1 , v2 , . . . , vm ) . The dispersions of the sample points within the same type and between the two types after projection, w(Z ) and b(Z ), are given respectively by w(Z ) =
ng 2
(Z gk − Z g ) , 2
b(Z ) =
g=1 k=1
2
n g (Z g − Z )2 .
g=1
This may be proved as follows: w(Z ) =
m m
wi j vi v j ,
i=1 i=1
here wi j =
ng 2
(x igk − x ig )(x j gk − x j g ).
g=1 k=1 m m
b(Z ) =
bi j vi v j ,
i=1 j =1
here bi j =
2
n g (x ig − x i )(x j g − x j ).
g=1
The ratio of the dispersions of the sample points within the same type and between the two types, r , is given by r = b(Z )/w(Z ). In order for r to attained the extremum, the necessary condition is ∂r/∂vi = 0: ∂w(Z ) ∂b(Z ) 1 = 0. − b(Z ) w(Z ) ∂vi ∂vi w2 (Z ) Rearranging gives ∂b(Z ) ∂w(Z ) −r = 0. ∂vi ∂vi Hence, ng j =1
bi j v j − r
ng
wi j v j = 0.
j =1
Or, using vector notation: (B − r W )v = 0. Thus, the problem of seeking the direction of projection became that of determining the eigenvector v. The best two directions of projection v1 and v2 were obtained by resolving the matrix equation. The two-dimensional plane spread obtained with v1 and v2 was the best recognition pattern.
XX are the Batsanov electronegativities of M, M and X respectively. Here the element with the larger cation was always defined as M and the smaller one as M in each system. The data from 75 known phase diagrams were used as a training set for the projection map [5, 6]. The sample parameter data are given in Table 1. The solid solutions of M X in MX were investigated. The systems with solid solutions of M X in MX were defined as type “1” samples; there were 37 systems: AgBr–CuBr, AgBr–LiBr, AgBr–NaBr, AgCl–CuCl, AgCl–LiCl, AgCl–NaCl, AgI–LiI, CsBr–KBr, CsBr–RbBr, CsBr–TlBr, CsCl–KCl, CsCl–RbCl, CsCl–TlCl, CsF–KF, CsF–RbF, CsI–KI, CsI–RbI, CuCl–LiCl, CuCl–NaCl, KBr–NaBr, KCl–NaCl, KF–NaF, KI–NaI, NaBr–LiBr, NaCl–LiCl, NaF–LiF, NaI–LiI, RbBr–KBr, RbCl–KCl, RbCl–NaCl, RbCl–TlCl, RbF–KF, RbI–KI, RbI–NaI, TlCl–KCl, TlCl–NaCl, TlI–KI. On the other hand, systems without solid solutions of M X in MX were defined as type “2” samples; there are 38 systems: CsBr–LiBr, CsBr–NaBr, CsCl–AgCl, CsCl–CuCl, CsCl–LiCl, CsCl–NaCl, CsF–LiF, CsF–NaF, CsI–LiI, CsI–NaI, HgCl–CuCl, KBr–AgBr, KBr–CuBr, KBr–LiBr, KCl–AgCl, KCl–CuCl, KCl–LiCl, KF–LiF, KI–AgI, KI–LiI, NH4 Cl–AgCl, NH4 Cl–CuCl, NH4 Cl–HgCl, NH4 Cl–LiCl, RbBr–AgBr, RbBr–LiBr, RbCl–AgCl, RbCl–CuCl, RbCl–LiCl, RbF–LiF, RbF–NaF, RbI–AgI, RbI–LiI, TlBr–AgBr, TlCl–AgCl, TlCl–CuCl, TlCl–LiCl, TlI–AgI. The systems for which predictions had not been made, RbBr–NaBr, CsBr–CuBr and RbBr–CuBr, were defined as type “0” samples. By the Fisher method, a rather good projection map could be obtained, as shown in Fig. 1. The solid solution formers for M X in MX and nonformers could be separated into different regions. The coordinate axes were given by v1 = −0.8901RX − 2.324RM + 2.387RM − 0.5769X X − 1.267E–2X M − 1.094X M + 5.609 v2 = 2.869RX − 0.7562RM + 0.8654RM + 1.561X X + 0.1114X M − 0.3474X M − 9.452. The criterion of formation for a solid solution of M X in MX for MX–M X systems can be roughly expressed as follows: 0.0763 ≤ v1 ≤ 1.2955,
and −0.0965 ≤ v2 ≤ 0.5642.
According to this criterion, the RbBr–NaBr system has a solid solution of NaBr in RbBr, and for the CsBr–CuBr, RbBr–CuBr systems there is negligible solid solubility. The latter result was confirmed by Wojakowska [7, 8]. It was reasonable to infer that the Fisher method was able to recognize whether a binary univalent metal halide system was one with solid solutions.
2.2. The solid solution prediction of M X in MX
2.3. The solid solution prediction for MX in M X
In addition to the atomic parameters, Pauling’s ionic radii and Batsanov’s electronegativities were also used in this work. RM , RM , RX are the ionic radii and XM , XM ,
The solid solution of MX in M X was investigated. The 32 systems with solid solutions of MX in M X were defined as type “1” samples and the other 43 systems were defined
J. Fang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 28 (2004) 9–14
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Table 1 The sample parameter data No
Name
Class
RX
RM
RM
XX
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
RbBr–NaBr AgBr–CuBr AgBr–LiBr AgBr–NaBr AgCl–CuCl AgCl–LiCl AgCl–NaCl AgI–LiI CsBr–KBr CsBr–RbBr CsBr–TlBr CsCl–KCl CsCl–RbCl CsCl–TlCl CsF–KF CsF–RbF CsI–KI CsI–RbI CuCl–LiCl CuCl–NaCl KBr–NaBr KCl–NaCl KF–NaF KI–NaI NaBr–LiBr NaCl–LiCl NaF–LiF NaI–LiI RbBr–KBr RbCl–KCl RbCl–NaCl RbCl–TlCl RbF–KF RbI–KI RbI–NaI TlCl–KCl TlCl–NaCl TlI–KI CsBr–CuBr CsBr–LiBr CsBr–NaBr CsCl–AgCl CsCl–CuCl CsCl–LiCl CsCl–NaCl CsF–LiF CsF–NaF CsI–LiI CsI–NaI HgCl–CuCl KBr–AgBr KBr–CuBr KBr–LiBr KCl–AgCl KCl–CuCl KCl–LiCl KF–LiF KI–AgI
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1.95 1.95 1.95 1.95 1.81 1.81 1.81 2.16 1.95 1.95 1.95 1.81 1.81 1.81 1.36 1.36 2.16 2.16 1.81 1.81 1.95 1.81 1.36 2.16 1.95 1.81 1.36 2.16 1.95 1.81 1.81 1.81 1.36 2.16 2.16 1.81 1.81 2.16 1.95 1.95 1.95 1.81 1.81 1.81 1.81 1.36 1.36 2.16 2.16 1.81 1.95 1.95 1.95 1.81 1.81 1.81 1.36 2.16
1.48 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 0.96 0.96 1.33 1.33 1.33 1.33 0.95 0.95 0.95 0.95 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.44 1.44 1.44 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.26 1.33 1.33 1.33 1.33 1.33 1.33 1.33 1.33
0.95 0.96 0.68 0.95 0.96 0.68 0.95 0.68 1.33 1.48 1.44 1.33 1.48 1.44 1.33 1.48 1.33 1.48 0.68 0.95 0.95 0.95 0.95 0.95 0.68 0.68 0.68 0.68 1.33 1.33 0.95 1.44 1.33 1.33 0.95 1.33 0.95 1.33 0.96 0.68 0.95 1.00 0.96 0.68 0.95 0.68 0.95 0.68 0.95 0.96 1.00 0.96 0.68 1.00 0.96 0.68 0.68 1.00
2.8 2.8 2.8 2.8 3.0 3.0 3.0 2.5 2.8 2.8 2.8 3.0 3.0 3.0 3.95 3.95 2.5 2.5 3.0 3.0 2.8 3.0 3.95 2.5 2.8 3.0 3.95 2.5 2.8 3.0 3.0 3.0 3.95 2.5 2.5 3.0 3.0 2.5 2.8 2.8 2.8 3.0 3.0 3.0 3.0 3.95 3.95 2.5 2.5 3.0 2.8 2.8 2.8 3.0 3.0 3.0 3.95 2.5
XM
XM
0.8 0.9 1.8 1.8 1.8 0.95 1.8 0.9 1.8 1.8 1.8 0.95 1.8 0.9 1.8 0.95 0.75 0.8 0.75 0.8 0.75 1.5 0.75 0.8 0.75 0.8 0.75 1.5 0.75 0.8 0.75 0.8 0.75 0.8 0.75 0.8 1.8 0.95 1.8 0.9 0.8 0.9 0.8 0.9 0.8 0.9 0.8 0.9 0.9 0.95 0.9 0.95 0.9 0.95 0.9 0.95 0.8 0.8 0.8 0.8 0.8 0.9 0.8 1.5 0.8 0.8 0.8 0.8 0.8 0.9 1.5 0.8 1.5 0.9 1.5 0.9 0.75 1.8 0.75 0.95 0.75 0.9 0.75 1.8 0.75 1.8 0.75 0.95 0.75 0.9 0.75 0.95 0.75 0.9 0.75 0.95 0.75 0.9 2.0 1.8 0.8 1.8 0.8 1.8 0.8 0.95 0.8 1.8 0.8 1.8 0.8 0.95 0.8 0.95 0.8 1.8 (continued on next page)
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J. Fang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 28 (2004) 9–14
Table 1 (continued) No
Name
Class
RX
RM
RM
XX
XM
XM
58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77
KI–LiI NH4 Cl–AgCl NH4 Cl–CuCl NH4 Cl–HgCl N4 Cl–LiCl RbBr–AgBr RbBr–CuBr RbBr–LiBr RbCl–AgCl RbCl–CuCl RbCl–LiCl RbF–LiF RbF–NaF RbI–AgI RbI–LiI TlBr–AgBr TlCl–AgCl TlCl–CuCl TlCl–LiCl TlI–AgI
2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2
2.16 1.81 1.81 1.81 1.81 1.95 1.95 1.95 1.81 1.81 1.81 1.36 1.36 2.16 2.16 1.95 1.81 1.81 1.81 2.16
1.33 1.43 1.43 1.43 1.43 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.44 1.44 1.44 1.44 1.44
0.68 1.00 0.96 1.26 0.68 1.00 0.96 0.68 1.00 0.96 0.68 0.68 0.95 1.00 0.68 1.00 1.00 0.96 0.68 1.00
2.5 3.0 3.0 3.0 3.0 2.8 2.8 2.8 3.0 3.0 3.0 3.95 3.95 2.5 2.5 2.8 3.0 3.0 3.0 2.5
0.8 0.96 0.96 0.96 0.96 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 1.5 1.5 1.5 1.5 1.5
0.95 1.8 1.8 2.0 0.95 1.8 1.8 0.95 1.8 1.8 0.95 0.95 0.9 1.8 0.95 1.8 1.8 1.8 0.95 1.8
Fig. 1. The projection map of the pattern recognition for the MX–M X system on the MX side.
J. Fang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 28 (2004) 9–14
13
Fig. 2. The projection map of pattern recognition for the MX–M X system on the M X side.
as type “2” samples. The systems for which predictions had not been made, RbBr–NaBr, CsBr–CuBr and RbBr–CuBr, were defined as type “0” samples. Fig. 2 also shows a rather good projection map with a different set of coordinates. The solid solution formers for MX in M X and nonformers could be separated into different regions. The coordinate axes were given by v1 = −1.341RX − 1.958RM + 2.141RM − 1.135X X + 2.406E–2X M − 0.9083X M + 7.575 v2 = 2.734RX − 1.322RM + 1.522RM + 1.233X X + 0.1233X M − 0.5719X M − 7.818. The criterion for formation of a solid solution of MX in M X for MX–M X systems can be expressed as follows: 0.1729 ≤ v1 ≤ 1.1231,
and 0.0227 ≤ v2 ≤ 0.9619.
The prediction results indicate that there is no solid solubility of RbBr in NaBr and that there are also no solid solutions for the CsBr–CuBr and RbBr–CuBr systems.
3. Experiments Fig. 3. Some DTA traces for the system.
Sample preparation was performed in an argon-filled dry box. The samples of RbBr and NaBr were first dried at 773 K in vacuum, and then the salts of desired composition were mixed and homogenized in an agate mortar. About 20 mg of each mixture was packed into a platinum crucible and hermetically covered by a crucible cap for the DTA measurements. DTA measurements were performed with a DTA-TGtype thermal analyser (WCT-1A Model, Beijing-Ricoh Corp.) under an argon atmosphere. The heating rate was 5 K min−1 . Initially a temperature calibration was performed with Al, Sn, Pb and Zn at the same heating rates. Alumina powder was used as the reference material. The melting points of RbBr and NaBr measured under the same conditions were 965 K and 1020 K, coinciding with the
thermochemical data for the pure substances reported by Barin [9]. TG analysis showed that it was reasonable to neglect the mass change for all samples. Due to the large degree of undercooling of the system, the transition and liquidus temperatures were taken only from the heating curves. The transition temperatures were derived from extrapolated peak onsets for the eutectic reactions and offsets for the liquidus. Typical DTA heating curves are shown in Fig. 3. In the range of 2 mol%–90 mol%RbBr (excluding the component of 55 mol%RbBr), there were apparently two exothermic peaks for each composition of the sample in the heating curve. The first sharp exothermic peak corresponds to the eutectic
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J. Fang et al. / Computer Coupling of Phase Diagrams and Thermochemistry 28 (2004) 9–14
and Tsusba [3]. The eutectic composition at 55 mol%RbBr agreed with that reported by Samuseva and Plyushchev [2]. 4. Conclusion
Fig. 4. The phase diagram of the RbBr–NaBr system.
reaction at about 786 K, and the second tailed exothermic peak corresponds to the liquidus which varies with the RbBr content of the samples. The two exothermic peaks for 50 mol%RbBr composition nearly completely overlapped. The only peak of the 55 mol%RbBr sample indicated the eutectic point, as was confirmed by extrapolation of liquidus curves and Tamman triangle methods. The first endothermic peak of the 95 mol%RbBr corresponds to the solidus temperature. The results indicated the extent of solid solution as about 8 mol%NaBr in RbBr at the eutectic temperature, but negligible solid solubility on the NaBr side of the diagram. On the basis of the data from the DTA analysis, the phase diagram of the RbBr–NaBr system was plotted; see Fig. 4. The eutectic temperature of 786 K was higher than those reported by Samuseva and Plyushchev [2] and Tovmas’yan
In this paper, the atomic parameter-pattern recognition Fisher method was applied for the first time to estimate the formation of solid solutions in the MX–M X systems (X = F, Cl, Br, I; M and M are monovalent metals). The chosen atomic parameters, Pauling’s ionic radii and Batsanov’s electronegativities, had the advantages of simplicity and credibility. On the basis of a criterion found in the paper, it was predicted successfully that a solid solution of NaBr would form in RbBr in the RbBr–NaBr system. The solubility of NaBr in RbBr at the eutectic temperature (786 K) was confirmed as about 8 mol% by DTA measurements. References [1] J. Sangster, A.D. Pelton, J. Phys. Chem. Ref. Data 16 (1987) 509. [2] R.G. Samuseva, V.E. Plyushchev, Zh. Neorg. Khim 9 (1964) 2436. [3] I.K. Tovmas’yan, T.M. Tsusba, V.P. Radina, Zh. Neorg. Khim 15 (1970) 2535. [4] Nianyi Chen, Wencong Lu, Ruiliang Chen, Pei Qin, P. Villars, J. Alloy Comp. 289 (1999) 120. [5] N.K. Voskresinskaya, Handbook for Fusibility of Anhydrous Inorganic Salt Systems, Publisher of Academy of Sciences of Soviet Union, Moscow, 1961. [6] F.E. Pasipaiko, E.A. Alexivoi, Phase Diagrams of Salt Systems, Metallurgy, Moscow, 1977. [7] A. Wojakowska, E. Krzyzak, A. Wojakowski, Thermochim. Acta 344 (2000) 55. [8] A. Wojakowska, E. Krzyzak, A. Wojakowski, J. Thermal Anal. Calorimetry 65 (2001) 491. [9] I. Barin, Thermochemical Data of Pure Substances, 2nd edition, VCH, 1993.