Heterogeneous Design. Structural diagrams of ternary systems
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JJ6.6.1
Heterogeneous Design. Structural diagrams of ternary systems Vasily I. Lutsyk, Vera P. Vorob'eva Buryat Scientific Center, Russian Academy of Sciences 8, Sakhyanova str., Ulan-Ude, 670047, RUSSIA ABSTRACT It is proposed to supplement a phase diagram by a structural diagram, which represents the mass portions of phases, conglomerates or their elements upon the system concentration at fixed temperature. Methods of structural diagrams and concentration maps construction are considered. Concentration map is a projection of structural diagram. It marks a concentration triangle by the lines of constant mass portions of a phase or its elements. INTRODUCTION Phase diagram of binary and ternary system is used to visualize the component interaction results and to store in compact form the data. It becomes more informative if to supplement its concentration simplex by a structural diagram. The last can serve also as an instrument to design heterogeneous material with a help of concentration maps marked by the lines of constant mass portions of microstructure elements or its conglomerates [1]. EXPERIMENTAL DETAILS Let's consider the structural diagrams of isobaric system Pb-Cd-Bi and its binary subsystems Pb-Cd и Pb-Bi (Figure 1). Experimental information about concentration of binary eutectics and peritectic [2], melt temperature of metals, binary eutectics and binary and ternary peritectics and about liquidus curvature [3] are required to simulate liquidus by the equations [4]: TPb = 327z1 − 689.24z 2 − 392.81z 3 + 1020.41z 1 z 2 + 554.02z 1 z 3 − 2072.19z 2 z 3 TCd = 154.80z 1 + 321z 2 − 535.05z 3 + 231.48z 1z 2 + 673.46z 1 z 3 + 849.38z 2 z 3 . (1) T = −64.31z + 13.98z + 271z − 43.42z z + 19.75z z + 66.12z z 3 1 2 1 3 2 3 TBi = 301.421 z + 432.269z − 50 .48z 3 − 1217z 1z 2 + 69.20z 1z 3 − 414.49z 2 z 3 1 2 Pb 3Bi Coordinates of ternary points had been calculated with a help of (1) and compared with experimental data (Table). Let’s signify as R=Pb3Bi, e1=ePb-Cd, e2=eCd-Bi, e3=ePb-Bi. DISCUSSION Structural diagram represents dependence "mass portion mI (I is a phase or its element) upon the concentration". The values of mI belongs the axis orthogonal to concentration simplex. Binary structural diagram is a rectangle and a ternary one is a straight prism. The height of both figures equal 1. A vertical line at every point of concentration simplex (ordinate in binary system and applicate in a ternary one) expresses a mass portion of microstructure element or their conglomerate. Its ends form a line in binary system and a surface in a ternary one. Table. Experimental and calculated coordinates (mol. portions, oC) Pb Cd Bi e1 e2 e3 p Eexp Ecalc Pexp Pcalc z1 1 0 0 0.72 0 0.45 0.62 0.377 0.44 0.675 0.65 z2 0 1 0 0.28 0.55 0 0 0.141 0.11 0.105 0.10 z3 0 0 1 0 0.45 0.55 0.38 0.482 0.45 0.220 0.25
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327 321 271 248
146
125
184
92
87.3
146
146
Figure 1. Liquidus projection and Pb-Cd-Pb3Bi, BiCd-Pb3Bi sybsystems Really a structural diagram supplements an isothermal section of phase diagram. Structural
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