Ternary and Higher Order Systems

Aluminum is an effective sintering aid for B4C and SiC ceramics if combined with elemental boron and carbon. Phase relations in the B-C-Al-Si system may hence indicate suitable procedures to initiate transient liquid phase or enhanced solid-state sintering. Furthermore, liquid A1 may be used to infiltrate porous B4C bodies acting as a reinforcing phase. 

The B-C-Si system was first treated by Kieffer et al. [91]. The experimental data indicated a ternary equilibrium between B4C, SiBg and SiC up to temperatures exceeding 1900°C. 

Thermodynamic calculations by Dorner [78], Lukas [93] and Lim and Lukas [52], however, clearly demonstrated the existence of a binary phase equilibrium of boron carbide and a Si- and B-containing melt above 1560°C. The theoretical results were confirmed by hot pressing, liquid phase sintering and infiltration experiments by Lange and Holleck [75], Telle [83], Telle and Petzow [94], and Telle [54], which also yielded more details on the extension of the homogeneity field of boron carbide towards the Si-rich corner of the system B-C-Si. 

Discrepancies between previous and recent experiments as well as calculations arise from the binary B-Si system, in particular from the various plausible equilibria at the Si-rich corner. Furthermore, experimental problems in the ternary phase studies are related to the high Si vapor pressure at 1400°C. 

The characteristics of the B-C-Si system as assessed today, comprise the stability of a B]2(B,C,Si)3 solid solution with a maximum of 2.5 at.-% Si [28, 82, 95] being 

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The crystal structures of the borides of the rare earth metals (M g) are describedand phase equilibria in ternary and higher order systems containing rare earths and B, including information on structures, magnetic and electrical properties as well as low-T phase equilibria, are available. Phase equilibria and crystal structure in binary and ternary systems containing an actinide metal and B are... 

Rogl, P. (1984) Phase equilibria in ternary and higher order systems with rare earth elements and boron. In Handbook on the Physics and Chemistry of Rare Earths, eds. Gschneidner Jr., K.A. and Eyring, L. (North-Holland, Amsterdam), Vol. 6, p. 335. 

They can also be made identical in the general case if the conditions t = —vB/vA and j — 1. The equivalences break down in ternary and higher-order systems as there is the introduction of more compositional variables in the associate model than for the two-sublattice case. This was considered (Hillert et al. 1985) to demonstrate the advantages of the sub-lattice model, but as mentioned previously it turns out that the number of excess terms to describe Fe-Mn-S is very similar. 

In vertical sections through ternary and higher-order systems or isothermal sections for quaternary and higher systems, the position becomes more complex as tie-lines do not lie in the plane of the diagram. They therefore cannot be used to define the positions of phase boundaries and the procedures described above become inoperative. New concepts are required, such as viewing the diagram in a... 

P. Rogl, Phase equilibria in ternary and higher order systems with rare earth elements and boron 335... 

Phase diagrams are calculated from these data using regular solution or other appropriate solution models. Some of the great strengths of the CALPHAD approach are that it provides immediate, approximate diagrams for new systems of interest and that it can be readily extended to ternary and higher order systems that would be prohibitively complex and expensive to study experimentally. A comparison of the... 

Margules Equations for Ternary and Higher Order Systems... 

PHASE EQUILIBRIA IN TERNARY AND HIGHER ORDER SYSTEMS WITH RARE EARTH ELEMENTS AND SILICON... 

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