Unary and binary multisystems; topologic classification of phase diagrams and relation to Euler's theorem on polyhedra

Roseboom, Eugene H.; Zen, E‐an

doi:10.2475/ajs.282.3.286

Cited by 5 publications

(16 citation statements)

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“…In order to demonstrate the capability and the efficiency of our method, it is compared with the most representative methods reported previously (Guo, 1980a; Roseboom & Zen, 1982) using some specific examples.…”

Section: Comparison With Previously Reported Methodsmentioning

confidence: 99%

“…Zen & Roseboom (1972) extended the same treatment to ternary n + 3‐phase multisystems. By making a new divariant field to extend the system, Roseboom & Zen (1982) derived the representation polyhedra of the unary multisystems with five to seven phases. However, this technique cannot be applied to multi‐component systems.…”

Section: Introductionmentioning

confidence: 99%

“…In past decades, many contributions have been made to the related study of closed nets of multisystems, e.g. Day (1972Day ( , 1976Day ( , 1978, Braun & Stout (1975), Barron & Barron (1977), Burt (1978), Chesworth (1980), Guo (1979Guo ( , 1980aGuo ( ,b,c, 1981aGuo ( ,b, 1984Guo ( , 1985, Cai (1981Cai ( , 1982, Cheng (1983Cheng ( , 1986, , Korzhinskii (1959); Kujava et al (1965), Kujava & Eugster (1966), Zen (1966aZen ( , 1967Zen ( , 1974, Guo & Jin (1980), Mohr & Stout (1980), Wang (1980), Guo & Cai (1982), Guo & Wang (1982), Roseboom & Zen (1982), Vielzeuf & Boivin (1984), Stout (1985Stout ( , 1990, Usdansky (1987Usdansky ( , 1989, , Tan (1990), Stout & Guo (1994), Hu (1998); Kletetschka & Stout (1999), Hu et al (2000), Guy & Pla (2002), Zharikov (1961), Zen & Roseboom (1972), etc. Zen (1966a) proposed the n...…”

Section: Introductionmentioning

confidence: 99%

“…However, this technique cannot be applied to multi-component systems. In view of that, Roseboom & Zen (1982) proposed the approach of Ôoverlapping stability fieldsÕ, and used it to derive closed-net-diagrams and representation polyhedra of the binary multisystems of five or six phases. Guo (1980a) initiated a study of the closed nets of n + 4-phase multisystems (Roseboom & Zen, 1982).…”

Section: Introductionmentioning

confidence: 99%

“…In view of that, Roseboom & Zen (1982) proposed the approach of Ôoverlapping stability fieldsÕ, and used it to derive closed-net-diagrams and representation polyhedra of the binary multisystems of five or six phases. Guo (1980a) initiated a study of the closed nets of n + 4-phase multisystems (Roseboom & Zen, 1982). Guo (1980a) put forward a fundamental theorem on univariant curves, which was re-stated by Guo (1984): ÔThe stable portion, if any, of a univariant curve can only be a segment between two adjacent stable invariant points, in spite of the number of the invariant points with which this univariant curve is associatedÕ.…”

Section: Introductionmentioning

confidence: 99%

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A new method for the derivation of the closed nets in the phase diagram space of multisystems. I. The absent phase substitution method

Hu¹,

Duan²

2004

Journal Metamorphic Geology

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A new convenient combinatorial method is developed here to derive the invariant points in multisystem closed nets -the absent phase substitution (APS) method. It substantially simplifies the derivation of the closed nets in multisystems with many components and phases. For the multisystems whose total phase number (N PS ) £ twice the number of the absent phases (m) in an invariant assemblage, the method can yield regular closed nets with or without globally absent phases; for other multisystems, the method can yield the regular closed nets with globally absent phases. As examples, the APS method was used to predict: (1) the regular closed nets of unary to quinary n + 4-phase multisystems, unary 6-phase multisystem and ternary 8-phase multisystem; (2) the basic properties of the regular closed nets of the quaternary and quinary multisystems with n + 4 and n + 5 phases. Two multisystems were chosen to demonstrate how to select a realistic closed net from the numerous possible closed nets of a complex multisystem, and how to derive a realistic partially closed-net, closed-net-diagram and the related realistic straight-line-net-diagram. Comparisons of our APS method for the derivation of complicated closed nets with other methods indicate that this method is much simpler and more efficient.

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Section: Comparison With Previously Reported Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%