Some topological relationships in multisystems of n+3 phases, III; ternary systems

Zen, E‐an; Roseboom, Eugene H.

doi:10.2475/ajs.272.8.677

Cited by 12 publications

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“…It will be much more difficult to derive the nets in Table 5 with the method of Guo (1980a). If the derivation of the above nets is done with the representation polyhedron approach of Zen (1966a); Zen & Roseboom (1972), the task will be very arduous.…”

Section: Derivation Of the Complete Systems Of Closed Nets Of Complexmentioning

confidence: 99%

“…(1965), Kujava & Eugster (1966), Zen (1966a, 1967, 1974), Guo & Jin (1980), Mohr & Stout (1980), Wang (1980), Guo & Cai (1982), Guo & Wang (1982), Roseboom & Zen (1982), Vielzeuf & Boivin (1984), Stout (1985, 1990), Usdansky (1987, 1989), Guo & Cheng (1989), Tan (1990), Stout & Guo (1994), Hu (1998); Kletetschka & Stout (1999), Hu et al. (2000), Guy & Pla (2002), Zharikov (1961), Zen & Roseboom (1972), etc.…”

Section: Introductionmentioning

confidence: 99%

“…Zen (1966a) proposed the n + 3‐phase closed net theory and derived closed‐net‐diagrams and straight‐line‐net‐diagrams of unary and binary n + 3‐phase multisystems using the so‐called ‘representation polyhedron’ approach. 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.…”

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%

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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: Derivation Of the Complete Systems Of Closed Nets Of Complexmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…Use of Zen and Roseboom's (1972) technique allows a shortcut to the desired diagram since the system in question has the chemography of their type Tb (Zen and Roseboom, 1972, p. 697), with two degenerate features. A multisystem net appropriate to current concerns is presented as Figure 1 points are (G) and (P).…”

Section: An Internally Consistent Phase Diagrammentioning

confidence: 99%

Mineral Metastability In the System Al₂O₃-SiO₂-H₂O: A Discussion

Chesworth

1994

Clays and clay miner.

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Phase equilibria among pumpellyite, lawsonite, epidote and associated minerals in low grade metamorphic rocks

Brown

1977

Contr. Mineral. and Petrol.

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Some topological relationships in multisystems of n+3 phases, III; ternary systems

Cited by 12 publications

References 0 publications

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

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

Mineral Metastability In the System Al₂O₃-SiO₂-H₂O: A Discussion

Phase equilibria among pumpellyite, lawsonite, epidote and associated minerals in low grade metamorphic rocks

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Some topological relationships in multisystems of n+3 phases, III; ternary systems

Cited by 12 publications

References 0 publications

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

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

Mineral Metastability In the System Al2O3-SiO2-H2O: A Discussion

Phase equilibria among pumpellyite, lawsonite, epidote and associated minerals in low grade metamorphic rocks

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Mineral Metastability In the System Al₂O₃-SiO₂-H₂O: A Discussion