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By A Vilenkin

Part transitions within the early universe can provide upward thrust to macroscopic topological defects: vacuum area partitions, strings, partitions bounded by way of strings, and monopoles attached via strings. this text stories the formation, actual houses and the cosmological evolution of assorted defects. a specific recognition is paid to strings and their cosmological results, together with the string state of affairs of galaxy formation and attainable observational results of strings.

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The bond energy criterion of Sun and Mackenzie (Sun, 1947, Baldwin, 1981) arises from similar considerations. For systems in which the bonding is at least partially ionic in character, the coordination polyhedra present are to a large extent determined by the relative sizes of their constituent ions, usually expressed as the radius ratio, in which A is the cation and X is the anion. ) For stability, the cation at the center of an AXn polyhedron should fill the cavity defined by the anions, and there exists a critical radius ratio at which the criterion is just fulfilled and below which the cation cannot remain in contact with all the anions and the A X n polyhedron is unstable.

A n d P o u l a i n , M a . (1982a). Mat. Res. Bull. 17, 1035-1043. 34 Marcel Poulain Matecki, M . , P o u l a i n , M i . , and P o u l a i n , M a . (1982b). Mat. Res. Bull. 17, 1275-1281. Matecki, M . , P o u l a i n , M i . , and P o u l a i n , M a . (1983). J. Non-Cryst. Solids 56, 8 1 - 8 6 . Matecki, M . , P o u l a i n , M i . , and P o u l a i n , M a . (1987a). Mat. Res. Bull. 22, 345-350. Matecki, M . , P o u l a i n , M i . , and P o u l a i n , M a . (1987b). Mat. Sei. Forum 19-20, 4 7 - 5 4 .

1986). Numerous other fluoroaluminate glasses have been synthesized in multicomponent 7. Fluoride Glass Composition and Processing 23 F I G . 11. Glass forming area in the (a) A l F 3 - B a F 3 - Y F 3 - C a F 2 , and (b) A l F 3 - B a F 2 - Y F 3 T h F 4 systems. systems including zinc (Matecki and Poulain, 1981), alkali, magnesium, and rare-earths (Poulain and Matecki, 1982). New fluoroaluminate glasses were prepared by Tick (1988) in the A l F 3 - C d F 2 - L i F - P b F 2 system. , 1987).

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