X-ray study of the second-order phase transition of Ag0.35TiS2: A phase transition characterized by two order parameters
| Autor: | Ga Wiegers, R.J. Haange, J.E. Zondag, J. L. de Boer, S. van Smaalen, Klaas Derk Bronsema |
|---|---|
| Rok vydání: | 1987 |
| Předmět: |
chemistry.chemical_classification
Phase transition Crystal structure Atmospheric temperature range Condensed Matter Physics Electronic Optical and Magnetic Materials Inorganic Chemistry Crystallography Mean field theory chemistry X-ray crystallography Materials Chemistry Ceramics and Composites Hexagonal lattice Physical and Theoretical Chemistry Inorganic compound Critical exponent |
| Zdroj: | Journal of Solid State Chemistry. 67:9-20 |
| ISSN: | 0022-4596 |
| DOI: | 10.1016/0022-4596(87)90332-x |
| Popis: | Ag 0.35 TiS 2 shows a second-order phase transition with T c = 298.0 K from a a √3 × a √3 × 2 c superstructure, space group P 3 1c , to a disordered Cd(OH) 2 NiAs intermediate structure with unit cell a × a × c and space group P 3 m1 . In the disordered structure silver atoms occupy fractionally the sites of triangular lattice planes. Below T c silver atoms occupy special sites in space group P 3 1c : Ag(α) at ±(0, 0, 1 4 ) , Ag(β) at ±( 2 3 , 1 3 , 1 4 ) , and Ag(γ) at ±( 1 3 , 2 3 , 1 4 ) . The order is characterized by two order parameters η 1 = n ( β ) − n ( γ ) and η 2 = n ( β ) + n ( γ ) − 2 n ( α ), where n ( α ), n ( β ), and n ( γ ) are the occupancies of the α, β, and γ sites, respectively. Single-crystal X-ray diffraction of the ordered structure showed the occupancies n ( α ) = 0.172, n ( β ) = 0.861, n ( γ ) = 0 at 100 K and n ( α ) = 0.180, n ( β ) = 0.786, n ( γ ) = 0.069 at 255 K. Critical exponents β 1 and β 2 of the order parameters η 1 and η 2 were determined from the temperature dependence of the intensities of the superreflections 101 and 102, respectively; the values obtained, β 1 = 0.41 and β 2 = 0.81, are between those predicted by P. Bak ( Phys. Rev. Lett. 44, 889 (1980)) from scaling laws: β 1 = 0.33 and β 2 = 0.86, and from mean field theory: β 1 = 0.5, β 2 = 1.0. The temperature dependence of the order parameters in the temperature range 100–298 K is compared with that from a Bragg-Williams (mean field) model, the energy being written in terms of nearest-neighbor repulsive interactions, e 1 for atoms at distance a and e 2 for atoms at distance c ; e 1 > e 2 because c > a . The space group of the observed structure, P 3 1c , is discussed in (3 + 1)D superspace, which gives an alternate description for the symmetry of this commensurately modulated phase. Finally, some related phases are discussed. |
| Databáze: | OpenAIRE |
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