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Fractal Interpretation of the Phase Transition of the Crystalline NH 4‐ x D x NO 3 System as Shown by the Critical Raman Intensity Behaviour of the Nitrate ν 1 and ν 4 Modes
Author(s) -
Ma Shuguo,
Wu Guozhen
Publication year - 1996
Publication title -
journal of raman spectroscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.748
H-Index - 110
eISSN - 1097-4555
pISSN - 0377-0486
DOI - 10.1002/(sici)1097-4555(199608)27:8<615::aid-jrs998>3.0.co;2-y
Subject(s) - raman spectroscopy , critical exponent , phase transition , intensity (physics) , fractal , exponent , critical point (mathematics) , phase (matter) , thermodynamics , critical phenomena , chemistry , materials science , physics , optics , geometry , mathematics , mathematical analysis , linguistics , philosophy , organic chemistry
The critical Raman intensities of the nitrate ν 1 and ν 4 modes are shown to behave as ∣ T ‐ T c ∣ β . This behaviour is interpreted from the fractal viewpoint. Deuteration is shown to affect the ν 1 and ν 4 modes differently through the exponent β. The exponent β is expressed as the product of two factors related to the energy barrier between the two co‐existing phases in the critical region and the degrees of the structural order of the respective phases. Therefore, using also the thermodynamic measurement of Δ H , it is possible to obtain parameters concerning the structural order of the phases in the critical region and the effect of deuteration. The Raman intensity ratios of the ν 1 to ν 4 modes also behave as power functions of ∣ T ‐ T c ∣ , suggesting that the size effect of micro‐domains of both phases, which fluctuate randomly due to thermal agitation, on the Raman cross‐sections in the critical region is significant and fractal.