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Critical Behavior in Fluids
Published in Ian L. Spain, Jac Paauwe, High Pressure Technology, 2017
Critical exponents are usually determined either by power-law analysis of the particular property studied along the appropriate path, or by fitting a scaled equation to any scalable physical property as a function of its variables, after which the desired exponent is extracted. In either case, there are many different ways in which critical- region properties can be measured, ranging from adapted conventional methods of often venerable age to new techniques that involve dielectric constant determination and interference or scattering of light. The direct power-law analysis is straightforward, although careful attention should be given to the rapidly decreasing relative accuracy of reduced properties (such as ∆ρ*, ∆T*, etc.) when the critical point is approached, and to the possible presence of “trends” in the apparent exponents when the range from the critical point is reduced; the presence of such trends indicates that the asymptotic range has been exceeded in the data fit.
Effects of Alcohol Chain Length and Salt on Phase Behavior and Critical Phenomena in SDS Microemulsions
Published in Promod Kumar, K. L. Mittal, Handbook of Microemulsion Science and Technology, 2018
Finally, the third important feature of critical phenomena highlighted by modern theories is the concept of universality. According to this, the critical exponents associated with the singularities are identical for all the systems within a given universality class. Pure fluids and fluid mixtures near normal critical points belong in the universality class of the three-dimensional Ising model. Renormalization group methods have yielded a detailed and accurate description of the critical thermodynamic behavior of such Ising-like systems. The Ising values for the exponents v, γ, β, and μ are v = 0.630 ± 0.001, γ = 1.240 ± 0.002, β = 0.325 ± 0.001, and μ = 1.260.
High-throughput analysis of magnetic phase transition by combining table-top sputtering, photoemission electron microscopy, and Landau theory
Published in Science and Technology of Advanced Materials: Methods, 2022
T. Nishio, M. Yamamoto, T. Ohkochi, D. Nanasawa, A. L. Foggiatto, M. Kotsugi
The second-order term Am2 is the demagnetization energy term, and the sign of the coefficient A corresponds to the ferromagneticparamagnetic transition. The fourth-order coefficient B is the magnetic anisotropy energy term, and h is the magnetic field. Note that the experimental MCD histograms remained asymmetric due to the remanent magnetisation. Therefore, we left the first-order term hm as a correction term to perform the fitting. It should also be noted that the Landau theory cannot wholly treat spatial inhomogeneity in magnetic domain structures because of the mean-field approximation [30]. Therefore, we abandoned the spatial information in the MCD-PEEM image and statistically treated the MCD data to investigate only the presence of a ferromagnetic/paramagnetic transition. We used data with clearly separated black and white contrast for fitting the curve. As a result of fitting the MCD histograms, the coefficient A changed from 2.00 × 10−3 in the ferromagnetic phase (Fe25Co40Cr35) to −6.99 × 10−3 in the paramagnetic phase (Fe30Co30Cr40), where the change in the sign indicates a magnetic phase transition. The coefficient B ranged from 1.90 × 10−5 (Fe25Co40Cr35) to 9.43 × 10−5 (Fe30Co30Cr40). Finally, we evaluated the critical exponent β to validate the analytical method. Critical exponent β is a fundamental constant that characterizes not only magnetic-phase transitions but also phase transitions. It is a universal parameter that is independent of materials. β can be expressed by the following equation