Critical behavior of the order-disorder phase transition inβ-brass investigated by x-ray scattering

Abstract

β-brass exhibits an archetypical example of an order-disorder transition with a critical behavior that was previously investigated by neutron scattering. The data were well described by the three-dimensional (3d) Ising model but the relatively crude experimental resolution prevented an in-depth examination of the single-length scaling hypothesis, a cornerstone in the theory of critical phenomena. With the development of synchrotron x-ray experiments, high-resolution data could be recorded and surprisingly it was found that the single-length scaling did not hold in most critical systems, possibly due to strain originating from surface defects and/or impurities. In this paper we demonstrate single-length critical behavior using high-resolution x-ray scattering in β-brass. The investigations confirm that β-brass behaves like a 3d Ising system over a wide range of length scales comprising correlated clusters of millions of atoms. To vary the surface sensitivity, experiments have been performed both in Bragg reflection and Laue transmission geometries but without any substantial differences observed in the scaling and critical behavior.

Effective medium approach in the renormalization group theory of phase transitions

“…As is known, the Ising model on a bipartite lattice in zero external field ordered antiferromagnetically can be mapped onto ferromagnetic model by flipping the spins on every second site and simultaneously changing signs of the 2, respectively; the upper horizontal dashed-dotted line is the best known universal value for the exponent [8], the lower line is the value used in [11].…”

“…Current non-perturbative RG approaches [9,6,10,8] suffer from poorly controlled approximations and so are not reliable enough to quantitatively predict non-universal quantities. Presumably because of this, phenomenological theories and the high-temperature expansions of simple model systems developed before the advent of the RG theory are still being invoked to interpret experimental data on the second-order phase transitions (see [11] and references therein).…”

“…It will be shown that the implementation of the self-consistent LPA scheme (SC-LPA) makes possible accurate calculation of non-universal quantities without use of arbitrary parameters. As a first physical application of the method, semi-quantitative arguments will be presented that the non-universal contributions may be responsible for the discrepancy between the universal value of the critical exponent β calculated within RG theory and the values obtained in recent experiments on ordering in beta-brass [11].…”

Simulations of single-particle imaging of hydrated proteins with x-ray free-electron lasers

“…X-ray free-electron lasers (XFELs) deliver ultra-short fs pulses of x-ray photons at fluences that exceed those of synchrotron radiation sources by many orders of magnitude. 1 These key characteristics (pulse durations of a few femtoseconds, of the order 10 12 photons per pulse, focussed to spot sizes of a few 100 nm in diameter) open scientific opportunities in many research fields, 2 including ultra-fast dynamics in atoms, molecules, and clusters, [3][4][5] condensed matter spectroscopy, 6,7 high energy density science, 8 materials research 9 , and structural biology. 10 In the latter case, the "probe-before-destruction" technique, i.e.…”

Three-Dimensional Imaging of Phase Ordering in an Fe-Al Alloy by Bragg Ptychography

“…This order-disorder phase transition has attracted much fundamental interest since it is regarded as a model system for second order phase transitions and critical behavior, e.g., the Heisenberg antiferromagnet and the Ising model, see Ref. [8] and references therein. Highresolution x-ray scattering has been instrumental in characterizing metallic alloys and determining their phase diagrams.…”