Near-surface critical x-ray scattering from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Al

Mailänder, L.; Dosch, H.; Peisl, J.; Johnson, R.L.

doi:10.1103/physrevlett.64.2527

Cited by 66 publications

(48 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the numerical point of view, the best investigated cases are n = 0 [45,46] and n = 1 (Ising) [47,17,18,48,8], whereas studies for n ≥ 2 are scarce [24,49,50,51]. The rather few experimental determinations of surface critical exponents at the ordinary transition, using for example x-ray scattering at grazing angle, yield values which are found to be compatible with the theoretical estimates [52,53,54,55].…”

Section: The Surface Universality Classessupporting

confidence: 52%

“…In these experiments [53,157] critical exponents compatible with the ordinary transition critical behaviour were measured, but at the same time the existence of residual longrange surface order was revealed at temperatures above the bulk critical temperature. This behaviour is readily explained by assuming that a weak surface field exists, yielding a surface structure factor governed by the ordinary behaviour in the case that l ord exceeds the bulk correlation length.…”

Section: Surfaces and Fieldsmentioning

confidence: 99%

See 1 more Smart Citation

Critical phenomena at perfect and non-perfect surfaces

Pleimling¹

2004

J. Phys. A: Math. Gen.

100

135

View full text Add to dashboard Cite

Abstract. In the past perfect surfaces have been shown to yield a local critical behaviour that differs from the bulk critical behaviour. On the other hand surface defects, whether they are of natural origin or created artificially, are known to modify local quantities. It is therefore important to clarify whether these defects are relevant or irrelevant for the surface critical behaviour.The purpose of this review is two-fold. In the first part we summarise some of the important results on surface criticality at perfect surfaces. Special attention is thereby paid to new developments as for example the study of surface critical behaviour in systems with competing interactions or of surface critical dynamics. In the second part the effect of surface defects (presence of edges, steps, quenched randomness, lines of adatoms, regular geometric patterns) on local critical behaviour in semi-infinite systems and in thin films is discussed in detail. Whereas most of the defects commonly encountered are shown to be irrelevant, some notable exceptions are highlighted. It is shown furthermore that under certain circumstances non-universal local critical behaviour may be observed at surfaces.

show abstract

Section: The Surface Universality Classessupporting

confidence: 52%

Section: Surfaces and Fieldsmentioning

confidence: 99%

Critical phenomena at perfect and non-perfect surfaces

Pleimling¹

2004

J. Phys. A: Math. Gen.

100

135

View full text Add to dashboard Cite

show abstract

“…In particular, the grazing incidence of x-rays and neutrons [3] has become a standard tool for probing critical behavior near surfaces and interfaces [5][6][7][8]. For instance, the decay of the two-point correlation function has been measured close to the surface of a Fe 3 Al crystal near its continuous order-disorder transition by the method of grazing incidence of x-rays [5]. The phenomenon of critical adsorption near columnar defects [4] has apparently been observed by small angle scattering of light in a NH 4 Br crystal near a continuous structural phase transition [12].…”

Section: Introductionmentioning

confidence: 99%

“…Theoretical predictions for surface criticality have been tested experimentally [5][6][7][8][9] and in simulations [10,11]. In particular, the grazing incidence of x-rays and neutrons [3] has become a standard tool for probing critical behavior near surfaces and interfaces [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Correlation functions near modulated and rough surfaces

Hanke

Kardar

2002

Phys. Rev. E

View full text Add to dashboard Cite

In a system with long-ranged correlations, the behavior of correlation functions is sensitive to the presence of a boundary. We show that surface deformations strongly modify this behavior as compared to a flat surface.The modified near surface correlations can be measured by scattering probes.To determine these correlations, we develop a perturbative calculation in the deformations in height from a flat surface. Detailed results are given for a regularly patterned surface, as well as for a self-affinely rough surface with roughness exponent ζ. By combining this perturbative calculation in height deformations with the field-theoretic renormalization group approach, we also estimate the values of critical exponents governing the behavior of the decay of correlation functions near a self-affinely rough surface. We find that for the interacting theory, a large enough ζ can lead to novel surface critical behavior.We also provide scaling relations between roughness induced critical exponents for thermodynamic surface quantities.

show abstract

“…Rh, 68.35.Ct, 05.70.Jk, 64.60.Fr Bulk properties, such as magnetization, as well as correlation functions are modified on approaching a surface. In particular, critical behavior near surfaces or defects, which is quite different from the bulk, has been extensively studied theoretically [1][2][3][4], by experiments [5][6][7], and in simulations [8]. Along with this development, the method of grazing incidence of x-rays and neutrons [3] has become a standard tool of probing critical behavior near surfaces and interfaces [5][6][7].…”

mentioning

confidence: 99%

Modified Critical Correlations Close to Modulated and Rough Surfaces

Hanke

Kardar

2001

Phys. Rev. Lett.

View full text Add to dashboard Cite

Correlation functions are sensitive to the presence of a boundary. Surface modulations give rise to modified near surface correlations, which can be measured by scattering probes. To determine these correlations, we develop a perturbative calculation in deformations in height from a flat surface. The results, combined with a renormalization group around four dimensions, are also used to predict critical behavior near a self-affinely rough surface. We find that a large enough roughness exponent can modify surface critical behavior.PACS numbers: 68.35. Rh, 68.35.Ct, 05.70.Jk, 64.60.Fr Bulk properties, such as magnetization, as well as correlation functions are modified on approaching a surface. In particular, critical behavior near surfaces or defects, which is quite different from the bulk, has been extensively studied theoretically [1][2][3][4], by experiments [5][6][7], and in simulations [8]. Along with this development, the method of grazing incidence of x-rays and neutrons [3] has become a standard tool of probing critical behavior near surfaces and interfaces [5][6][7].Most theoretical studies have been restricted to flat surfaces. However, real surfaces mostly deviate from this idealized picture. Possible deviations can be divided into two classes: (i) advanced experimental methods, e.g., lithographic preparation, allow one to endow surfaces with specific, regular geometrical patterns down to the nanometer scale, with important applications in technology and material science [9]; (ii) surfaces or interfaces can be naturally rough, e.g., due to growth, fracture, or erosion. Most common are self-affinely rough surfaces, in which the root mean square height fluctuations on a length scale L grow as L ζ , where ζ < 1 is the so-called roughness exponent. Self-affine scaling is predicted by many numerical and analytical models of surface growth [10], and is also observed in a number of experiments [11].In this work we show that the shape of the surface has a distinct influence on the properties of an adjacent medium with long-range correlations. This is demonstrated for two-point correlation functions near a critical point of the medium, for both cases (i) and (ii) outlined above. The diffuse scattering of x-rays and neutrons at grazing incidence due to such correlations appears in addition to what would have been observed if the surface was separating two homogeneous media [12]. The modified correlations may thus provide an additional and indirect means of characterizing the surface profile. This may be of value when other techniques are not possible, as in the case of the interior surface of a glass, or an internal crack, whereas scattering from a critical fluid or binary alloy coating the surface may be feasible.In order to study the effects of the surface shape, we develop a perturbative expansion of two-point correlation functions in the deformations of the height profile. Initially for a Gaussian field, the calculations are carried out to second order. Already at the first order, the two-point correlatio...

show abstract

Near-surface critical x-ray scattering fromFe3Al

Cited by 66 publications

References 7 publications

Critical phenomena at perfect and non-perfect surfaces

Critical phenomena at perfect and non-perfect surfaces

Correlation functions near modulated and rough surfaces

Modified Critical Correlations Close to Modulated and Rough Surfaces

Contact Info

Product

Resources

About