Escherization with a Distance Function Focusing on the Similarity of Local Structure

2018 ◽  
pp. 108-120
Author(s):  
Yuichi Nagata
Keyword(s):  
Distance Function ◽  
Local Structure

X-ray microprobe for materials science

1994 ◽  
Vol 52 ◽  
pp. 56-57
Author(s):  
G.E. Ice
Keyword(s):  
Crystallographic Orientation ◽  
Local Structure ◽  
Materials Science ◽  
Chemical Information ◽  
X Ray Diffraction ◽  
Ray Optics ◽  
X Ray ◽  
Novel Materials ◽  
New Information ◽  
Elemental Sensitivity

The increasing availability of synchrotron x-ray sources has stimulated the development of advanced hard x-ray (E≥5 keV) microprobes. With new x-ray optics these microprobes can achieve micron and submicron spatial resolutions. The inherent elemental and crystallographic sensitivity of an x-ray microprobe and its inherently nondestructive and penetrating nature will have important applications to materials science. For example, x-ray fluorescent microanalysis of materials can reveal elemental distributions with greater sensitivity than alternative nondestructive probes. In materials, segregation and nonuniform distributions are the rule rather than the exception. Common interfaces to whichsegregation occurs are surfaces, grain and precipitate boundaries, dislocations, and surfaces formed by defects such as vacancy and interstitial configurations. In addition to chemical information, an x-ray diffraction microprobe can reveal the local structure of a material by detecting its phase, crystallographic orientation and strain.Demonstration experiments have already exploited the penetrating nature of an x-ray microprobe and its inherent elemental sensitivity to provide new information about elemental distributions in novel materials.

DETERMINATION OF THE LOCAL STRUCTURE OF METALLIC GLASSES BY EXAFS

1982 ◽  
Vol 43 (C9) ◽  
pp. C9-43-C9-46 ◽  
Author(s):  
A. Sadoc ◽  
A. M. Flank ◽  
D. Raoux ◽  
P. Lagarde
Keyword(s):  
Metallic Glasses ◽  
Local Structure

LOCAL STRUCTURE IN InGaAsP QUATERNARY ALLOYS

1986 ◽  
Vol 47 (C8) ◽  
pp. C8-423-C8-426
Author(s):  
H. OYANAGI ◽  
Y. TAKEDA ◽  
T. MATSUSHITA ◽  
T. ISHIGURO ◽  
A. SASAKI
Keyword(s):  
Local Structure ◽  
Quaternary Alloys

LOCAL STRUCTURE AND THERMODYNAMICS OF II-VI AND III-V SEMICONDUCTORS BY EXAFS

1986 ◽  
Vol 47 (C8) ◽  
pp. C8-403-C8-406
Author(s):  
N. MOTTA ◽  
A. BALZAROTTI ◽  
P. LETARDI
Keyword(s):  
Local Structure

Parallel Residues

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Distance Function ◽  
Length Function ◽  
Coxeter System ◽  
Vertex Set ◽  
Ordered Pairs

This chapter considers the notion of parallel residues in a building. It begins with the assumption that Δ‎ is a building of type Π‎, which is arbitrary except in a few places where it is explicitly assumed to be spherical. Δ‎ is not assumed to be thick. The chapter then elaborates on a hypothesis which states that S is the vertex set of Π‎, (W, S) is the corresponding Coxeter system, d is the W-distance function on the set of ordered pairs of chambers of Δ‎, and ℓ is the length function on (W, S). It also presents a notation in which the type of a residue R is denoted by Typ(R) and concludes with the condition that residues R and T of a building will be called parallel if R = projR(T) and T = projT(R).

On Asymmetric Distances

2013 ◽  
Vol 1 ◽  
pp. 200-231 ◽  
Author(s):  
Andrea C.G. Mennucci
Keyword(s):  
Total Variation ◽  
Calculus Of Variations ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Geodesic Segment ◽  
Intrinsic Metric ◽  
Typical Application ◽  
Variation Formula

Abstract In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.

Engineering Porosity Through Defects in a Giant Pore Metal–Organic Framework

2020 ◽  
Author(s):  
Adam Sapnik ◽  
Duncan Johnstone ◽  
Sean M. Collins ◽  
Giorgio Divitini ◽  
Alice Bumstead ◽  
...  
Keyword(s):  
Distribution Function ◽  
Ball Milling ◽  
Local Structure ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Metal Organic Framework ◽  
Metal Organic Frameworks ◽  
Defect Engineering ◽  
Metal Organic ◽  
Unsaturated Metal Sites

<p>Defect engineering is a powerful tool that can be used to tailor the properties of metal–organic frameworks (MOFs). Here, we incorporate defects through ball milling to systematically vary the porosity of the giant pore MOF, MIL-100 (Fe). We show that milling leads to the breaking of metal–linker bonds, generating more coordinatively unsaturated metal sites, and ultimately causes amorphisation. Pair distribution function analysis shows the hierarchical local structure is partially</p><p>retained, even in the amorphised material. We find that the solvent toluene stabilises the MIL-100 (Fe) framework against collapse and leads to a substantial rentention of porosity over the non-stabilised material.</p>

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