scholarly journals Symmetry and Asymmetry in Quasicrystals or Amorphous Materials

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1326
Author(s):  
Enrique Maciá Barber
Keyword(s):  
Long Range ◽  
Amorphous Materials ◽  
Recent Literature ◽  
Range Order ◽  
Translation Invariance ◽  
Variable Range Hopping ◽  
Interference Effects ◽  
Quasiperiodic Systems ◽  
Diffraction Patterns ◽  
Weak Interference

Quasicrystals (QCs) are long-range ordered materials with a symmetry incompatible with translation invariance. Accordingly, QCs exhibit high-quality diffraction patterns containing a collection of discrete Bragg reflections. Notwithstanding this, it is still common to read in the recent literature that these materials occupy an intermediate position between amorphous materials and periodic crystals. This misleading terminology can be understood as probably arising from the use of models and notions borrowed from the amorphous solid’s conceptual framework (such us tunneling states, weak interference effects, variable range hopping, or spin glass) in order to explain certain physical properties observed in QCs. On the other hand, the absence of a general, full-fledged theory of quasiperiodic systems certainly makes it difficult to clearly distinguish the features related to short-range order atomic arrangements from those stemming from long-range order correlations.

scholarly journals Synthesis of Paracrystalline Diamond

2021 ◽  
Author(s):  
Howard Sheng ◽  
Hu Tang ◽  
Xiaohong Yuan ◽  
Yong Cheng ◽  
Hongzhan Fei ◽  
...  
Keyword(s):  
Long Range ◽  
Amorphous Materials ◽  
Nearest Neighbor ◽  
Structural Characteristics ◽  
Range Order ◽  
Dynamics Simulation ◽  
X Ray Diffraction ◽  
Transmission Microscopy ◽  
Nucleation Sites ◽  
High Pressure High Temperature

Abstract Solids in nature can be generally classified into crystalline and non-crystalline states, depending on whether long-range lattice periodicity is present in the material. The differentiation of the two states, however, could face fundamental challenges if the degree of long-range order in crystals is significantly reduced. Here we report a unique paracrystalline state of diamond that is distinct from either crystalline or amorphous diamond. The paracrystalline diamond reported in this work, consisting of sub-nanometer-sized paracrystals that possess a well-defined crystalline medium-range order up to a few atomic shells, was synthesized in high-pressure high-temperature conditions (e.g., 30 GPa, 1600 K) employing fcc-C60 as a precursor. The structural characteristics of paracrystalline diamond was identified through a combination of X-ray diffraction, high-resolution transmission microscopy, and advanced molecular dynamics simulation. The formation of paracrystalline diamond is a result of densely distributed nucleation sites developed in compressed C60 as well as pronounced second-nearest-neighbor short-range order in amorphous diamond due to strong sp3 bonding. The discovery of paracrystalline diamond adds a new diamond form to the enriched carbon family, which exhibits distinguishing physical properties and can be furthered exploited to develop new materials. Furthermore, this work reveals the missing link in the length-scale between amorphous and crystalline states across the structural landscape, which has profound implications for recognizing complex structures arising from amorphous materials.

EXAFS Studies of Semiconductor Microstructure

MRS Bulletin ◽  
1988 ◽  
Vol 13 (2) ◽  
pp. 36-39 ◽  
Author(s):  
Bruce A. Bunker
Keyword(s):  
Absorption Coefficient ◽  
Long Range ◽  
Amorphous Materials ◽  
Diluted Magnetic Semiconductors ◽  
Condensed Matter ◽  
Range Order ◽  
Long Range Order ◽  
X Ray ◽  
Atomic Species ◽  
X Ray Absorption

Extended X-Ray Absorption Fine Structure (EXAFS) is a technique capable of probing local structure in condensed- matter systems, determining distances, coordination numbers, and species of atoms near an x-ray excited atom. Further, this information is obtained separately for each constituent atomic species. EXAFS can be applied equally well to crystals, alloys, or even systems having no long-range order such as liquids, gases, and amorphous materials.Here we review EXAFS spectroscopy and its use in studying semiconductors. First, we show EXAFS in the study of impurities to determine the local environment of Fe implanted in Si. Second, we show how EXAFS can be used to determine local structural distortion in diluted magnetic semiconductors. We next demonstrate that EXAFS can determine the nature of the phase transition in ferroelectric Pb1-x Gex Te, where the transition is revealed to have an order-disorder character in contrast to GeTe where the transition is purely displacive. The theme of these examples is that EXAFS can determine the relative positions of atoms in condensed matter and that the short-range order as determinedn by EXAFS often differs from the long-range order or theoretical expectations.In the EXAFS technique, one measures the x-ray absorption coefficient as a function of x-ray energy. The absorption spectrum shows a number of x-ray edges corresponding to the threshold of excitation of core electrons from the sample's various atomic species. At energies above each of these edges, oscillations in the absorption coefficient are due to backscattering of the photoelectron from the neighboring atoms.

scholarly journals A modulation wave approach to the long range order hidden in nominal 'disorder'

2014 ◽  
Vol 70 (a1) ◽  
pp. C36-C36
Author(s):  
Ray Withers
Keyword(s):  
Long Range ◽  
Range Order ◽  
Local Order ◽  
Long Range Order ◽  
Diffuse Intensity ◽  
Crystalline Materials ◽  
Modulated Structures ◽  
Close Relationship ◽  
Diffraction Patterns ◽  
Definition Of

While the definition of a crystal in terms of pure point diffraction/sharp Bragg reflections only is undoubtedly an excellent approximation for many crystalline materials, there exists a large and growing family of phases for which such a description is grossly inadequate: namely crystalline materials whose reciprocal spaces exhibit highly structured, continuous, diffuse intensity distributions which are essentially long range ordered in at least one or more dimensions (see e.g. Fig.1). To gain insight into both the local order, as well as the long range order, hidden in disordered materials of this type it is very helpful, if not essential, to use the language of modulated structures. An approach of this type automatically emphasizes the close relationship between the crystallography of disordered structures and aperiodic crystallography in general. In this contribution, the use of such an approach to understand the often highly structured shapes of such diffuse distributions, the characteristic extinction conditions frequently associated with them and the long range crystal chemical rules underlying their existence will be highlighted. Fig.1: <11-2> and <-110> zone axis electron diffraction patterns of (a) β-cristobalite and (b) SiO2-tridymite.

Fluctuation Microscopy: A New Class of Microscopy Techniques for Probing Medium Range Order in Amorphous Materials

1998 ◽  
Vol 4 (S2) ◽  
pp. 702-703
Author(s):  
J. M. Gibson ◽  
M. M. J. Treacy ◽  
P. M. Voyles
Keyword(s):  
Long Range ◽  
Short Range ◽  
Amorphous Materials ◽  
Short Range Order ◽  
Nearest Neighbor ◽  
Range Order ◽  
Regular Tetrahedron ◽  
Long Range Order ◽  
Medium Range Order ◽  
Medium Range

Amorphous materials are devoid of periodic long range order, but at the nearest-neighbor level they possess a high degree of short-range order. In amorphous tetrahedral semiconductors, such as Si and Ge, this short-range order arises because each atom attempts to satisfy four bonds arranged as a regular tetrahedron. It is the rotations about each bond, from the second-nearest-neighbor outwards, that result in the loss of long-range order. It is apparent from modeling of amorphous materials, that there is considerable flexibility as to how rapidly the medium-range-order diminishes. The continuous random network (CRN) is a hypothetical tetrahedral extended structure wherein the atoms possess full four-connected coordination, but have minimal medium-range order. However, real amorphous materials infrequently exhibit true CRN-like topologies. Traditionally, diffraction has been used to study short- and medium-range order in amorphous materials. Assuming kinematical scattering, and that every atom has a similar environment, a radial distribution function (RDF) can be extracted which is sensitive only to the averaged atom pair-correlations out to ∼1 nm.

A transmission electron microscope and X-ray diffraction study of muscovite and chlorite

1973 ◽  
Vol 39 (302) ◽  
pp. 176-188 ◽  
Author(s):  
G. Oertel ◽  
C. D. Curtis ◽  
P. P. Phakey
Keyword(s):  
Long Range ◽  
Stacking Faults ◽  
Range Order ◽  
Long Range Order ◽  
X Rays ◽  
Transmitted Radiation ◽  
High Background ◽  
Rock Types ◽  
Transmission Electron ◽  
Diffraction Patterns

SummarySingle-crystal diffraction patterns produced by transmitted radiation, both X-rays and electrons, reveal varying degrees of disorder and long-range order in common phyllosilicates from several different rock types. The transmission electron micrographs and their selected-area diffraction patterns demonstrate the presence of numerous stacking faults parallel to (001) of muscovite and chlorite. Individual stacking faults can be recognized by the diffraction-contrast fringe patterns they cause, and partial dislocations can be seen where such faults terminate inside a crystal. Long-range order of muscovite explains what seemed to be spurious, high ‘background’ levels that are sometimes encountered in the analysis of rock fabrics by transmitted X-rays.

Analysis of Dark-Field Images of Disordered Materials

1972 ◽  
Vol 30 ◽  
pp. 560-561
Author(s):  
J. M. Cowley
Keyword(s):  
Amorphous Materials ◽  
Careful Analysis ◽  
Dark Field ◽  
Minimum Diameter ◽  
Statistical Fluctuations ◽  
Bright Spots ◽  
Sufficient Detail ◽  
Random Arrangement ◽  
Diffraction Patterns ◽  
Imaging Conditions

Recently a number of authors have reported detail in dark-field images obtained from diffuse-scattering regions of electron diffraction patterns. Bright spots in images from short-range order diffuse peaks of disordered binary alloys have been interpreted as evidence for the existence of microdomains of ordered lattice or of segragated clusters of one component. Spotty contrast in dark field images of near-amorphous materials has been interpreted as evidence for the existense of microcrystals. Without a careful analysis of the imaging conditions such conclusions may be invalid. Usually the conditions of the experiment have not been specified in sufficient detail to allow evaluation of the conclusions.Elementary considerations show that even for a completely random arrangement of atoms the statistical fluctuations of density will give a spotty contrast with spots of minimum diameter determined by the dark field aperture size and other factors influencing the minimum resolvable distance under darkfield imaging conditions, including fluctuations and drift over long exposure times (resolution usually 10Å or more).

Ordering in Ni4Mo by TEM and APFIM

1987 ◽  
Vol 45 ◽  
pp. 214-215
Author(s):  
E.A. Kenik ◽  
T.A. Zagula ◽  
M.K. Miller ◽  
J. Bentley
Keyword(s):  
Electron Irradiation ◽  
Low Temperatures ◽  
Short Range ◽  
Atom Probe ◽  
Range Order ◽  
Considerable Time ◽  
Probe Field ◽  
Disordered Phase ◽  
Transmission Electron ◽  
Diffraction Patterns

The state of long-range order (LRO) and short-range order (SRO) in Ni4Mo has been a topic of interest for a considerable time (see Brooks et al.). The SRO is often referred to as 1½0 order from the apparent position of the diffuse maxima in diffraction patterns, which differs from the positions of the LRO (D1a) structure. Various studies have shown that a fully disordered state cannot be retained by quenching, as the atomic arrangements responsible for the 1½0 maxima are present at temperatures above the critical ordering temperature for LRO. Over 20 studies have attempted to identify the atomic arrangements associated with this state of order. A variety of models have been proposed, but no consensus has been reached. It has also been shown that 1 MeV electron irradiation at low temperatures (∼100 K) can produce the disordered phase in Ni4Mo. Transmission electron microscopy (TEM), atom probe field ion microscopy (APFIM), and electron irradiation disordering have been applied in the current study to further the understanding of the ordering processes in Ni4Mo.

Multislice calculations for quasi-periodic and non-periodic objects

1990 ◽  
Vol 48 (4) ◽  
pp. 138-139
Author(s):  
R. Herrera ◽  
A. Gómez
Keyword(s):  
Electron Diffraction ◽  
Computer Simulations ◽  
Periodic Table ◽  
Amorphous Materials ◽  
Space Group ◽  
Essential Step ◽  
Shape Effects ◽  
Atomic Scattering ◽  
Diffraction Patterns ◽  
Periodic Continuation

Computer simulations of electron diffraction patterns and images are an essential step in the process of structure and/or defect elucidation. So far most programs are designed to deal specifically with crystals, requiring frequently the space group as imput parameter. In such programs the deviations from perfect periodicity are dealt with by means of “periodic continuation”.However, for many applications involving amorphous materials, quasiperiodic materials or simply crystals with defects (including finite shape effects) it is convenient to have an algorithm capable of handling non-periodicity. Our program “HeGo” is an implementation of the well known multislice equations in which no periodicity assumption is made whatsoever. The salient features of our implementation are: 1) We made Gaussian fits to the atomic scattering factors for electrons covering the whole periodic table and the ranges [0-2]Å−1 and [2-6]Å−1.

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