scholarly journals Pinning of dislocations in disordered alloys: effects of dislocation orientation

2022 ◽  
Vol 6 (1) ◽  
Author(s):  
Michael Zaiser ◽  
Ronghai Wu
Keyword(s):  
Long Range ◽  
Random Distribution ◽  
Spatial Correlations ◽  
Third Order ◽  
High Entropy ◽  
Disordered Alloys ◽  
Power Law Decay ◽  
The Mean ◽  
Edge Dislocations ◽  
Solute Hardening

AbstractThe current interest in compositionally complex alloys including so called high entropy alloys has caused renewed interest in the general problem of solute hardening. It has been suggested that this problem can be addressed by treating the alloy as an effective medium containing a random distribution of dilatation and compression centers representing the volumetric misfit of atoms of different species. The mean square stresses arising from such a random distribution can be calculated analytically, their spatial correlations are strongly anisotropic and exhibit long-range tails with third-order power law decay (Geslin and Rodney 2021; Geslin et al. 2021). Here we discuss implications of the anisotropic and long-range nature of the correlation functions for the pinning of dislocations of arbitrary orientation. While edge dislocations are found to follow the standard pinning paradigm, for dislocations of near screw orientation we demonstrate the co-existence of two types of pinning energy minima.

scholarly journals Homogenization approximations for unidirectional transport past randomly distributed sinks

2019 ◽  
Vol 85 (2) ◽  
pp. 161-189 ◽  
Author(s):  
Matthew J Russell ◽  
Oliver E Jensen
Keyword(s):  
Long Range ◽  
Spatial Correlations ◽  
First Order ◽  
First Order Kinetics ◽  
Random Structures ◽  
Non Local ◽  
The Mean ◽  
Higher Order Corrections ◽  
Mean Concentration ◽  
Random Sink

Abstract Transport in biological systems often occurs in complex spatial environments involving random structures. Motivated by such applications, we investigate an idealized model for solute transport past an array of point sinks, randomly distributed along a line, which remove solute via first-order kinetics. Random sink locations give rise to long-range spatial correlations in the solute field and influence the mean concentration. We present a non-standard approach in evaluating these features based on rationally approximating integrals of a suitable Green’s function, which accommodates contributions varying on short and long lengthscales and has deterministic and stochastic components. We refine the results of classical two-scale methods for a periodic sink array (giving more accurate higher-order corrections with non-local contributions) and find explicit predictions for the fluctuations in concentration and disorder-induced corrections to the mean for both weakly and strongly disordered sink locations. Our predictions are validated across a large region of parameter space.

Stochastic homogenization and macroscopic modelling of composites and flow through porous media

2002 ◽  
pp. 337-378 ◽  
Author(s):  
Jozef Telega ◽  
Wlodzimierz Bielski
Keyword(s):  
Porous Medium ◽  
Random Distribution ◽  
Flow Through Porous Media ◽  
Macroscopic Models ◽  
Linear Elastic ◽  
Multi Scale ◽  
Convergence Method ◽  
Flow Through ◽  
The Mean ◽  
Random Porous Medium

The aim of this contribution is mainly twofold. First, the stochastic two-scale convergence in the mean developed by Bourgeat et al. [13] is used to derive the macroscopic models of: (i) diffusion in random porous medium, (ii) nonstationary flow of Stokesian fluid through random linear elastic porous medium. Second, the multi-scale convergence method developed by Allaire and Briane [7] for the case of several microperiodic scales is extended to random distribution of heterogeneities characterized by separated scales (stochastic reiterated homogenization). .

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

scholarly journals Preparation of high-entropy carbides by different sintering techniques

2021 ◽  
Vol 56 (19) ◽  
pp. 11237-11247 ◽  
Author(s):  
Johannes Pötschke ◽  
Manisha Dahal ◽  
Mathias Herrmann ◽  
Anne Vornberger ◽  
Björn Matthey ◽  
...  
Keyword(s):  
Grain Size ◽  
Single Phase ◽  
X Ray Diffraction ◽  
Vacuum Sintering ◽  
X Ray ◽  
High Entropy ◽  
Mean Grain Size ◽  
The Mean ◽  
Gas Pressure Sintering ◽  
Hardness Values

AbstractDense (Hf, Ta, Nb, Ti, V)C- and (Ta, Nb, Ti, V, W)C-based high-entropy carbides (HEC) were produced by three different sintering techniques: gas pressure sintering/sinter–HIP at 1900 °C and 100 bar Ar, vacuum sintering at 2250 °C and 0.001 bar as well as SPS/FAST at 2000 °C and 60 MPa pressure. The relative density varied from 97.9 to 100%, with SPS producing 100% dense samples with both compositions. Grain size measurements showed that the substitution of Hf with W leads to an increase in the mean grain size of 5–10 times the size of the (Hf, Ta, Nb, Ti, V,)C samples. Vacuum-sintered samples showed uniform grain size distribution regardless of composition. EDS mapping revealed the formation of a solid solution with no intermetallic phases or element clustering. X-ray diffraction analysis showed the structure of mostly single-phase cubic high-entropy carbides. Hardness measurements revealed that (Hf, Ta, Nb, Ti, V)C samples possess higher hardness values than (Ta, Nb, Ti, V, W)C samples.

scholarly journals Lattice Distortion and Phase Stability of Pd-Doped NiCoFeCr Solid-Solution Alloys

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 900 ◽  
Author(s):  
Fuxiang Zhang ◽  
Yang Tong ◽  
Ke Jin ◽  
Hongbin Bei ◽  
William Weber ◽  
...  
Keyword(s):  
Long Range ◽  
Lattice Distortion ◽  
Maximum Pressure ◽  
Local Lattice Distortion ◽  
X Ray ◽  
High Entropy ◽  
Local Lattice ◽  
Pd Doping ◽  
Fcc Phase ◽  
The Stability

In the present study, we have revealed that (NiCoFeCr)100−xPdx (x= 1, 3, 5, 20 atom%) high-entropy alloys (HEAs) have both local- and long-range lattice distortions by utilizing X-ray total scattering, X-ray diffraction, and extended X-ray absorption fine structure methods. The local lattice distortion determined by the lattice constant difference between the local and average structures was found to be proportional to the Pd content. A small amount of Pd-doping (1 atom%) yields long-range lattice distortion, which is demonstrated by a larger (200) lattice plane spacing than the expected value from an average structure, however, the degree of long-range lattice distortion is not sensitive to the Pd concentration. The structural stability of these distorted HEAs under high-pressure was also examined. The experimental results indicate that doping with a small amount of Pd significantly enhances the stability of the fcc phase by increasing the fcc-to-hcp transformation pressure from ~13.0 GPa in NiCoFeCr to 20–26 GPa in the Pd-doped HEAs and NiCoFeCrPd maintains its fcc lattice up to 74 GPa, the maximum pressure that the current experiments have reached.

scholarly journals Developing and Demonstrating Climate Indicators for Monitoring the Changing Water Cycle

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Xia Feng ◽  
Paul Houser
Keyword(s):  
Water Cycle ◽  
Spatial Scales ◽  
Atmospheric Moisture ◽  
Spatial Correlations ◽  
Climate Indicators ◽  
Terrestrial Water ◽  
The Mean ◽  
Atmospheric Moisture Content ◽  
Daily Total

In this study, we developed a suite of spatially and temporally scalable Water Cycle Indicators (WCI) to examine the long-term changes in water cycle variability and demonstrated their use over the contiguous US (CONUS) during 1979–2013 using the MERRA reanalysis product. The WCI indicators consist of six water balance variables monitoring the mean conditions and extreme aspects of the changing water cycle. The variables include precipitation (P), evaporation (E), runoff (R), terrestrial water storage (dS/dt), moisture convergence flux (C), and atmospheric moisture content (dW/dt). Means are determined as the daily total value, while extremes include wet and dry extremes, defined as the upper and lower 10th percentile of daily distribution. Trends are assessed for annual and seasonal indicators at several different spatial scales. Our results indicate that significant changes have occurred in most of the indicators, and these changes are geographically and seasonally dependent. There are more upward trends than downward trends in all eighteen annual indicators averaged over the CONUS. The spatial correlations between the annual trends in means and extremes are statistically significant across the country and are stronger forP,E,R, andCcompared todS/dtanddW/dt.

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