On the Relationship between Calculations and Measurements of the Free Volume of Grain Boundaries

1994 ◽  
Vol 343 ◽  
Author(s):  
S. C. Mehta ◽  
D. A. Smith
Keyword(s):  
Grain Boundary ◽  
Single Crystal ◽  
Free Volume ◽  
Experimental Measurement ◽  
Boundary Energy ◽  
Experimental Measurements ◽  
Grain Boundary Energy ◽  
Computer Calculations ◽  
The Difference ◽  
The Relationship

ABSTRACTGrain boundary free volume, simply defined as the difference between the volume of a bicrystal and that of a single crystal containing an equal number of atoms, provides a good measure of average grain boundary coordination. Free volume is useful because (a) computer calculations suggest that the grain boundary free volume scales with the grain boundary energy and (b) experimental measurement of free volume may be relatively easier and more direct than that of grain boundary energy. The objective of this paper is to compare the predictions from computer models of grain boundary free volume with experimental measurements.

Fractional phase-field crystal modelling: analysis, approximation and pattern formation

2020 ◽  
Vol 85 (2) ◽  
pp. 231-262
Author(s):  
Mark Ainsworth ◽  
Zhiping Mao
Keyword(s):  
Pattern Formation ◽  
Grain Boundary ◽  
Fractional Order ◽  
Phase Field ◽  
Boundary Energy ◽  
Classical Case ◽  
Experimental Measurements ◽  
Grain Boundary Energy ◽  
Material Interface ◽  
Phase Field Crystal

Abstract We consider a fractional phase-field crystal (FPFC) model in which the classical Swift–Hohenberg equation (SHE) is replaced by a fractional order Swift–Hohenberg equation (FSHE) that reduces to the classical case when the fractional order $\beta =1$. It is found that choosing the value of $\beta $ appropriately leads to FSHE giving a markedly superior fit to experimental measurements of the structure factor than obtained using the SHE ($\beta =1$) for a number of crystalline materials. The improved fit to the data provided by the fractional partial differential equation prompts our investigation of a FPFC model based on the fractional free energy functional. It is shown that the FSHE is well-posed and exhibits the same type of pattern formation behaviour as the SHE, which is crucial for the success of the PFC model, independently of the fractional exponent $\beta $. This means that the FPFC model inherits the early successes of the FPC model such as physically realistic predictions of the phase diagram etc. and, therefore, provides a viable alternative to the classical PFC model. While the salient features of PFC and FPFC are identical, we expect more subtle features to differ. The prediction of grain boundary energy arising from a mismatch in orientation across a material interface is another notable success of the PFC model. The grain boundary energy can be evaluated numerically from the PFC model and compared with experimental measurements. The grain boundary energy is a derived quantity and is more sensitive to the nuances of the model. We compare the predictions obtained using the PFC and FPFC models with experimental observations of the grain boundary energy for several materials. It is observed that the FPFC model gives superior agreement with the experimental observation than those obtained using the classical PFC model, especially when the mismatch in orientation becomes larger.

A Comparison between ∑3 Asymmetrical Tilt Grain Boundary Energies in Niobium Obtained Analytically and through Molecular Dynamics Based Simulations

2020 ◽  
Vol 998 ◽  
pp. 179-184
Author(s):  
Divya Singh ◽  
Avinash Parashar
Keyword(s):  
Grain Boundary ◽  
Inclination Angle ◽  
Boundary Energy ◽  
Accurate Method ◽  
Grain Boundary Energy ◽  
Tilt Axis ◽  
Pressure Tubes ◽  
Tilt Grain Boundary ◽  
The Relationship ◽  
Important Constituent

Niobium is an important constituent of Zr-Nb alloys being used widely in the nuclear industries as fuel claddings and pressure tubes. In this article, MD based simulations are performed to obtain grain boundary (GB) energies in ∑3 symmetrical and asymmetrical tilt grain boundaries (ATGBs) along <110> tilt axis. Grain boundary energies are also obtained analytically by utilizing the equation establishing the relationship between inclination angle and grain boundary energy for ATGBs. It is observed that in both the cases the GB energies increase with the increase in inclination angle of the ATGBs. The increase in the GB energy follows the same trend with a little offset between the results obtained analytically and MD based simulations. The offset between both the results can be attributed to the limitations of the potentials employed for the simulations. MD based simulations thus provide an accurate method to calculate the GB energies.

Grain Boundary Structure and Its Energy of Symmetric Tilt Boundary in Copper

2004 ◽  
Vol 467-470 ◽  
pp. 807-812 ◽  
Author(s):  
Naoki Takata ◽  
Kenichi Ikeda ◽  
Fusahito Yoshida ◽  
H. Nakashima ◽  
Hiroshi Abe
Keyword(s):  
Grain Boundary ◽  
Free Volume ◽  
Atomic Structure ◽  
Boundary Energy ◽  
Tilt Boundary ◽  
Grain Boundary Energy ◽  
Structural Units ◽  
Symmetric Tilt ◽  
Tilt Boundaries ◽  
Symmetric Tilt Boundary

In the present study, grain boundary energy and atomic structure of <110> symmetric tilt boundaries in copper were evaluated by molecular dynamics (MD) simulation. From the simulations, the grain boundary energy of <110> symmetric tilt boundaries depended on misorientation angle and there were large energy cusps at the misorientation angles which corresponded to (111) S 3 and (113) S 11 symmetric tilt boundaries. It was found that the atomic structure of each <110> symmetric tilt boundary was described by the combination of three kinds of structural units which consisted of (331) S 19, (111) S 3 and (113) S 11 symmetric tilt boundaries and two single crystal units which consisted of (110) S 1and (001) S 1 single crystals. From the the analysis of the excess free volume in each grain boundary, it was found that the energy of structural units depended on the excess free volume of the units and that the misorientation dependence of grain boundary energy agreed with that of the free volume in grain boundaries.

OS0116 Relationship between grain boundary energy and free volume in magnesium : first-principles study

2014 ◽  
Vol 2014 (0) ◽  
pp. _OS0116-1_-_OS0116-3_
Author(s):  
Naoki MIYAZAWA ◽  
Motohiro YUASA ◽  
Masataka HAKAMADA ◽  
Mamoru MABUCHI ◽  
Yasumasa CHINO
Keyword(s):  
Grain Boundary ◽  
Free Volume ◽  
First Principles ◽  
Boundary Energy ◽  
Grain Boundary Energy ◽  
First Principles Study

The Relationship between Grain Boundary Energy, Grain Boundary Complexion Transitions, and Grain Size in Ca-Doped Yttria

2013 ◽  
Vol 753 ◽  
pp. 87-92 ◽  
Author(s):  
Stephanie A. Bojarski ◽  
Jocelyn Knighting ◽  
Shuai Lei Ma ◽  
William Lenthe ◽  
Martin P. Harmer ◽  
...  
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Size Distribution ◽  
Grain Growth ◽  
Lower Energy ◽  
Boundary Energy ◽  
Grain Boundary Energy ◽  
Entire Sample ◽  
Small Grains ◽  
The Relationship

The thermal groove technique has been used to measure relative grain boundary energies in two 100 ppm Ca-doped yttria samples. The first has a normal grain size distribution and the boundaries have a bilayer of segregated Ca. In the second sample, there is a combination of large grains and small grains. The boundaries around the large grains are known to have an intergranular film. The results show that the relative energies of boundaries in the sample with normal grain growth and the boundaries around small grains far from larger grains in the second sample are similar. Also, boundaries surrounding the largest grains and small grains immediately adjacent to them have the same and significantly lower energies. The results indicate that grain boundaries with an intergranular film have a lower energy than those with bilayer segregation and that the intergranular film extends beyond the periphery of the largest grains, but not throughout the entire sample.

Grain boundary energy in /φ Pure Ice Bicrystals Samples

2021 ◽  
pp. 111094
Author(s):  
C.L. Di Prinzio ◽  
D. Stoler ◽  
Aguirre Varela ◽  
E. Druetta
Keyword(s):  
Grain Boundary ◽  
Boundary Energy ◽  
Grain Boundary Energy

Dihedral angles in Cu–1wt.% Pb: Grain boundary energy and grain boundary triple line effects

2009 ◽  
Vol 57 (8) ◽  
pp. 2527-2537 ◽  
Author(s):  
D. Empl ◽  
L. Felberbaum ◽  
V. Laporte ◽  
D. Chatain ◽  
A. Mortensen
Keyword(s):  
Grain Boundary ◽  
Boundary Energy ◽  
Triple Line ◽  
Dihedral Angles ◽  
Grain Boundary Energy ◽  
Boundary Triple

Grain boundary energy function for α iron

Materialia ◽  
2021 ◽  
pp. 101186
Author(s):  
Rajchawit Sarochawikasit ◽  
Cong Wang ◽  
Poom Kumam ◽  
Hossein Beladi ◽  
Taira Okita ◽  
...  
Keyword(s):  
Grain Boundary ◽  
Energy Function ◽  
Boundary Energy ◽  
Grain Boundary Energy
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