Stress Generation during Grain Boundary Interdiffusion

2011 ◽  
Vol 309-310 ◽  
pp. 19-28 ◽  
Author(s):  
Leonid Klinger ◽  
Eugen Rabkin
Keyword(s):  
Stress Field ◽  
Grain Boundary ◽  
Diffusion Coefficients ◽  
Concentration Distribution ◽  
Boundary Diffusion ◽  
Elastic Stress ◽  
Bulk Diffusion ◽  
Stress Generation ◽  
Additional Material ◽  
Coupled Diffusion

A grain boundary interdiffusion in a semi-infinite bicrystal under the conditions of negligible bulk diffusion is considered. We show that the inequality of intrinsic grain boundary diffusion coefficients of the two components leads to plating out of additional material at the grain boundary in the form of extra material wedge, which generates an elastic stress field in the vicinity of the grain boundary. We solved a coupled diffusion/elasticity problem and determined the time-dependent stress field and concentration distribution in the vicinity of the grain boundary.

scholarly journals Grain boundary diffusion and its relation to segregation of multiple elements in yttrium aluminum garnet

2020 ◽  
Vol 32 (6) ◽  
pp. 675-696
Author(s):  
Joana Polednia ◽  
Ralf Dohmen ◽  
Katharina Marquardt
Keyword(s):  
Grain Boundary ◽  
Boundary Diffusion ◽  
Yttrium Aluminum Garnet ◽  
Bulk Diffusion ◽  
Element Distribution ◽  
Grain Boundary Diffusion ◽  
Yttrium Aluminum ◽  
Detectable Concentration ◽  
Thin Film Diffusion ◽  
Strong Segregation

Abstract. We studied grain boundary diffusion and segregation of La, Fe, Mg, and Ti in a crystallographically defined grain boundary in yttrium aluminum garnet (YAG). Bi-crystals were synthesized by wafer bonding. Perpendicular to the grain boundary, a thin-film diffusion source of a La3.60Al4.40O12 was deposited by pulsed laser deposition. Diffusion anneals were performed at 1000 and 1450 ∘C. Via a gas phase small amounts of elements were added during the experiment. The element concentration distributions in our bi-crystals were mapped using analytical transmission electron microscopy (ATEM). Our results show strong segregation of La and Ti at the grain boundary. However, in the presence of Ti, the La concentrations dropped below the detection limit. Quantitative element distribution profiles along and across the grain boundary were fitted by a numerical diffusion model for our bi-crystal geometry that considers the segregation of elements into the grain boundary. The shape of the diffusion profiles of Fe requires the presence of two diffusion modes, e.g., the co-diffusion of Fe2+ as well as Fe3+. The absence of a detectable concentration gradient along the grain boundary in many experiments allows a minimum value to be determined for the product of sDgb. The resulting sDgb are a minimum of 7 orders of magnitude larger than their respective volume diffusion coefficient, specifically for La = 10−14 m2 s−1, Fe = 10−11 m2 s−1, Mg = Si = 10−12 m2 s−1, and Ti = 10−14 m2 s−1 at 1450 ∘C. Additionally, we model the effect of convolution arising from the given spatial resolution of our analysis with the resolution of our modeled system. Such convolution effects result in a non-unique solution for the segregation coefficient, e.g., for example for Mg between 2–3. Based on our data we predict that bulk diffusion of impurities in a mono-phase polycrystalline aggregate of YAG is effectively always dominated by grain boundary diffusion.

Diffusion and solubility of holmium ions in barium titanate ceramics

2004 ◽  
Vol 19 (12) ◽  
pp. 3512-3520 ◽  
Author(s):  
Junichi Itoh ◽  
Hajime Haneda ◽  
Shunichi Hishita ◽  
Isao Sakaguchi ◽  
Naoki Ohashi ◽  
...  
Keyword(s):  
Barium Titanate ◽  
Grain Boundary ◽  
Diffusion Coefficients ◽  
Boundary Diffusion ◽  
Diffusion Mechanism ◽  
Annealed Sample ◽  
Lattice Diffusion ◽  
Grain Boundary Diffusion ◽  
A Site ◽  
Titanate Ceramics

Ho ion solubility and diffusivity were evaluated in barium titanate ceramics in which Ho ions were implanted with an accelerating voltage of 500 keV. The depth profile of the ions was composed of three regions in the post-annealed sample: the first was the precipitation region, the second was a region created by lattice diffusion of Ho ions, and the third was a region created by grain-boundary diffusion. The Ho lattice diffusion characteristics were similar to those of Ni ion diffusion in barium titanate ceramics, and we concluded that the diffusion mechanism was the same as that responsible for Ni ions. The Ho ions diffused through the B-site (Ti-site) and were then exchanged with A-site ions. This mechanism suggests that a small number of Ho ions dissolved in the B-site. Preferential grain-boundary diffusion was also observed. The grain-boundary diffusion coefficients were four to five orders of magnitude larger than the volume diffusion coefficients. The solubility of Ho ions was estimated to be a few thousand parts per million in barium titanate ceramics.

Mechanistic Two Stage Fission Gas Release Model

2002 ◽  
Author(s):  
Yong-Soo Kim ◽  
Chan-Bok Lee
Keyword(s):  
Grain Boundary ◽  
Diffusion Coefficients ◽  
Boundary Diffusion ◽  
Diffusion Processes ◽  
Lattice Diffusion ◽  
Grain Boundary Diffusion ◽  
Factor Α ◽  
Two Stages ◽  
Grain Surface ◽  
Release Model

In this study, a mechanistic two stages model is developed which analytically simulates the two-step diffusion processes, grain lattice diffusion and grain boundary diffusion, coupled with the bubbles trap/resolution. Mathematical manipulation reveals that the release at high burn-up depend on the ratio of the diffusivities in the both processes, i.e., α ≅ Dveff/Dgbeff where Dveff and Dgbeff are effective volume and grain boundary diffusion coefficients, respectively. Thus, the ratio α is incorporated in the time-dependent third kind boundary condition at the equivalent grain surface. This model brings forth analytical solutions of the fractional release which are identical to that of either ANS5.4 or modified ANS5.4 model when α goes to the infinity. It turns out that this model describes the release behavior well in the high burn-up fuel and puts out a comparable prediction to the solution of FRAPCON-3 model under the same condition. It is also demonstrated that the new factor α not only ease the computational treatment for the high burn-up fuel performance evaluation, but also enables us to possibly separate the burn-up enhancement from the diffusion coefficients and to easily simulate the bubble-related phenomena in the grain boundary.

Diffusion Mechanisms in Nanocrystalline and Nanolaminated Au-Cu

2007 ◽  
Vol 266 ◽  
pp. 13-28 ◽  
Author(s):  
Alan F. Jankowski
Keyword(s):  
Low Temperature ◽  
Grain Boundary ◽  
Grain Growth ◽  
Boundary Diffusion ◽  
Bulk Diffusion ◽  
Grain Boundary Diffusion ◽  
Dominant Mechanism ◽  
Temperature Range ◽  
Diffusion Mechanisms ◽  
Kinetics Of

Thermal anneal treatments are used to identify the temperature range of the two dominant diffusion mechanisms – bulk and grain boundary. To assess the transition between mechanisms, the low temperature range for bulk diffusion is established utilizing the decay of static concentration waves in composition-modulated nanolaminates. These multilayered structures are synthesized using vapor deposition methods as thermal evaporation and magnetron sputtering. However, at low temperature the kinetics of grain-boundary diffusion are much faster than bulk diffusion. The synthesis of Au-Cu alloys (0-20 wt.% Cu) with grain sizes as small as 5 nm is accomplished using pulsed electro-deposition. Since the nanocrystalline grain structure is thermally unstable, these structures are ideal for measuring the kinetics of grain boundary diffusion as measured by coarsening of grain size with low temperature anneal treatments. A transition in the dominant mechanism for grain growth from grain boundary to bulk diffusion is found with an increase in temperature. The activation energy for bulk diffusion is found to be 1.8 eV·atom-1 whereas that for grain growth at low temperatures is only 0.2 eV·atom-1. The temperature for transitioning from the dominant mechanism of grain boundary to bulk diffusion is found to be 57% of the alloy melt temperature and is dependent on composition.

scholarly journals Determination of Grain Boundary Diffusion Coefficients in C-Regime by Hwang-Balluffi Method: Silver Diffusion in Pd

2009 ◽  
Vol 289-292 ◽  
pp. 763-767 ◽  
Author(s):  
Z. Balogh ◽  
Z. Erdélyi ◽  
Dezső L. Beke ◽  
Alain Portavoce ◽  
Christophe Girardeaux ◽  
...  
Keyword(s):  
Grain Boundary ◽  
Diffusion Coefficients ◽  
Boundary Diffusion ◽  
Grain Boundary Diffusion ◽  
Controlled Processes ◽  
Diffusion Controlled ◽  
Arrhenius Function ◽  
Data Points ◽  
Accumulation Kinetics

Diffusion controlled processes play a crucial role in the degradation of technical materials. At low temperatures the most significant of them is the diffusion along grain boundaries. In thin film geometry one of the best methods for determining the grain boundary (GB) diffusion coefficient of an impurity element is the Hwang-Balluffi method, in which a surface sensitive technique is used to follow the surface accumulation kinetics. Results of grain boundary diffusion measurements, carried out in our laboratory by this method in three different materials systems (Ag/Pd, Ag/Cu and Au/Ni) are reviewed. In case of Ag diffusion along Pd GBs the surface accumulation was followed by AES method. The data points can be well fitted by an Arrhenius function with an activation energy Q=0.99eV

Zinc Self-Diffusion in ZnO

2005 ◽  
Vol 237-240 ◽  
pp. 163-168 ◽  
Author(s):  
M.A.N. Nogueira ◽  
Antônio Claret Soares Sabioni ◽  
Wilmar Barbosa Ferraz
Keyword(s):  
Diffusion Coefficient ◽  
Grain Boundary ◽  
Diffusion Coefficients ◽  
Boundary Diffusion ◽  
Volume Diffusion ◽  
Grain Boundary Diffusion ◽  
Polished Surface ◽  
Self Diffusion ◽  
Zinc Diffusion ◽  
Diffusion Profiles

This work deals with the study of zinc self-diffusion in ZnO polycrystal of high density and of high purity. The diffusion experiments were performed using the 65Zn radioactive isotope as zinc tracer. A thin film of the tracer was deposited on the polished surface of the samples, and then the diffusion annealings were performed from 1006 to 1377oC, in oxygen atmosphere. After the diffusion treatment, the 65Zn diffusion profiles were established by means of the Residual Activity Method. From the zinc diffusion profiles were deduced the volume diffusion coefficient and the product dDgb for the grain-boundary diffusion, where d is the grain-boundary width and Dgb is the grain-boundary diffusion coefficient. The results obtained for the volume diffusion coefficient show good agreement with the most recent results obtained in ZnO single crystals using stable tracer and depth profiling by secondary ion mass spectrometry, while for the grain-boundary diffusion there is no data published by other authors for comparison with our results. The zinc grain-boundary diffusion coefficients are ca. 4 orders of magnitude greater than the volume diffusion coefficients, in the same experimental conditions, which means that grain-boundary is a fast path for zinc diffusion in polycrystalline ZnO.

Study of Oxygen Diffusion in Polycrystalline ZnO by SIMS

2009 ◽  
Vol 289-292 ◽  
pp. 523-530
Author(s):  
Antônio Claret Soares Sabioni ◽  
Antônio Márcio J.M. Daniel ◽  
Anne Marie Huntz ◽  
Wilmar Barbosa Ferraz ◽  
François Jomard
Keyword(s):  
Grain Boundary ◽  
Oxygen Pressure ◽  
Diffusion Coefficients ◽  
Effective Charge ◽  
Oxygen Diffusion ◽  
Secondary Ion Mass Spectrometry ◽  
Diffusion Mechanism ◽  
Bulk Diffusion ◽  
Interstitial Oxygen ◽  
Exchange Method

Oxygen diffusion coefficients were measured in polycrystalline ZnO by means of the gas-solid exchange method using the isotope 18O as the oxygen tracer. The diffusion annealings were performed at 892oC and 992oC, in an Ar+18O2 atmosphere under oxygen partial pressures from 0.1 to 1atm. After the diffusion annealings, the 18O diffusion profiles were established by secondary ion mass spectrometry (SIMS). Increasing the oxygen pressure leads to an increase of the oxygen diffusion in ZnO. The bulk diffusion coefficients depends on oxygen pressure according to , at 882oC, or , at 992oC, which indicates that the oxygen bulk diffusion mechanism should preferentially take place by means of interstitial oxygen having a null effective charge. The grain boundary diffusion coefficients show little dependence on oxygen pressure at 882oC, given by , which should correspond to a diffusion mechanism by means of interstitial oxygen, with a double negative charge, but at 992oC this dependence is corresponding to a diffusion mechanism by interstitial oxygen having a null effective charge. The results also show that the grain boundary is a fast path for the oxygen diffusion in polycrystalline ZnO.

Glancing angle x-ray study of the effect of oxygen on interface reactions in Al/Ni bilayers

1991 ◽  
Vol 6 (5) ◽  
pp. 935-942 ◽  
Author(s):  
S.M. Heald ◽  
E.V. Barrera
Keyword(s):  
Grain Boundary ◽  
Boundary Diffusion ◽  
Bulk Diffusion ◽  
Diffusion Path ◽  
Initial Reaction ◽  
X Ray ◽  
Interface Reactions ◽  
Glancing Angle ◽  
Effect Of Oxygen ◽  
Oxygen Impurities

Glancing angle x-ray reflectivity and EXAFS measurements have been made on a series of UHV prepared Al/Ni bilayers with varying amounts of oxygen impurities. These samples show an intrinsic reacted region prior to annealing, and for clean samples further reaction occurs at 250 °C. Oxygen is found to influence strongly the course of the reaction with an effect which depends on its location. A few percent O impurity within the Al film strongly suppresses the grain boundary diffusion path, which allows the growth of a smooth NiAl3 layer. Interfacial O exposures of 60 and 600 Langmuir both inhibit the initial reaction and raise the temperature at which further reaction occurs to as much as 300 °C with an effect which depends on exposure. The thickness of the intrinsic reaction zone is about 60 Å for clean samples, and is nearly eliminated for contaminated interfaces. The results indicate that surface/interface, grain boundary, and bulk diffusion all play important roles in the formation of these interfaces, and that each of these is influenced by O impurities.

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