Grain Boundary Diffusion Research Articles

Analysis of the magnetization reversal mechanism of heterogenous grain boundary diffused Nd-Fe-B sintered magnets

The grain boundary diffusion (GBD) method could effectively improve the coercivity of Nd-Fe-B sintered magnets, but the uneven distribution of heave rare earth (HRE) elements would lead to the decrease of squareness factor of the demagnetization curve of the magnets, which limited the application of this method. In this paper, three typical-structure regions were summarized based on microstructure characterization, and the magnetic properties and magnetization reversal mechanism were analyzed. The differences in nucleation positions and magnetization reversal processes of the three regions were discussed, and it found that the remarkable differences among them resulted in the low squareness factor of GBD Nd-Fe-B sintered magnets. In addition, the efficiency of Tb elements could be further improved to enhance the coercivity of Nd-Fe-B sintered magnets by forming homogeneous and complete core-shell structure grains, which could strengthen the nucleation field and even transfer the nucleation position from the grain surface defect layer to the grain interior region. Our results could provide guidance and reference for further improving the permanent magnetic properties of Nd-Fe-B sintered magnets by optimized GBD method.

Accelerated phase growth kinetics during interdiffusion of ultrafine-grained Ni and Sn

The phase growth is investigated during the interdiffusion of an ultra-fine grained Ni (UFG) (grain size, d ∼ 320 nm) and coarse-grained Sn diffusion couple in the temperature range of 175–215 °C. The UFG Ni was produced through spark plasma sintering (SPS) of ball-milled Ni powder. Formation of only Ni3Sn4 intermetallic phase is observed, as confirmed by electron probe microanalysis (EPMA), micro-x-ray diffraction (XRD), and Transmission Kikuchi Diffraction (TKD) measurements. Using the CALPHAD approach, the driving forces for the formation of possible intermetallic phases in the Ni-Sn system were estimated and the highest value was found for Ni3Sn4, which matches the experimental observations. Time-dependent measurements at 200 °C revealed an acceleration in the growth (∼2 orders of magnitude) of Ni3Sn4 compared to the scenario prevalent in the coarse-grained (CG) Ni/Sn diffusion couple. This is reflected in the calculated integrated diffusivities for the UFG-Ni/Sn diffusion couple. The accelerated phase growth kinetics are attributed to the increased fraction of grain boundaries (GBs) in the UFG-Ni, which leads to an increased contribution of GB diffusion to the overall diffusion flux. The formation of Ni3Sn4 at GB was further ascertained using correlative microscopy strategy including transmission electron microscopy, transmission Kikuchi diffraction and scanning transmission electron microscopy.

Simultaneous enhancement of coercivity and electric resistivity of Nd-Fe-B magnets by Pr-Tb-Al-Cu synergistic grain boundary diffusion toward high-temperature motor rotors

To high-power permanent magnetic motors, it is critical for Nd-Fe-B magnets to maintain the desirable coercivity at high-temperature operating conditions. To address this, two approaches have been proven effective: (1) enhancing the room temperature coercivity; (2) reducing the eddy current loss. However, these two items are difficult to be simultaneously achieved. Here, the grain boundary diffusion (GBD) of the Pr-Tb-Al-Cu-based source is applied to enhance the coercivity and electric resistivity at room temperature from 1101 kA m-1 and 2.13 × 10–6 Ω m to 1917 kA m-1 and 2.60 × 10–6 Ω m, and those at 120 °C from 384 kA m-1 and 4.31 × 10–6 Ω m to 783 kA m-1 and 4.86 × 10–6 Ω m, respectively. Such optimization is ascribed to the improved formation depth of Tb-rich 2:14:1 shells with large magnetocrystalline anisotropy and the increased intergranular Pr-based oxides with high electric resistivity, induced by the coordination effects of Tb and Pr, as proven by the atomic-scale observations and the first principles calculations. It thus results in the simultaneously improved output power and energy efficiency of the motor because of the combination of magnetic thermal stability enhancement and eddy current loss reduction, as theoretically confirmed by electromagnetic simulation.

Grain-Boundary Diffusion of 57Сo in Niobium

The grain-boundary diffusion of Co in Nb has been studied by a layer-by-layer radiometric analysis in the temperature range of 723–873 K. The diffusion annealing modes corresponded to the kinetic C mode, which implies that the diffusion proceeds only along grain boundaries. The coefficients of grain-boundary diffusion of Co in Nb have been determined for several temperatures from diffusion profiles. An expression for the Arrhenius dependence of Co diffusion coefficient along the grain boundaries of Nb has been determined. The temperature dependence of coefficient of grain-boundary segregation of Co in Nb is constructedbased on the temperature dependence of coefficient of grain-boundary diffusion of Co in Nb and the data in the literature on the temperature dependence of the triple product.

Enhancement of coercivity and thermal stability of Pr85Al15 doped NdFeB sintered magnets followed with grain boundary diffusion

Magnetic-property modification and thermal stability improvement for high-performance NdFeB magnets by dual-alloy (DA) sintering with Pr85Al15 (PrAl) together with grain boundary diffusion (GBD) with Tb55Pr20Cu25 (TbPrCu) is demonstrated. The coercivity is increased from 14.9 to 16.4–18.0 kOe for the magnet DA sintering with 2–4 % PrAl. Pr and Al at grain boundary strengthens magnetic decoupling effect. In addition, a thin layer of (Nd, Pr)2Fe14B with higher magnetocrystalline anisotropy field (HA) is formed at grain surface. Both effects contribute to the coercivity enhancement for the magnets prepared by DA sintering with PrAl. Furthermore, remarkable coercivity enhancement, from 14.9 to 18.0 kOe to 22.7–27.1 kOe, with improved thermal stability is attained for the above magnets after GBD with Tb55Pr20Cu25 alloy. Besides, the increased Curie temperature of 2:14:1 phase indicates the entrance of Tb into 2:14:1 phase and helps to improve thermal stability. Most importantly, various magnetic levels of high-performance NdFeB magnets, including 48–52 M, 45H, 50SH and 40-45UH, can be easily attained by modifying the amount of PrAl for DA sintered magnets and/or GBD with TbPrCu alloys.

Substantial coercivity enhancement in Dy-free Nd-Fe-B sintered magnet by Dy grain boundary diffusion

To date, the highest coercivity reported for Dy-free Nd–Fe–B sintered magnets under the Dy grain boundary diffusion (GBD) process is ∼2.4 T. Therefore, exploring various approaches for achieving higher coercivity is beneficial for eliminating the dependence on the scarce and expensive heavy rare-earth elements, Dy and Tb. In this study, we report record-breaking high coercivity by separately diffusing Dy70Cu30 and then Pr68Cu32 eutectic alloys through grain boundaries in fine-grained Dy-free sintered magnets. The two-step GBD-processed sample containing a low Dy content (only 0.9 wt%) exhibited a high coercivity of 2.8 T and an excellent temperature coefficient of coercivity of β = -0.447%/ °C. The second GBD process facilitated Dy infiltration from the bulk surface toward the center by chemically induced liquid film migration to form a uniform Dy-rich shell throughout the bulk. Pr was also enriched in the Dy-rich shell near the surface of Nd2Fe14B grains in the two-step GBD-processed sample. However, the Pr-enrichment in the shell did not cause the degradation of the coercivity at high temperatures. This unique shell structure strengthened the anisotropy field to achieve 2.8 T coercivity without alloying Dy to the initial sintered magnet.

The Algorithm to Predict the Grain Boundary Diffusion in Non-Dilute Metallic Systems

The analysis of grain boundary (GB) diffusion in metallic systems based on Cu, Ni, Ag and Al was made to set demonstrate the common behavior. It was shown that the slow penetration for 11 systems can be connected with negative segregation or specific interatomic interaction. Two energetic parameters such as energy of interaction with GB and energy of interatomic interaction are proposed as main characteristics. The analysis of a tendency toward segregation and tendency of intermediate phase formation in these terms allows us to divide the systems on four groups and formulate a qualitative way to predict the behavior of the diffusing elements in a non-dilute solution. Mathematical formulation of GB diffusion problem and typical solutions are presented.

New grain boundary diffusion strategy of Nd-Fe-B sintered magnets to achieve breakthroughs in Tb-availability and thick limitation

Grain boundary diffusion (GBD) Nd-Fe-B sintered magnets were prepared using a newly developed solid-liquid phase separation diffusion (SepD) technique, as well as a currently popular solid-liquid phase simultaneous diffusion (SimD) technique. The magnetic properties, microstructures, and magnetic domain morphologies of the magnets with different Tb contents diffused using the two techniques were then investigated. A SepD magnet using 0.25 wt% Tb exhibited a similar coercivity and a stronger maximum energy product compared to a SimD magnet with 0.50 wt% Tb, demonstrating high Tb availability. Moreover, by using the new diffusion technique, Tb could diffuse deeper into the magnet and distribute more homogeneously around the surface region of the Nd2Fe14B crystal grains, forming the crucial core-shell structure without undesirable enrichment in the surface area of the magnet. As a result, the squareness factor increased noticeably from 0.842 for the current technique diffused magnet to 0.925 for the new technique diffused magnet with a thickness of 8 mm.

High-coercivity heavy-rare-earth-free NdFeB sintered magnets developed by doping Ce85Al15 and grain boundary diffusion with Pr70Cu15Al15

Traditional NdFeB sintered magnets with coercivity larger than 20 kOe, called super-high (SH) level, usually contains considerable amount of high-cost heavy rare earth (HRE), such as Dy or Tb. In this work, high coercivity of 21.4 kOe, which corresponds to SH level, is achieved for HRE-free NdFeB magnet by doping with Ce85Al15 (CeAl) alloy and grain boundary diffusion (GBD) with Pr70Cu15Al15 (PrCuAl) alloy powders, where Ce/RE ratio is about 15% within the magnet. After GBD treatment with PrCuAl on Ce-containing NdFeB magnets, the formation of Pr-containing shell at 2:14:1 grain surface can increase the local magnetic anisotropy filed and therefore enhance the coercivity. Most of Cu and Al, and parts of Ce and Pr appear at grain boundary and triple junction, which can reduce the magnetization of grain boundary phase, strengthen the decoupling effect between grains and thus contribute to high coercivity. This study provides a cost-effective way to obtain high coercivity for HRE-free NdFeB sintered magnet via doping Ce85Al15 and then GBD with Pr70Cu15Al15.

Synergy of grain boundary and interface diffusion during intermediate compound formation

ABSTRACT The kinetics of reactive growth of a compound with a columnar structure with frozen bulk diffusion is revisited. The finite rate of redistribution and reaction along moving interfaces between reagents and growing compound is taken into account. Cases of planar and curved inter-phase interfaces are discussed. A new kinetic equation for the phase growth with evolving grain boundaries is suggested. Three cases are considered: (1) frozen grain structure, (2) normal lateral grain growth which does not depend on phase growth and on diffusion fluxes, (3) flux-driven grain growth which is induced by grain-boundary diffusion fluxes across the growing compound layer. The latter model provides the best fit to the experimental data.

Surface modification of alloys by high-energy pulsed particle beams

The effect of particle beams on the surface of alloys is often used to obtain a material with desired characteristics. Mathematical modeling of such surface modification leads to the study of diffusion in the presence of an intense external source of diffusant. In this case peculiarities in material structure may be of great importance. A special role belongs to inter-grain boundaries in metals, the vicinities of which are regions of accelerated diffusion. Moreover, if the surface treatment by particle beam is carried out with short impulses comparable with relaxation times of diffusion and chemical processes to their equilibrium course, it may be necessary to explicitly consider the particle transfer rate in the material, for example, using the non-classical laws.In this paper we discuss the model of the treatment process by particle beam, which takes into account both the feature of grain boundary diffusion and finiteness of relaxation times of diffusion fluxes in the boundaries and in the volumes of grains. The problem is considered in two-dimensional formulation. The grains and their boundaries are treated as separate phases with different diffusion properties. The grains are represented in the form of rectangles, located at equal distances from each other. The relative size of the boundary phase may vary. Using generalized equations for diffusion fluxes with finite time of relaxation, we come to diffusion equations of hyperbolic type for the volume and the grain-boundary phases. It is assumed that between the diffusant and the treated material a summary chemical reaction occurs with formation of a summary product. A numerical study allowed us for the first time to establish the features of grain-boundary diffusion and to study the dynamics of reaction product formation for treatment times comparable to relaxation times. The effect of pulse duration and grain size on the diffusant concentration distribution for these conditions was investigated.

Peculiarities of Fe and Ni Diffusion in Polycrystalline Cu.

The peculiarities of Ni and Fe diffusion in polycrystalline Cu and Cu-Fe alloys at a 650-750 °C temperature range were studied. It was shown that the bulk diffusion coefficients were in a good agreement with the available literature data obtained for different temperature concentration ranges. The obtained values of the Ni GB diffusion triple product could be described as sδDb=8.8×10-13×exp(-165 kJmol-1RT)m3s-1. The obtained values were an order of magnitude less than the values obtained by the radiotracer method. This fact was explained by the negative segregation of Ni at the Cu GB. A stronger negative segregation of Fe in the copper GB reduced the penetration depth of iron along the GB because of an additional (negative) "driving" force; this explained why there was no advanced grain boundary diffusion. Another peculiarity of the Fe diffusion that was confirmed was the significant supersaturation of the Cu-based solid solution near the Fe/Cu interface.

Elevated corrosion resistance and improved magnetic properties of sintered Nd-Fe-B magnets via the infiltration of DyCr film

The low coercivity at high temperature and poor corrosion resistance limit the application field of Nd-Fe-B magnets. In this work, a DyCr film was prepared on the surface of Nd-Fe-B magnet through magnetron sputtering, and then subjected to grain boundary diffusion (GBD) to improve magnetic properties and enhance corrosion resistance. The results show that the residual Cr-rich film exists on the surface of NdFeB magnets, acting as a protective coating to enhance the corrosion resistance, which is evidenced by the weight loss experiment and scanning electron microscopy (SEM) image. Moreover, Cr element in the grain boundary phase increase the electrochemical potential from − 0.985 to − 0.733 V, which is also beneficial in improving corrosion resistance. Transmission electron microscope (TEM) analysis confirmed that the crystal structure of intergranular phase remained unchanged after diffusion, i.e. BCC-RE2O3 (RE=Rare Earth) phase. The coercivity was improved significantly, obtaining an increment of 19.4% comparing to that of initial magnet, which is attributed to the formed Dy-rich shell with high magnetocrystalline anisotropy field and the improved distribution of grain boundary phase. This suggests that it is feasible to fabricate high coercivity magnets and strong corrosion resistance only through grain boundary diffusion, which is expected to further shorten the processing flow of Nd-Fe-B magnets.

Atomic simulations on the deformation mechanisms in nano-crystalline Ni–Al series Ni-based superalloy based on grain size, strain rate and temperature

Molecular Dynamic (MD) simulations were used to investigate the tensile properties of nanocrystalline Ni–Al series Ni-based superalloy at different grain sizes (6.54–20 nm), strain rates (1 × 107–5 × 108 s−1) and temperatures (300–1000 K). Results indicate that plastic deformation of nanocrystalline Ni–Al series Ni-based superalloy was governed by stacking faults and FCC-to-HCP martensitic phase transformation, which was significantly different from twinning-dominated plastic deformation in nanocrystalline Ni. Nevertheless, the conventional Hall-Petch breakdown occurred at a critical grain size in both nanocrystalline Ni and Ni–Al series Ni-based superalloy. Moreover, the critical mean grain size was little influenced by the strain rate in the strain-rate range of 107 to 5 × 108 s−1. Strain rate sensitivity m was closely related to grain size and strain rate. Grains combination can be observed at lower strain rate, while at higher strain rate, GB diffusion was visible. Besides, flow stress and Young's modulus were both strongly affected by temperature, and an increase in temperature can accelerate GB diffusion and GB migration. The current study provides an atomic perspective on the deformation process and mechanisms in nanocrystalline Ni–Al series Ni-based superalloy, as well as new perspectives on designing novel superalloys with excellent mechanical properties.

On the anisotropic grain boundary diffusion of sintered Nd-Fe-B magnets

• Anisotropic diffusion of heavy rare earth can be avoided for sintered Nd-Fe-B magnets. • The alloying of diffusion source distinctly enhance diffusion efficiency of Tb along a -axis. • The alloying of diffusion source inhibits the excessive lattice diffusion of Tb. Grain boundary diffusion (GBD) efficiency of heavy rare earths (HREs) for sintered Nd-Fe-B magnets along the easy magnetization direction ( c -axis) was reported to be higher than that along the difficult one ( a -axis). However, this conclusion is challenged by the present results, which indicate that the anisotropic diffusion does not exist, at least for some low-melting HRE-based diffusion sources. The alloying of Tb by Pr, Al and Cu can distinctly enhance the diffusion efficiency of Tb along the a -axis, resulting in quite similar coercivity enhancement to that diffused along the c -axis. The diffusion kinetic analysis and microstructure characterizations demonstrate that the alloying lowers the melting point of diffusion source and wets the intergranular phase as effective diffusion paths for Tb. This suppresses the excessive lattice diffusion of Tb and the formation of over-thick Tb-rich shells, which is beneficial to enhancing the Tb diffusion efficiency along the a -axis and reducing the total Tb consumption.

Point-defect avalanches mediate grain boundary diffusion

Grain boundary diffusion in polycrystalline materials is a physical phenomenon of great fundamental interest and practical significance. Although accelerated atomic transport along grain boundaries has been known for decades, atomic-level understanding of diffusion mechanisms remains poor. Previous atomistic simulations focused on low temperatures where the grain boundary structure is ordered or high temperatures where it is highly disordered. Here, we conduct molecular dynamics simulations of grain boundary diffusion at intermediate temperatures most relevant to applications. A surprising result of this work is the observation of intermittent GB diffusion behavior and its strong system-size dependence unseen in previous work. Both effects are found to originate from thermally activated point-defect avalanches. We identify the length and time scales of the avalanches and link their formation to dynamic heterogeneity in partially disordered systems. Our findings have implications for future computer modeling of grain boundary diffusion and mass transport in nano-scale materials.

Molecular dynamics simulation on creep-ratcheting behavior of columnar nanocrystalline aluminum

Creep-ratcheting deformation behavior of columnar nanocrystalline (NC) Al varying in grain sizes have been studied using molecular dynamics simulations at three different temperatures (300 K, 467 K, and 653 K). The underlying deformation mechanisms of columnar NC Al for two stress ratios of ratcheting are also evaluated in this study. The highest strain accumulation and rapid hysteresis loop proliferation are attained at 653 K. The dislocation density is low at 653 K in contrast to the other two deformation temperatures. The perfect dislocations support the creep-deformation process followed by Shockley partial dislocations. It is observed that the cyclic hardening phenomenon at 300 K and the cyclic softening phenomenon at 653 K dominate during creep-ratcheting loading. The specimen fails earlier at higher temperatures owing to the change in the shape of hysteresis loops. The predominant grain boundary-based deformation mechanisms of columnar NC Al specimens are grain boundary (GB) migration, GB diffusion, GB widening, GB sliding, and GBs merging for all the deformation temperatures. The variation in the extent of deformation with respect to temperatures depends on strain accumulation in the plastic region under creep-ratcheting loading.

Dy-based dual-alloy grain boundary diffusion for sintered Nd-Fe-B magnets with improved magnetic performance and corrosion resistance

Grain boundary diffusion (GBD) is an effective process to enhance the thermal stability and coercivity of sintered Nd-Fe-B magnets, but the low diffusion efficiency and high consumption of heavy rare earth (HRE) elements prevent further performance improvement and cost reduction of the magnets. Here, a Ni-containing dual-alloy Pr-Ni-Al/Dy-Ni-Al diffusion source is used to enhance both the diffusion efficiency of the Dy element and the anti-corrosion properties of Nd-Fe-B magnets. Pr-Ni-Al and Dy-Ni-Al alloys with different melting points exhibit different diffusion behaviors. The diffused low-melting Pr-Ni-Al alloy can construct continuous grain boundary, acting as an effective diffusion channel for the GBD of Dy-Ni-Al. As a result, the coercivity was enhanced from 1057 to 1662 kA/m by dual-alloy diffusion. For comparison, the coercivity increased only to 1548 kA/m by the diffusion of Pr-Dy-Ni-Al single-alloy with the same element contents. It was confirmed by composition and microstructure characterizations that Pr-Ni-Al/Dy-Ni-Al diffusion leads to a deeper diffusion of Dy. The constitution of continuous grain boundary phase and core-shell structure attributed to the enhancement of coercivity. Different from many HRE-based diffusion sources, the present Ni-containing sources can also greatly enhance the anti-corrosion properties of Nd-Fe-B magnets after GBD. The dual-alloy diffusion with low consumption and high diffusion efficiency of HREs, thus, shows good prospect for practical applications.

Do smaller oxide particles sinter worse? Paradoxes of the initial stages of sintering of zirconia nanoparticles

The effect of particle size on the dominant densification mechanism at the initial stage of sintering of tetragonal zirconia nanoparticles was investigated. It has been found that a decrease in the particle size of zirconia leads to a change in the diffusion mechanism. The volume diffusion mechanism identified by the value of densification parameter n = 0.5 was dominant in zirconia nanoparticles with the average particle size 32 and 26.2 nm. The grain-boundary diffusion mechanism (n = 0.3) dominated during the sintering zirconia nanoparticles with the average particle size 21.7 nm. It was established that the change in densification parameter n from 0.5 to 0.3 caused by the increase in the value of particle surface to volume ratio due to the particles size decrease from 32 to 21 nm. A further decrease in the particle size to 17–12 nm led to a decrease in the densification parameter n to 0.17–0.11, respectively. This may be due to an increase in the influence of the particle surface on the sintering process (large values of particle surface to volume ratio) and, accordingly, the action of the surface diffusion mechanism.

Reducing the process consumption of Tb in grain boundary diffusion of Nd-Fe-B magnets by sputtering deposition instead of adhesive coating

Grain boundary diffusion (GBD) can enhance the coercivity of Nd-Fe-B magnets with relatively low consumption of heavy rare earths (HREs). Most of previous investigations on GBD focused on improving the efficiency of diffusion source, but less attention has been paid on reducing the process consumption of HRE. Here, a comparative study on coating methods of adhesive coating and sputtering deposition is carried out to evaluate the surface state of diffused magnet and the process consumption of HRE during surface cleaning. The results suggest that 0.9 wt.% sputtering deposited Tb-Cu alloy can enhance the coercivity of the magnet from 1053 kA/m to 1668 kA/m, due to the formation of high-anisotropy (Nd,Tb)2Fe14B phase and the optimized intergranular phases. To obtain smooth magnet surface for the subsequent surface protection process, the surface of the diffused magnet is polished, which leads to the reductions of magnet thickness and coercivity of ∼40 µm and 25 kA/m, respectively. In comparison, when 0.9 wt.% Tb-Cu source was coated by adhesive coating, although a comparable coercivity of 1663 kA/m can be obtained, the as-diffused magnet shows a rough surface and the polishing process leads to the reductions of magnet thickness and coercivity of ∼140 µm and 81 kA/m, respectively. By fitting the concentration-depth curves based on Fick’s second law, Tb contents in the diffused magnets decrease by 74 % and 13 % after surface cleaning for adhesive coating and sputtering deposition processes, respectively. The results suggest that the process consumption of Tb in GBD of Nd-Fe-B magnets can be greatly saved by sputter deposition.