Grain Boundary Layer Research Articles

The corrosion behavior of Sc2O3-Y2O3 co-doped ZrO2 influenced by Sc2O3 content in CMAS at 1300 °C

The effect of Sc2O3 content on the corrosion behaviors of xSc2O3-3.5Y2O3 co-doped ZrO2 (ScYSZ, x = 4.5, 5.5 and 6.5 mol.%) in calcium-magnesium-alumino-silicate (CMAS) at 1300 °C was investigated in this paper. It is shown that the ScYSZ ceramic exhibits better resistance to molten CMAS attack when doping with more Sc2O3. The CMAS penetration depth in the ScYSZ ceramic decreases with increasing Sc2O3. It is about 18 µm of CMAS penetrated depth in the 6.5Sc3.5YSZ after corrosion for 4 h at 1300 °C, including an 11 µm and 7 µm for the reaction-reprecipitation and grain-boundary infiltration layers, respectively. High thermochemical stability and weak reactivity of the ScYSZ to the glassy CMAS melt are beneficial to enhance the high temperature corrosion resistance, attributing to the low solubility in molten CMAS and the weak affinity to Ca2+ for small ionic radius Sc3+. The mechanism of enhancing the resistance to CMAS is discussed.

Microstructures and intergranular corrosion resistances of hot-rolled austenitic stainless steel clad plates

In this study, two stainless steel clad plates (STS 316L/A516-70N and STS 304L/A516-70N) were fabricated without Ni interlayers by hot rolling and normalizing under the same conditions, and their microstructures and intergranular corrosion resistances were comparatively evaluated. Although a similar amount of C diffused from carbon steel to stainless steel during clad fabrication, the thickness of the grain-boundary carburized layer was thinner in STS 316L due to Mo atoms segregated at the grain boundaries. The stainless steel parts of both clad plates had carbides even at their free surfaces and STS 304L also had some amount of δ ferrite. Nevertheless, the corrosion resistance of the free surfaces of both stainless steels was not undermined.

Evaluation of core-shell structure and grain boundary structure in multi-main-phase Nd-Y-Fe-B sintered magnet by grain boundary modification

The grain boundary modification by Pr64Fe12Al9Ga15 addition was performed in the B-lean Nd-Y-Fe-B multi-main-phase (MMP) magnets. The effects of the additive on the microstructure and magnetic properties were investigated. A pronounced coercivity enhancement was achieved from 4.96 kOe to 8.15 kOe with 2 wt% Pr64Fe12Al9Ga15 addition, while the coercivity tended to be invariable with further increasing of Pr64Fe12Al9Ga15 content to 4, 6, and 8 wt%. Detailed microstructure analysis revealed that the significant amounts of RE6Fe13(Ga, Al)1 intergranular phase were generated by introducing Pr64Fe12Al9Ga15 additive in the B-lean Nd-Y-Fe-B MMP magnets. The formation of RE6Fe13(Ga, Al)1 contributed to the optimization of the distribution of grain boundary (GB) phase, strengthening the intergrain magnetic isolation. However, the further increases of the additive content led to the agglomeration of RE6Fe13(Ga, Al)1 in the triple junction region, which caused a reduction in remanence. Meanwhile, excessive addition for additives revealed that the thicker GB layer was unessential to further increase in coercivity, the intergranular exchange coupling had already been decoupled in magnets with adequate addition. In addition, more Pr atoms were primarily substituting the Nd atoms, but Y atoms were not substituted by Pr in the shell region of matrix grains. It was deemed that the magnetic anisotropy of the grain shell was essentially unchanged even with the formation of Pr-rich shell. These results reported here enlighten the microstructure design of Nd-Y-Fe-B MMP magnets.

Construction of high-performance multi-main-phase LaCe-based sintered magnets by chemical heterogeneity enhancement

• The H cj + (BH) max of the 40 wt% LaCe substituted Nd magnet reached 47.34. • The Pr-rich phase with a lower melting point optimized GB phases' wettability. • The high H A Pr 2 Fe 14 B grains provided strong chemical heterogeneity. • The continuous GB layers and chemical heterogeneity guarantee high performance. To further optimize the comprehensive magnetic properties of LaCe-based sintered magnets prepared by constructing a multi-main-phase (MMP) structure, Pr-Fe-B was used as a LaCe-free alloy to prepare MMP sintered magnets with 40 wt% LaCe substitution. Due to the high anisotropy field ( H A ) of Pr 2 Fe 14 B grains, strong chemical heterogeneity could be provided in MMP magnets. In addition, the Pr-rich phase with a lower melting point enters the MMP magnet, optimizing the composition and structure of the grain boundary (GB) phase. It is beneficial to improve the wettability and promote the formation of continuous GB layers. As a result, the H cj and (BH) max of the MMP magnets reached 9.64 kOe and 37.70 MGOe, leading to an excellent overall magnetic performance of (BH) max (MGOe) + H cj (kOe) = 47.34. This will serve as a reference for the high performance of MMP LaCe-based magnets.

Coercivity enhancement of Nd-La-Ce-Fe-B sintered magnets: Synergistic effects of grain boundary regulation and chemical heterogeneity

Retaining the chemical heterogeneity of 2:14:1 main phase grains and forming continuous grain boundary (GB) layers are considered two significant contributions to high coercivity in multi-main-phase (MMP) Nd-La-Ce-Fe-B sintered magnets. In this work, the trade-off between chemical heterogeneity and the GB layers in MMP Nd-La-Ce-Fe-B sintered magnets was tackled by designing the composition of LaCe-free alloys. The coercivity of the MMP LaCe-40 (LaCe/TRE = 40 wt.%, TRE: total rare earth) magnets prepared by replacing conventional Nd30.5FebalM1.8B0.96 (Nd-normal) with Nd42.1FebalB0.79 (Nd-rich) as a LaCe-free alloy increased by 52.7%, reaching an ultra-high coercivity of 11.10 kOe. Analysis of the microstructure showed that chemical heterogeneity was retained in the MMP LaCe-40 sintered magnets prepared with Nd42.1FebalB0.79. In addition, thick Nd-rich hard magnetic shells and continuous GB layers were constructed. On the one hand, magnetization reversal of the LaCe-rich grains was hindered by the adjacent strongly magnetic LaCe-free grains. On the other hand, this enhanced the anisotropic field of the LaCe-rich grains and weakened the ferromagnetic coupling effect. These provided a guarantee for preventing the nucleation and propagation of reversed domains, thereby achieving high coercivity. This study offers a new solution for the contradiction between the retention of chemical heterogeneity and the regulation of the GB structure in the MMP Nd-La-Ce-Fe-B sintered magnets, creating the conditions for further improving the coercivity of magnets.

Uncovering the softening mechanism and exploring the strengthening strategies in extremely fine nanograined metals: A molecular dynamics study

• Softening and strengthening in extremely fine nanograined metals are governed by grain boundary (GB) stability. • Atomic sliding in GB layer induces the softening while dislocation activity in grain interior plays the role of coordinator to fit the deformation dominated by GBs. • The solid solution exerts the negative strengthening (the softening) effect to the nanoscale metals. • The GB segregation gives rise to a notable improvement in strength, and this improvement can be further enhanced by optimizing solute concentration and GB excess. The strength of polycrystalline metals increases with decreasing grain size, following the classical Hall-Petch relationship. However, this relationship fails when softening occurs at very small grain sizes (typically less than 10 to 20 nm), which limits the development of ultrahigh-strength materials. In this work, using columnar-grained nanocrystalline Cu-Ag ‘samples’, molecular dynamics simulations were performed to investigate the softening mechanism and explore the strengthening strategies (e.g., formation of solid solution or grain boundary (GB) segregation) in extremely fine nanograined metals. Accordingly, the softening of pure metals is induced by atomic sliding in the GB layer, rather than dislocation activities in the grain interior, although both occur during deformation. The solid solution lowers the stacking fault energy and increases the GB energy, which leads to the softening of NC metals. GB segregation stabilizes GB structures, which causes a notable improvement in strength, and this improvement can be further enhanced by optimizing the solute concentration and GB excess. This work deepens the understanding of the softening mechanism due to atomic sliding in the GB layer and the strengthening mechanism arising from tailoring the GB stability of immiscible alloys and provides insights into the design of ultrahigh-strength materials.

The Grain Boundary Wetting Phenomena in the Ti-Containing High-Entropy Alloys: A Review

In this review, the phenomenon of grain boundary (GB) wetting by melt is analyzed for multicomponent alloys without principal components (also called high-entropy alloys or HEAs) containing titanium. GB wetting can be complete or partial. In the former case, the liquid phase forms the continuous layers between solid grains and completely separates them. In the latter case of partial GB wetting, the melt forms the chain of droplets in GBs, with certain non-zero contact angles. The GB wetting phenomenon can be observed in HEAs produced by all solidification-based technologies. GB leads to the appearance of novel GB tie lines Twmin and Twmax in the multicomponent HEA phase diagrams. The so-called grain-boundary engineering of HEAs permits the use of GB wetting to improve the HEAs’ properties or, alternatively, its exclusion if the GB layers of a second phase are detrimental.

A Critical Examination of the Mott–Schottky Model of Grain-Boundary Space-Charge Layers in Oxide-Ion Conductors

The electrical properties of grain boundaries in ionic conductors are studied most frequently and most easily by Electrochemical Impedance Spectroscopy (EIS). The resistance data obtained in this manner are typically analyzed with the Mott–Schottky space-charge model to extract a space-charge potential. In this study, taking CeO2 containing acceptor-dopant cations and oxygen vacancies as our model system, we calculate impedance spectra by solving the drift–diffusion equation for oxygen vacancies for a bicrystal geometry with space-charge layers at the grain boundary. Three different cases are considered for the behavior of the acceptor-dopant cations: a uniform distribution (Mott–Schottky), an equilibrium distribution (Gouy–Chapman), and a distribution frozen-in from a much higher temperature (restricted equilibrium). Analyzing our impedance data for the restricted-equilibrium case with the Mott–Schottky model, we find that the obtained space-charge potentials are substantially underestimated. In view of such a discrepancy not normally being apparent (the true values being unknown), we propose a specific set of EIS experiments that allow the Mott–Schottky model to be discounted.

A Multi-Scale Approach for Phase Field Modeling of Ultra-Hard Ceramic Composites.

Diamond-silicon carbide (SiC) polycrystalline composite blends are studied using a computational approach combining molecular dynamics (MD) simulations for obtaining grain boundary (GB) fracture properties and phase field mechanics for capturing polycrystalline deformation and failure. An authentic microstructure, reconstructed from experimental lattice diffraction data with locally refined discretization in GB regions, is used to probe effects of local heterogeneities on material response in phase field simulations. The nominal microstructure consists of larger diamond and SiC (cubic polytype) grains, a matrix of smaller diamond grains and nanocrystalline SiC, and GB layers encasing the larger grains. These layers may consist of nanocrystalline SiC, diamond, or graphite, where volume fractions of each phase are varied within physically reasonable limits in parametric studies. Distributions of fracture energies from MD tension simulations are used in the phase field energy functional for SiC-SiC and SiC-diamond interfaces, where grain boundary geometries are obtained from statistical analysis of lattice orientation data on the real microstructure. An elastic homogenization method is used to account for distributions of second-phase graphitic inclusions as well as initial voids too small to be resolved individually in the continuum field discretization. In phase field simulations, SiC single crystals may twin, and all phases may fracture. The results of MD calculations show mean strengths of diamond-SiC interfaces are much lower than those of SiC-SiC GBs. In phase field simulations, effects on peak aggregate stress and ductility from different GB fracture energy realizations with the same mean fracture energy and from different random microstructure orientations are modest. Results of phase field simulations show unconfined compressive strength is compromised by diamond-SiC GBs, graphitic layers, graphitic inclusions, and initial porosity. Explored ranges of porosity and graphite fraction are informed by physical observations and constrained by accuracy limits of elastic homogenization. Modest reductions in strength and energy absorption are witnessed for microstructures with 4% porosity or 4% graphite distributed uniformly among intergranular matrix regions. Further reductions are much more severe when porosity is increased to 8% relative to when graphite is increased to 8%.

Micromagnetic study of sphericity effect in bulk permanent magnets

The sphericity, κ, is introduced to describe the morphology of the magnetic grains. The effect of κ on the magnetic properties of rare earth-transition metal (RE-TM) permanent magnets was investigated using the micromagnetic simulation, where randomly aligned, irregular-shaped grains with ferromagnetic/non-ferromagnetic grain boundary (GB) phases were considered. For the simulated RE-TM systems, the coercivity increases significantly with the increase in κ. In particular, with 10 nm thick non-ferromagnetic GB phase, the coercivity, 1.74 MA/m, for к = 0.9 increases by 22% compared to 1.43 MA/m for к = 0.6 in the Nd2Fe14B system. Among the simulated materials, the SmCo5 system displays the largest increment in coercivity, increasing by 0.82 MA/m from 7.61 MA/m for к = 0.6 to 8.43 MA/m for к = 0.9. Magnetization reversal patterns under different external fields indicate that the dependence of coercivity on κ is attributed to the formation of local reversals at different regions and mechanisms of reversal propagation. Meanwhile the effect of κ cannot be neglected even at elevated temperatures. The simulated results of (Dy0.47Nd0.53)2Fe14B systems with the non-ferromagnetic GB layer of 4 nm at a temperature of 450 K show that the coercivity for к = 0.9 (1.88 MA/m) increased by 23% compared with that of к = 0.6 (1.52 MA/m). Our study demonstrates that the sphericity can be used as a key parameter to design high-coercivity RE-TM magnets.

Prospects for the use of ferrites with high magnetic permeability and permittivity as radio-absorbing materials

The paper presents an overview of studies on the influence of the main parameters of ferrites on their ability to absorb electromagnetic radiation in the megahertz range (more than 10 dB). The main advantage of ferrites is a high refractive index (more than 1000) in the megahertz range due to the combination of high values of magnetic and dielectric permeability, which makes it possible to produce radio-absorbing coatings of small thickness (less than 10 mm) that effectively absorb electromagnetic radiation. Studies show that the attenuation of the power of electromagnetic radiation reflected from the surface of the ferrite is due to both interference processes and the processes of dissipation of electromagnetic energy during propagation in the ferrite. The inversely proportional relationship between the refractive index and the frequency of electromagnetic radiation in the megahertz range provides the condition for the interference minimum of the reflected radiation at a constant thickness of the ferrite coatings. A high refractive index slows down the speed of propagation of electromagnetic waves in ferrites, which enhances the processes of dissipation of their energy. The paper presents studies on the influence of the basic chemical composition of ferrites, alloying additives, microstructure parameters and technological modes on their magnetic and dielectric permeability. Studies have shown that an excess of iron oxide in excess of stoichiometry, which provides the semiconducting properties of ferrite grains, significantly increases the dielectric constant. High values of the dielectric constant of ferrites are provided by a combination of the dielectric properties of grain-boundary layers and the semiconducting properties of the grains themselves, which form the barrier capacity of grain boundaries according to the Okazaki mechanism. Alloying ferrites with oxides TiO 2 , Bi 2 O 3 , CaO in an amount of up to 1 wt.% allows increasing the electrical resistance and dielectric constant of grain-boundary layers, providing an increase in the dielectric constant of ferrite as a whole. It has been established that the formation of a dense coarse-grained structure provides an increase in both the magnetic permeability and permittivity.

Significantly improving the giant dielectric properties of CaCu3Ti4O12 ceramics by co-doping with Sr2+ and F- ions

Improved dielectric properties of CaCu3Ti4O12 ceramics were produced by co-doping with Sr2+/F- cation/anions. The grain sizes of the Ca1-xSrxCu3Ti4O12-xFx ceramics were considerably decreased, producing a large amount of insulating grain boundary (GB) layers. Optimized dielectric properties with a high dielectric permittivity of ε′∼6.44 × 104 and a low loss tangent (tanδ∼0.030) were produced. The non-Ohmic properties also improved. The Schottky barrier height (ΦB) of the GBs increased by co-doping with Sr2+/F- ions. The electrical properties of the semiconducting grains changed slightly. Accordingly, the increase in the total GB resistance (Rgb) significantly decreased the tanδ and increased the breakdown electric field. The increased Rgb resulted from the improved intrinsic properties of the GBs (that is, ΦB increased) and the controlled microstructure (that is, the insulating GB layers increased). The macroscopic giant dielectric and electrical properties were described using an internal barrier layer capacitor model related to the Schottky barrier height at the GBs.

Atomically Sharp Dual Grain Boundaries in 2D WS2 Bilayers.

It is shown that tilt grain boundaries (GBs) in bilayer 2D crystals of the transition metal dichalcogenide WS2 can be atomically sharp, where top and bottom layer GBs are located within sub-nanometer distances of each other. This expands the current knowledge of GBs in 2D bilayer crystals, beyond the established large overlapping GB types typically formed in chemical vapor deposition growth, to now include atomically sharp dual bilayer GBs. By using atomic-resolution annular dark-field scanning transmission electron microscopy (ADF-STEM) imaging, different atomic structures in the dual GBs are distinguished considering bilayers with a 3R (AB stacking)/2H (AA' stacking) interface as well as bilayers with 2H/2H boundaries. An in situ heating holder is used in ADF-STEM and the GBs are stable to at least 800 °C, with negligible thermally induced reconstructions observed. Normal dislocation cores are seen in one WS2 layer, but the second WS2 layer has different dislocation structures not seen in freestanding monolayers, which have metal-rich clusters to accommodate the stacking mismatch of the 2H:3R interface. These results reveal the competition between maintaining van der Waals bilayer stacking uniformity and dislocation cores required to stitch tilted bilayer GBs together.

Copper enriched by dealloying as external cathode in intergranular corrosion of aluminium alloy AA6005

The purpose of this work is to understand the role of Cu in the propagation mechanism of IGC on extruded alloy AA6005-T5. The constituent Cu segregates as a Cu-rich nanolayer, together with the formation of a solute depleted zone, along the grain boundaries during thermomechanical processing of the alloy. While the α-phase particles corrode in acidified chloride test solution, additional Cu becomes enriched as nanoscale particles and layer segments by dealloying on the external surface and fissure walls formed by IGC. While the grain-boundary layer functions as the internal cathode, enriched Cu acts as effective external cathodes in IGC propagation.

Molecular Dynamics Studies on the Lithium Ion Conduction Behaviors Depending on Tilted Grain Boundaries with Various Symmetries in Garnet-Type Li7La3Zr2O12

Grain boundary (GB) structure is a critical parameter that significantly affects the macroscopic properties of materials; however, the evaluation of GB characteristics by modern analytical methods remains an extremely challenging task. In this work, Li+ conductivity degradation at the GBs of cubic Li7La3Zr2O12 (LLZO) with a garnet framework (which represents the most promising candidate material for solid electrolytes utilized in all-solid-state batteries) has been investigated by various molecular dynamics approaches combined with newly developed analytical techniques. It was found that the transboundary diffusion of Li ions was generally slower than their diffusion in the bulk regardless of the GB symmetry; however, this effect strongly depended on the concentration of Li-deficient sites (trapping Li vacancies) in the GB layer. Furthermore, the compactness and density of the combined GB regions represent the key parameters affecting the overall Li+ conductivity of polycrystalline LLZO films.

Oxygen vacancy formation in the SrTiO3 Σ5 [001] twist grain boundary from first‐principles

AbstractThe SrTiO3 5 [001] twist grain boundary (GB) is studied using first‐principles density functional theory calculations. Three types of GB structures, SrO/SrO (S/S), SrO/TiO2 (S/T), and TiO2/TiO2 (T/T), are modeled and their relative thermodynamic stabilities are examined. Our calculations show that the S/S and S/T structures can be formed within appropriate synthesis conditions, with the S/S structure thermodynamically favored over the S/T structure within a wide range of chemical potentials, while the T/T structure is unlikely to form. The segregation behavior of oxygen vacancies is also investigated by calculating oxygen vacancy formation energies with respect to the distance from GB plane. In the S/S system, oxygen vacancies tend to segregate to the layer adjacent to the GB layer, while in the S/T system, oxygen vacancies tend to segregate to the GB layer itself. In both S/S and S/T systems, oxygen vacancy formation energy is lower than that in bulk SrTiO3. To clearly show the experimental conditions necessary to promote oxygen vacancy formation in the 2 GB systems, we also generate grain boundary phase diagrams for oxygen vacancy with respect to synthesis temperature and oxygen partial pressure. Our calculations reveal different segregation behaviors and distributions of oxygen vacancies in the S/S and S/T systems, providing a possible avenue for GB engineering.

Post-sinter annealing influences on coercivity of multi-main-phase Nd-Ce-Fe-B magnets

Post-sinter annealing (PSA) plays an essential role on enhancing coercivity of the single-main-phase (SMP) Nd2Fe14B-based magnets due to the formation of continuous Nd-rich grain boundary (GB) layers to decouple the adjacent grains. Here we investigated the PSA effects on coercivity of the multi-main-phase (MMP) [(Nd,Pr)0.55Ce0.45]30.5FebalM1.0B1.0 (wt.%) magnet prepared by sintering the mixture of Ce-free and Ce-containing 2:14:1 powders, which has shown superior magnetic properties to the SMP one at the same average composition. The annealing temperature dependent investigation showed that the coercivity can be enhanced when annealing at low temperatures, but becomes even lower than that of the as-sintered state when annealing at higher temperatures, despite that continuous RE-rich GB layers are formed after annealing. When raising the annealing temperature, the RE gradients within the 2:14:1 phase grains are reduced to reach the ‘‘close to equilibrium (or SMP)’’ state due to the further elemental inter-diffusions among the Ce-lean and Ce-rich 2:14:1 grains, which weakens the magnetic impedance effect among them. These findings suggest a unique clue to enhance coercivity of the MMP RE-Fe-B magnets by PSA, i.e. the competitive contributions between the formation of continuous GB layers and the gradual chemical homogenization should be balanced.

Mechanically Driven Grain Boundary Formation in Nickel Nanowires.

Metallic nanomaterials are widely used in micro/nanodevices. However, the mechanically driven microstructure evolution in these nanomaterials is not clearly understood, particularly when large stress and strain gradients are present. Here, we report the in situ bending experiment of Ni nanowires containing nanoscale twin lamellae using high-resolution transmission electron microscopy. We found that the large, localized bending deformation of Ni nanowires initially resulted in the formation of a low-angle tilt grain boundary (GB), consisting of randomly distributed dislocations in a diffuse GB layer. Further bending intensified the local plastic deformation and thus led to the severe distortion and collapse of local lattice domains in the GB region, thereby transforming a low-angle GB to a high-angle GB. Atomistic simulations, coupled with in situ atomic-scale imaging, unravelled the roles of bending-induced strain gradients and associated geometrically necessary dislocations in GB formation. These results offer a valuable understanding of the mechanically driven microstructure changes in metallic nanomaterials through GB formation. The work also has implications for refining the grains in bulk nanocrystalline materials.

Thickness‐dependent domain wall reorientation in 70/30 lead magnesium niobate‐ lead titanate thin films

AbstractContinued reduction in length scales associated with many ferroelectric film‐based technologies is contingent on retaining the functional properties as the film thickness is reduced. Epitaxial and polycrystalline lead magnesium niobate‐lead titanate (70PMN‐30PT) thin films were studied over the thickness range of 100‐350 nm for the relative contributions to property thickness dependence from interfacial and grain‐boundary low permittivity layers. Epitaxial PMN‐PT films were grown on SrRuO3/(001)SrTiO3, while polycrystalline films with {001}‐Lotgering factors >0.96 were grown on Pt/TiO2/SiO2/Si substrates via chemical solution deposition. Both film types exhibited similar relative permittivities of ~300 at high fields at all measured thicknesses with highly crystalline electrode/dielectric interfaces. These results, with the DC‐biased and temperature‐dependent dielectric characterization, suggest irreversible domain wall mobility is the major contributor to the overall dielectric response and its thickness dependence. In epitaxial films, the irreversible Rayleigh coefficients reduced 85% upon decreasing thickness from 350 to 100 nm. The temperature at which a peak in the relative permittivity is observed was the only measured small signal quantity which was more thickness‐dependent in polycrystalline than epitaxial films. This is attributed to the relaxor nature present in the films, potentially stabilized by defect concentrations, and/or chemical inhomogeneity. Finally, the effective interfacial layers are found to contribute to the measured thickness dependence in the longitudinal piezoelectric coefficient.

Spin Structures of Textured and Isotropic Nd-Fe-B-Based Nanocomposites: Evidence for Correlated Crystallographic and Spin Textures

We report the results of a comparative study of the magnetic microstructure of textured and isotropic $\mathrm{Nd}_2\mathrm{Fe}_{14}\mathrm{B}/\alpha$-$\mathrm{Fe}$ nanocomposites using magnetometry, transmission electron microscopy, synchrotron x-ray diffraction, and, in particular, magnetic small-angle neutron scattering (SANS). Analysis of the magnetic neutron data of the textured specimen and computation of the correlation function of the spin misalignment SANS cross section suggests the existence of inhomogeneously magnetized regions on an intraparticle nanometer length scale, about $40-50 \, \mathrm{nm}$ in the remanent state. Possible origins for this spin disorder are discussed: it may originate in thin grain-boundary layers (where the materials parameters are different than in the $\mathrm{Nd}_2\mathrm{Fe}_{14}\mathrm{B}$ grains), or it may reflect the presence of crystal defects (introduced via hot pressing), or the dispersion in the orientation distribution of the magnetocrystalline anisotropy axes of the $\mathrm{Nd}_2\mathrm{Fe}_{14}\mathrm{B}$ grains. X-ray powder diffraction data reveal a crystallographic texture in the direction perpendicular to the pressing direction -- a finding which might be related to the presence of a texture in the magnetization distribution, as inferred from the magnetic SANS data.