Materialia最新文献

{"title":"Incorporating elasticity into the thermodynamics and phase diagrams of multi-component systems","authors":"Niklas Marschall ,&nbsp;Jegatheesan Murugan ,&nbsp;Reza Darvishi Kamachali","doi":"10.1016/j.mtla.2025.102546","DOIUrl":"10.1016/j.mtla.2025.102546","url":null,"abstract":"<div><div>Elastic energy plays a critical role in determining phase stability in compositionally complex alloys. However, quantifying elastic contributions in multi-component systems and incorporating them into phase diagram construction remain challenging. In this study, we present a generalized elastic energy formalism tailored for multi-component alloys, which can be directly and efficiently integrated with CALPHAD thermodynamic databases and existing frameworks such as Thermo-Calc (Andersson et al., 2002), Pandat (Cao et al., 2009) or FactSage (Bale et al., 2016). This elasticity formalism can also be introduced as a post-processing layer in open-source software such as pyCALPHAD (Otis and Liu, 2017) and Kawin (Ury et al., 2023) , enabling elastic assessments in multi-component systems.</div><div>We apply our framework for constructing the phase diagram of quinary Fe–Mn–Ni–Co–Cu alloy system, utilizing convex hull and Hessian matrix under elastic considerations. Our results reveal that incorporating elastic energy leads to an expansion of both the spinodal region and the miscibility gap. These are governed by the intricate interplay of chemical and elastic driving forces: We found that Mn and Ni contribute strongly to chemical stabilization, while Cu and Co tend to destabilize the alloy, especially at low Mn concentrations. The stabilizing effect of Fe is also pronounced in Mn-deficient regions. Acting as a destabilizing factor, the elastic energy is primarily driven by the presence of Mn, underscoring its multifaceted role in thermodynamic stability. In Mn-rich compositions, Cu markedly reduces the elastic energy contribution. Combined with CALPHAD infrastructures, the current framework offers a practical pathway to improve the predictive accuracy of phase stability and transformations in complex multi-component alloys.</div></div>","PeriodicalId":47623,"journal":{"name":"Materialia","volume":"44 ","pages":"Article 102546"},"PeriodicalIF":2.9,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Phase decomposition in the equiatomic CoCrNi alloy","authors":"Sakshi Bajpai ,&nbsp;Xin Wang ,&nbsp;Bijun Xie ,&nbsp;Hangman Chen ,&nbsp;Jize Zhang ,&nbsp;Calvin Belcher ,&nbsp;Benjamin MacDonald ,&nbsp;Julia Ivanisenko ,&nbsp;Yu Zhong ,&nbsp;Penghui Cao ,&nbsp;Enrique J. Lavernia ,&nbsp;Diran Apelian","doi":"10.1016/j.mtla.2025.102554","DOIUrl":"10.1016/j.mtla.2025.102554","url":null,"abstract":"<div><div>Complex, concentrated alloys (CCAs) are composed of multiple principal elements in significant proportions and have attracted substantial interest due to their distinctive properties. It was initially thought that CCAs formed primarily as single-phase structures; however, subsequent research has revealed that CCAs may undergo phase decomposition when subjected to intermediate temperatures over extended durations. This study investigates the phase stability of equiatomic CoCrNi alloy, commonly recognized as a single-phase face-centered cubic (FCC) material. The alloy was subjected to severe plastic deformation, resulting in a high density of grain boundaries and deformation-induced structures. Guided by the calculation of phase diagrams (CALPHAD) predictions, prolonged annealing at a selected temperature was conducted to evaluate its phase stability. Microstructural characterization from the micro- to atomic-scale revealed that the FCC matrix undergoes structural decomposition into an HCP phase, accompanied by elemental partitioning within this phase. Transmission electron microscopy confirmed the presence of the HCP phase, while high-throughput CALPHAD and hybrid Monte Carlo/Molecular Dynamics simulations provided mechanistic insights into its formation. The emergence of this HCP phase, and the associated redistribution of elements, explains the observed differences in phase constitution compared to previously studied alloys. These findings highlight the critical role of processing-dependent phase evolution and elemental partitioning in dictating the performance of complex concentrated alloys (CCAs), thereby influencing their mechanical properties and long-term reliability in demanding applications.</div></div>","PeriodicalId":47623,"journal":{"name":"Materialia","volume":"44 ","pages":"Article 102554"},"PeriodicalIF":2.9,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigation of creep cavitation mechanisms in ferritic Grade 91 steel","authors":"E.C. Galliopoulou ,&nbsp;S. He ,&nbsp;G.T. Martinez ,&nbsp;P.J. Thomas ,&nbsp;L. Coghlan ,&nbsp;H. Shang ,&nbsp;C. Jones ,&nbsp;M. Zimina ,&nbsp;J. Siefert ,&nbsp;J.D. Parker ,&nbsp;G.M. Hughes ,&nbsp;N. Grilli ,&nbsp;A. Cocks ,&nbsp;T.L. Martin","doi":"10.1016/j.mtla.2025.102547","DOIUrl":"10.1016/j.mtla.2025.102547","url":null,"abstract":"<div><div>The majority of premature failures in Grade 91 steel components used in high-temperature applications, such as power plants, are attributed to creep cavity nucleation. This study examined creep cavity nucleation in ferritic P91 ex-service material during its early formation stages through interrupted creep tests at 4% and 10% strain, as well as in later stages by analysing a failed creep-tested specimen with 35.6% strain at failure. While cavity growth under high-temperature exposure did not require applied stress, cavity interlinkage was more pronounced in high-stress regions. It was found that manganese sulfide (MnS) inclusions were highly prone to damage and were responsible for the nucleation of the first cavities during early creep life stages. This process was facilitated by the presence of M₂₃C₆ carbides and Laves phase located at the interface between the MnS inclusions and the ferrite matrix. Grain boundary misorientation was highly associated with cavitation with grain boundaries of misorientations <span><math><mrow><mn>45</mn><mo>−</mo><mn>5</mn><msup><mrow><mn>5</mn></mrow><mrow><mo>∘</mo></mrow></msup></mrow></math></span> being the predominant type in the ferritic microstructure and, consequently, the most frequently cavitating. Although less frequent in the microstructure, lower-angle GBs with misorientations <span><math><mrow><mo>&lt;</mo><mn>15</mn><mo>−</mo><mn>2</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>∘</mo></mrow></msup></mrow></math></span> exhibited the highest cavitation ratios. Localized deformation was found to be strongly correlated with cavitation, whereas the Schmid factor did not exhibit a statistically significant link to damage. A dense dislocation structure, observed using TEM and SEM imaging at early creep life stages, was significantly reduced at the failure stage, likely due to dislocation relief during cavity formation and crack propagation.</div></div>","PeriodicalId":47623,"journal":{"name":"Materialia","volume":"44 ","pages":"Article 102547"},"PeriodicalIF":2.9,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Performance of layered morphology in tribological applications and its two-dimensional modification with MoS2 for the enhanced performance in lubrication","authors":"M.S. Darris","doi":"10.1016/j.mtla.2025.102555","DOIUrl":"10.1016/j.mtla.2025.102555","url":null,"abstract":"<div><div>Li₂TiO₃'s distinctive layered structure holds promise for augmenting the wear resistance of industrial coating systems. The present work outlined the influence of 2D assembled MoS₂ on layered structure for enhancing the tribological performance of Li₂TiO₃. The synthesis of Li₂TiO₃ was carried out using the sol-gel method and the Li₂TiO₃/MoS₂ composite coating was developed by Phosphate conversion coating. The phase purity of the generated materials has been validated using X-ray diffraction (XRD) analysis. The composite material exhibited a lack of additional phases, hence precluding any possible interactions among the oxides. The confirmation of the effective integration of the composites into the coating was achieved by employing XRD and energy-dispersive X-ray spectroscopy (EDS) methods. SEM and optical surface profilometry was used to examine the shape and roughness of coating surface. The hardness of the Li₂TiO₃/MoS₂ composite coating has been observed to exhibit a significantly elevated value of 750 HV, along with low friction coefficient and enhanced wear resistance when compared to pure Li₂TiO₃. The utilization of a cost-effective technique for coating preparation, along with the incorporation of a composite material including Li₂TiO₃/MoS₂ into the hot-dip galvanization process, presents an innovative approach for exploring prospective materials suitable for industrial applications.</div></div>","PeriodicalId":47623,"journal":{"name":"Materialia","volume":"44 ","pages":"Article 102555"},"PeriodicalIF":2.9,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145119283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigations on the effect of Nb on acicular ferrite dominant weld metal microstructure and toughness","authors":"Wenguang Liao,&nbsp;Xun Liu","doi":"10.1016/j.mtla.2025.102551","DOIUrl":"10.1016/j.mtla.2025.102551","url":null,"abstract":"<div><div>Despite the recognized benefits of Niobium (Nb) as a micro-alloying element in high-strength low-alloy (HSLA) steels, its adverse impact on weld metal toughness has been consistently observed and yet not fully understood. This study employs multiscale microstructural and properties characterization to investigate the effects of Nb on HSLA weld metal with a predominantly acicular ferrite (AF) microstructure. Based on nanoindentation results, the addition of Nb increases the hardness of AF phase in weld metal by 11.3 % - 13.1 % through solid solution strengthening, while exhibiting no significant enhancement in non-AF micro-constituents. In AF regions, Nb reduces the fraction of AF and promotes the formation of more equiaxed granular bainite (GB) by lowering the γ to α transformation temperature and inhibiting AF growth through a solute drag effect. Nb not only promotes the formation of low temperature transformation products such as martensite-austenite constituent (MA) and bainitic micro-constituent (BC) but also refines the distribution of MA within the microstructure. Analysis suggests the microstructural modifications associated with Nb cannot fully explain the toughness deterioration. The Nb-induced material strengthening, along with the intrinsic balance between strength and toughness in metallic materials, is likely the dominant factor in the reduction of toughness caused by Nb.</div></div>","PeriodicalId":47623,"journal":{"name":"Materialia","volume":"44 ","pages":"Article 102551"},"PeriodicalIF":2.9,"publicationDate":"2025-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling the dielectric spectra of silicon dioxide for passive radiative cooling applications","authors":"Antoine Patt ,&nbsp;Jorge S. Dolado","doi":"10.1016/j.mtla.2025.102536","DOIUrl":"10.1016/j.mtla.2025.102536","url":null,"abstract":"<div><div>Passive radiative cooling (PRC) is a promising strategy for sustainable thermal regulation that relies on materials with tailored infrared emissivity. Silica (SiO₂) is a key component in many PRC applications due to its high transparency in the solar spectrum and strong infrared phonon absorption near 9<!--> <!-->µm, aligning with the atmospheric transparency window. However, effective integration of silica into advanced PRC systems – such as photonic coatings, aerogels, and composite networks – requires accurate knowledge of its intrinsic dielectric properties. In this work, the complex dielectric function of silica is derived from atomistic simulations, with an emphasis on infrared-active vibrational modes. We optimize a polarizable force field against available experimental data, including vibrational spectra, elastic moduli, and dielectric constants. The resulting force field provides a robust basis for predictive simulations of silica-based nanostructures relevant to PRC applications.</div></div>","PeriodicalId":47623,"journal":{"name":"Materialia","volume":"44 ","pages":"Article 102536"},"PeriodicalIF":2.9,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influence of layer orientation on the mechanical properties of fused deposition modelling using PLA and PETG","authors":"Lucas L.B. Ramos,&nbsp;Kelvin M.K. Iwasaki,&nbsp;Rafael Beck,&nbsp;Wellinton C. Scheffer,&nbsp;Felipe Ruivo Fuga,&nbsp;Ricardo De Medeiros","doi":"10.1016/j.mtla.2025.102541","DOIUrl":"10.1016/j.mtla.2025.102541","url":null,"abstract":"<div><div>The rapid advancement of Fused Deposition Modelling (FDM) technology has enabled researchers to optimise processing parameters and enhance the performance of thermoplastic components. However, the anisotropic behaviour induced by the layer-by-layer deposition process requires a comprehensive understanding of the mechanical response and failure mechanisms. This study investigates the mechanical properties and fracture behaviour of polylactic acid (PLA) and polyethylene terephthalate glycol (PETG) specimens fabricated using FDM, with print orientations of [<span><math><mrow><mn>0</mn><mo>°</mo></mrow></math></span>], [<span><math><mrow><mo>±</mo><mn>45</mn><mo>°</mo></mrow></math></span>], and [<span><math><mrow><mn>90</mn><mo>°</mo></mrow></math></span>]. By treating the printed structures as orthotropic materials, characterisation was conducted following the ASTM D3039 and ASTM D3518 standards, which represent a key methodological contribution of this work. Uniaxial tensile tests were performed in conjunction with Digital Image Correlation (DIC) to determine elastic moduli, Poisson’s ratios, and tensile strength. PLA exhibited 21.1% higher maximum tensile strength than PETG in the [<span><math><mrow><mn>0</mn><mo>°</mo></mrow></math></span>] orientation. Conversely, PETG outperformed PLA in the [<span><math><mrow><mn>90</mn><mo>°</mo></mrow></math></span>] and [<span><math><mrow><mo>±</mo><mn>45</mn><mo>°</mo></mrow></math></span>] orientations, with 13.7% and 12.3% higher strength, respectively. Post-failure analysis using optical microscopy and scanning electron microscopy (SEM) revealed brittle fracture features in PLA and ductile behaviour in PETG, with filament rupture for layers at 0<span><math><mo>°</mo></math></span> and filament detachment for 45<span><math><mo>°</mo></math></span> and 90<span><math><mo>°</mo></math></span>. Therefore, Hashin’s failure criteria predictions were confronted with experimental data, showing agreement with not only strength values but also associated failure mechanisms. These findings contribute to the understanding of anisotropic mechanical performance in FDM-fabricated polymers, providing insights for performance-oriented design in FDM applications.</div></div>","PeriodicalId":47623,"journal":{"name":"Materialia","volume":"44 ","pages":"Article 102541"},"PeriodicalIF":2.9,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Orientation dependence of the deformation behaviors of multilayered Cu/CuZr coating","authors":"Hang Xu ,&nbsp;Tao Guo ,&nbsp;Kewei Gao ,&nbsp;Xiaolu Pang","doi":"10.1016/j.mtla.2025.102553","DOIUrl":"10.1016/j.mtla.2025.102553","url":null,"abstract":"<div><div>In multilayered crystalline/amorphous structures, improving deformation capacity hinges on how effectively the crystalline layer inhibits main shear band formation in the amorphous layer. Here, we propose utilizing crystalline layers with varying deformation capabilities, controlled via crystallographic orientation, to coordinate amorphous layer deformation. Without altering the deposition parameters, we fabricated two types of crystalline Cu/amorphous CuZr nanocomposites with distinct textures by using differently oriented substrates, followed by micropillar compression tests. (200)-textured samples exhibited higher strength without softening. The (200)-textured Cu and CuZr layers showed stronger coupling, and the Cu layer’s higher hardening capacity facilitated multiple shear bands in the CuZr layer, enhancing plasticity. In contrast, (111)-textured samples exhibited catastrophic shear localization. In addition, molecular dynamics (MD) simulations confirmed these findings and revealed the underlying deformation mechanisms. This study provides a new strategy for improving the mechanical performance of crystalline/amorphous composites.</div></div>","PeriodicalId":47623,"journal":{"name":"Materialia","volume":"44 ","pages":"Article 102553"},"PeriodicalIF":2.9,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hybrid additive manufactured tool steels: Microstructural modifications and mechanical enhancements through heat treatments","authors":"Meysam Mashhadikarimi ,&nbsp;Yahya Aghayar ,&nbsp;Parisa Moazzen ,&nbsp;Mohammad Masoumi ,&nbsp;SeyedAmirReza Shamsdini ,&nbsp;Mohsen Mohammadi","doi":"10.1016/j.mtla.2025.102552","DOIUrl":"10.1016/j.mtla.2025.102552","url":null,"abstract":"<div><div>This study investigates the microstructural and mechanical evolution of hybrid steel components produced via laser powder bed fusion (LPBF), wherein maraging steel (MS1) was deposited onto an S7 tool steel substrate. Two heat treatment schedules—heat treatment 1 (HT1: austenitizing at 880 °C for 1 h, air cooling), to enhance elemental diffusion and promote partial recrystallization, and heat treatment 2 (HT2: HT1 followed by aging at 500 °C for 2 h), to induce precipitation hardening in MS1—were performed. Comprehensive microstructural characterization was conducted on the as-built and heat-treated samples using optical microscopy, scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and energy dispersive x-ray spectroscopy (EDS). Vickers microhardness measurements and uniaxial tensile testing evaluated the effects of heat treatments. In the as-built condition, a narrow transition zone (∼300 μm) near the interface exhibited steep hardness gradients (from ∼250 HV in S7 to ∼650 HV in MS1); high dislocation density was observed. HT1 shifted the fracture location from the S7 substrate to the MS1 deposit. HT2 further refined the microstructure and resulted in an ultimate tensile strength (UTS) of ∼1730 MPa and a uniform hardness distribution across the interface. Fracture consistently occurred away from the interface, confirming a sound metallurgical bond. These findings demonstrate the effectiveness of tailored heat treatments in tuning the mechanical performance of hybrid additively manufactured components, offering a promising route for structural repair in tooling applications. Finally, this research highlights the potential of hybrid additive manufacturing for advanced tool inserts with improved cooling capabilities and durability.</div></div>","PeriodicalId":47623,"journal":{"name":"Materialia","volume":"44 ","pages":"Article 102552"},"PeriodicalIF":2.9,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Unified mobility model for grain‑boundary‑limited transport in polycrystalline thermoelectric materials","authors":"Gbadebo Taofeek Yusuf ,&nbsp;Sukhwinder Singh ,&nbsp;Alexandros Askounis ,&nbsp;Zlatka Stoeva ,&nbsp;Fideline Tchuenbou-Magaia","doi":"10.1016/j.mtla.2025.102550","DOIUrl":"10.1016/j.mtla.2025.102550","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Grain-boundary-limited charge transport is a fundamental bottleneck in polycrystalline thermoelectric materials, where reduced carrier mobility degrades electrical conductivity and suppresses power factors. This degradation arises from the interplay of scattering mechanisms: grain-boundary barriers dominate at low temperatures; thermionic activation enables partial barrier crossing at intermediate temperatures; and phonon scattering limits the mean free path at high temperatures. Hence, there remains a need for a physically transparent framework to quantitatively extract these microstructural parameters. In this study, a semi-empirical mobility model that explicitly integrates these grain-boundary mechanisms was developed and validated, expressed as: &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/msub&gt;&lt;mtext&gt;exp&lt;/mtext&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mfrac&gt;&lt;msub&gt;&lt;mstyle&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mstyle&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/msub&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the weighted mobility, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mstyle&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mstyle&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the grain‑boundary barrier height, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is Boltzmann’s constant, &lt;span&gt;&lt;math&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is temperature, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is the bulk mean free path and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the boundary width. This model was validated for oxide semiconductor, intermetallic, chalcogenide and heuslers polycrystalline materials, achieving excellent agreement with experimental data (&lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;= 0.97–0.99) and yielding physically consistent parameters: &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mstyle&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mstyle&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; ≈ 0–0.056 eV and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mn&gt;300&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; ≈ 6–368 nm. A case study for Ta doped ZnO thermoelectric material shows that barrier passivation (reduction of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mstyle&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mstyle&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; from 0.056 eV to 0.03 eV) combined with modest grain-interior improvement (&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mn&gt;300&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;→60 nm) can significantly enhance carrier mobility across the entire temperature range. The analysis predicts that, at ∼1000 K, grain engineering could nearly double mobility and electrical conductivity. ","PeriodicalId":47623,"journal":{"name":"Materialia","volume":"44 ","pages":"Article 102550"},"PeriodicalIF":2.9,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}