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Atomic Scale Investigation of Defects in High-Performance Materials
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Properties.ORCID iD: 0000-0002-3726-9869
2025 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Transition metal carbides of groups 4 and 5 (TiC, ZrC, HfC, VC, NbC, TaC) with the rocksalt (B1) structure are critical refractory materials for extreme temperature applications due to their exceptional hardness, high melting points, and thermal stability. This high-temperature behavior governed by point defects and diffusion has long been preplexing, with experimental metal self-diffusion activation energies ( 7.5 eV in TiC and ZrC) and anomalously high prefactors (entropy 10–14.5 𝑘𝐵 in TiC)conflicting with traditional ab initio predictions assuming unreconstructed vacancies.

This thesis focuses on these discrepancies through systematic density functional theory (DFT) investigations, revealing that metal vacancies in group 4 and certain group 5 carbides spontaneously reconstruct by displacing neighboring carbon atoms to form strong C–C bonds. A combinatorial enumeration in TiC identified a rich landscape of reconstructed configurations, with the ground-state structure featuring a planar graphene-like C dimer lowering the Ti vacancy formation energy by 3.5 eV relative to the unreconstructed state. This reconstruction dramatically reduces Schottky defect formation energies from 7–8 eV (unreconstructed) to 3.98 eV (TiC), 6.08 eV (ZrC), 7.14 eV (HfC), and 1.97 eV (VC), while NbC and TaC retain unreconstructed vacancies ( 2.7 eV). Trends across the MeX (X = C, N, O) series correlate with valence electron count and bond covalency. Ab initio molecular dynamics (AIMD) at 1500–3000 K demonstrate that the C-dimer in the 2G structure undergoes thermally activated rotation above 1500 K, periodically opening the vacancy site and enabling Ti jumps into metastable open configurations with migration barriers of 3.5–4.0 eV. The resulting activation energy of 7.5 eV in agreement with experimental values. The anomalously high diffusion entropy arises from the large configurational and vibrational entropy of the reconstructed vacancy ensemble, particularly the dimer’s rotational degree of freedom (rotational diffusion coefficient 1.5 × 1012 s−1 at 2500 K) and numerous low-energy C-bonded metastable states. Reconstruction also induces strong short range repulsion between vacancies,preventing clustering and restoring the classical dissociated Schottky picture contrary to earlier cluster-based models. These findings establish a monovacancy mediated diffusion mechanism driven by dynamic carbon reconstruction as the dominant metal transport pathway in group 4 carbides. The insights are extended to technologically vital WC–Co cemented carbides, where vacancy-reconstruction-mediated processes at the surface of WC particles and WC/Co interfaces control Ostwald ripening,abnormal grain growth, and phase stability during liquid-phase sintering. The reconstructed vacancy framework provides a new atomic-scale foundation for defect engineering of refractory carbides, enabling predictive modeling of creep, sintering,and microstructural evolution in ultra-high-temperature ceramics and cemented carbides for aerospace, nuclear, and cutting-tool applications.

Abstract [sv]

Övergångsmetallkarbider i grupp 4 och 5 (TiC, ZrC, HfC, VC, NbC, TaC) med bergsaltstrukturen (B1) är –tack vare deras exceptionella hårdhet, höga smältpunkter och termiska stabilitet– viktiga eldfasta material för extrema högtemperaturtillämpningar. Detta högtemperaturbeteende, som styrs av punktdefekter och diffusion, har länge varit förbryllande eftersom experimentella aktiveringsenergier för metalsjälvdiffusion ( 7,5 eV i TiC och ZrC) och onormalt höga prefaktorer (entropi 14.5 𝑘𝐵 i TiC) står i konflikt med traditionella ab initio-förutsägelser som pekar på icke-rekonstruerade vakansstrukturer. Denna avhandling fokuserar på dessa avvikelser genom systematiska beräkningar med täthetsfunktionalteori (DFT). De visar att platser där metall är vakant i grupp 4 och vissa grupp 5-karbider spontant rekonstrueras genom att närliggande kolatomer förskjuts och bildar starka C–C-bindningar. En kombinatorisk numrering i TiC identifierade flera rekonstruerade konfigurationer, där grundtillstånds strukturen uppvisar en plan, grafenliknande C-dimer som sänker bildningsenergin för en Ti-vakans med 3,5 eV jämfört med det icke-rekonstruerade tillståndet. Denna rekonstruktion reducerar Schottkydefekternas bildningsenergier drastiskt från 7–8 eV (icke-rekonstruerat) till 3,98 eV (TiC), 6,08 eV (ZrC), 7,14 eV (HfC) och 1,97 eV(VC), medan NbC och TaC bibehåller icke-rekonstruerade vakanser ( 2,7 eV). Trenderöver MeX-serien (X = C, N, O) korrelerar med valenselektrontal och bindningskovalens. Ab initio-molekyldynamik (AIMD) vid 1500–3000 K visar att C-dimern i 2G-strukturen genomgår termiskt aktiverad rotation över 1500 K, vilket periodiskt öppnar en vakant plats och möjliggör Ti-hopp till metastabila öppna konfigurationer med migrationsbarriärer på 3,5–4,0 eV. Den resulterande aktiveringsenergin på 7,5 eV stämmer perfekt överens med experimentellt uppmätta värden. Den onormalt höga diffusionsentropin härrör från den stora konfigurationsoch vibrationsentropin i det rekonstruerade vakans-ensemblet. Särskilt härör den från dimerns rotationsfrihetsgrad (rotationsdiffusionskoefficient 1.5 × 1012 s−1 vid 2500 K) och de många lågenergi C-bindningar i metastabila tillstånd.

Rekonstruktionen inducerar också en stark kortdistansrepulsion mellan vakanser, vilket förhindrar klustring och återställer den klassiska bilden av dissocierade Schottkydefekter – i motsats till tidigare klusterbaserade modeller. Dessa resultat fastställer en monovakansmedierad diffusionsmekanism, driven av dynamisk kolrekonstruktion, som den dominerande vägen för metalltransport i grupp 4-karbider. Insikterna utvidgas till teknologiskt viktiga WC–Co-hårdmetaller, där rekonstruktionsmedierade vakansprocesser vid ytan av WC-partiklar och WC/Co-gränsytor styr Ostwald-mognad, onormal korn-växt och fasstabilitet under sintring i vätskefas. Det rekonstruerade vakansramverket tillhandahåller en ny atomskalig grund för utvärdering av defekter i eldfasta karbider och möjliggör prediktiv modellering av kryp, sintring och mikrostrukturell utveckling i ultrahögtemperaturkeramer och hårdmetaller för rymd-, kärn-och skärverktygstillämpningar.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2025. , p. xvii, 121
Series
TRITA-ITM-AVL ; 2026:1
National Category
Materials Engineering
Research subject
Materials Science and Engineering
Identifiers
URN: urn:nbn:se:kth:diva-374648ISBN: 978-91-8106-508-4 (print)OAI: oai:DiVA.org:kth-374648DiVA, id: diva2:2023591
Public defence
2026-01-30, https://kth-se.zoom.us/j/66026793395, Kollegiesalen, Brinellvägen 8, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2026-01-07 Created: 2025-12-19 Last updated: 2026-01-28Bibliographically approved
List of papers
1. Internal structure of metal vacancies in cubic carbides
Open this publication in new window or tab >>Internal structure of metal vacancies in cubic carbides
2024 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 109, no 6, article id L060103Article in journal (Refereed) Published
Abstract [en]

A combinatorial approach is employed to investigate the atomic and electronic structures of a metal vacancy in titanium carbide. It turns out that the usual relaxed geometry of the vacancy is just a metastable state representing a local energy minimum. Using ab initio calculations and by systematically searching through the configurational space of a Ti monovacancy, we identify a multitude of local minima with reconstructed geometry that are lower in energy. Among them, there is a planar configuration with two displaced carbons forming a dimer inside the vacancy. This structure has the optimal number and order of C-C bonds making it the global minimum. Further calculations show that this reconstructed geometry is also the ground state of metal vacancies in other carbides such as ZrC, HfC, and VC. The reconstructed metal vacancies are characterized by localized electron states due to the relatively short C-C bonds. The defect states lie just below the upper and lower valence bands. The existence of reconstructed vacancy configurations is essential for understanding the mechanism of metal self-diffusion in transition-metal carbides.

Place, publisher, year, edition, pages
American Physical Society (APS), 2024
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-343672 (URN)10.1103/PhysRevB.109.L060103 (DOI)001314558600001 ()2-s2.0-85184662338 (Scopus ID)
Note

QC 20240222

Available from: 2024-02-22 Created: 2024-02-22 Last updated: 2025-12-22Bibliographically approved
2. Configuration of Schottky defects in transition metal carbides
Open this publication in new window or tab >>Configuration of Schottky defects in transition metal carbides
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Vacancy defects in Group 4 and 5 transition metal carbides are studied employing ab initio calculations to obtain the energies of formation of Schottky defects as well as the interaction energies for the pair of vacancies in various spatial arrangements. The present calculations take into account the recently established fact that metal vacancies in these compounds may undergo a reconstruction where the octahedron of carbons surrounding the metal vacancy transforms into a lower-symmetry structure stabilized by formed C–C bonds. This reconstruction significantly lowers the formation energy of Schottky defects in cubic carbides of transition metals and also qualitatively changes the interactions between a metal vacancy and a carbon vacancy, from strong attraction to strong repulsion in the nearest-neighbor shell. The latter result removes the problem of vacancy clustering, that results from the assumption of unreconstructed geometry, and restores the usual view of a Schottky defect as a pair of dissociated vacancies in the studied equiatomic compounds.

National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-374139 (URN)
Note

QC 20251217

Available from: 2025-12-15 Created: 2025-12-15 Last updated: 2025-12-22Bibliographically approved
3. Dynamics of metal vacancies in TiC
Open this publication in new window or tab >>Dynamics of metal vacancies in TiC
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Metal self-diffusion in cubic transition-metal carbides exhibits anomalously high activation entropy(∼10–14.5 kB ), unexplained by conventional vacancy or cluster models. Using ab initio molecular dynamics (AIMD), we reveal that the reconstructed ground-state metal vacancy in TiC—a planarC–C dimer (2G structure)—undergoes thermally activated dimer rotation above 1800 K. This dynamic degree of freedom generates significant configurational entropy, contributing up to 8 kB pervacancy. We further compute temperature-dependent Schottky defect formation free energies from 500 to 3000 K, showing a reduction from 7.4 eV at 0 K to ∼3.8 eV at 2500 K due to vibrational and configurational contributions. Supercell size effects are clarified: 2×2×2 cells yield a 1.5 eV overestimate due to artificial vacancy–vacancy repulsion under periodic boundaries, resolved using 3×3×3cells. These findings establish a monovacancy-mediated diffusion mechanism with high entropy, resolving a decades-long discrepancy in TiC and related carbides

National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-374140 (URN)
Note

QC 20251217

Available from: 2025-12-15 Created: 2025-12-15 Last updated: 2025-12-22Bibliographically approved
4. Carbon trapping at the solid–liquid interface in cemented carbides
Open this publication in new window or tab >>Carbon trapping at the solid–liquid interface in cemented carbides
2026 (English)In: Computational materials science, ISSN 0927-0256, E-ISSN 1879-0801, Vol. 262, article id 114388Article in journal (Refereed) Published
Abstract [en]

Inter-diffusion between the hard ceramic and ductile metallic phases in composite materials such as cemented carbides governs their mechanical properties. Understanding atomic-scale diffusion at these interfaces is key to uncovering the mechanisms that dictate microstructure evolution, establishing a foundation for tailoring the properties of WC Co composites through precise interfacial control. The interface between tungsten carbide (WC) and liquid cobalt (Co) is investigated using molecular dynamics simulations. An integrated approach is presented for computing the solid–liquid interfacial free energy by combining computer vision aided interface detection with the Capillary fluctuation method. Significant inter-diffusion is observed, with atomic displacements primarily localized at the interface for W and C, while Co exhibits homogeneous behavior in the liquid phase. The formation of C C bonded structures at the interface is identified as a critical factor influencing diffusion, introducing localized structural rigidity that reduces atomic mobility. Additionally, premelting phenomena below bulk melting temperatures gives rise to a heterogeneous interfacial zone containing residual solid WC patches and molten W-Co alloy. The inter-diffusion coefficients for W, C, and Co compare well with prior computational and experimental studies, validating the methodology. These findings offer new insights into the atomic-scale mechanisms driving interface evolution and provide a foundation for tailoring the properties of WC Co composites through precise interfacial control.

Place, publisher, year, edition, pages
Elsevier BV, 2026
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-373823 (URN)10.1016/j.commatsci.2025.114388 (DOI)001630604900002 ()2-s2.0-105023512379 (Scopus ID)
Funder
Swedish Research Council, 2022-06725Swedish Research Council, 2018-05973Vinnova, 2016- 00668KTH Royal Institute of Technology
Note

QC 20251215

Available from: 2025-12-10 Created: 2025-12-10 Last updated: 2025-12-22Bibliographically approved
5. Premelting in dissolution of cemented carbides
Open this publication in new window or tab >>Premelting in dissolution of cemented carbides
2025 (English)In: Physical Review Materials, E-ISSN 2475-9953, Vol. 9, no 10, article id 103404Article in journal (Refereed) Published
Abstract [en]

The dissolution behavior of tungsten carbide (WC) particles in liquid cobalt is investigated using ab initio and classical molecular-dynamics calculations. It turns out that at the atomic level there is a complex interplay between surface properties, bulk diffusion, and dissolution. It is found that carbon-rich shells form around dissolving WC particles, creating a semidissolved state. The dissolution process is decelerated by trapping carbon atoms via the formation of carbon-carbon bonds, both on the surface of dissolving particles and in the surrounding semidissolved shell. Upon reaching a critical particle radius, the dissolution rate sharply increases, driven by changes in the number of carbon-carbon bonds, resulting in a premelting behavior. The existence of a semidissolved shell and premelting behavior advance our understanding of dissolution mechanisms at the atomic scale and can be applicable for controlling dissolution processes that are an important part of coarsening of WC particles, a phenomenon taking place during cemented carbide manufacturing.

 

Place, publisher, year, edition, pages
American Physical Society (APS), 2025
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-373824 (URN)10.1103/35tp-fss7 (DOI)001613264900003 ()2-s2.0-105022974917 (Scopus ID)
Funder
Vinnova, 2016-00668KTH Royal Institute of TechnologySwedish Research Council, 2022-06725Swedish Research Council, 2018-05973
Note

QC 20251215

Available from: 2025-12-10 Created: 2025-12-10 Last updated: 2025-12-22Bibliographically approved
6. C–C bonding in metal vacancies in WC
Open this publication in new window or tab >>C–C bonding in metal vacancies in WC
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Focusing on the reconstruction of metal (W) and carbon (C) vacancies, we systematically analyze their impact on diffusion processes critical to microstructural evolution in WC-Co cemented carbides. We investigate the role of vacancy-mediated diffusion in hexagonal tungsten carbide (WC) using a combination of ab initio molecular dynamics (AIMD) and classical molecular dynamics (MD )simulations. AIMD simulations reveal spontaneous formation of C–C bonds within W vacancies, forming dimers, trimers, and tetramers with bond lengths of 1.4 ˚A to 1.9 ˚A, which stabilize defect structures and hinder carbon diffusion. Classical MD simulations, employing an analytical bond-order potential, demonstrate a nonlinear reduction in carbon diffusion coefficients by up to 40% at moderate W vacancy concentrations (up to 0.06%) and temperatures below 2800 K, following a power-law dependence D ∝ N −αv (α ≈ 0.6). In contrast, C vacancies exhibit minimal C–C bonding and diffusion coefficients close to defect free WC. At higher temperatures (≥ 2800 K) and vacancy counts (≥ 2500), thermal energy disrupts C–C bonds, leading to enhanced, Arrhenius diffusion. These findings shed light on the atomic-scale mechanisms governing diffusion in WC, offering insights into optimizing sintering processes and mechanical properties of cemented carbides.

National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-374141 (URN)
Note

QC 20251217

Available from: 2025-12-15 Created: 2025-12-15 Last updated: 2025-12-22Bibliographically approved

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