4.7 Article

Effects of notches on the deformation behavior of submicron sized metallic glasses: Insights from in situ experiments

Journal

ACTA MATERIALIA
Volume 154, Issue -, Pages 172-181

Publisher

PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.actamat.2018.05.041

Keywords

Metallic glass; Notch sensitivity; Strength; Ductility; Nano mechanical test; In situ TEM

Funding

  1. Carnegie Mellon University
  2. Natural Science Foundation of China [51501144]
  3. China Postdoctoral Science Foundation [2015M580842]
  4. Alexander von Humboldt foundation

Ask authors/readers for more resources

Reducing the size of metallic glasses (MG) to submicron or nanoscale levels improves their strength and ductility. However, there is no clear consensus in the literature regarding their mechanical behavior in the presence of a flaw or notch. In this work, quantitative tensile tests on notched submicron sized CuZr MG specimens were conducted inside a transmission electron microscope to study their deformation characteristics. Strength was found to be notch insensitive for shallow notched thick specimens, although reducing specimen dimensions and increasing notch sharpness enhances it by 14%. It was reasoned that the severity with which shear bands are geometrically constrained determines the strength and fracture morphology of notched specimens. Softening, accompanied with a transition to necking failure, occurs when the width of ligament that connects the notches is smaller than 80 nm. The competition between shear band propagation and plastic zone growth-mediated homogeneous activation of shear transformation zones was found to be responsible for this brittle to ductile transition. Current results provide unique insights into the various design aspects to be considered for reliable engineering of small scale components. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.7
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

Article Materials Science, Multidisciplinary

Oxidation assisted recrystallization and cracking at grain boundaries in Nimonic 80 A during elevated temperature service

Wang Chao, Lou Yuming, Wang Xu, Peng Yichao, Huang Yijun, Bao Ting, Li Jixue, R. Lakshmi Narayan

Summary: The oxidation and cracking at the grain boundary of wrought Nimonic 80 A alloy under high temperature and load conditions are studied. It is found that the grain boundary forms cracks and transforms into a hierarchical structure, with a nanoscale recrystallized nickel layer in the center and ambilateral NiCr2O4/NiCrO3 layers on both sides. The recrystallized nickel layer oxidizes, and its formation is influenced by the oxidation of Cr and externally applied stress.

CORROSION SCIENCE (2022)

Article Metallurgy & Metallurgical Engineering

A Critical Appraisal of the Role of Oxygen in Phase Evolution and Mechanical Properties of Additively Manufactured Bulk Metallic Glasses

K. S. N. Satish Idury, R. Lakshmi Narayan

Summary: Additive manufacturing techniques have the potential to produce large-size bulk metallic glass components, but the presence of oxygen during fabrication can affect their glass forming ability and mechanical properties. This review explores the issue of oxygen pick-up in BMGs during AM fabrication and discusses its impact on crystal nuclei formation, glass forming ability, and mechanical properties.

TRANSACTIONS OF THE INDIAN INSTITUTE OF METALS (2023)

Article Chemistry, Physical

Enhanced plasticity in laser additive manufactured Nb-reinforced bulk metallic glass composite

Weihua Hu, Zejiang Yu, Yunzhuo Lu, Juntao Huo, Zuoxiang Qin, Xing Lu, R. Lakshmi Narayan

Summary: This study investigates the microstructures and mechanical properties of 50 wt% Nb-reinforced Zr-based bulk metallic glass composites (BMGCs) manufactured via laser directed energy deposition (LDED) with two different laser powers, and compares them with those of LDED manufactured monolithic bulk metallic glass (BMG). The results show that both BMGCs have a multi-component microstructure, while the monolithic BMG contains only one component. The nanocrystals at the melt-pool boundaries embrittle the monolithic BMG, resulting in higher yield strength but negligible plastic deformation. In contrast, both BMGCs exhibit significant plastic deformation due to the reinforcement of Nb, which improves plasticity and reduces the volume fraction of nanocrystallites at the melt-pool boundaries. The BMGC manufactured at higher laser power exhibits higher shear band plasticity, despite having higher volume fraction of nanocrystallites and lower enthalpy of relaxation. The load transfer characteristics of the Nb-BMG matrix interfaces in the two BMGCs are analyzed and rationalized.

JOURNAL OF ALLOYS AND COMPOUNDS (2022)

Article Materials Science, Multidisciplinary

Effects of Al addition and cryogenic cyclic treatment on impact toughness of phase-transformable Ti-based bulk metallic glass composites

Tingyi Yan, Long Zhang, R. Lakshmi Narayan, Jingyu Pang, Yi Wu, Huameng Fu, Hong Li, Upadrasta Ramamurty, Haifeng Zhang

Summary: This study investigates the influence of different microstructures and cryogenic cyclic treatment (CCT) on the impact toughness of bulk metallic glass composites (BMGCs). It is found that at 298 K, the intrinsic toughness of the glass matrix and deformation-induced martensitic transformation (DIMT) are the key mechanisms, while at 77 K, the toughness is primarily determined by the glass matrix itself. The addition of Al affects the phase stability and impact toughness of BMGCs at 298 K, but it causes embrittlement at 77 K. CCT can rejuvenate the BMGCs and enhance the impact toughness at 298 K, but it decreases the toughness at 77 K with increasing CCT cycles.

JOURNAL OF MATERIALS SCIENCE & TECHNOLOGY (2023)

Article Metallurgy & Metallurgical Engineering

Investigation of Crystallographic Orientation and Mechanical Behaviour in Laser-Welded Stainless Steel 316L Additive Components

S. Pradeep Kumar, V Chakkravarthy, A. Mahalingam, R. Rajeshshyam, N. Sriraman, P. Marimuthu, R. Lakshmi Narayan, P. Dinesh Babu

Summary: The main limitation of selective laser melting (SLM)-based additive manufacturing is the smaller build size and the lack of standard rework techniques. This study explores the weldability of SLM-built stainless steel samples and evaluates the quality of the weld. The results show that laser-welded SLM samples exhibit superior tensile strength and hardness, providing a novel solution for reworking defective SLM components.

TRANSACTIONS OF THE INDIAN INSTITUTE OF METALS (2023)

Article Nanoscience & Nanotechnology

Microstructure-property correlations in as-built and heat-treated compositionally graded stainless steel 316L-Inconel 718 alloy fabricated by laser powder bed fusion

Yaojie Wen, Jianbao Gao, Ramasubramanian Lakshmi Narayan, Pei Wang, Lijun Zhang, Baicheng Zhang, Upadrasta Ramamurty, Xuanhui Qu

Summary: The microstructures and mechanical properties of a laser powder bed fusion manufactured compositionally graded alloy of SS316L and Inconel 718 were studied. Heat treatment caused changes in the microstructure and mechanical properties of the alloy, including coarsening of Laves phases and precipitation of gamma and gamma' phases. The alloy exhibited increased hardness, yield strength, and tensile strength but decreased ductility after heat treatment.

MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING (2023)

Article Multidisciplinary Sciences

Microfluidic study of retention and elimination of abnormal red blood cells by human spleen with implications for sickle cell disease

Yuhao Qiang, Abdoulaye Sissoko, Zixiang L. Liu, Ting Dong, Fuyin Zheng, Fang Kong, John M. Higgins, George E. Karniadakis, Pierre A. Buffet, Subra Suresh, Ming Dao

Summary: This article introduces the clearance of altered red blood cells by the spleen and the mechanisms underlying these processes. By studying sickle cell disease, it is found that the retention and adhesion of red blood cells are faster in blood samples from patients with sickle cell disease compared to healthy individuals. Additionally, under hypoxic conditions, the phagocytosis process of sickled red blood cells is different from non-sickled red blood cells. It is also observed that reoxygenation significantly alleviates RBC retention and leads to rapid unsickling of ingested sickled red blood cells. These findings provide insights into the maintenance of homeostatic balance in the spleen and the potential clinical manifestations in hematologic diseases.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2023)

Article Chemistry, Multidisciplinary

In Situ Study of Twin Boundary Stability in Nanotwinned Copper Pillars under Different Strain Rates

Shou-Yi Chang, Yi-Chung Huang, Shao-Yi Lin, Chia-Ling Lu, Chih Chen, Ming Dao

Summary: The nanoscopic deformation of < 111 > nanotwinned copper nanopillars under different strain rates was investigated using in situ transmission electron microscopy. The study found that the deformation mechanism, including dislocation activity and twin boundary migration, is influenced by strain rates. At higher strain rates, dislocations accumulate in the nanotwinned copper, resulting in significant hardening. At lower strain rates, detwinning occurs and the hardening is reduced. Different deformation mechanisms, such as dislocation activity and twin boundary migration via atom motion, are proposed based on the experimental results.

NANOMATERIALS (2023)

Article Engineering, Mechanical

Modeling of magnetic cilia carpet robots using discrete differential geometry formulation

Weicheng Huang, Mingchao Liu, K. Jimmy Hsia

Summary: A numerical framework based on discrete differential geometry (DDG) is used to analyze the dynamics of bio-inspired cilia carpet robots powered by an external magnetic field. The model accurately captures the behavior of the active cilia and the carpet, and provides insights for the optimal design of cilia-inspired soft robots for biomedical applications. The framework is computationally efficient and can simulate dynamic locomotion such as crawling and rolling. (c) 2023 Elsevier Ltd. All rights reserved.

EXTREME MECHANICS LETTERS (2023)

Article Biophysics

In silico and in vitro study of the adhesion dynamics

Guansheng Li, Yuhao Qiang, He Li, Xuejin Li, Ming Dao, George Em Karniadakis

Summary: Erythrophagocytosis is a critical process in the spleen for removing senescent and diseased red blood cells from circulation. However, the biophysical interaction between red blood cells and macrophages in pathological conditions like sickle cell disease has not been well studied. This study combines computational simulations and microfluidic experiments to investigate the adhesion dynamics between red blood cells and macrophages under flow conditions similar to those in the spleen.

BIOPHYSICAL JOURNAL (2023)

Article Multidisciplinary Sciences

Safe drugs with high potential to block malaria transmission revealed by a spleen-mimetic screening

Mario Carucci, Julien Duez, Joel Tarning, Irene Garcia-Barbazan, Aurelie Fricot-Monsinjon, Abdoulaye Sissoko, Lucie Dumas, Pablo Gamallo, Babette Beher, Pascal Amireault, Michael Dussiot, Ming Dao, Mitchell V. Hull, Case W. McNamara, Camille Roussel, Papa Alioune Ndour, Laura Maria Sanz, Francisco Javier Gamo, Pierre Buffet

Summary: Malaria parasites multiply in red blood cells, but can be eliminated when the cells become stiff. Through screening, two safe drugs were found that can block the transmission of malaria.

NATURE COMMUNICATIONS (2023)

Article Multidisciplinary Sciences

Evolution of surface area and membrane shear modulus of matured human red blood cells during mechanical fatigue

Qiaodong Wei, Xiaolong Wang, Ce Zhang, Ming Dao, Xiaobo Gong

Summary: In this study, we investigated the morphological changes and mechanical behavior of red blood cells (RBCs) during aging using an in vitro mechanical fatigue model. We identified three typical shape transformations of RBCs during mechanical fatigue, which are strongly associated with the loss of surface area. Mathematical models were constructed to describe the evolution of surface area and membrane shear modulus, and an ensemble parameter was developed to quantitatively evaluate the aging status of RBCs. This study provides a novel in vitro fatigue model for studying the mechanical behavior of RBCs and a quantitative index for differentiating individual RBCs based on their age and physical properties.

SCIENTIFIC REPORTS (2023)

Article Chemistry, Multidisciplinary

Modeling Fretting Wear Resistance and Shakedown of Metallic Materials with Graded Nanostructured Surfaces

Ting Yang, T. A. Venkatesh, Ming Dao

Summary: In this study, the mechanical responses of materials with graded nanostructured surfaces during fretting sliding are compared to homogeneous materials. The results show that metallic materials with a graded nanostructured surface exhibit superior fretting damage resistance by reducing the plastically deformed surface areas and volumes by more than 80%. By decreasing the friction coefficient, optimal fretting resistance can be achieved in the graded nanostructured material.

NANOMATERIALS (2023)

Article Engineering, Mechanical

A discrete model for the geometrically nonlinear mechanics of hard-magnetic slender structures

Weicheng Huang, Mingchao Liu, K. Jimmy Hsia

Summary: Hard-magnetic soft materials and structures have attracted wide attention in various engineering applications due to their rapid configurational transformation under non-contact magnetic stimuli. Predicting their mechanical responses is crucial for realizing their full potentials. In this work, we propose a discrete magneto-elastic rod model to analyze the mechanical behaviors of slender structures made of HMS materials. The model considers the dipole-dipole interaction and viscous effect and significantly improves the computational efficiency for simulating the mechanical, especially dynamic, behaviors of hard-magnetic slender structures.

EXTREME MECHANICS LETTERS (2023)

Article Materials Science, Multidisciplinary

A statistical analysis of the second 'pop-in' behaviour of the spherical-tip nanoindentation of Zr-based bulk metallic glasses

Priyanka Saini, Shankha Nag, Jae-il Jang, In-Chul Choi, Upadrasta Ramamurty, R. L. Narayan

Summary: Statistical analysis is often conducted to understand the micromechanisms of plasticity by analyzing the shear stresses at which the first 'pop-ins' occur during nano-indentation. This study focuses on the second 'pop-in' stress and finds that the 3-parameter Weibull distribution is the best descriptor for its stochasticity. The study also provides insight into the development of plasticity in bulk metallic glasses during nano-indentation.

MATERIALIA (2023)

Article Materials Science, Multidisciplinary

Transmission electron microscopy of the rapid solidification microstructure evolution and solidification interface velocity determination in hypereutectic Al-20at.%Cu after laser melting

Y. Liu, K. Zweiacker, C. Liu, J. T. McKeown, J. M. K. Wiezorek

Summary: The evolution of rapid solidification microstructure and solidification interface velocity of hypereutectic Al-20at.%Cu alloy after laser melting has been studied experimentally. It was found that the formation of microstructure was dominated by eutectic, alpha-cell, and banded morphology grains, and the growth modes changed with increasing interface velocity.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

Mechanisms for high creep resistance in alumina forming austenitic (AFA) alloys

Bharat Gwalani, Julian Escobar, Miao Song, Jonova Thomas, Joshua Silverstein, Andrew Chihpin Chuang, Dileep Singh, Michael P. Brady, Yukinori Yamamoto, Thomas R. Watkins, Arun Devaraj

Summary: Castable alumina forming austenitic alloys exhibit superior creep life and oxidation resistance at high temperatures. This study reveals the mechanism behind the enhanced creep performance of these alloys by suppressing primary carbide formation and offers a promising alloy design strategy for high-temperature applications.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

Achieving atomically flat copper surface: Formation of mono-atomic steps and associated strain energy mechanisms

Jian Song, Qi Zhang, Songsong Yao, Kunming Yang, Houyu Ma, Jiamiao Ni, Boan Zhong, Yue Liu, Jian Wang, Tongxiang Fan

Summary: Recent studies have shown that achieving an atomically flat surface for metals can greatly improve their oxidation resistance and enhance their electronic-optical applications. Researchers have explored the use of graphene as a covering layer to achieve atomically flat surfaces. They found that high-temperature deposited graphene on copper surfaces formed mono-atomic steps, while annealed copper and transferred graphene on copper interfaces formed multi-atomic steps.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

Modeling and measurements of creep deformation in laser-melted Al-Ti-Zr alloys with bimodal grain size

Jennifer A. Glerum, Jon-Erik Mogonye, David C. Dunand

Summary: Elemental powders of Al, Ti, Sc, and Zr are blended and processed via laser powder-bed fusion to create binary and ternary alloys. The microstructural analysis and mechanical testing show that the addition of Ti results in the formation of primary precipitates, while the addition of Sc and Zr leads to the formation of fine grain bands. The Al-0.25Ti-0.25Zr alloy exhibits comparable strain rates to Al-0.5Zr at low stresses, but significantly higher strain rates at higher stresses during compressive creep testing. Finite element modeling suggests that the connectivity of coarse and fine grain regions is a critical factor affecting the creep resistance of the alloys.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

Characterizing stable nanocrystalline Cu-Ta behavior and failure dynamics under extremes of strain rate, strain, temperature and pressure by modified dynamic tensile extrusion

P. Jannotti, B. C. Hornbuckle, J. T. Lloyd, N. Lorenzo, M. Aniska, T. L. Luckenbaugh, A. J. Roberts, A. Giri, K. A. Darling

Summary: This work characterizes the thermo-mechanical behavior of bulk nanocrystalline Cu-Ta alloys under extreme conditions. The experiments reveal that the alloys exhibit unique mechanical properties, behaving differently from conventional nanocrystalline Cu. They do not undergo grain coarsening during extrusion and exhibit behavior similar to coarse-grained Cu.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

Phase-dependent microstructure modification leads to high thermoelectric performance in n-type layered SnSe2

Yiqing Wei, Jingwei Li, Daliang Zhang, Bin Zhang, Zizhen Zhou, Guang Han, Guoyu Wang, Carmelo Prestipino, Pierric Lemoine, Emmanuel Guilmeau, Xu Lu, Xiaoyuan Zhou

Summary: This study proposes a new strategy to modify microstructure by phase regulation, which can simultaneously enhance carrier mobility and reduce lattice thermal conductivity. The addition of Cu in layered SnSe2 induces a phase transition that leads to increased grain size and reduced stacking fault density, resulting in improved carrier mobility and lower lattice thermal conductivity.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

Selective oxidation and nickel enrichment hinders the repassivation kinetics of multi-principal element alloy surfaces

Jia Chen, Zhengyu Zhang, Eitan Hershkovitz, Jonathan Poplawsky, Raja Shekar Bhupal Dandu, Chang-Yu Hung, Wenbo Wang, Yi Yao, Lin Li, Hongliang Xin, Honggyu Kim, Wenjun Cai

Summary: In this study, the structural origin of the pH-dependent repassivation mechanisms in multi-principal element alloys (MPEA) was investigated using surface characterization and computational simulations. It was found that selective oxidation in acidic to neutral solutions leads to enhanced nickel enrichment on the surface, resulting in reduced repassivation capability and corrosion resistance.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

Rate-dependent transition of dislocation mechanisms in a magnesium alloy

X. Y. Xu, C. P. Huang, H. Y. Wang, Y. Z. Li, M. X. Huang

Summary: The limited slip systems of magnesium (Mg) and its alloys hinder their wide applications. By conducting tensile straining experiments, researchers discovered a rate-dependent transition in the dislocation mechanisms of Mg alloys. At high strain rates, glissile dislocations dominate, while easy-glide dislocations dominate at low strain rates. Abundant glissile dislocations do not necessarily improve ductility.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

The effect of temperature on detwinning and mechanical properties of face-centered cubic deformation twins

M. S. Szczerba, M. J. Szczerba

Summary: Inverse temperature dependences of the detwinning stress were observed in face-centered cubic deformation twins in Cu-8at.%Al alloy. The detwinning stress increased with temperature when the pi detwinning mode was involved, but decreased when the pi/3 mode was involved. The dual effect of temperature on the detwinning stress was due to the reduction of internal stresses pre-existing within the deformation twins. The complete reduction of internal stresses at about 530 degrees C led to the equivalence of the critical stresses of different detwinning modes and a decrease in the yield stress anisotropy of the twin/matrix structure.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

Nature of the electric double layer to modulate the electrochemical behaviors of Fe2O3 electrode

Taowen Dong, Tingting Qin, Wei Zhang, Yaowen Zhang, Zhuoran Feng, Yuxiang Gao, Zhongyu Pan, Zixiang Xia, Yan Wang, Chunming Yang, Peng Wang, Weitao Zheng

Summary: The interaction between the electrode and the electric double layer (EDL) significantly influences the energy storage mechanism. By studying the popular alpha-Fe2O3 electrode and the EDL interaction, we find that the energy storage mechanism of the electrode can be controlled by modulating the EDL.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

Grain scale bursts of plasticity in Mg-4Zn via high energy X-rays: Towards twin observation in real-time

Matthew R. Barnett, Jun Wang, Sitarama R. Kada, Alban de Vaucorbeil, Andrew Stevenson, Marc Fivel, Peter A. Lynch

Summary: The elastic-plastic transition in magnesium alloy Mg-4.5Zn exhibits bursts of deformation, which are characterized by sudden changes in grain orientation. These bursts occur in a coordinated manner among nearby grains, with the highest burst rate observed at the onset of full plasticity. The most significant burst events are associated with twinning, supported by the observation of twinned structures using electron microscopy. The bursts are often preceded and followed by a stasis in peak movement, indicating a certain "birth size" for twins upon formation and subsequent growth at a later stage.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

Atomistic simulations and machine learning of solute grain boundary segregation in Mg alloys at finite temperatures

Vaidehi Menon, Sambit Das, Vikram Gavini, Liang Qi

Summary: Understanding solute segregation thermodynamics is crucial for investigating grain boundary properties. The spectral approach and thermodynamic integration methods can be used to predict solute segregation behavior at grain boundaries and compare with experimental observations, thus aiding in alloy design and performance control.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

Integrating abnormal thermal expansion and ultralow thermal conductivity into (Cd,Ni)2Re2O7 via synergy of local structure distortion and soft acoustic phonons

Feiyu Qin, Lei Hu, Yingcai Zhu, Yuki Sakai, Shogo Kawaguchi, Akihiko Machida, Tetsu Watanuki, Yue-Wen Fang, Jun Sun, Xiangdong Ding, Masaki Azuma

Summary: This study reports on the negative and zero thermal expansion properties of Cd2Re2O7 and Cd1.95Ni0.05Re2O7 materials, along with their ultra-low thermal conductivity. Through investigations of their structures and phonon calculations, the synergistic effect of local structure distortion and soft phonons is revealed as the key to achieving these distinctive properties.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

Semi-automatic miniature specimen testing method to characterize the plasticity and fracture properties of metals

Thomas Beerli, Christian C. Roth, Dirk Mohr

Summary: A novel testing system for miniature specimens is designed to characterize the plastic response of materials for which conventional full-size specimens cannot be extracted. The system has an automated operation process, which reduces the damage to specimens caused by manual handling and improves the stability of the test results. The experiments show that the miniature specimens extracted from stainless steel and aluminum have high reproducibility, and the results are consistent with those of conventional-sized specimens. A correction procedure is provided to consider the influence of surface roughness and heat-affected zone caused by wire EDM.

ACTA MATERIALIA (2024)

Article Materials Science, Multidisciplinary

The effect of microstructure and film composition on the mechanical properties of linear antenna CVD diamond thin films

Rani Mary Joy, Paulius Pobedinskas, Nina Baule, Shengyuan Bai, Daen Jannis, Nicolas Gauquelin, Marie-Amandine Pinault-Thaury, Francois Jomard, Kamatchi Jothiramalingam Sankaran, Rozita Rouzbahani, Fernando Lloret, Derese Desta, Jan D'Haen, Johan Verbeeck, Michael Frank Becker, Ken Haenen

Summary: This study investigates the influence of film microstructure and composition on the Young's modulus and residual stress in nanocrystalline diamond thin films. The results provide insights into the mechanical properties and intrinsic stress sources of these films, and demonstrate the potential for producing high-quality nanocrystalline diamond films under certain conditions.

ACTA MATERIALIA (2024)