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Crystal Dislocations: Their Impact on Physical Properties of Crystals

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A special issue of Crystals (ISSN 2073-4352). This special issue belongs to the section "Inorganic Crystalline Materials".

Deadline for manuscript submissions: closed (31 January 2018) | Viewed by 89827

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Prof. Dr. Peter Lagerlof

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Department of Materials Science and Engineering, Case Western Reserve University, Cleveland, OH, USA
Interests: slip and twinning in ceramics and metals; X-ray diffraction; electron microscopy; microstructural development; mechanical properties
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Dear Colleagues,

The proposed existance of the edge and screw dislcoation, in the 1930s, and the subsequent work showing that dislocation theory could explain the plastic deformation of crystals, represent an important step in developing our understanding of materials into a science. The continued work involved with characterization of dislocations, and linking them to a variety of physical properties, in both single and poly crystals, have made enormous progress over the past 50 years. It is rare to find a technical application involving a material with any crystal structure that is not impacted by dislocations; mechanical properties, massive phase transformations, interphases, crystal growth, electronic properties, and the list goes on. In many systems, the properties are controlled by the formation of partial dislocations separated by a stacking fault; for example, plastic deformation via deformation twinning. Finally, giant strides have been made in characterization and modeling of systems containing dislcocations.

The Special Issue on Crystal Dislocations is intended to provide a unique international forum aimed at covering a broad range of results involving dislocations and their importance in crystal properties and crystal growth. Scientists working in a wide range of disciplines are invited to contribute to this cause.

The list of key words shown below cover only a limited range of areas in which dislocations play an intrical part; this Special Issue of Crystals is open for any innovative contributions involving dislocations.

Prof. Dr. K. Peter D. Lagerlof
Guest Editor

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Crystals is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Crystal dislocations
Partial dislocations
Crystal defect structures and properties
Deformation twinning
Massive phase transformations
Characterization of dislocations
Crystal growth

Related Special Issue

Crystal Dislocations: Their Impact on Physical Properties of Crystals II in Crystals (2 articles)

Published Papers (15 papers)

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Editorial

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3 pages, 172 KiB

Open AccessEditorial

Crystal Dislocations: Their Impact on Physical Properties of Crystals

by Peter Lagerlof

Crystals 2018, 8(11), 413; https://doi.org/10.3390/cryst8110413 - 03 Nov 2018

Cited by 4 | Viewed by 2980

Abstract

It is rare to find technical applications involving a material of any crystal structure that is not impacted by dislocations—which affect the material’s mechanical properties, interfaces, martensitic phase transformations, crystal growth, and electronic properties, to name a few. [...] Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

Research

Jump to: Editorial, Review

10 pages, 2828 KiB

Open AccessArticle

Structure of the Basal Edge Dislocation in ZnO

by Atsutomo Nakamura, Eita Tochigi, Ryota Nagahara, Yuho Furushima, Yu Oshima, Yuichi Ikuhara, Tatsuya Yokoi and Katsuyuki Matsunaga

Crystals 2018, 8(3), 127; https://doi.org/10.3390/cryst8030127 - 08 Mar 2018

Cited by 5 | Viewed by 6224

Abstract

Basal dislocations having a Burgers vector of 1/3<2

\bar{1}

\bar{1}

0> in zinc oxide (ZnO) with the wurtzite structure are known to strongly affect physical properties in bulk. However, the core structure of the basal dislocation remains unclear. In the present [...] Read more.

Basal dislocations having a Burgers vector of 1/3<2

\bar{1}

\bar{1}

\bar{1}

\bar{1}

0}/<01

\bar{1}

0> 2° low-angle tilt grain boundary were fabricated by diffusion bonding. The resultant dislocation core structure was observed by using scanning transmission electron microscopy (STEM) at an atomic resolution. It was found that a basal edge dislocation in α-type is dissociated into two partial dislocations on the (0001) plane with a separation distance of 1.5 nm, indicating the glide dissociation. The Burgers vectors of the two partial dislocations were 1/3<1

\bar{1}

00> and 1/3<10

\bar{1}

0>, and the stacking fault between the two partials on the (0001) plane has a formation energy of 0.14 J/m². Although the bicrystals have a boundary plane of {2

\bar{1}

\bar{1}

0}, the boundary basal dislocations do not exhibit dissociation along the boundary plane, but along the (0001) plane perpendicular to the boundary plane. From DFT calculations, the stacking fault on the (0001) plane was found to be much more stable than that on {2

\bar{1}

\bar{1}

0}. Such an extremely low energy of the (0001) stacking fault can realize transverse dissociation of the basal dislocation of ZnO. Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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11 pages, 10354 KiB

Open AccessArticle

Anisotropic Deformation in the Compressions of Single Crystalline Copper Nanoparticles

by Jianjun Bian, Hao Zhang, Xinrui Niu and Gangfeng Wang

Crystals 2018, 8(3), 116; https://doi.org/10.3390/cryst8030116 - 01 Mar 2018

Cited by 9 | Viewed by 4168

Abstract

Atomistic simulations are performed to probe the anisotropic deformation in the compressions of face-centred-cubic metallic nanoparticles. In the elastic regime, the compressive load-depth behaviors can be characterized by the classical Hertzian model or flat punch model, depending on the surface configuration beneath indenter. On the onset of plasticity, atomic-scale surface steps serve as the source of heterogeneous dislocation in nanoparticle, which is distinct from indenting bulk materials. Under [111] compression, the gliding of jogged dislocation takes over the dominant plastic deformation. The plasticity is governed by nucleation and exhaustion of extended dislocation ribbons in [110] compression. Twin boundary migration mainly sustain the plastic deformation under [112] compression. This study is helpful to extract the mechanical properties of metallic nanoparticles and understand their anisotropic deformation behaviors. Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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11 pages, 419 KiB

Open AccessArticle

Interface Effects on Screw Dislocations in Heterostructures

by Jianwei Wang, Ting Sun, Weiwei Xu, Xiaozhi Wu and Rui Wang

Crystals 2018, 8(1), 28; https://doi.org/10.3390/cryst8010028 - 10 Jan 2018

Cited by 15 | Viewed by 3496

Abstract

The governing equation of screw dislocations in heterostructures is constructed using image method. The interface type (

- 1 \leq γ \leq 1

) and distance between dislocation and interface h are considered in the new equation. The Peierls–Nabarro equations for screw dislocations [...] Read more.

The governing equation of screw dislocations in heterostructures is constructed using image method. The interface type (

- 1 \leq γ \leq 1

) and distance between dislocation and interface h are considered in the new equation. The Peierls–Nabarro equations for screw dislocations in bulk and semi-infinite materials can be recovered when

γ = 0

and

γ = - 1

. The soft (

γ < 0

) and hard (

γ > 0

) interfaces can enhance and reduce the Peierls stress of screw dislocations near the interface, respectively. The interface effects on dislocations decrease with the increasing of distance h. The Al/TiC heterostructure is investigated as a model interface to study the unstable stacking fault energy and dislocation properties of the interface. The mismatch of lattice constants and shear modulus at the interface results in changes of the unstable stacking fault energy. Then, the changes of the unstable stacking fault energy also have an important effect on dislocation properties, comparing with

γ

and h. Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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5391 KiB

Open AccessArticle

Stable Stacking Faults Bounded by Frank Partial Dislocations in Al7075 Formed through Precipitate and Dislocation Interactions

by Sijie Li, Hongyun Luo, Hui Wang, Pingwei Xu, Jun Luo, Chu Liu and Tao Zhang

Crystals 2017, 7(12), 375; https://doi.org/10.3390/cryst7120375 - 13 Dec 2017

Cited by 6 | Viewed by 8940

Abstract

Through high-resolution electron microscopy, stacking faults (SFs) due to Frank partial dislocations were found in an aluminum alloy following deformation with low strain and strain rate, while also remaining stable during artificial aging. Extrinsic stacking faults were found surrounded by dislocation areas and precipitates. An intrinsic stacking fault was found between two Guinier-Preston II (GP II) zones when the distance of the two GP II zones was 2 nm. Defects (precipitates and dislocations) are considered to have an influence on the formation of the SFs, as their appearance may cause local strain and promote the gathering of vacancies to lower the energy. Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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2227 KiB

Open AccessArticle

Study of Anisotropic Plastic Behavior in High Pressure Torsion of Aluminum Single Crystal by Crystal Plasticity Finite Element Method

by Peitang Wei, Cheng Lu, Huaiju Liu, Lihong Su, Guanyu Deng and Kiet Tieu

Crystals 2017, 7(12), 362; https://doi.org/10.3390/cryst7120362 - 06 Dec 2017

Cited by 7 | Viewed by 4290

Abstract

In this study, a crystal plasticity finite element method (CPFEM) model has been developed to investigate the anisotropic plastic behavior of (001) aluminum single crystal during high-pressure torsion (HPT). The distributions of equivalent plastic strain and Mises stress recorded on the sample surface are presented. The directional variations of plastic strain and Mises stress with the development of four-fold symmetry pattern are observed along the sample circumference. The crystallographic orientation evolution along the tangential direction is studied, and the corresponding lattice rotation and slip trace are predicted, respectively. The plastic anisotropy mechanism is discussed in detail based on the theory of crystal plasticity. The simulation results reveal that the differences in slip systems activation (dominant slip and multiple slips) are responsible for the anisotropic plastic deformation in HPT. Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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3943 KiB

Open AccessArticle

Room-Temperature Plastic Deformation of Strontium Titanate Crystals Grown from Different Chemical Compositions

by Atsutomo Nakamura, Kensuke Yasufuku, Yuho Furushima, Kazuaki Toyoura, K. Peter D. Lagerlöf and Katsuyuki Matsunaga

Crystals 2017, 7(11), 351; https://doi.org/10.3390/cryst7110351 - 22 Nov 2017

Cited by 14 | Viewed by 4554

Abstract

Oxide materials have the potential to exhibit superior mechanical properties in terms of high yield point, high melting point, and high chemical stability. Despite this, they are not widely used as a structural material due to their brittle nature. However, this study shows enhanced room-temperature plasticity of strontium titanate (SrTiO₃) crystals through the control of the chemical composition. It is shown that the deformation behavior of SrTiO₃ crystals at room temperature depends on the Sr/Ti ratio. It was found that flow stresses in deforming SrTiO₃ crystals grown from a powder with the particular ratio of Sr/Ti = 1.04 are almost independent of the strain rate because of the high mobility of dislocations in such crystals. As a result, the SrTiO₃ crystals can deform by dislocation slip up to a strain of more than 10%, even at a very high strain rate of 10% per second. It is thus demonstrated that SrTiO₃ crystals can exhibit excellent plasticity when chemical composition in the crystal is properly controlled. Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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3010 KiB

Open AccessArticle

Morphology Dependent Flow Stress in Nickel-Based Superalloys in the Multi-Scale Crystal Plasticity Framework

by Shahriyar Keshavarz, Zara Molaeinia, Andrew Reid and Stephen Langer

Crystals 2017, 7(11), 334; https://doi.org/10.3390/cryst7110334 - 02 Nov 2017

Cited by 5 | Viewed by 5041

Abstract

This paper develops a framework to obtain the flow stress of nickel-based superalloys as a function of γ-γ’ morphology. The yield strength is a major factor in the design of these alloys. This work provides additional effects of γ’ morphology in the design scope that has been adopted for the model developed by authors. In general, the two-phase γ-γ’ morphology in nickel-based superalloys can be divided into three variables including γ’ shape, γ’ volume fraction and γ’ size in the sub-grain microstructure. In order to obtain the flow stress, non-Schmid crystal plasticity constitutive models at two length scales are employed and bridged through a homogenized multi-scale framework. The multi-scale framework includes two sub-grain and homogenized grain scales. For the sub-grain scale, a size-dependent, dislocation-density-based finite element model (FEM) of the representative volume element (RVE) with explicit depiction of the γ-γ’ morphology is developed as a building block for the homogenization. For the next scale, an activation-energy-based crystal plasticity model is developed for the homogenized single crystal of Ni-based superalloys. The constitutive models address the thermo-mechanical behavior of nickel-based superalloys for a large temperature range and include orientation dependencies and tension-compression asymmetry. This homogenized model is used to obtain the morphology dependence on the flow stress in nickel-based superalloys and can significantly expedite crystal plasticity FE simulations in polycrystalline microstructures, as well as higher scale FE models in order to cast and design superalloys. Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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1827 KiB

Open AccessArticle

Phase Transformation and Hydrogen Storage Properties of an La_7.0Mg_75.5Ni_17.5 Hydrogen Storage Alloy

by Lin Hu, Rui-hua Nan, Jian-ping Li, Ling Gao and Yu-jing Wang

Crystals 2017, 7(10), 316; https://doi.org/10.3390/cryst7100316 - 18 Oct 2017

Cited by 5 | Viewed by 3872

Abstract

X-ray diffraction showed that an La_7.0Mg_75.5Ni_17.5 alloy prepared via inductive melting was composed of an La₂Mg₁₇ phase, an LaMg₂Ni phase, and an Mg₂Ni phase. After the first hydrogen absorption/desorption process, the phases of the alloy turned into an La–H phase, an Mg phase, and an Mg₂Ni phase. The enthalpy and entropy derived from the van’t Hoff equation for hydriding were −42.30 kJ·mol⁻¹ and −69.76 J·K⁻¹·mol⁻¹, respectively. The hydride formed in the absorption step was less stable than MgH₂ (−74.50 kJ·mol⁻¹ and −132.3 J·K⁻¹·mol⁻¹) and Mg₂NiH₄ (−64.50 kJ·mol⁻¹ and −123.1 J·K⁻¹·mol⁻¹). Differential thermal analysis showed that the initial hydrogen desorption temperature of its hydride was 531 K. Compared to Mg and Mg₂Ni, La_7.0Mg_75.5Ni_17.5 is a promising hydrogen storage material that demonstrates fast adsorption/desorption kinetics as a result of the formation of an La–H compound and the synergetic effect of multiphase. Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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Review

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16 pages, 4007 KiB

Open AccessReview

Dislocation-Free SiGe/Si Heterostructures

by Francesco Montalenti, Fabrizio Rovaris, Roberto Bergamaschini, Leo Miglio, Marco Salvalaglio, Giovanni Isella, Fabio Isa and Hans Von Känel

Crystals 2018, 8(6), 257; https://doi.org/10.3390/cryst8060257 - 19 Jun 2018

Cited by 21 | Viewed by 5565

Abstract

Ge vertical heterostructures grown on deeply-patterned Si(001) were first obtained in 2012 (C.V. Falub et al., Science2012, 335, 1330–1334), immediately capturing attention due to the appealing possibility of growing micron-sized Ge crystals largely free of thermal stress and hosting dislocations only in a small fraction of their volume. Since then, considerable progress has been made in terms of extending the technique to several other systems, and of developing further strategies to lower the dislocation density. In this review, we shall mainly focus on the latter aspect, discussing in detail 100% dislocation-free, micron-sized vertical heterostructures obtained by exploiting compositional grading in the epitaxial crystals. Furthermore, we shall also analyze the role played by the shape of the pre-patterned substrate in directly influencing the dislocation distribution. Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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77 pages, 25036 KiB

Open AccessReview

Influence of Dislocations in Transition Metal Oxides on Selected Physical and Chemical Properties

by Kristof Szot, Christian Rodenbücher, Gustav Bihlmayer, Wolfgang Speier, Ryo Ishikawa, Naoya Shibata and Yuichi Ikuhara

Crystals 2018, 8(6), 241; https://doi.org/10.3390/cryst8060241 - 04 Jun 2018

Cited by 53 | Viewed by 10145

Abstract

Studies on dislocations in prototypic binary and ternary oxides (here TiO₂ and SrTiO₃) using modern TEM and scanning probe microscopy (SPM) techniques, combined with classical etch pits methods, are reviewed. Our review focuses on the important role of dislocations in the insulator-to-metal transition and for redox processes, which can be preferentially induced along dislocations using chemical and electrical gradients. It is surprising that, independently of the growth techniques, the density of dislocations in the surface layers of both prototypical oxides is high (10⁹/cm² for epipolished surfaces and up to 10¹²/cm² for the rough surface). The TEM and locally-conducting atomic force microscopy (LCAFM) measurements show that the dislocations create a network with the character of a hierarchical tree. The distribution of the dislocations in the plane of the surface is, in principle, inhomogeneous, namely a strong tendency for the bundling and creation of arrays or bands in the crystallographic <100> and <110> directions can be observed. The analysis of the core of dislocations using scanning transmission electron microscopy (STEM) techniques (such as EDX with atomic resolution, electron-energy loss spectroscopy (EELS)) shows unequivocally that the core of dislocations possesses a different crystallographic structure, electronic structure and chemical composition relative to the matrix. Because the Burgers vector of dislocations is per se invariant, the network of dislocations (with additional d¹ electrons) causes an electrical short-circuit of the matrix. This behavior is confirmed by LCAFM measurements for the stoichiometric crystals, moreover a similar dominant role of dislocations in channeling of the current after thermal reduction of the crystals or during resistive switching can be observed. In our opinion, the easy transformation of the chemical composition of the surface layers of both model oxides should be associated with the high concentration of extended defects in this region. Another important insight for the analysis of the physical properties in real oxide crystals (matrix + dislocations) comes from the studies of the nucleation of dislocations via in situ STEM indentation, namely that the dislocations can be simply nucleated under mechanical stimulus and can be easily moved at room temperature. Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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53 pages, 6835 KiB

Open AccessReview

Dislocations and Plastic Deformation in MgO Crystals: A Review

by Jonathan Amodeo, Sébastien Merkel, Christophe Tromas, Philippe Carrez, Sandra Korte-Kerzel, Patrick Cordier and Jérôme Chevalier

Crystals 2018, 8(6), 240; https://doi.org/10.3390/cryst8060240 - 31 May 2018

Cited by 61 | Viewed by 10489

Abstract

This review paper focuses on dislocations and plastic deformation in magnesium oxide crystals. MgO is an archetype ionic ceramic with refractory properties which is of interest in several fields of applications such as ceramic materials fabrication, nano-scale engineering and Earth sciences. In its bulk single crystal shape, MgO can deform up to few percent plastic strain due to dislocation plasticity processes that strongly depend on external parameters such as pressure, temperature, strain rate, or crystal size. This review describes how a combined approach of macro-mechanical tests, multi-scale modeling, nano-mechanical tests, and high pressure experiments and simulations have progressively helped to improve our understanding of MgO mechanical behavior and elementary dislocation-based processes under stress. Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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31 pages, 13543 KiB

Open AccessReview

Peak Broadening Anisotropy and the Contrast Factor in Metal Alloys

by Thomas Hadfield Simm

Crystals 2018, 8(5), 212; https://doi.org/10.3390/cryst8050212 - 13 May 2018

Cited by 37 | Viewed by 6879

Abstract

Diffraction peak profile analysis (DPPA) is a valuable method to understand the microstructure and defects present in a crystalline material. Peak broadening anisotropy, where broadening of a diffraction peak doesn’t change smoothly with 2θ or d-spacing, is an important aspect of these methods. There are numerous approaches to take to deal with this anisotropy in metal alloys, which can be used to gain information about the dislocation types present in a sample and the amount of planar faults. However, there are problems in determining which method to use and the potential errors that can result. This is particularly the case for hexagonal close packed (HCP) alloys. There is though a distinct advantage of broadening anisotropy in that it provides a unique and potentially valuable way to develop crystal plasticity and work-hardening models. In this work we use several practical examples of the use of DPPA to highlight the issues of broadening anisotropy. Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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14 pages, 2566 KiB

Open AccessReview

Dislocation Structures in Low-Angle Grain Boundaries of α-Al₂O₃

by Eita Tochigi, Atsutomo Nakamura, Naoya Shibata and Yuichi Ikuhara

Crystals 2018, 8(3), 133; https://doi.org/10.3390/cryst8030133 - 12 Mar 2018

Cited by 22 | Viewed by 8244

Abstract

Alumina (α-Al₂O₃) is one of the representative high-temperature structural materials. Dislocations in alumina play an important role in its plastic deformation, and they have attracted much attention for many years. However, little is known about their core atomic structures, with a few exceptions, because of lack of experimental observations at the atomic level. Low-angle grain boundaries are known to consist of an array of dislocations, and they are useful to compose dislocation structures. So far, we have systematically fabricated several types of alumina bicrystals with a low-angle grain boundary and characterized the dislocation structures by transmission electron microscopy (TEM). Here, we review the dislocation structures in

{11 \bar{2} 0} / [0001]

{11 \bar{2} 0} / 〈 1 \bar{1} 00 〉

{1 \bar{1} 00} / 〈 11 \bar{2} 0 〉

(0001) / 〈 1 \bar{1} 00 〉

{\bar{1} 104} / 〈 11 \bar{2} 0 〉

, and

(0001) / [0001]

low-angle grain boundaries of alumina. Our observations revealed the core atomic structures of b =

1 / 3 〈 11 \bar{2} 0 〉

edge and screw dislocations,

〈 1 \bar{1} 00 〉

edge dislocation, and

1 / 3 〈 \bar{1} 101 〉

edge and mixed dislocations. Moreover, the stacking faults on

{11 \bar{2} 0}

{1 \bar{1} 00}

, and

(0001)

planes formed due to the dissociation reaction of the dislocations are discussed, focusing on their atomic structure and formation energy. Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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24 pages, 10027 KiB

Open AccessReview

Study on Dislocation-Dopant Ions Interaction in Ionic Crystals by the Strain-Rate Cycling Test during the Blaha Effect

by Yohichi Kohzuki

Crystals 2018, 8(1), 31; https://doi.org/10.3390/cryst8010031 - 12 Jan 2018

Cited by 1 | Viewed by 3540

Abstract

The interaction between a dislocation and impurities has been investigated by measurements of yield stress and proof stress, micro-hardness tests, direct observations of dislocation, internal friction measurements, or stress relaxation tests so far. A large number of investigations has been carried out by the separation of the flow stress into effective and internal stresses on the basis of the temperature dependence of yield stress, the strain rate dependence of flow stress, and stress relaxation. Nevertheless, it is difficult to investigate the interaction between a dislocation and obstacles during plastic deformation by the mentioned methods. As for the original method which combines strain-rate cycling tests with the Blaha effect measurement, the original method is different from above-mentioned ones and would be possible to clear it up. The strain-rate cycling test during the Blaha effect measurement has successively provided the information on the dislocation motion breaking away from the strain fields around dopant ions with the help of thermal activation, and seems to separate the contributions arising from the interaction between dislocation and the point defects and those from dislocations themselves during plastic deformation of ionic crystals. Such information on dislocation motion in bulk material cannot be obtained by the widely known methods so far. Furthermore, the various deformation characteristics derived from the original method are sensitive to a change in the state of dopant ions in a specimen by heat treatment, e.g., the Gibbs free energy (G₀) for overcoming of the strain field around the dopant by a dislocation at absolute zero becomes small for the annealed KCl:Sr²⁺ single crystal (G₀ = 0.26 eV) in comparison with that for the quenched one (G₀ = 0.39 eV). Full article

(This article belongs to the Special Issue Crystal Dislocations: Their Impact on Physical Properties of Crystals)

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