Special Issue "Crystallography of Structural Phase Transformations"

A special issue of Crystals (ISSN 2073-4352). This special issue belongs to the section "Crystal Engineering".

Deadline for manuscript submissions: closed (15 September 2020).

Special Issue Editor

Dr. Cyril Cayron
E-Mail Website
Guest Editor
Swiss Federal Institute of Technology EPFL, Lausanne, Lausanne, Switzerland
Interests: metallurgy; EBSD; TEM; crystallography; martensitic transformations; twinning; variants; group theory
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Special Issue Information

Dear Colleagues,

Solid-solid phase transformations generally imply a crystallographic orientation relationship (OR). The precipitates at the nucleation stage are often in OR with the surrounding matrix; the martensite products are in OR with their parent austenite; and the annealing twins and deformation twins are two crystals of the same species linked by an OR. The symmetries of the phases combined with the OR generate complex microstructures made of variants or twins that can be described mathematically with group theory, linear algebra, coset and multiple cosets, graphs, groupoids, or high-dimension spaces, etc. A lot of efforts have been devoted over the last century to establishing bridges between this “descriptive” crystallography and the “predictive” thermodynamics, but full unification remains to be achieved. For the moment, the models are not well balanced. On the crystallographic side, the phenomenological of theory of martensitic crystallography (PTMC), the edge-to-edge matching model, the disconnection “topological” model, etc. are well developed, but they are often limited to using the generalized Clausius–Clapeyron formula to make the link with thermodynamics. On the thermodynamic side, one can find the famous Landau and Ginzburg–Landau theories, but crystallographic complexity is often reduced to the symmetries of the polynomial form of the free energy introduced with group representation theory. It is not easy to find a way to marry all the different approaches, even if phase field has made a lot of progress over the last decades.

As it is important for research in this field to continue, all experimental and theoretical contributions about phase transformations and crystallography are welcome in this Special Issue, regardless of the type of materials (piezo and ferroelectrics, structurally hardened alloys, martensitic alloys, ordered alloys, shape memory alloys, polymorphic minerals, mechanically twinned materials, etc).

Dr. Cyril Cayron
Guest Editor

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Keywords

  • Phase transformation
  • Twins
  • Variants
  • Algebra
  • Orientation relationship

Published Papers (14 papers)

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Research

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Article
Reproducible Orientation Relationships Developed from Phase Transformations—Role of Interfaces
Crystals 2020, 10(11), 1042; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst10111042 - 16 Nov 2020
Cited by 2 | Viewed by 842
Abstract
The orientation relationship (OR) between phases related by a phase transformation is often reproducible. This study interprets and predicts the reproducible ORs with a two-stage approach. The initial OR formed at the nucleation stage tends to allow a periodic structure of a preferred [...] Read more.
The orientation relationship (OR) between phases related by a phase transformation is often reproducible. This study interprets and predicts the reproducible ORs with a two-stage approach. The initial OR formed at the nucleation stage tends to allow a periodic structure of a preferred state to form in the interface. A matching correspondence of either a one-to-one or n-to-m nature can be specified in the periodic structure. An initial OR will become the final reproducible OR if there is no misfit. Otherwise, a reproducible OR developed at the growth stage tends to permit a singular dislocation structure to form in an interface where the preferred state must be sustained locally. The actual change in the OR is subject to the given material system and the phase-transformation condition. Various singular dislocation structures and their constraints on the ORs are analyzed, with thermodynamics and kinetics applied conceptually. The resulting ORs can be specified by following one or more Δg parallelism rules. A set of workable steps is provided to facilitate the interpretation of observed reproducible ORs. Some unsolved problems are identified, which call for further studies that can quantitatively combine the thermodynamics, kinetics and crystallography of phase transformations. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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Article
Synthesis, Structure, and Dielectric Properties of (3-Nitroanilinium) (18-Crown) (PF6)
Crystals 2020, 10(11), 1028; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst10111028 - 11 Nov 2020
Cited by 1 | Viewed by 560
Abstract
(3-Nitroanilinium) (18-crown) (PF6) (1), which is an organic-inorganic hybrid containing one-dimensional chains of hydrogen-bonded supramolecular cations, was synthesized under slow evaporation conditions and subjected to differential scanning calorimetry, temperature-dependent dielectric measurements, and variable-temperature single-crystal X-ray diffraction analysis. These analyses [...] Read more.
(3-Nitroanilinium) (18-crown) (PF6) (1), which is an organic-inorganic hybrid containing one-dimensional chains of hydrogen-bonded supramolecular cations, was synthesized under slow evaporation conditions and subjected to differential scanning calorimetry, temperature-dependent dielectric measurements, and variable-temperature single-crystal X-ray diffraction analysis. These analyses revealed the occurrence of a reversible structural phase transition [P21/n P21/c] at 223 K and a dielectric anomaly, which, based on the results of structural analysis and potential energy calculations, was attributed to the synergistic effect between the pendulum-like motion of the nitro group in the supramolecular cation, (3-nitroanilinium)(18-crown), and the order-disorder motion of PF6 anions. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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Article
Shear Deformation Helps Phase Transition in Pure Iron Thin Films with “Inactive” Surfaces: A Molecular Dynamics Study
Crystals 2020, 10(10), 855; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst10100855 - 23 Sep 2020
Cited by 1 | Viewed by 654
Abstract
In a previous study, it was shown that the (111)fcc, (110)fcc and (111)bcc free surfaces do not assist the phase transitions as nucleation sites upon heating/cooling in iron (Fe) thin slabs. In the present work, the three surfaces are [...] Read more.
In a previous study, it was shown that the (111)fcc, (110)fcc and (111)bcc free surfaces do not assist the phase transitions as nucleation sites upon heating/cooling in iron (Fe) thin slabs. In the present work, the three surfaces are denoted as “inactive” free surfaces. The phase transitions in Fe thin films with these “inactive” free surfaces have been studied using a classical molecular dynamics simulation and the Meyer–Entel potential. Our results show that shear deformation helps to activate the free surface as nucleation sites. The transition mechanisms are different in dependence on the surface orientation. In film with the (111)fcc free surface, two body-centered cubic (bcc) phases with different crystalline orientations nucleate at the free surface. In film with the (110)fcc surface, the nucleation sites are the intersections between the surfaces and stacking faults. In film with the (111)bcc surface, both heterogeneous nucleation at the free surface and homogeneous nucleation in the bulk material are observed. In addition, the transition pathways are analyzed. In all cases studied, the unstrained system is stable and no phase transition takes place. This work may be helpful to understand the mechanism of phase transition in nanoscale systems under external deformation. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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Article
Phase Transitions of N-(4-methoxybenzylidene)-4-butylaniline (MBBA) Confined within Mesoporous Silica
Crystals 2020, 10(9), 792; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst10090792 - 08 Sep 2020
Cited by 1 | Viewed by 1188
Abstract
We have used differential scanning calorimetry (DSC) to investigate the phase transition of a liquid crystal, N-(4-methoxybenzylidene)-4-butylaniline (MBBA), confined within porous silica materials with one- and three-dimensional pore architectures. Each phase-transition temperature of the confined MBBA linearly decreased with the inverse pore [...] Read more.
We have used differential scanning calorimetry (DSC) to investigate the phase transition of a liquid crystal, N-(4-methoxybenzylidene)-4-butylaniline (MBBA), confined within porous silica materials with one- and three-dimensional pore architectures. Each phase-transition temperature of the confined MBBA linearly decreased with the inverse pore size compared with that of bulk MBBA. However, the degree of temperature shift varied owing to differences in the pore architectures. In addition, when MBBA was confined within one-dimensional pores, the thermal anomaly associated with the phase transition from the nematic phase to the isotropic liquid phase was not observed in the DSC measurements. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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Article
Crystallographic Texture Analysis of As-Built and Heat-Treated Ti6Al4V (ELI) Produced by Direct Metal Laser Sintering
Crystals 2020, 10(8), 699; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst10080699 - 12 Aug 2020
Cited by 1 | Viewed by 921
Abstract
This paper reports on an investigation of crystallographic texture of as-built and heat-treated Ti6Al4V (ELI) produced by direct metal laser sintering (DMLS). The texture analyses were conducted using electron backscatter diffraction (EBSD). The β-phase texture from the obtained EBSD data was ascertained based [...] Read more.
This paper reports on an investigation of crystallographic texture of as-built and heat-treated Ti6Al4V (ELI) produced by direct metal laser sintering (DMLS). The texture analyses were conducted using electron backscatter diffraction (EBSD). The β-phase texture from the obtained EBSD data was ascertained based on a reconstruction method using the Automatic Reconstruction of Parent Grain for EBSD data (ARPGE) program. A significant improvement of the maximum intensity of the texture from the pole figure was also noted upon heat treatment. The as-built samples and samples heat-treated just below the α→β transformation temperature showed a stronger fibrous texture of the reconstructed β-grains with the ⟨100⟩ directions almost parallel to the build direction. The alignment of the fibrous texture in the build direction disappeared after heat treatment above the α→β-grain transformation temperature. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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Article
Vibrational Dynamics of a Chiral Smectic Liquid Crystal Undergoing Vitrification and Cold Crystallization
Crystals 2020, 10(8), 655; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst10080655 - 30 Jul 2020
Cited by 5 | Viewed by 812
Abstract
Vibrational dynamics in the glass transition and the cold crystallization process of (S)-4′-(1-methyloctyloxycarbonyl) biphenyl-4-yl 4-[7-(2,2,3,3,4,4,4-heptafluorobutoxy) heptyl-1-oxy]-benzoate (3F7HPhH7) was studied by Fourier transform infrared spectroscopy (FTIR) during cooling/heating experimental runs. The measured spectra processing was supported by quantum chemical density functional theory (DFT) calculations [...] Read more.
Vibrational dynamics in the glass transition and the cold crystallization process of (S)-4′-(1-methyloctyloxycarbonyl) biphenyl-4-yl 4-[7-(2,2,3,3,4,4,4-heptafluorobutoxy) heptyl-1-oxy]-benzoate (3F7HPhH7) was studied by Fourier transform infrared spectroscopy (FTIR) during cooling/heating experimental runs. The measured spectra processing was supported by quantum chemical density functional theory (DFT) calculations (frequency assignments). The perturbation-correlation moving window two-dimensional analysis (PCMW2D) was performed to examine how the height of individual absorption bands change under with temperature. Two-dimensional correlation analysis (2D-COS) was used to detect freezing-in or activation of the stochastic movements during the vitrification and the cold crystallization processes. Upon cooling, the vitrification process involves freezing-in of the stochastic movements of ester groups. Upon heating, as the cold crystallization process begins, the first to respond are the vibrations of the C–O–C and C=O groups in the rigid core. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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Article
What EBSD and TKD Tell Us about the Crystallography of the Martensitic B2-B19′ Transformation in NiTi Shape Memory Alloys
Crystals 2020, 10(7), 562; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst10070562 - 01 Jul 2020
Cited by 3 | Viewed by 1225
Abstract
The complex and intricate microstructure of B19′ martensite in shape memory nickel titanium alloys is generally explained with the Phenomenological Theory of Martensitic Crystallography (PTMC). Over the last decade, we have developed an alternative approach that supposes the existence of a “natural” parent–daughter [...] Read more.
The complex and intricate microstructure of B19′ martensite in shape memory nickel titanium alloys is generally explained with the Phenomenological Theory of Martensitic Crystallography (PTMC). Over the last decade, we have developed an alternative approach that supposes the existence of a “natural” parent–daughter orientation relationship (OR). As the previous TEM studies could not capture the global crystallographic characteristics of the B2→B19′ transformation required to discriminate the models, we used Electron BackScatter Diffraction (EBSD) and Transmission Kikuchi Diffraction (TKD) to investigate a polycrystalline NiTi alloy composed of B19′ martensite. The EBSD maps show the large martensite plates and reveal the coexistence of different ORs. The TKD maps permit us to image the “twins” and confirm the continuum of orientations suspected from EBSD. The results are interpreted with the alternative approach. The predominant OR in EBSD is the “natural” OR for which the dense directions and dense planes of B2 and B19′ phases are parallel—i.e., (010)B19′//(110)B2 and [101]B19′//[ 1 ¯ 11]B2. The natural OR was used to automatically reconstruct the prior parent B2 grains in the EBSD and TKD maps. From the distortion matrix associated with this OR, we calculated that the habit plane could be (1 1 ¯ 2)B2//(10 1 ¯ )B19′. The traces of these planes are in good agreement with the EBSD maps. We interpret the other ORs as “closing-gap” ORs derived from the natural OR to allow the compatibility between the distortion variants. Each of them restores a parent symmetry element between the variants that was lost by distortion but preserved by correspondence. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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Article
Bicrystallography and Beyond: Example of Group–Subgroup Phase Transformations
Crystals 2020, 10(7), 560; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst10070560 - 01 Jul 2020
Viewed by 545
Abstract
This paper presents the basic elementary tools for describing the global symmetry obtained by overlapping two or more crystal variants of the same structure, differently oriented and displaced one with respect to the other. It gives an explicit simple link between the concepts [...] Read more.
This paper presents the basic elementary tools for describing the global symmetry obtained by overlapping two or more crystal variants of the same structure, differently oriented and displaced one with respect to the other. It gives an explicit simple link between the concepts used in the symmetry studies on grain boundaries on one side and group–subgroup transformations on the other side. These questions are essentially of the same nature and boil down to the resolution of the same problem: identifying the permutation groups that are images of the corresponding applications. Examples are given from both domains, classical grain boundaries with coincidence lattices and group–subgroup phase transformations that illustrate the profound similarities between the two approaches. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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Article
Ordering Phase Transition with Symmetry-Breaking from Disorder over Non-Equivalent Sites: Calorimetric and Crystallographic Study of Crystalline d-Sorbose
Crystals 2020, 10(5), 361; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst10050361 - 01 May 2020
Cited by 1 | Viewed by 920
Abstract
Phase transitions in the crystalline state of chiral sorbose were examined using precise heat capacity calorimetry and X-ray crystallography. The calorimetry established heat capacity below room temperature. Besides the known transition (main transition) at 199.5 K, the calorimetry detected plural thermal anomalies assignable [...] Read more.
Phase transitions in the crystalline state of chiral sorbose were examined using precise heat capacity calorimetry and X-ray crystallography. The calorimetry established heat capacity below room temperature. Besides the known transition (main transition) at 199.5 K, the calorimetry detected plural thermal anomalies assignable to new phase transitions (around 210 K) and a glass transition (at ca. 120 K). The X-ray diffraction at low temperatures established the crystal structure of the lowest temperature phase. The identification of the broken symmetry upon the main transition solves an apparent contradiction that the structural disorder reported previously does not contribute seemingly to the symmetrization. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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Article
Structural Dynamics of An ELM-11 Framework Transformation Accompanied with Double-Step CO2 Gate sorption: An NMR Spin Relaxation Study
Crystals 2020, 10(4), 328; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst10040328 - 22 Apr 2020
Viewed by 1188
Abstract
[Cu(4,4'-bipyridine)2(BF4)2] (ELM-11), an elastic layer-structured MOF (metal-organic framework), is expected to be a sophisticated CO2 reservoir candidate because of its high capacity and recovery efficiency for CO2 sorption. While ELM-11 shows a unique double-step gate [...] Read more.
[Cu(4,4'-bipyridine)2(BF4)2] (ELM-11), an elastic layer-structured MOF (metal-organic framework), is expected to be a sophisticated CO2 reservoir candidate because of its high capacity and recovery efficiency for CO2 sorption. While ELM-11 shows a unique double-step gate sorption for CO2 gas, the dynamics of the structural transition have not yet been clarified. In this study, the dynamics of the 4,4'-bipyridine linkers and the BF4- anions were studied by determining 1H spin-lattice relaxation times (T1). The ELM-11 structural transition accompanying CO2 sorption was also examined through the CO2 uptake dependence of the 1H spin–spin relaxation time (T2), in addition to T1. In its closed form, the temperature dependence of the 1H T1 of ELM-11 was analyzed by considering the contributions of both paramagnetic and dipolar relaxations, which revealed the isotropic reorientation of BF4- and the torsional flipping of the 4,4'-bipyridine moieties. The resultant activation energy of 32 kJ mol-1 for the isotropic BF4 reorientation is suggestive of strong (B-F...Cu2+) interactions between Cu(II) and the F atoms in BF4. Furthermore, the CO2 uptake dependence of T1 was found to be dominated by competition between the increase in the longitudinal relaxation time of the electron spins and the decrease in the spin density in the unit cell. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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Article
Near Atomic Row Matching in the Interface Analyzed in Both Direct and Reciprocal Space
Crystals 2020, 10(3), 192; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst10030192 - 11 Mar 2020
Cited by 2 | Viewed by 755
Abstract
Reproducible crystallographic features between new phase and matrix are often observed during phase transformation, including orientation relationship, interfacial orientation, morphology, and so on. The geometrical matching in the interface is the key to understanding the preferred transformation crystallography. Recently, a new geometrical method [...] Read more.
Reproducible crystallographic features between new phase and matrix are often observed during phase transformation, including orientation relationship, interfacial orientation, morphology, and so on. The geometrical matching in the interface is the key to understanding the preferred transformation crystallography. Recently, a new geometrical method emphasizing the atomic row matching in the interface, the so-called near row matching method, has been proposed to predict the preferred orientations between two arbitrary crystals. In this work, this method originally expressed in direct space was further extended to the reciprocal space. These two methods were implemented in our free software PTClab (version 1.19). It is found that these two expressions are nearly equivalent. As the near row matching in reciprocal space could be directly measured by the diffraction patterns with transmission electron microscopy (TEM), the condition of atomic row matching would be easily identified in reciprocal space during TEM work, and could be applied to rationalize the experimental observations. Several examples in bothsmall and large misfit alloy systems are shown to apply the near tow matching method in both direct and reciprocal space. Furthermore, the row matching method is compared with other models, and there are some crucial aspects that need extra attention when being applied to prediction. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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Article
Revisit the Role of Steps/Disconnections on Misfit Cancellation at Semi-Coherent Interface—Bridging the O-Line Model and the Topological Model
Crystals 2019, 9(10), 525; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst9100525 - 13 Oct 2019
Cited by 3 | Viewed by 1258
Abstract
It has been a long-standing topic how the lattice misfit is cancelled at a semi-coherent interphase boundary consisting of terraces and steps. Apart from a set of misfit dislocations separating the coherent patches, the role of steps (which is frequently called ‘disconnections’) on [...] Read more.
It has been a long-standing topic how the lattice misfit is cancelled at a semi-coherent interphase boundary consisting of terraces and steps. Apart from a set of misfit dislocations separating the coherent patches, the role of steps (which is frequently called ‘disconnections’) on misfit cancellation remains ambiguous because these steps do not destroy the continuity of lattice planes across the interface. This paper aims to clarify such ambiguity through identification of a set of secondary dislocations through a rigorous constrained coincidence site lattice (CCSL)/constrained displacive shift complete lattice (CDSCL) analysis. A semi-coherent interface between body-centred cubic (BCC) Cr-rich precipitate and face-centred cubic (FCC) Cu-rich matrix that holds a near N-W orientation relationship (OR) is used as an example to demonstrate the procedure to determine the secondary dislocations that are coincident with steps along the interface. The current approach does not only redefine the disconnections in the topological model, but also extends the description of interface structure from the O-line model. As a result, the ‘discrepancy’ between these two popular crystallographic models can be completely eliminated when the interface is required to contain a pair of parallel close-packed directions. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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Article
Low-Temperature Polymorphic Transformation of β-Lactam Antibiotics
Crystals 2019, 9(9), 460; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst9090460 - 02 Sep 2019
Cited by 2 | Viewed by 1412
Abstract
Abstract: Polymorphic screening and transformation of molecular crystals are presently popular research areas in pharmaceutical studies. In this study, we developed an ab initio method to examine the structures, spectra, and stabilities of β-lactam (trans-13-azabicyclo[10.2.0]tetradecan-14-one), an important component of antibiotics. Based on [...] Read more.
Abstract: Polymorphic screening and transformation of molecular crystals are presently popular research areas in pharmaceutical studies. In this study, we developed an ab initio method to examine the structures, spectra, and stabilities of β-lactam (trans-13-azabicyclo[10.2.0]tetradecan-14-one), an important component of antibiotics. Based on the density functional theory (DFT) and second-order Møller-Plesset perturbation (MP2) methods, the present work demonstrated that forms I and II have isomorphic structures but can be distinguished by their Gibbs free energies and vibrational spectra. Forms I and II show a low-temperature polymorphic transformation at 308 K, where form I is stable below 308 K and form II is stable above 308 K. The proposed method suggests that the theoretical calculation can be used as a tool to effectively distinguish the isomorphic structures, and temperature-induced polymorphic transformation has far-reaching significance for drug storage and design. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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Review

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Review
A Short Review of One-Dimensional Wigner Crystallization
Crystals 2021, 11(1), 20; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst11010020 - 29 Dec 2020
Cited by 3 | Viewed by 898
Abstract
The simplest possible structural transition that an electronic system can undergo is Wigner crystallization. The aim of this short review is to discuss the main aspects of three recent experimets on the one-dimensional Wigner molecule, starting from scratch. To achieve this task, the [...] Read more.
The simplest possible structural transition that an electronic system can undergo is Wigner crystallization. The aim of this short review is to discuss the main aspects of three recent experimets on the one-dimensional Wigner molecule, starting from scratch. To achieve this task, the Luttinger liquid theory of weakly and strongly interacting fermions is briefly addressed, together with the basic properties of carbon nanotubes that are required. Then, the most relevant properties of Wigner molecules are addressed, and finally the experiments are described. The main physical points that are addressed are the suppression of the energy scales related to the spin and isospin sectors of the Hamiltonian, and the peculiar structure that the electron density acquires in the Wigner molecule regime. Full article
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
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