Solid-solid Transition Research Articles

Mixed-order phase transition in a colloidal crystal

Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and nonequilibrium systems, but their experimental observation has remained elusive. Here, we analytically predict and experimentally realize a mixed-order equilibrium phase transition. Specifically, a discontinuous solid-solid transition in a 2D crystal of paramagnetic colloidal particles is induced by a magnetic field [Formula: see text] At the transition field [Formula: see text], the energy landscape of the system becomes completely flat, which causes diverging fluctuations and correlation length [Formula: see text] Mean-field critical exponents are predicted, since the upper critical dimension of the transition is [Formula: see text] Our colloidal system provides an experimental test bed to probe the unconventional properties of mixed-order phase transitions.

Structure and Thermodynamics of Metal Clusters on Atomically Smooth Substrates.

We analyze the structure of model NiN and CuN clusters (N = 55, 147) supported on a variety of atomically smooth van der Waals surfaces. The global minima are mapped in the space of two parameters: (i) the laterally averaged surface stickiness, γ, which controls the macroscopic wetting angle, and (ii) the surface microstructure, which produces more subtle but important templating via epitaxial stresses. We find that adjusting the substrate lattice (even at constant γ) can favor different crystal plane orientations in the cluster, stabilize hexagonal close-packed order, or induce various defects, such as stacking faults, twin boundaries, and five-fold disclinations. Thermodynamic analysis reveals substrate-dependent solid-solid transitions in cluster morphology, with tunable transition temperature and sometimes exhibiting re-entrant behavior. These results shed new light on the extent to which a supporting surface can be used to influence the equilibrium behavior of nanoparticles.

Dipolar Crystals: The Crucial Role of the Clinohexagonal Prism Phase.

We report a new phase called clinohexagonal prism (CHP) that accounts for all the ground states of dipolar hard spheres prepared at any density. This phase merely consists of an oblique prismatic lattice with a hexagonal base. Our calculations show that at intermediate densities, a special close packed body-centered orthorhombic phase coincides with the CHP phase in the ground state for a wide density window. In the high packing regime, i.e., in the vicinity of the density of the hexagonal close packed phase, it is a limiting case of the CHP phase with vanishing obliquity that emerges. These findings provide a unified and clarified view of the solid-solid transitions occurring at zero temperature in dipolar systems and should be relevant in other related molecular or soft matter systems governed by anisotropic (and possibly isotropic) soft potentials.

Signature of f -electron conductance in α -Ce single-atom contacts

Cerium is a fascinating element exhibiting, with its different phases, long-range magnetic order and superconductivity in bulk form. The coupling of the 4f electron to sd conduction electrons and to the lattice is responsible for unique structural and electronic properties like the isostructural first-order solid-solid transition from the cubic $\gamma$ phase to the cubic $\alpha$ phase, which is accompanied by a huge volume collapse of 14 %. While the $\gamma - \alpha$ phase transition has been investigated for decades, experiments aiming at disentangling the 4f contribution to the electric conductance of the different phases have not been performed. Here we report on the strongly enhanced conductance of single-atom Ce contacts. By controlling the content of $\alpha$-Ce employing different rates of cooling, we find a strong correlation between the fraction of $\alpha$-Ce and the magnitude of the last conductance plateau before the contact breaks. We attribute the enhanced conductance of $\alpha$-Ce to the additional contribution of the 4f level.

Co-crystal of suberic acid and 1,2-bis(4-pyridyl)ethane: A new case of packing polymorphism

The polymorphic behaviour of a co-crystal composed of neutral suberic acid and 1,2-bis(4-pyridyl)ethane is reported. A multidisciplinary approach has been employed, using thermal analysis methods (differential scanning calorimetry and polarized light thermomicroscopy), spectroscopic methods (infrared spectroscopy) and X-ray single crystal and powder diffraction. Two new polymorphs, I and III; have been identified, and for one of them the crystal structure has been elucidated and compared to that of a known polymorph, form II, showing that the assembling of the molecules in chains via H-bonds is a common feature of both polymorphs. Polymorph II, obtained by crystallization from an aqueous or ethanol solution or by grinding, undergoes a solid-solid transition to polymorph I, which melts at 180.5 °C. Upon cooling from the melt, polymorph I is obtained, and a solid-solid transformation also occurs, to polymorph III'. Polymorph III was obtained serendipitously in an attempt to prepare a Nd(III) complex. The relative stability of the three polymorphic forms was established.

Thermoanalytical study of sweetener myo-inositol: α and β polymorphs

This work investigates the thermal behavior of α and β myo-inositol polymorphs. The inositol is a natural compound widely used in the food industry due to its presence in carbohydrate metabolism and its sweet taste. The occurrence of polymorphism could change some physico-chemical properties, such as melting and sublimation temperatures, and solubility. Therefore, the thermal study of polymorphism is important to ensure better conditions for synthesis, storage, and transportation of food that contains the myo-inositol. Simultaneous Termogravimetry-Differential Thermal Analysis, Photovisual Differential Scanning Calorimetry, Polarized Light Thermomicroscopy, and Powder X-ray Diffraction were used in investigation. The data show a new thermal event associated to β myo-inositol melting at 221.43°C, suggesting that the solid-solid transition at 185.68°C was incomplete. The kinetics data made it possible to determine the transition lifetime of myo-inositol to occur 5% of solid-solid transition at 20°C and 37°C: 126 and 8years, respectively.

Diffusive and martensitic nucleation kinetics in solid-solid transitions of colloidal crystals

Solid–solid transitions between crystals follow diffusive nucleation, or various diffusionless transitions, but these kinetics are difficult to predict and observe. Here we observed the rich kinetics of transitions from square lattices to triangular lattices in tunable colloidal thin films with single-particle dynamics by video microscopy. Applying a small pressure gradient in defect-free regions or near dislocations markedly transform the diffusive nucleation with an intermediate-stage liquid into a martensitic generation and oscillation of dislocation pairs followed by a diffusive nucleus growth. This transformation is neither purely diffusive nor purely martensitic as conventionally assumed but a combination thereof, and thus presents new challenges to both theory and the empirical criterion of martensitic transformations. We studied how pressure, density, grain boundary, triple junction and interface coherency affect the nucleus growth, shape and kinetic pathways. These novel microscopic kinetics cast new light on control solid–solid transitions and microstructural evolutions in polycrystals.

Nanothermodynamics of iron clusters: Small clusters, icosahedral and fcc-cuboctahedral structures.

The study of the thermodynamics and structures of iron clusters has been carried on, focusing on small clusters and initial icosahedral and fcc-cuboctahedral structures. Two combined tools are used. First, energy intervals are explored by the Monte Carlo algorithm, called σ-mapping, detailed in the work of Soudan et al. [J. Chem. Phys. 135, 144109 (2011), Paper I]. In its flat histogram version, it provides the classical density of states, gp(Ep), in terms of the potential energy of the system. Second, the iron system is described by a potential which is called "corrected EAM" (cEAM), explained in the work of Basire et al. [J. Chem. Phys. 141, 104304 (2014), Paper II]. Small clusters from 3 to 12 atoms in their ground state have been compared first with published Density Functional Theory (DFT) calculations, giving a complete agreement of geometries. The series of 13, 55, 147, and 309 atom icosahedrons is shown to be the most stable form for the cEAM potential. However, the 147 atom cluster has a special behaviour, since decreasing the energy from the liquid zone leads to the irreversible trapping of the cluster in a reproducible amorphous state, 7.38 eV higher in energy than the icosahedron. This behaviour is not observed at the higher size of 309 atoms. The heat capacity of the 55, 147, and 309 atom clusters revealed a pronounced peak in the solid zone, related to a solid-solid transition, prior to the melting peak. The corresponding series of 13, 55, and 147 atom cuboctahedrons has been compared, underscoring the unstability towards the icosahedral structure. This unstability occurs clearly in several steps for the 147 atom cluster, with a sudden transformation at a transition state. This illustrates the concerted icosahedron-cuboctahedron transformation of Buckminster Fuller-Mackay, which is calculated for the cEAM potential. Two other clusters of initial fcc structures with 24 and 38 atoms have been studied, as well as a 302 atom cluster. Each one relaxes towards a more stable structure without regularity. The 38 atom cluster exhibits a nearly glassy relaxation, through a cascade of six metastable states of long life. This behaviour, as that of the 147 atom cluster towards the amorphous state, shows that difficulties to reach ergodicity in the lower half of the solid zone are related to particular features of the potential energy landscape, and not necessarily to a too large size of the system. Comparisons of the cEAM iron system with published results about Lennard-Jones systems and DFT calculations are made. The results of the previous clusters have been combined with that of Paper II to plot the cohesive energy Ec and the melting temperature Tm in terms of the cluster atom number Nat. The Nat-1/3 linear dependence of the melting temperature (Pawlow law) is observed again for Nat > 150. In contrast, for Nat < 150, the curve diverges strongly from the Pawlow law, giving it an overall V-shape, with a linear increase of Tm when Nat goes from 55 to 13 atoms. Surprisingly, the 38 atom cluster is anomalously below the overall curve.

Shape-driven solid–solid transitions in colloids

Solid-solid phase transitions are the most ubiquitous in nature, and many technologies rely on them. However, studying them in detail is difficult because of the extreme conditions (high pressure/temperature) under which many such transitions occur and the high-resolution equipment needed to capture the intermediate states of the transformations. These difficulties mean that basic questions remain unanswered, such as whether so-called diffusionless solid-solid transitions, which have only local particle rearrangement, require thermal activation. Here, we introduce a family of minimal model systems that exhibits solid-solid phase transitions that are driven by changes in the shape of colloidal particles. By using particle shape as the control variable, we entropically reshape the coordination polyhedra of the particles in the system, a change that occurs indirectly in atomic solid-solid phase transitions via changes in temperature, pressure, or density. We carry out a detailed investigation of the thermodynamics of a series of isochoric, diffusionless solid-solid phase transitions within a single shape family and find both transitions that require thermal activation or are "discontinuous" and transitions that occur without thermal activation or are "continuous." In the discontinuous case, we find that sufficiently large shape changes can drive reconfiguration on timescales comparable with those for self-assembly and without an intermediate fluid phase, and in the continuous case, solid-solid reconfiguration happens on shorter timescales than self-assembly, providing guidance for developing means of generating reconfigurable colloidal materials.

Interrelations Between Side Chain and Main Chain Packing in Different Crystal Modifications of Alkoxylated Polyesters

Interrelations between main chain and side chain packing are studied in a series of comb-like poly(1,4-phenylene-2,5-n-dialkyloxy terephthalate)s (PPAOTs) with C = 6-12 alkyl carbons per side chain by X-ray diffractometry. Two different polymorphic states, called modification A and modification B, are observed depending on thermal treatment and side chain length. For PPAOTs with short side chains (C ≤ 8), modification A is commonly observed. "As synthesized" (solution crystallized) PPAOTs with longer side chains (C ≥ 10) contain mostly modification B while modification A is growing during melt cooling. A solid-solid transition from modification B to modification A is observed above ≈70 °C for the decyl member (C = 10, PPDOT) while modification A converts under ambient conditions slowly to modification B. This indicates that modification B is thermodynamically stable at low temperature while modification A is stable at higher temperature. Crystallographic analysis shows that both modifications are characterized by an orthorhombic unit cell and a long-range ordered layered structure with alternating main chain and alkyl nanodomains. This is confirmed by 2D diffration data for shear oriented PPDOT fibers. The main difference between both modifications is the packing of the side chains which are in a crystalline state for modification B but disordered for modification A. This is concluded from values for the volume per CH2 unit VCH2 in alkyl nanodomains calculated without further assumptions from the obtained lattice parameters. Interestingly, the crystalline packing of the side chains in modification B leads to a significant increase (≈ 20%) in the application relevant π-π spacings within the main chain domains as compared to those for modification A. It is argued that the structure formation process and thermodynamic equilibrium in comb-like polymers might be strongly influenced by a competition of the individual packing tendencies of main and side chains.

Thermal study of ZrO2 nanoparticles: Effect of heating and cooling cycles on solid-solid transition

This study investigates the influence of particle size on the solid-solid transition in zirconium (ZrO2) nanoparticles. The Simultaneous Thermogravimetry/Derivate Thermogravimetric-Differential Thermal Analysis (TG/DTG-DTA) was used to evince the phase transitions processes as well as the quantity of volatile compounds and the residual organic matter formed during the synthesis of nanoparticles. Field Emission Scanning Electron Microscopy (FE-SEM) and Transmission Electron Microscopy (TEM) were used to prove the increase and agglomeration ;1;of particle size after each thermal cycle.

Decoding heat capacity features from the energy landscape.

A general scheme is derived to connect transitions in configuration space with features in the heat capacity. A formulation in terms of occupation probabilities for local minima that define the potential energy landscape provides a quantitative description of how contributions arise from competition between different states. The theory does not rely on a structural interpretation for the local minima, so it is equally applicable to molecular energy landscapes and the landscapes defined by abstract functions. Applications are presented for low-temperature solid-solid transitions in atomic clusters, which involve just a few local minima with different morphologies, and for cluster melting, which is driven by the landscape entropy associated with the more numerous high-energy minima. Analyzing these features in terms of the balance between states with increasing and decreasing occupation probabilities provides a direct interpretation of the underlying transitions. This approach enables us to identify a qualitatively different transition that is caused by a single local minimum associated with an exceptionally large catchment volume in configuration space for a machine learning landscape.

Janus particle rotator-to-lamellar nucleation and growth kinetics

We determine the free energy barrier, critical nucleus size, and kinetics of a Janus particle solid-solid transition by nucleation and growth of lamellar clusters within a metastable rotator phase. The transition involves negligible change in particle position and phase volume and entails only particle orientational ordering. Fast kinetics enable the analysis of unbiased crystal growth and shrinkage trajectories from Brownian dynamic simulations. By fitting simulation trajectories to a diffusion-migration equation, the nucleus free energy and growth coefficient as a function of nucleus size are extracted. Observed transition times are on the order of hundreds of characteristic particle rotation times. Lamellar crystal nuclei are oblate rather than spherical, but otherwise classical nucleation theory applies, with the bulk free energy contribution following closely the Maier-Saupe theory for purely orientational transitions and the interfacial energy contribution following trends from 3-dimensional Ising spin kinetics.

A further discussion on solid-liquid equilibrium in complex synthetic paraffinic systems with the effects of solid-solid transition

A predictive thermodynamic model for the prediction of wax precipitation in paraffinic mixtures is developed, on the basis of the wax prediction model (RSFV-IRSW) established by Yang et al. (2016), where the liquid phase is described by the combination of regular solution model and Flory free-volume equation, and the solid phase is modelled by the combination of improved regular solution model and Wilson equation. Advancements are adopted in the present work: 1. The influence of transition enthalpy between disorder and order solid phases on liquid-solid fugacity ratio of pure component is considered; 2. A method for the precise calculation of fusion enthalpy and transition enthalpy is suggested; 3. The boundary condition to decide whether one component would precipitate out to form the solid phase is added. The predictive model, RSFV-IRSW, predictive Wilson and regular solution model are tested against the experimental data of complex synthetic paraffinic systems. Results show that the predictive model behaves the best with high prediction accuracy in terms of the characteristics of wax precipitation curve and the composition of solid phase.

Contrasting the dynamics of elastic and non-elastic deformations across an experimental colloidal Martensitic transition.

We present a framework to segregate the roles of elastic and non-elastic deformations in the examination of real-space experiments of solid-solid Martensitic transitions. The Martensitic transformation of a body-centred-tetragonal (BCT) to a body-centred-orthorhombic (BCO) crystal structure has been studied in a model system of micron-scale ionic microgel colloids (P. S. Mohanty, P. Bagheri, S. Nöjd, A. Yethiraj and P. Schurtenberger, Phys. Rev. X, 2015, 5, 011030). Non-affine fluctuations, i.e., displacement fluctuations that do not arise from purely elastic (affine) deformations, are detected in particle configurations acquired from the experiment. Tracking these fluctuations serves as a highly sensitive tool in signaling the onset of the Martensitic transition and precisely locating particle rearrangements occurring at length scales of a few particle diameters. Particle rearrangements associated with non-affine displacement modes become increasingly favorable during the transformation process. The nature of the displacement fluctuation modes that govern the transformation are shown to be different from those predominant in an equilibrium crystal. We show that BCO crystallites formed through shear may, remarkably, co-exist with those resulting from local rearrangements within the same sample.

Formation of a solid solution between [N(C2H5)4][BF4] and [N(C2H5)4][PF6] in crystal and plastic crystal phases.

The phase behavior of [N2222][BF4] and [N2222][PF6] (N2222+ = tetraethylammonium cation) binary systems has been investigated in the present study. Differential scanning calorimetry revealed that the crystal-to-plastic-crystal transition temperature decreases upon mixing the two salts, with a minimum at x([N2222][PF6]) = 0.4, where x([N2222][PF6]) denotes the molar fraction of [N2222][PF6]. Powder X-ray diffraction analysis indicated the formation of a solid solution with a rock-salt type structure in the plastic crystal phase at all ratios and the lattice parameter a changes according to Vegard's law. In the crystal phase, two solid solution phases based on the structures of the single salts are observed. Raman spectroscopy confirmed the changes in the solid-solid transition temperature as observed by differential scanning calorimetry. Consequently, in the resulting phase diagram, the solid solution is formed in a wide x([N2222][PF6]) range for both the crystal and plastic crystal phases.

Semifluorinated alkanes and alkanes: A phase study of the perfluorohexyloctane – Tetradecane system

The binary system perfluorohexyloctane (F6H8)–tetradecane (C14) was investigated in order to increase understanding of interactions of semifluorinated alkanes (SFAs) with hydrophobic molecules. The thermal phase behavior for F6H8 and C14 and their mixtures was determined using DSC. The activity coefficients for both components in the mixtures were calculated and Gibbs energy of mixing was determined. Furthermore, enthalpies of mixing were determined with ITC and structural investigations of the solid and the liquid phases were performed with SAXS and SWAXD. It was found that F6H8 displays one solid-solid transition at −42.3°C (ΔH=1.1kJ/mol) and one solid-liquid transition at −5.9°C (ΔH=16.6kJ/mol). Due to the low enthalpy of the solid-liquid transition it is likely that F6H8 is not fully crystallized in the solid phase but partly amorphous. The F6H8–C14 system displays a eutectic phase behavior and the liquid mixtures display a positive deviation from ideal mixing. C14 crystalizes in a triclinic unit cell as shown before, whereas crystallization of F6H8 in a lamellar rippled phase is shown for the first time. This ripple phase comprises a bilayer of tilted alternating heavily interdigitated F6H8 molecules in an oblique subunit cell.

New Melting Data of the Two Polymorphs of Prednisolone.

Prednisolone is known to exist in two anhydrous solid polymorphic forms. The substance is known to degrade upon melting, resulting in erroneous melting data, as shown by the widely scattered results reported in the literature. In this article, thermal analyses carried out at different scan rates show that the onset temperature and the enthalpy value of the signal increase with the scan rate and reach plateau values for high scan rates. Owing to flash scanning calorimetry, the plateau value for the temperature has been identified as the "true" temperature of melting of both polymorphs. This consistent set of new thermodynamic data on the two solid forms leads to the conclusion that both forms are unambiguously enantiotropes of each other. The solid-solid transition has been observed experimentally for the first time and has been confirmed by calculation.

Solid-solid phase transitions via melting in metals.

Observing solid–solid phase transitions in-situ with sufficient temporal and spatial resolution is a great challenge, and is often only possible via computer simulations or in model systems. Recently, a study of polymeric colloidal particles, where the particles mimic atoms, revealed an intermediate liquid state in the transition from one solid to another. While not yet observed there, this finding suggests that such phenomena may also occur in metals and alloys. Here we present experimental evidence for a solid–solid transition via the formation of a metastable liquid in a ‘real' atomic system. We observe this transition in a bulk glass-forming metallic system in-situ using fast differential scanning calorimetry. We investigate the corresponding transformation kinetics and discuss the underlying thermodynamics. The mechanism is likely to be a feature of many metallic glasses and metals in general, and may provide further insight into phase transition theory.

Modes of surface premelting in colloidal crystals composed of attractive particles.

Crystal surfaces typically melt into a thin liquid layer at temperatures slightly below the melting point of the crystal. Such surface premelting is prevalent in all classes of solids and is important in a variety of metallurgical, geological and meteorological phenomena. Premelting has been studied using X-ray diffraction and differential scanning calorimetry, but the lack of single-particle resolution makes it hard to elucidate the underlying mechanisms. Colloids are good model systems for studying phase transitions because the thermal motions of individual micrometre-sized particles can be tracked directly using optical microscopy. Here we use colloidal spheres with tunable attractions to form equilibrium crystal-vapour interfaces, and study their surface premelting behaviour at the single-particle level. We find that monolayer colloidal crystals exhibit incomplete premelting at their perimeter, with a constant liquid-layer thickness. In contrast, two- and three-layer crystals exhibit conventional complete melting, with the thickness of the surface liquid diverging as the melting point is approached. The microstructures of the surface liquids differ in certain aspects from what would be predicted by conventional premelting theories. Incomplete premelting in the monolayer crystals is triggered by a bulk isostructural solid-solid transition and truncated by a mechanical instability that separately induces homogeneous melting within the bulk. This finding is in contrast to the conventional assumption that two-dimensional crystals melt heterogeneously from their free surfaces (that is, at the solid-vapour interface). The unexpected bulk melting that we observe for the monolayer crystals is accompanied by the formation of grain boundaries, which supports a previously proposed grain-boundary-mediated two-dimensional melting theory. The observed interplay between surface premelting, bulk melting and solid-solid transitions challenges existing theories of surface premelting and two-dimensional melting.