Incommensurate Phase Transition Research Articles

Crystal structure of the incommensurate modulated high-pressure phase of the potassium guaninate monohydrate.

The crystal structure of the incommensurate modulated phase of potassium guaninate monohydrate has been solved on the basis of high-pressure single-crystal X-ray diffraction data. The modulated structure was described as a `mosaic' sequence of three different local configurations of two neighbouring guaninate rings. In contrast to known examples of incommensurate modulated organic compounds, the modulation functions of all atoms are discontinuous. This is the first example of the experimental detection of an incommensurate modulated crystal structure that can be modelled using the special `soliton mode' modulation function proposed by Aramburu et al. [(1995), J. Phys. Condens. Matter, 7, 6187-6196].

Phase transitions and magnetoelectricity in Fe implanted TlInS2 and TlGaSe2 ferroelectric crystals

The dielectric constant measurements of Fe implanted TlInS2 and TlGaSe2 crystals without and under application of constant magnetic field have been performed. It has been observed that the implantation of the crystals with Fe ions caused the formation of ferromagnetic layer in the irradiated region, which leads to considerable shifts of the successive incommensurate and commensurate phase transitions to high temperatures in the heating regime. Remarkable shifts of the phase transition temperatures back to the low temperature region on heating of the samples were observed on applying the magnetic field perpendicularly to the implanted surface. None changes of the phase transition temperature points on measurements of the samples have been observed in cooling regime. The obtained results are interpreted as magnetodielectric effects that resulted from magnetoelectric coupling between ferromagnetic and ferroelectric constituents of the composite structure.

Field-induced strain engineering to optimize antiferroelectric ceramics in breakdown strength and energy storage performance

The unique filed-induced phase transition makes antiferroelectric (AFE) ceramics naturally advantageous in exploiting advanced capacitors with ideal energy storage performance. However, low breakdown strength (BDS) has become one key restriction on energy storage performance of AFE ceramic and there have fewer research been carried out focused on optimizing breakdown strength with the design strategy based on regulating field-induced strain behavior. Here, we first propose introducing Nd3+ to induce incommensurate modulated AFE phase in Pb0.98Sr0.02Zr0.75Sn0.25O3 (PSrZS) matrix. Benefited from this strategy, the field-induced strain was well dispersed that the strain rate under electric field (strain/electric field) significantly decreased. Accordingly, inducing incommensurate modulated AFE phase in matrix by introducing Nd3+ greatly enhanced the BDS from 350 kV/cm to 540 kV/cm by regulating strain behavior combined with the delayed saturated polarization and significantly optimized several key parameters including hysteresis width and phase-switching field. As a result, outstanding recoverable energy density of 14.21 J/cm3 accompanying with high efficiency of 87.35% were obtained in 0.03 Nd-doped PSrZS ceramics at 530 kV/cm at room temperature. The actual discharge performance is also prominent. Ultrahigh current density of 2111 A/cm2 and power density of 507 MW/cm3 were obtained in PSrNd0.03ZS ceramics. The sample also exhibited a high discharge energy density of 9.11 J/cm3. The great energy storage properties obtained in this work provides a novel strategy to further enhance the energy storage performance and demonstrates the extremely potential of AFE ceramics in exploiting advanced ceramic capacitors for pushing on the miniaturization and integration of electronic devices.

Calculation of charge density wave phase diagram by interacting eigenmodes method

Patterns and periods of charge density waves (CDWs) in transition metal dichalcogenides exhibit complex phase diagrams that depend on pressure, temperature, metal intercalation, or chalcogen alloying. The phase diagrams have been understood in the context of Landau free energy model which explains the lock-in behavior in the commensurate–incommensurate phase transition and rotational symmetry breaking (stripe phase) in CDW phase. Here, we present that our interatomic potential energy function has not only reproduced the above behaviors in the temperature-dependent phase diagram of monolayer H-TaSe2 without adjustable parameters, but also predict a new commensurate–commensurate phase transition. For the calculation, eigenmodes of the lattice potential were used for variables in the interatomic potential and CDWs are obtained as ground states of interacting eigenmodes. Unlike Landau model, the parameters in our potential energy function are directly calculated from first-principles. Our work explicitly shows how the aforementioned behaviors in CDW phase transition are related with the lattice anharmonicity.

Normal to In-Commensurate Phase Transition in Sr2nb2o7 Single Crystal as Studied by Inelastic Light Scattering

Normal to In-Commensurate Phase Transition in Sr2nb2o7 Single Crystal as Studied by Inelastic Light Scattering

Mode Coupling at around M-Point in PZT.

The question of the microscopic origin of the M-superstructure and additional satellite peaks in the Zr-rich lead zirconate-titanate is discussed for nearly 50 years. Clear contradiction between the selection rules of the critical scattering and the superstructure was found preventing unambiguous attributing of the observed superstructure either to the rotation of the oxygen octahedra or to the antiparallel displacements of the lead cations. Detailed analysis of the satellite pattern explained it as the result of the incommensurate phase transition rather than antiphase domains. Critical dynamics is the key point for the formulated problems. Recently, the oxygen tilt soft mode in the PbZrTiO (PZT2.4) was found. But this does not resolve the extinction rules contradiction. The results of the inelastic X-ray scattering study of the phonon spectra of PZT2.4 around M-point are reported. Strong coupling between the lead and oxygen modes resulting in mode anticrossing and creation of the wide flat part in the lowest phonon dispersion curves is identified. This flat part corresponds to the mixture of the displacements of the lead and oxygen ions and can be an explanation of the extinction rules contradiction. Moreover, a flat dispersion surface is a typical prerequisite for the incommensurate phase transition.

Direct-space-self-consistent-phonon treatment of monolayer structures and dynamics.

Computations, which would have been intractable just a few years ago, are now possible on desktop workstations. Such is the case for the application of the Self-Consistent-Phonon (SCP) approximation to large monolayer clusters on structured surfaces, combining a SCP approach to the system dynamics with a random walk approach to finding the optimum positions of the adsorbed atoms. This combination of techniques enables the investigation of the stability, structure, and dynamics of incommensurate adsorbed monolayers at low temperatures. We refer to this approach as the Direct-Space-Self-Consistent-Phonon framework. We present the application of this framework to the study of rare-gas and molecular hydrogen adsorbates on the graphite basal-plane surface and (for xenon) the Pt(111) surface. The largest cluster size consists of 4096 particles, a system that is large enough to examine incommensurate phases without significant adverse boundary effects. The existence of "pseudo-gaps" in the phonon spectrum of nearly commensurate monolayers is demonstrated, and the implication of such "pseudo-gaps" for the determination of the location of any commensurate ↔ incommensurate phase transition is explored. The stability of striped incommensurate structures vs hexagonal incommensurate structures is examined. The inherent difficulties of using this approach for the highly quantum monolayer solids is shown to generate some particular problems. Nevertheless, we demonstrate that this approach to the stability, structure, and dynamics of quantum monolayer solids is a very useful tool in the theorist's arsenal. By implication, this approach should also be useful in the study of adsorption on graphene and carbon nanotubes at low temperatures.

Incommensurate Crystallization of Neutron Matter in Neutron Stars

The composition of the neutron stars from its surface region, outer-core, inner-core, and to its center is still being investigated. One can only surmise on the properties of neutron stars from the spectroscopic data that may be available from time to time. A few models have suggested that the matter at the surface region of the neutron star is composed of atomic nuclei that get crushed under extremely large pressure and gravitational stress, and this leads to the creation of solid lattice with a sea of electrons, and perhaps some protons, flowing through the gaps between them. Nuclei with high mass numbers, such as ferrous, gold, platinum, uranium, may exist in the surface region or in the outer-core region. It is found that the structure of the neutron star changes very much as one goes from the surface to the core of the neutron star. The surface region is extremely hard and very smooth. Surface irregularities are hardly of the order of 5 mm, whereas the interior of the neutron star may be superfluid and composed of neutron-degenerate matter. However, the neutron star is highly compact crystalline systems, and in terrestrial materials under pressure, many examples of incommensurate phase transitions have been discovered. Consequently, the properties of incommensurate crystalline neutron star have been studied. The composition of the neutron stars in the super dense state remains uncertain in the core of the neutron star. One model describes the core as superfluid neutron-degenerate matter, mostly, composed of neutrons , and a small percentage of protons and electrons More exotic forms of matter are possible, including degenerate strange matter. It could also be incommensurate crystalline neutron matter that could be BCC or HCP. Using principles of quantum statistical mechanics, the specific heat and entropy of the incommensurate crystalline neutron star has been calculated assuming that the temperature of the star may vary between to . Two values for the temperature T that have been arbitrarily chosen for which the calculations have been done are and . The values of specific heat and entropy decrease as the temperature increases, and also, their magnitudes are very small. This is in line with the second law of thermodynamics.

Iodine Adsorption on Ni(110): 2D-Phase Transitions and NiI2 Growth

Scanning tunneling microscopy, low-energy electron diffraction, Auger electron spectroscopy, and density functional theory calculations have been used to investigate I2 adsorption on the Ni(110) surface. Dissociative adsorption takes place rapidly to form a c(2 × 2) layer at an iodine coverage of 0.5 ML. DFT calculations show that hollow sites are energetically preferable for iodine adsorption on the Ni(110) surface. Increase of iodine coverage above 0.5 ML leads to the commensurate–incommensurate phase transition via nucleation of loops of domain walls and to their subsequent ordering into the striped superstructure. At saturation, a striped domain-wall phase degenerates into the uniaxially compressed quasi-hexagonal phase. Further iodine dosing leads to the nucleation and growth of 2D nickel iodide islands.

Incommensurate Phase Transition and Electronic Properties of BaMnF4

We present the ab initio study the electronic, mechanical and structural properties of BaMnF4. We duscuss the trends in the electronic and mechanical properties of BaMnF4 under pressure up to 80 GPa. BaMnF4 belongs to the family of BaMF4-type fluorides (M = Mn, Fe, Co, Ni, Mg, Zn) which share the same orthorhombic structure. The main focus of this study is to elaborate the changes brought about in the electronic and the structural properties by applied pressure. The calculated lattice parameters have been in agreement with the available experimental and theoretical value. Band gap of BaMnF4 in our calculation is about 2.0 eV, separating the empty upper-Hubbard t2g bands and occupied lower-Hubbard eg bands. The total and partial DOS corresponding to the electronic band structure are calculated. Comparative analysis of the results of these calculations shows that the band-gap energy of BaMnF4 decreases with increasing pressure and has a minima value at a critical pressure (appr. 65 GPa), after which it increases again. Some fundamental physical parameters such as elastic constants, bulk modulus, Poisson’s ratio, sound velocities and Debye temperature were calculated and interpreted, too.

New modulated structures of solid bromine at high pressure

Crystal structures of bromine under pressure have been studied through the advanced structure search method in combination with first-principles calculations. At 10 and 90 GPa, we successfully reproduced the experimentally observed molecular phase I and monatomic body-centred orthorhombic phase II, respectively. At 120 and 200 GPa, the lowest-enthalpy structures predicted are body centered tetragonal and face-centered cubic phase, respectively, which are also consistent with previously theoretical study. Interestingly, in the pressure range of 50–80 GPa, our structural searches predicted four structurally similar and modulated structures, oF20, oC24, oF28 and oC12, whose magnitude of the modulation vectors k are 2/5, 1/6, 2/7 and 1/3, respectively. Enthalpy calculations show that oF20, oC24, oF28 and oC12 are thermaldynamically stable in the pressure range of 52–53, 53–58, 58–65 and 65–79 GPa, respectively. Through comparison of the structural characterization and X-ray diffraction patterns of the predicted oF28, oC12 in bromine and the known incommensurate modulated phase V in iodine, we suggest that bromine might also adopt an incommensurate modulated structure. In addition, the prediction of two new phases (oF20 and oC24) between molecular phase I and incommensurate phases are consistent with Raman scattering and X-ray absorption spectroscopy (XAS) experimental results. For the first time, we presented the structure information between molecular phase I and monatomic phase II in bromine. The calculated elastic stiffness coefficients indicate that the four modulated phases are mechanically stable. The calculated electronic density of states for these four predicted phases show that they are all metallic.

Chemical versus conformational entropies at the incommensurate and lock-in phase transitions of morpholinium tetrafluoroborate

Chemical <i>versus</i> conformational entropies at the incommensurate and lock-in phase transitions of morpholinium tetrafluoroborate

Influence of cobalt substitution on the magnetism of NiBr2

Co-substituted ${\mathrm{Ni}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}{\mathrm{Br}}_{2}$ ($0\ensuremath{\le}x\ensuremath{\le}1$) single crystals were synthesized using vapor transport. The physical properties of the crystals were characterized by x-ray powder diffraction, magnetization, and specific-heat measurements. Room-temperature x-ray powder diffraction data indicate that a change from the ${\mathrm{CdCl}}_{2}$ structure type to the ${\mathrm{CdI}}_{2}$ structure type occurs within $0.56&lt;x&lt;0.76$. ${\mathrm{NiBr}}_{2}$ has a commensurate antiferromagnetic phase below ${T}_{\mathrm{N}}\ensuremath{\approx}46\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and an incommensurate magnetic ground state below ${T}_{\mathrm{IC}}\ensuremath{\approx}20\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. Both magnetic transitions are affected by cobalt substitution, and the incommensurate phase transition is present up to at least $x=0.56$. The evolution of magnetism has been studied as a function of cobalt content and is summarized in the temperature-composition phase diagram.

Magnetic-field-induced incommensurate to collinear spin order transition in NiBr2

The triangular spin lattice of NiBr2 is a canonical example of the frustrated helimagnet that shows a collinear commensurate antiferromagnetic to an incommensurate spin helix phase transition on cooling. Herein, we have studied a self-flux grown NiBr2 single crystal by neutron diffraction and low temperature magnetization measurements at fields up to 14 T. Experimental findings enable the deduction of the driving force responsible for the spin spiral ordering. The neutron diffraction data reveal satellite peaks representing characteristic features of an incommensurate magnetic state. The satellites develop symmetrically below TN=44.0(1)K, replacing the main magnetic reflections. Interestingly, a field-induced incommensurate to commensurate spin phase transition has been successfully demonstrated, which enforces the spin helix to restore the high temperature compensated antiferromagnetic structure. This reorientation can be described by a spin-flop in the (a–b) basal plane of a triangular spin lattice system. The findings offer a novel way for spin helix control of incommensurate phases, having immense scientific and technological implications in the next-generation data storage devices.

Incommensurate instability and diffuse scattering at Brillouin zone boundary in Zr-rich lead zirconate titanate

Detailed study of the X-ray diffuse scattering in the paraelectric phase of the PbZr0.985Ti0.015O3 was carried out. We concentrated on the analysis of the scattering peculiarities in the vicinities of M- and R- points of the Brillouin zone. We have observed a critical increase of the diffuse scattering at the position Q ≈ (0.47 + h 0.53 + k l) slightly aside of M point on cooling to the intermediate phase. We attribute observed critical scattering to a mixed mode containing both oxygen octahedral tilts and antiparallel cationic displacements. Tentative conclusion is made describing earlier reported complicated set of the satellite peaks around M-point as the result of the soft-mode driven incommensurate phase transition.

Impact of the Flexoelectric Coupling and Electrostriction on the Dispersion of Soft Phonon Modes and Neutron Scattering in Ferroelectrics

Within the Landau–Ginzburg–Devonshire (LGD) theory framework, the impact of the flexocoupling and electrostriction on the soft phonon dispersion and neutron scattering spectra is analyzed, and analytical expressions are derived. The impact of the higher gradient term in the LGD functional is studied analytically. The existence of incommensurate modulations in a temperature interval higher than the Curie temperature TC, but lower than the temperature of incommensurate phase transition TIC, TC &lt; T &lt; TIC, and under the condition of the flexocoefficient magnitude ranging over the critical value, |f| &gt; fcr(T), is established. The influence of the dynamic flexocoefficient M, suggested in [1], on phonon spectra is studied. We consider various parameters of the free energy functional; especially, we have discovered a significant contribution of the electrostriction to the appearance of a commensurate phase. In the recent years, the various methods based on the neutron scattering acquire more applications to study phonons in solid crystals. We have analyzed neutron scattering spectra and shown that theoretical predictions are in a very good agreement with observed data.

Realization of the axial next-nearest-neighbor Ising model in U3Al2Ge3

Here we report small-angle neutron scattering (SANS) measurements and theoretical modeling of U$_3$Al$_2$Ge$_3$. Analysis of the SANS data reveals a phase transition to sinusoidally modulated magnetic order, at $T_{\mathrm{N}}=63$~K to be second order, and a first order phase transition to ferromagnetic order at $T_{\mathrm{c}}=48$~K. Within the sinusoidally modulated magnetic phase ($T_{\mathrm{c}} < T < T_{\mathrm{N}}$), we uncover a dramatic change, by a factor of three, in the ordering wave-vector as a function of temperature. These observations all indicate that U$_3$Al$_2$Ge$_3$ is a close realization of the three-dimensional Axial Next-Nearest-Neighbor Ising model, a prototypical framework for describing commensurate to incommensurate phase transitions in frustrated magnets.

Incommensurate Chirality Density Wave Transition in a Hybrid Molecular Framework.

Using single-crystal x-ray diffraction we characterize the 235K incommensurate phase transition in the hybrid molecular framework tetraethylammonium silver(I) dicyanoargentate, [NEt_{4}]Ag_{3}(CN)_{4}. We demonstrate the transition to involve spontaneous resolution of chiral [NEt_{4}]^{+} conformations, giving rise to a state in which molecular chirality is incommensurately modulated throughout the crystal lattice. We refer to this state as an incommensurate chirality density wave (XDW) phase, which represents a fundamentally new type of chiral symmetry breaking in the solid state. Drawing on parallels to the incommensurate ferroelectric transition of NaNO_{2}, we suggest the XDW state arises through coupling between acoustic (shear) and molecular rotoinversion modes. Such coupling is symmetry forbidden at the Brillouin zone center but symmetry allowed for small but finite modulation vectors q=[0,0,q_{z}]^{*}. The importance of long-wavelength chirality modulations in the physics of this hybrid framework may have implications for the generation of mesoscale chiral textures, as required for advanced photonic materials.

Incommensurately modulated structure of morpholinium tetrafluoroborate and configurational versus chemical entropies at the incommensurate and lock-in phase transitions.

Morpholinium tetrafluoroborate, [C4H10NO]+[BF4]-, belongs to a class of ferroelectric compounds ABX4. However, [C4H10NO]+[BF4]- does not develop ferroelectric properties because the incommensurate phase below Tc,I = 153 K is centrosymmetric with superspace group Pnam(σ100)00s and σ1 = 0.42193 (12) at T = 130 K; the threefold superstructure below Tc,II = 117-118 K possesses the acentric but non-ferroelectric space group P212121. At ambient conditions, [C4H10NO]+[BF4]- comprises orientationally disordered [BF4]- anions accommodated in cavities between four morpholinium cations. A structure model for the incommensurately modulated phase, which involves modulated orientational ordering of [BF4]- together with modulated distortions and displacements of the morpholinium ions is reported. A mechanism is proposed for the phase transitions, whereby at low temperatures morpholinium cations are shaped around the tetrafluoroborate anion in order to optimize the interactions with one orientation of this anion and, thus, forcing [BF4]- into this orientation. This mechanism is essentially different from a pure order-disorder phase transition. It is supported by consideration of the transition entropy. The difference in configurational entropy between the disordered and incommensurate phases has been computed from the structure models. It is shown to be much smaller than the experimental transition entropy reported by Owczarek et al. [Chem. Phys. (2011), 381, 11-20]. These features show that the order-disorder contribution is only a minor contribution to the transition entropy and that other factors, such as conformational changes, play a larger role in the phase transitions.

Quantum incommensurate skyrmion crystals and commensurate to in-commensurate transitions in cold atoms and materials with spin–orbit couplings in a Zeeman field

In this work, we study strongly interacting spinor atoms in a lattice subject to a two dimensional (2d) anisotropic Rashba type of spin orbital coupling (SOC) and an Zeeman field. We find the interplay between the Zeeman field and the SOC provides a new platform to host rich and novel classes of quantum commensurate and in-commensurate phases, excitations and phase transitions. These commensurate phases include two collinear states at low and high Zeeman field, two co-planar canted states at mirror reflected SOC parameters respectively. Most importantly, there are non-coplanar incommensurate Skyrmion (IC-SkX) crystal phases surrounded by the four commensurate phases. New excitation spectra above all the five phases, especially on the IC-SKX phase are computed. Three different classes of quantum commensurate to in-commensurate transitions from the IC-SKX to its four neighboring commensurate phases are identified. Finite temperature behaviors and transitions are discussed. The critical temperatures of all the phases can be raised above that reachable by current cold atom cooling techniques simply by tuning the number of atoms N per site. In view of recent impressive experimental advances in generating 2d SOC for cold atoms in optical lattices, these new many-body phenomena can be explored in the current and near future cold atom experiments. Applications to various materials such as MnSi, Si, especially the complex incommensurate magnetic ordering in Li2IrO3 are given.