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At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Dynamical effects from anomalies: Modified electrodynamics in Weyl semimetals

Here, we discuss the modified quantum electrodynamics from a time-reversal-breaking Weyl semimetal coupled with a U⁡(1) gauge (electromagnetic) field. A key role is played by the soft dispersion of the photons in a particular direction, say $\hat{z}$, due to the Hall conductivity of the Weyl semimetal. Due to the soft photon, the fermion velocity in $\hat{z}$ is logarithmically reduced under renormalization group flow, together with the fine-structure constant. Meanwhile, fermions acquire a finite lifetime from spontaneous emission of the soft photon, namely, the Cherenkov radiation. At low-energy E, the inverse of the fermion lifetime scales as τ -1 ~E/PolyLog⁡(E). Therefore, even though fermion quasiparticles are eventually well-defined at very low energy, over a wide intermediate energy window the Weyl semimetal behaves like a marginal Fermi liquid. Phenomenologically, our results are more relevant for emergent Weyl semimetals, where the fermions and photons all emerge from strongly correlated lattice systems. Possible experimental implications are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Quantum many-body calculations using body-centered cubic lattices

It is often computationally advantageous to model space as a discrete set of points forming a lattice grid. This technique is particularly useful for computationally difficult problems such as quantum many-body systems. For reasons of simplicity and familiarity, nearly all quantum many-body calculations have been performed on simple cubic lattices. Since the removal of lattice artifacts is often an important concern, it would be useful to perform calculations using more than one lattice geometry. In this paper we show how to perform quantum many-body calculations using auxiliary-field Monte Carlo simulations on a three-dimensional body-centered cubic (BCC) lattice. As a benchmark test we compute the ground state energy of 33 spin-up and 33 spin-down neutrons in the unitary limit, which is an idealized limit where the interaction range is zero and scattering length is infinite. As a fraction of the free Fermi gas energy E FG , we find that the ground state energy is E 0 /E FG =0.369(2),0.371(2), using two different definitions of the finite-system energy ratio. This is in excellent agreement with recent results obtained on a cubic lattice [He et al., Phys. Rev. A 101, 063615 (2020)]. We find that the computational effort and performance on a BCC lattice is approximately the same as that for a cubic lattice with the same number of lattice points. We discuss how the lattice simulations with different geometries can be used to constrain the size of lattice artifacts in simulations of continuum quantum many-body systems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Imaging surface topography with coherent x-ray reflectivity: Theory, kinematics, and simulations

A theoretical formalism is described for understanding coherent x-ray reflectivity (CXR) from the surface of a semi-infinite crystal having a variable surface topography, described by the height profile ℎ(𝑥,𝑦). The surface topography is imaged as a complex “effective density,” obtained from the phasing and inversion of the coherent x-ray reflectivity data, measured through a rocking scan centered at a vertical momentum transfer 𝑄$^{0}_{𝑧}$ and a vertical range Δ⁢𝑄 𝑧 . The formalism predicts that the effective density has an amplitude with a maximum located at the surface height for each position within the surface plane. The phase of the effective density has a lateral variation that is controlled by the surface height and a vertical variation that reflects a combination of the interfacial structure and specific choice of measurement conditions. This understanding enables direct observation of nanometer-scale interfacial topography, i.e., ℎ⁡(𝑥,𝑦)⁢𝑐 𝑠 (where 𝑐 𝑠 is the vertical substrate lattice parameter) with Å-scale sensitivity to surface height. Numerical simulations illustrate and confirm the theoretical results. These results show how the interpretation of the interfacial density phase obtained by CXR data inversion (i.e., surface topography with respect to a flat surface) is conceptually similar to that previously known for Bragg coherent diffraction imaging (BCDI) measurements of isolated nanoparticles (i.e., lattice displacements with respect to an ideal crystal lattice). This suggests that CXR can be thought of as a form of dark field imaging with respect to the bright field BCDI approach. An implication of these results is that interfacial imaging may bypass some of the significant challenges associated with BCDI imaging of multiple particles having different orientations.

X-ray imaging↗
DOE OSTI2021

Magnetoelastic coupling and spin contributions to entropy and thermal transport in biferroic yttrium orthochromite

Direct engineering of material properties through exploitation of spin, phonon, and charge-coupled degrees of freedom is an active area of development in materials science. However, the relative contribution of the competing orders to controlling the desired behavior is challenging to decipher. In particular, the independent role of phonons, magnons, and electrons, quasiparticle coupling, and relative contributions to the phase transition free energy largely remain unexplored, especially for magnetic phase transitions. Here, we study the lattice and magnetic dynamics of biferroic yttrium orthochromite using Raman, infrared, and inelastic neutron spectroscopy techniques, supporting our experimental results with first-principles lattice dynamics and spin-wave simulations across the antiferromagnetic transition at T N ~ 138 K. Spectroscopy data and simulations together with the heat capacity (C p ) measurements, allow us to quantify individual entropic contributions from phonons (0.01 ± 0.01k B atom -1 ), dilational (0.03 ± 0.01k B atom -1 ), and magnons (0.11 ± 0.01k B atom -1 ) across TN. High-resolution phonon measurements conducted in a magnetic field show that anomalous T-dependence of phonon energies across TN originates from magnetoelastic coupling. Additionally, phonon scattering is primarily governed by the phonon–phonon coupling, with little contribution from magnon–phonon coupling, short-range spin correlations, or magnetostriction effects; a conclusion further supported by our thermal conductivity measurements conducted up to 14 T, and phenomenological modeling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Role of electromagnetic gauge-field fluctuations in the selection between chiral and nematic superconductivity

Motivated by the observation of nematic superconductivity in several systems, we revisit the problem of the leading pairing instability of two-component unconventional superconductors on the triangular lattice—such as (p x , p y )-wave and (d x 2 –y 2 , d xy )-wave superconductors. Such a system has two possible superconducting states: the chiral state (e.g., p + ip or d + id), which breaks time-reversal symmetry, and the nematic state (e.g., p + p or d + d), which breaks the threefold rotational symmetry of the lattice. Weak-coupling calculations generally favor the chiral over the nematic superconducting state, raising the question of what mechanism can stabilize the latter. Here, we show that the electromagnetic field fluctuations can play a crucial role in selecting between these two states. Specifically, we derive and analyze the effective free energy for the two-component superconducting order parameter after integrating out the gauge-field fluctuations, which is formally justified if the spatial order parameter fluctuations can be neglected. A nonanalytic cubic term arises, as in the case of a conventional s -wave superconductor. However, unlike the latter, the cubic term depends on the relative phase and on the relative amplitudes between the two order parameter components, in such a way that it generally favors the nematic state. This result is a direct consequence of the fact that the stiffness of the superconducting order parameter is not isotropic. Competition with the quartic term, which favors the chiral state, leads to a renormalized phase diagram in which the nematic state displaces the chiral state over a wide region in the parameter space. Here, we analyze the stability of the fluctuation-induced nematic phase, generalize our results to tetragonal lattices, and discuss their applicability to candidate nematic superconductors, including twisted bilayer graphene.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Trends in electronic structures and s ± -wave pairing for the rare-earth series in bilayer nickelate superconductor R 3 Ni 2 O 7

The recent discovery of pressure-induced superconductivity in the bilayer La 3 Ni 2 O 7 (LNO) has opened a new platform for the study of unconventional superconductors. In this publication, we investigate theoretically the whole family of bilayer 327-type nickelates R 3 Ni 2 O 7 (R = rare-earth elements) under pressure. From La to Lu, the lattice constants and volume decrease, leading to enhanced in-plane and out-of-plane hoppings, resulting in an effectively reduced electronic correlation U / W. Furthermore, the Ni's t 2g states shift away from the e g states, while the crystal-field splitting between d 3z 2 -r 2 and d x 2 -y 2 is almost unchanged. In addition, six candidates were found to become stable in the Fmmm phase, with increasing values of critical pressure as the atomic number increases. Similar to the case of LNO, the s ± -wave pairing tendency dominates in all candidates, due to the nesting between the M = (π , π) and the X = (π , 0) and Y = (0 , π) points in the Brillouin zone. Then, T c is expected to decrease as the radius of rare-earth (RE) ions decreases. In conclusion, our results suggest that LNO is already the “optimal” candidate, with Ce a close competitor, among the whole of the RE bilayer nickelates, and to increase T c we suggest growing on special substrates with larger in-plane lattice spacings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Multimodal Approach Reveals the Symmetry-Breaking Pathway to the Broken Helix in EuIn 2 ⁢As 2

Understanding and manipulating emergent phases, which are themes at the forefront of quantum-materials research, rely on identifying their underlying symmetries. This general principle has been particularly prominent in materials with coupled electronic and magnetic degrees of freedom, in which magnetic order influences the electronic band structure and can lead to exotic topological effects. However, identifying symmetry of a magnetically ordered phase can pose a challenge, particularly in the presence of small domains. Here we introduce a multimodal approach for determining magnetic structures, which combines symmetry-sensitive optical probes, scattering, and group-theoretical analysis. We apply it to EuIn 2 ⁢As 2 , a material that has received attention as a candidate axion insulator. While first-principles calculations predict this state on the assumption of a simple collinear antiferromagnetic structure, subsequent neutron-scattering measurements reveal a much more intricate magnetic ground state characterized by two coexisting magnetic wave vectors reached by successive thermal phase transitions. The proposed high- and low-temperature phases are a spin helix and a state with interpenetrating helical and Néel antiferromagnetic order termed a “broken helix,” respectively. Employing a multimodal approach, we identify the magnetic structure associated with these two phases of EuIn 2 ⁢As 2 . We find that the higher-temperature phase is characterized by a variation of the magnetic moment amplitude from layer to layer, with the moment vanishing entirely in every third Eu layer. The lower-temperature structure is similar to the broken helix, with one important difference: Because of local strain, the relative orientation of the magnetic structure and the lattice is not fixed. Consequently, the symmetry required to protect the axion phase is not generically protected in EuIn 2 ⁢As 2 , but we show that it can be restored if the magnetic structure is tuned with uniaxial strain. Finally, we present a spin Hamiltonian that identifies the spin interactions that account for the complex magnetic order in EuIn 2 ⁢As 2 . Our work highlights the importance of a multimodal approach in determining the symmetry of complex order parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Residual lattice strain in quartzites as a potential palaeo-piezometer

SUMMARY If a crystal lattice is subjected to a stress, it becomes distorted and no longer represents the ideal crystal symmetry, and if the stress introduces defects such as dislocations, some of this distortion is preserved after the applied stress is removed. In this study, we investigate lattice distortion in quartz at the micron scale with synchrotron X-ray Laue diffraction. From Laue images the local deviatoric strain tensor is derived and corresponding stresses are calculated based on elastic properties. The method is applied to metasedimentary quartzites from the Bergell Alps that were deformed at conditions of greenschist facies metamorphism. The residual palaeostrain is represented in maps of the deviatoric strain tensor components and with deviatoric strain axis pole figures. Data suggest overall shortening perpendicular to the schistosity plane but with considerable asymmetry relative to foliation and lineation, probably attributed to simple shear. Crystallographic pole figures from Laue diffraction agree with neutron diffraction and EBSD measurements and display quartz c-axes girdle distributions with maxima also perpendicular to schistosity. The method shows promise to be used as a palaeo-piezometer to unravel the stress field during tectonic deformation.

58 GEOSCIENCES↗
DOE OSTI2024

Dynamic magnetic phase transition induced by parametric magnon pumping

Uncovering pathways to optically drive magnetic order-disorder transitions on ultrashort timescales can lead to the realization of novel out-of-equilibrium quantum phenomena. A long-sought pathway is to directly excite a highly nonthermal energy-momentum distribution of magnons, bypassing both charge and lattice degrees of freedom. However, this remains elusive owing to the weak coupling and large momentum mismatch between photons and magnons. Here we demonstrate strong parametric excitation of magnons across the entire Brillouin zone of the antiferromagnetic insulator Sr 2 ⁢Cu 3 ⁢O 4 ⁢Cl 2 by periodically modulating the superexchange interaction with the electric field of light. The excitation efficiency is greatly enhanced by tuning to the van Hove singularity in the magnon spectrum, sufficient to transiently collapse the antiferromagnetic state using a pulsed laser field of 10 9 V/m. The order parameter recovery timescale increases by over 1000 times as a function of excitation density, reflecting a crossover from high- to low-energy magnon dominated decay dynamics. This electric-field induced parametric magnon pumping mechanism is applicable to a broad range of magnetic insulators and opens up the possibility of dynamically engineering magnon distributions by design.

antiferromagnetism↗
DOE OSTI2025

Dynamical logical qubits in the Bacon-Shor code

The Bacon-Shor code is a quantum error correcting subsystem code composed of weight-2 check operators that admits a single logical qubit, and has distance 𝑑 on a 𝑑×𝑑 square lattice. We show that when viewed as a Floquet code, by choosing an appropriate measurement schedule of the check operators, it can additionally host several dynamical logical qubits. Specifically, we identify a period-4 measurement schedule of the check operators that preserves logical information between the instantaneous stabilizer groups. Such a schedule not only measures the usual stabilizers of the Bacon-Shor code, but also measures and promotes gauge operators of the parent subsystem code to additional temporary stabilizers that protect the dynamical logical qubits against errors. We show that the code distance of these Floquet-Bacon-Shor codes scales as Θ⁢(𝑑/√𝑘) on an 𝑛=𝑑×𝑑 lattice with 𝑘 dynamical logical qubits, along with the logical qubit of the parent subsystem code. Unlike the usual Bacon-Shor code, the Floquet-Bacon-Shor code family introduced here can therefore saturate the subsystem bound 𝑘⁢𝑑=𝑂⁡(𝑛). Moreover, several errors are shown to be self-corrected purely by the measurement schedule itself. This work provides insights into the design space for dynamical codes and expands the known approaches for constructing Floquet codes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Theoretical tools for neutrino scattering: interplay between lattice QCD, EFTs, nuclear physics, phenomenology, and neutrino event generators

Maximizing the discovery potential of increasingly precise neutrino experiments will require an improved theoretical understanding of neutrino-nucleus cross sections over a wide range of energies. Low-energy interactions are needed to reconstruct the energies of astrophysical neutrinos from supernovae bursts and search for new physics using increasingly precise measurement of coherent elastic neutrino scattering. Higher-energy interactions involve a variety of reaction mechanisms including quasi-elastic scattering, resonance production, and deep inelastic scattering that must all be included to reliably predict cross sections for energies relevant to DUNE and other accelerator neutrino experiments. Refined nuclear interaction models in these energy regimes will also be valuable for other applications, such as measurements of reactor, solar, and atmospheric neutrinos. This manuscript discusses the theoretical status, challenges, required resources, and path forward for achieving precise predictions of neutrino-nucleus scattering and emphasizes the need for a coordinated theoretical effort involved lattice QCD, nuclear effective theories, phenomenological models of the transition region, and event generators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

$Ξ$ 𝑏 → $Ξ$ form factors from lattice QCD and standard-model predictions for $Ξ$ 𝑏 → $Ξ$⁢𝜇 + ⁢𝜇 − and $Ξ$ 𝑏 → $Ξ$⁢𝛾 decays

We present the first lattice QCD determination of the $Ξ$ 𝑏 → $Ξ$ vector, axial-vector, and tensor form factors, which are relevant for the theory of rare decays including $Ξ$ 𝑏 → $Ξ$⁢ℓ + ⁢ℓ − and $Ξ$ 𝑏 → $Ξ$⁢𝛾. The calculation is performed with 2+1 flavors of domain-wall fermions at three different lattice spacings and pion masses in the range from approximately 430 to 230 MeV. The bottom quark is implemented using an anisotropic clover action. Three-point functions with a wide range of source-sink separations and model averaging are used to extract the ground-state contributions. We fit the dependence of the form factors on the momentum transfer, the pion mass, and the lattice spacing using modified 𝑧 expansions that account for subthreshold branch cuts, and apply dispersive bounds and asymptotic behavior constraints to achieve controlled uncertainties in the full semileptonic kinematic region. Using our form factor results, we present standard model predictions for the $Ξ$$^{−}_{𝑏}$ → $Ξ$ − ⁢𝛾 and $Ξ$$^{−}_{𝑏}$ → $Ξ$ − ⁢𝜇 + ⁢𝜇 − branching fractions and two angular observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Breakdown of order fractionalization in the CPT model

Here, we present an analysis of the half-filled CPT model, an analytically tractable Kondo lattice model with Yao-Lee spin-spin interactions on a 3D hyperoctagon lattice, proposed by Coleman, Panigrahi, and Tsvelik. Previous studies have established that the CPT model exhibits odd-frequency triplet superconductivity and order fractionalization. Through asymptotic analyses in the small- and large- Kondo coupling limits, we identify a quantum critical point at , marking a transition from a superconductor to a Kondo insulator. By estimating the vison gap energy to account for thermal gauge fluctuations, we determine the energy scales governing the thermal breakdown of order fractionalization. Moreover, at large the Kondo insulator undergoes orbital decoupling, leading to the formation of a decoupled Kitaev orbital liquid. These findings and analogies with the -gauged model lead us to propose a tentative phase diagram for the CPT model at half-filling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Single photon emitters in van der Waals solids for quantum photonics: materials, theory and molecular-scale characterization probes

Strong light–matter interactions in two-dimensional layered materials (2D materials) have attracted the interest of researchers from interdisciplinary fields for more than a decade now. A unique phenomenon in some 2D materials is their large exciton binding energies (BEs), increasing the likelihood of exciton survival at room temperature. It is this large BE that mediates the intense light–matter interactions of many of the 2D materials, particularly in their monolayer limit, where the interplay of excitonic phenomena poses a wealth of opportunities for high-performance optoelectronics and quantum photonics. Within quantum photonics, quantum information science (QIS) is growing rapidly, where photons are a promising platform for information processing due to their low-noise properties, excellent modal control, and long-distance propagation. A central element for QIS applications is a single photon emitter (SPE) source, where an ideal on-demand SPE emits exactly one photon at a time into a given spatiotemporal mode. Recently, 2D materials have shown practical appeal for QIS which is directly driven from their unique layered crystalline structure. This structural attribute of 2D materials facilitates their integration with optical elements more easily than the SPEs in conventional three-dimensional solid state materials, such as diamond and SiC. In this review article, we will discuss recent advances made with 2D materials towards their use as quantum emitters, where the SPE emission properties maybe modulated deterministically. Here, the use of unique scanning tunneling microscopy tools for the in-situ generation and characterization of defects is presented, along with theoretical first-principles frameworks and machine learning approaches to model the structure-property relationship of exciton–defect interactions within the lattice towards SPEs. Given the rapid progress made in this area, the SPEs in 2D materials are emerging as promising sources of nonclassical light emitters, well-poised to advance quantum photonics in the future.

2D layered materials↗
DOE OSTI2025

Effect of Propagating Dopant Reactivity on Lattice Oxygen Loss in LLZO Solid Electrolyte Contacted with Lithium Metal

Lithium lanthanum zirconium oxide (LLZO) is widely known as the most stable solid electrolyte against lithium metal electrodes. This thermodynamic stability can be lost by the presence of dopants which are required to stabilize the cubic phase of LLZO and can be reduced by lithium metal. However, the role of oxygen in such reactions is taken for granted. In this work, the reduction of Nb-substituted LLZO (Nb-LLZO) is explored by Li metal and shows that interfacial reactions propagate and lead to the decomposition with substantial Nb 5+ reduction deep into the bulk electrolyte. Scanning Transmission Electron Microscopy with Energy Dispersive X-ray Spectroscopy and thermogravimetric analyses show much of the reduction is due to oxygen vacancies formed, leading to increased electronic conductivity mapped with conductive Atomic Force Microscopy. Density functional theory calculations indicate oxygen release is favored by increased excess lithiation of Nb-LLZO. Electrochemical impedance of polycrystalline Nb-LLZO shows the continuous evolution of ionically resistive interphases near the lithium metal interface with Nb-LLZO while single crystals show little reactivity at room temperature and self-limiting reduction at 60°C. This work underlines the role of grain boundaries in propagating destructive solid electrolyte reactions and highlights previously unseen mechanisms involving lattice oxygen in LLZO.

Li metal, solid-state electrolytes↗
DOE OSTI2024

Stealth dark matter spectrum using Laplacian Heaviside smearing and irreducible representations

We present nonperturbative lattice calculations in the quenched approximation of the low-lying meson and baryon spectrum of the SU(4) gauge theory with fundamental fermion constituents. This theory is one instance of stealth dark matter, a class of strongly coupled theories, where the lowest mass stable baryon is the dark matter candidate. This work constitutes the first milestone in the program to study stealth dark matter self-interactions. Here, we focus on reducing excited state contamination in the single-baryon channel by applying the Laplacian Heaviside method, as well as projecting our baryon operators onto the irreducible representations of the octahedral group. We compare our resulting spectrum to previous work involving Gaussian smeared nonprojected operators and find good agreement with reduced statistical uncertainties. We also present the spectrum of the low-lying odd-parity baryons for the first time.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Tunable magnetic order in low-symmetry SeO 3 ligand linked TM 3 (SeO 3 ) 3 H 2 O ( TM =Mn , Co, and Ni) compounds

The ability to design crystal lattices with specific sublattice geometries has long been sought after especially in the context of harnessing magnetic frustration to elicit emergent physics. One approach which has seen some success recently is to design magnetic sublattices chemically through the use of nonmagnetic linker ligands as scaffolding for the magnetic ions. In this work we report the magnetic properties of one such family of materials, the transition metal (TM) selenite hydrates with chemical formula TM 3 (SeO 3 ) 3 H 2 O. These materials link highly distorted TMO 6 octahedra via nonmagnetic [SeO 3 ] 2+ linkers. Studying members with TM = Mn, Co, and Ni we use magnetic susceptibility and neutron powder diffraction to identify antiferromagnetic order in all three compounds with moderate frustration indexes. A comparison of the magnetic structures suggests that while the overall structure of the SeO 3 scaffolding remains unchanged the TM effects changes in the magnetic properties through tuning the internal bonding parameters and the single-ion physics. Changing from Mn to Co is found to be particularly consequential manifesting changes in both the ordered-moment direction and in the direction of the ordering vector. Field-dependent measurements of the susceptibility and heat capacity reveal metamagnetic transitions in both Mn 3 (SeO 3 ) 3 H 2 O and Co 3 (SeO 3 ) 3 H 2 O indicating nearby magnetic ground states accessible under relatively small applied fields. Density functional theory calculations broadly confirm these results, showing both a sensitivity of the magnetic structure to the TM and its local environment. Although no spin liquid behavior is achieved, these results suggest the fruitfulness of such synthesis philosophies and encourage future work to engender higher frustration in these materials via doping, field, pressure, or larger linker ligands.

36 MATERIALS SCIENCE↗
NASA NTRS2004

Notes on Interface Growth Kinetics 50 Years after Burton, Cabrera and Frank

This overview is devoted to some unresolved basic problems in crystal growth kinetics. The density wave approach to propagation of a spatially diffuse interface between a growing crystal and its simple (e.g., metallic) melt is discussed is Section 2. This approach allows for the calculation of kinetic coefficients and is an alternative to the localized interface concept in which each atom belongs to either a solid or a liquid. Sections 3 and 4 deals mainly with layer growth from solution. Mutual retardation of the growth steps via their bulk and d a c e diffusion fields is the major subject. The influence of solution flow on step bunching (Section 4) suggests the essential influence of bulk diffusion on the surface morphology. The flow within the solution boundary layer enhances step-step interaction, influences the step bunching process and the resulting step pattern morphology on the growing surface. Recent experiments on the rates at which strongly polygonized steps on protein and small molecule crystals propagate during growth from solution are analyzed in Section 5 . We have shown that the step segments may be "singular" and that "one-dimensional nucleation" may be the rate limiting stage for the segments that are shorter or comparable in length to the thermodynamically equilibrium interlink distance. In this case, the reciprocal dependence of the segment propagation rate on the segment length that follow from the Gibbs-Thompson law, should be replaced by an abrupt switch from zero to a finite constant velocity. Until recently, the Kossel crystal remained the only model used in crystal growth theory. In such Kossel Gibbs-Thomson law, should be replaced by an abrupt switch &om zero to a finite constant velocity. crystals, all kinks at the steps are identical and the kink rate is a linear function of the supersaturation. In the non-Kossel crystals, there may be several kink configurations characterized by different geometries and energies. These configurations should appear in a specific sequence when each new lattice unit cell is filled. As a result of such a cooperative interaction within the unit cell, a non-linear dependence of the kink rate on the vapor pressure or solution concentration in excess over the equilibrium value should be expected.

Chernov, A. A.↗