Diffraction Patterns Of Crystals Research Articles

Radial nanotubes for nanoelectronics elements: structure and diffraction

Formulation of the problem. Nanotubes are promising objects for the development of nanoelectronic elements. The range of electronic properties of nanotubes can be significantly expanded by synthesizing structures on their surface. Such structures have a radial cylindrical lattice; a number of nanowires have a similar lattice. Radial crystals are a new group of cylindrical structures, the study of which is at an early stage. Therefore, it is necessary to develop both ideas about the structure of radial crystals and a method for their structural analysis. The aim. Consider the simplest radial structures and the features of diffraction by them. Results. A description of the close-packed structure of nanowires and atomic layers with bcc, fcc, and hcp radial lattices sorbed on the nanotube surfaces is proposed, taking into account the effect of radial relaxation. A linear approximation is proposed that makes it possible to quantitatively describe radial relaxation at the initial stage of block growth. The quantitative kinematic theory of Fraunhofer diffraction on achiral radial structures is considered as the basis for their structural analysis, and formulas relating the parameters of the direct and reciprocal lattices are obtained. The results of model calculations of scattering intensity distributions by layer planes of the reciprocal lattice of radial crystals and along the layer lines of their diffraction patterns are presented. Schemes of diffraction patterns of radial crystals with bcc, fcc, and hcp radial lattices are presented. The applicability of traditional selection rules and the significant dependence of the positions of pseudo-orthogonal reflections on the crystal size are shown. Practical significance. The proposed description of radial structures with bcc, fcc, and hcp radial lattices and the diffraction method of structural analysis of their achiral varieties will provide structural control of the products of their synthesis, which is necessary when carrying out a wide range of studies both at the stage of development work on the synthesis of nanoelectronic elements, and for technological control during their industrial production.

Synthesis of Nanomagnetite/Crosslinked Carboxymethyl kappa Carrageenan Nickel Imprinted Composite

Nickel(II) ions are carcinogenic water pollutants. To increase the accuracy of instrumental analysis of Ni(II) content, several analytical preparation methods have been developed, including solid phase adsorption extraction. The development of magnetic solid phase extraction adsorbents for metal ions is required, to support the application of magnetic solid phase adsorption as a method of separating metal ions in aqueous samples. This research describes the synthesis of Magnetic Solid Phase Extraction adsorbents as Ni(II) ion adsorbents, nano magnetite/carboxymethyl kappa-carrageenan (CMKC) crosslinked bisphenol A diglycidyl ether (BADGE) imprinted Ni(II)-IIP ion composites. This research was carried out in several stages, synthesis and characterization of nano magnetite (NM), synthesis and characterization of CMKC, and synthesis of NM/CMKCNi(II)-IIP adsorbents. The results of the synthesis were analyzed for morphological characteristics, magnetic strength, spectral characteristics, crystallinity, and composition using SEM, FTIR, XRD, and XRF instruments. The adsorption ability of Ni(II) of the adsorbent was tested. Determination of Ni(II) ion content in the sample before and after adsorption was carried out using a flame atomic absorption spectrophotometer (FAAS). Based on the results of spectral character analysis, crystal diffraction patterns, magnetic strength, and morphology, it is confirmed that nano-magnetite has been successfully synthesized. The diameter of the nano magnetite grains is 21.8 nm, the adsorbent NM/CMKCNi(II)-IIP has magnetic properties and wavy surface morphology. The optimum adsorption ability of Ni(II) for the NM/CMKCNi(II)-IIP composite was 2.44 mg Ni(II)/g adsorbent. To evaluate the tendency of the adsorption ability of the adsorbent towards Ni(II) ions in the presence of competitor ions, the adsorption ability of the adsorbent to adsorp Ni(II) ions in samples containing Ni(II) ions, Pb(II) ions and a mixture of Ni(II) ions. and Pb(II) were determined, based on the results of the analysis, the ability of the adsorbent to adsorb Ni(II) ions was higher than the ability of the adsorbent to adsorb Pb(II) ions, in all types of samples.

Experimental Revelation of Surface and Bulk Lattices in Faceted Cu2 O Crystals.

Semiconductor crystals have generally shown facet-dependent electrical, photocatalytic, and optical properties. These phenomena have been proposed to result from the presence of a surface layer with bond-level deviations. To provide experimental evidence of this structural feature, synchrotron X-ray sources areused to obtain X-ray diffraction (XRD) patterns of polyhedral cuprous oxide crystals. Cu2 O rhombic dodecahedra display two distinct cell constants from peak splitting. Peak disappearance during slow Cu2 O reduction to Cu with ammonia borane differentiates bulk and surface layer lattices. Cubes and octahedra also show two peak components, while diffraction peaks of cuboctahedra are comprised of three components. Temperature-varying lattice changes in the bulk and surface regions also show shape dependence. From transmission electron microscopy (TEM) images, slight plane spacing deviations in surface and inner crystal regions are measured. Image processing provides visualization of the surface layer with depths of about 1.5-4nm giving dashed lattice points instead of dots from atomic position deviations. Close TEM examination reveals considerable variation in lattice spot size and shape for different particle morphologies, explaining why facet-dependent properties are emerged. Raman spectrum reflects the large bulk and surface lattice difference in rhombic dodecahedra. Surface lattice difference can change the particle bandgap.

Intrinsic stacking fault of the ilmenite type in the structure of lithium niobate crystals of various compositions

X-ray diffraction (XRD) patterns of lithium niobate crystals doped with zinc (Zn2+) and crystals double doped with cations (Zn2+:Mg2+) as well as the spectrum of a nominally pure one were studied. Doping was carried out using a method of direct and homogeneous introduction of impurities into a charge. It was found that in all XRD patterns of the studied samples in the range of scattering angles from 11° to 22° and from 25° to 31° weak additional reflections, which are forbidden by the symmetry space group R3c, appeared. We established that the appearance of weak reflections was due to the ordering of intrinsic extended superstructural defects. In the double cell (a' = 2a, c' = c) an ilmenite type defect was formed. The calculated concentration of these defects was about 5% over the entire structure.

Crystal diffraction prediction and partiality estimation using Gaussian basis functions.

The recent diversification of macromolecular crystallographic experiments including the use of pink beams, convergent electron diffraction and serial snapshot crystallography has shown the limitations of using the Laue equations for diffraction prediction. This article gives a computationally efficient way of calculating approximate crystal diffraction patterns given varying distributions of the incoming beam, crystal shapes and other potentially hidden parameters. This approach models each pixel of a diffraction pattern and improves data processing of integrated peak intensities by enabling the correction of partially recorded reflections. The fundamental idea is to express the distributions as weighted sums of Gaussian functions. The approach is demonstrated on serial femtosecond crystallography data sets, showing a significant decrease in the required number of patterns to refine a structure to a given error.

Analysis on the caged structure of polyhedral oligomeric dodecaphenyl silsesquioxane and its condensation mechanism

Polyhedral oligomeric dodecaphenyl silsesquioxane (DPS) and octaphenyl silsesquioxane (OPS) are two kinds of caged inorganic-organic hybrids and high thermal stable compounds. Concerning the caged structure of DPS, there remain some inconformity among researchers’ conclusions. Some researchers hold that the structure is in the shape of a gem containing 4 tetragons and 4 pentagons, while other articles consider the structure to be a cyclic ladder with 6 tetragons and 2 hexagons. In this paper, the correct structure of DPS is found to be gem‑like, deduced by detailed NMR spectra analysis and Euler's formula calculation, and proved by a single crystal diffraction pattern. A simulation calculation by Materials Studio (MS) proves that the gem‑like structure (Etotal=41.57 kcal·mol-1) is more stable than the cyclic ladder-like one (Etotal=43.37 kcal·mol-1). For the DPS and OPS, the distances between adjacent phenyl groups are considered to influence the chemical shifts of H, C and Si atoms in NMR due to shielding effects, deshielding effects and electron densities. The cyclic tetramer with Etotal=20.40kcal·mol-1 is proved to be the stable cyclic oligomeric phenyl silsesquioxanes with the smallest polymerization degree by the simulations. The linear dimer with Etotal=14.49 kcal·mol-1 is proved to be the stable linear oligomeric silsesquioxanes with the smallest polymerization degree. A condensation mechanism of DPS and OPS is proposed based on the simulation results.

Synthesis, crystal structure and spectroscopic investigations of heteronuclear Co(III)/Cu(II), Co(III)/Cd(II) and Fe(III)/Cd(II) 3D coordination polymers with 4-(2-aminoethyl)pyridine

The cyanide complexes of transition metals with 4-(2-aminoethyl)pyridine (4aepy) of {[Cu(H2O)(µ-4aepy)Cu(µ-4aepy)2Cu(µ-4aepy)Co2(µ-CN)6(CN)6]·3H2O}n (1), (NH4)[Cd(µ-4aepy)2Co(µ-CN)2(CN)4]n (2) and (NH4)[Cd(µ-4aepy)2Fe(µ-CN)2(CN)4]n (3) were synthesized and investigated by vibrational (FT-IR and Raman), powder X-ray diffraction (PXRD), elemental and thermal analysis techniques. The crystal structures of the complexes have been determined by the single crystal X-ray diffraction (SC-XRD) patterns. The crystallographic analysis reveals that complex 1 crystallizes in the monoclinic system, space group P21, whereas; complexes 2 and 3 crystallize in the tetragonal system, space group P42/ncm. The asymmetric unit of heterometallic complex 1 consists of three Cu(II) ions, two Co(III) ions, four 4aepy ligands, twelve cyanide ligands, one aqua ligand and three non-coordinated water molecules. The asymmetric unit of heterometallic complexes 2–3 consists of one Cd(II) ion, one M ion [M = Co(III) in 2 and Fe(III) in 3], two cyanide ligands, half 4aepy ligand and one ammonium ion. Each Cd(II) ion is located at a center of symmetry and is coordinated by two nitrogen atoms by the cyanide ligands and by four nitrogen atoms by the 4aepy ligands. As a result, they show distorted octahedral coordination geometries. In complex 1, the intermolecular O–H⋯N, N–H⋯N, N–H⋯O and C–H⋯N hydrogen bonds and CN⋯π and π⋯π interactions play a crucial role in the architecture of 3D network. The intermolecular CN···π interaction between cyanide ligand and pyridine ring of the 4aepy ligand is the most striking feature of complex 1. Heterometallic complexes 2–3 have 3D coordination polymers.

Computing diffraction patterns of microstructures from phase-field simulations

The diffraction pattern of a material contains information not only on the crystal structures of its constituting phases, but also on its mesoscale spatial distributions of phases, grains, and ferroelastic, ferroelectric, and ferromagnetic domains. While diffraction patterns from experiments such as X-ray diffraction are presented in the reciprocal or Fourier space, mesoscale microstructure models such as the phase-field method naturally produce real-space images of spatial distribution of chemical composition, structural, and ferroic domains. Although one could rather readily compute the Fourier amplitudes of chemical and structural domain distributions generated by mesoscale simulations, they only contain information about the length scale and alignment of the real-space chemical and structure domains. Therefore, a direct comparison between diffraction experiments and mesoscale microstructure simulations is not possible. Here, we develop a theoretical approach to directly compute the crystal diffraction patterns of microstructures predicted by phase-field simulations. In particular, we consider five representative examples of microstructure patterns involving purely compositional domains, a single pair of tetragonal twin structures, multiple twin variants in a hexagonal system, ferroelectric polar vortices, and polycrystalline grains. The results are compared with previous experimental observations as well as X-ray diffraction experiments performed in the present study. The theoretical framework allows one to directly connect material microstructures and diffraction patterns predicted from phase-field simulations and the corresponding diffraction patterns from experiments, and thus providing guidance to experimental diffraction characterization and interpretation of microstructures.

Investigasi pola XRD dan ukuran kristal pada TiO2 terdoping vanadium menggunakan aplikasi VESTA

Visualization of crystal structure and simulation of X-ray diffraction patterns of TiO2 (Titanium dioxide) was successfully performed by VESTA application. The purpose of this research is to obtain the relation of lattice parameter and composition to the diffraction pattern. The program on VESTA needs several input parameters that can be found on Crystallography Open Database (COD). The obtained output of the VESTA application are in the form of crystal structure and diffraction pattern graph. The data obtained by VESTA can be used to estimate the size of the crystal. The result showed that TiO2 has a tetragonal shape crystal structure. The addition of dopant such as Vanadium does not change the crystal structure and does not change the peak position of diffraction pattern graph.

Preparation and Characterization of a Hybrid Complex of Cyclodextrin-Based Metal-Organic Frameworks-1 and Ascorbic Acid Derivatives.

Cyclodextrin-based metal–organic frameworks-1 (CD-MOF-1) prepared using potassium hydroxide, ethanol, and γ-cyclodextrin (γ-CD) has been reported as a new type of MOF for the development of pharmaceutical formulations. The present study aimed to investigate the physicochemical properties of ascorbic acid derivatives (L-ascorbyl 6-palmitate (ASCP); L-ascorbyl 2,6-palmitate (ASCDP)) complexed with CD-MOF-1 by a solvent evaporation method. Powder X-ray diffraction revealed that the crystal diffraction pattern of CD-MOF-1 changed from α-type to β-type when prepared by a solvent evaporation method. For ASCP/CD-MOF-1 = 1/2 and ASCDP/CD-MOF-1 = 1/4 evaporated samples, the crystal diffraction peaks derived from ASCP and ASCDP disappeared, indicating a β-like behavior. Differential scanning calorimetry results revealed that the endothermic peaks of evaporated samples (ASCP/CD-MOF-1 = 1/2 and ASCDP/CD-MOF-1 = 1/4) were not detected due to melting. Furthermore, intermolecular interactions were observed in the hydrogen bonds between the CH groups of the side chains of ASCP and ASCDP and the OH group of CD-MOF-1 in (ASCP/CD-MOF-1 = 1/2) and EVP (ASCDP/CD-MOF-1 = 1/4), based on the near-infrared absorption spectroscopy analysis. CD-MOF-1 did not form inclusion complexes with the lactone rings of ASCP and ASCDP, but with the lipophilic side chains. These results suggested that CD-MOF-1 may be useful in preparing novel drug carriers for ASCP and ASCDP.

Theoretical investigation of the growth of small crystals in single liquid droplets by analyzing their diffraction patterns

The article presents a method of observing and measurement the size of the growth of small crystalline particles in a solution droplet. Size measurement of small crystals in early stage of their growth is based on the analysis of optical diffraction patterns. The great advantage of this measurement method is the fact that it has no effect on the growth of the investigated crystals and, compared to microscopic methods, it provides a much larger area of observation. How to interpret diffraction patterns to use them to measure the size of the crystalline particles is illustrated by using a few examples of crystals with selected shapes and different orientations of their faces in space. All methods of interpreting diffraction patterns are justified by numerical calculations based on Fourier optics. The common features of diffraction patterns of crystals of different shapes and different orientations in space show that the presented method can be used to observe a small crystal of any shape and orientation growing in a droplet of solution.

Fluorine-substituted cyclobutenes in the solid state: Crystal structures, vibrational spectra and mechanical and thermodynamic properties

The crystal structures, infrared and Raman spectra, and mechanical and thermodynamic properties of four important fluorine-substituted cyclobutene derivatives in the solid state are investigated using first-principles solid-state methods based on density functional theory. These compounds are hexafluorocyclobutene (HFCB, C4F6), 1,3,3,4,4-pentafluoro-2-methoxycyclobut-1-ene (PFMCB, C4F5OCH3), 3,3,4,4-tetrafluoro-1,2-dimethoxycyclobut-1-ene [TFDMCB, C4F4(OCH3)2] and 1,2-dichloro-3,3,4,4-tetrafluorocyclobut-1-ene (DCTFCB, C4Cl2F4). Although some of the properties of the corresponding molecules in the gas phase have been studied, and the structures of the corresponding molecular crystals have been determined by refinement from X-ray diffraction data, their vibrational spectra and properties have not yet been reported. The computed crystal structures and X-ray diffraction patterns are in excellent agreement with their experimental counterparts. The infrared and Raman spectra are calculated from the computed crystal structures using density functional perturbation theory. The results are highly consistent with the corresponding spectra measured experimentally in the gas or liquid phases and, therefore, appropriate normal coordinate analyses of the theoretical results are employed to rigorously assign all the vibrational bands. The elasticity matrices of these materials are computed using the finite deformation technique and a complete set of relevant mechanical properties is determined. Their equations of state are also obtained. These compounds are shown to be weak, highly anisotropic materials displaying the negative Poisson's ratio phenomenon. The TFDMCB also exhibits the negative linear compressibility (NLC) phenomenon for external isotropic pressures in the range of 0.64–1.76 GPa. The computed minimum compressibility, found at P = 0.73 GPa, is substantial (k=−192.9 TPa−1). The NLC effect in TFDMCB is due to a collective rotation of the molecules within the crystal under increasing pressure. Finally, the thermodynamic properties of these materials are determined as a function of temperature using phonon calculations. The computed specific heats of HFCB, PFMCB, TFDMCB and DCMCB at T = 250 K are 127.5, 150.4, 169.9 and 134.8 J·K−1·mol−1, respectively, and corresponding entropies are 152.8, 173.3, 195.4 and 186.6 J·K−1·mol−1.

Simulation of electron diffraction patterns of organic crystals under continuous rotation

Simulation of electron diffraction patterns of organic crystals under continuous rotation

Formation of Cs3Cu2I5 microcrystals in CsI crystals through the aggregation of Cu+ ions

We have investigated X-ray diffraction (XRD) patterns of CsI bulk crystals highly doped with Cu+ ions (1 and 10 mol%) and a Cs3Cu2I5 bulk crystal in order to clarify the formation of microcrystals of Cu-based compounds through the aggregation of Cu+ ions in CsI host crystals. We have also measured photoluminescence (PL) and photoluminescence excitation (PLE) spectra of the above three crystals and a CsI bulk crystal lowly doped with Cu+ ions (0.001 mol%) at 10 K. The XRD patterns, PL, and PLE spectra show that the CsI bulk crystals doped with Cu+ ions (1 and 10 mol%) comprise Cs3Cu2I5 microcrystals formed in CsI crystals. On the basis of those results, we discuss the formation of microcrystals of Cu-based compounds through the aggregation of Cu+ ions in CsI bulk crystals with CsCl-type structure.

Influence of softwood cellulose fiber and chitosan on the film-forming properties of collagen fiber

Collagen fiber films were prepared with the addition of softwood cellulose fiber (SWCF) and chitosan (CHS). The modulus, viscosity and yield stress of collagen fiber dispersions (CFD) increased or decreased with the addition of SWCF or CHS, respectively. The addition of SWCF significantly improved the film flexibility at dry, wet state and decreased the swelling ratio of films. The addition of CHS significantly increased the tensile strength (TS) of films at different states and decreased the swelling ratio and shrinkage ratio. For the blending of the two polymers, the CHS has more improvement effect than SWCF in TS (wet, boiled), swelling ratio and shrinkage ratio. The thermodynamic properties of films were improved by adding SWCF and CHS. Optical microscope images showed that some of the SWCF could appeared on the film surface and the CHS could well dispersed in the collagen fiber network. The SEM observation indicated that the collagen fiber formed layered network and the addition of SWCF made the fiber network irregular, while the CHS made the fiber layer denser. Electrostatic interactions excited between CHS and collagen and the addition of SWCF and CHS changed the crystal diffraction patterns to a certain extent.

Ultrahigh Hydrogen Uptake in an Interpenetrated Zn 4 O-Based Metal–Organic Framework

As a highly promising candidate for hydrogen storage, crucial to vehicles powered by fuel cells, metal–organic frameworks (MOFs) have attracted the attention of chemists in recent decades. H2 uptak...

X-ray Diffraction Study of Deformational Evolution of Stacking Faults in Nanocrystalline Metals

The evolution of stacking faults (SF) during the mechanical activation (MA) of metals with a different energy of SF (γ): Co (7 mJ/m2), Cu (45 mJ/m2), Ni (125 mJ/m2),—was studied by X-ray diffraction analysis using (i) a complex for processing diffraction patterns and (ii) simulation of crystal diffraction patterns (DIFFaX). The study was performed to understand the connection of the evolution mentioned with plastic deformation mechanisms and depending on grain size. The values ​​of the energy yields of stacking faults (G) upon MA for nanocrystalline Co and Cu are in agreement with the values of ​​ γ for these metals in the coarse crystalline state (the lower the γ, the higher the G). The increased G for nanocrystalline nickel is associated with the effect of impurities. When decreasing the sizes of Co, Cu, and Ni crystallites in the course of MA to 30, 77, and 60 nm respectively, the maximum G are observed, which is a consequence of deformation by the mechanism of the generation of partial Shockley dislocations by nanograin boundaries and their sliding in the grain body with the formation of SF. A scheme of the deformation-induced shear transformation in nanocrystalline cobalt is proposed.

Diffraction pattern of Bacillus subtilis CotY spore coat protein 2D crystals

Bacillus subtilis spore coat is a bacterial proteinaceous structure with amazing characteristics of self-organization, unique resiliency, toughness and flexibility in the same time. The spore coat represents a complex multilayered protein structure which is composed of over 80 coat proteins. Some of these proteins form two dimensional crystal structures who’s low resolution ternary structure as was determined by electron microscopy. However, there are no 3D structure of these proteins known, due to a problem of preparing 3D crystals which could be analyzed by synchrotron X-ray sources. In the present study, Grazing-Incidence Wide-Angle X-ray Scattering (GIWAXS) was applied to investigate a diffraction pattern of CotY 2D crystals formed on Langmuir monolayer films. We observed two distinct diffraction rings and their position corresponds to a structure with the lattice spacing of 10.6 Å and 5.0 Å, respectively. Obtaining diffractions of 2D crystals pave the way to determination of 3D structure of coat proteins by using strong X-ray sources.

Preparation of a Novel Transplant Material, Zirconium Oxide (ZrO₂) Nanotubes, and Characterizations Research.

BackgroundZirconia is one of the most widely used ceramic materials for transplanting and treating caries. This study aimed to synthesize zirconium oxide (ZrO2) nanotubes and evaluated their characteristics.Material/MethodsZr film was prepared using an ion plating method. Nanoarray film was constructed with anodizing. Photocatalytic properties of nnanotubes were assessed by evaluating decolorization of methyl orange. Elemental analysis and structural morphology for coatings were evaluated using x-ray analysis and scanning electron microscopy (SEM). Dimensions for layers were measured with SEM imaging. X-ray diffraction (XRD) was measured using Empyrean x-ray diffractometry.ResultsThere were irregular cavities on the surface of ZrO2 nanotubes undergoing anodizing of 30V. Anodizing voltage of 45 V (with regular nano-pore arrays and smooth nanotube walls) and anodic oxidation duration of 60 min (ZrO2 nanotubes clearly formed atop ZrO2-coated substrate surface) were the optimal condition for ZrO2 nanotube formation. TEM illustrated tube length of ZrO2 nanotubes was approximately 2.01 μm. Nanotube diameter was 51.06 nm, and wall thickness was 13 to 14 nm. Annealed nanotubes showed an obvious crystal diffraction pattern. TEM diffraction ring showed nanotube array without obvious transistor structure before annealing, but with good crystallinity post-annealing. Increased annealing temperatures result in enhanced intensity for the monoclinic phase (400–800°C). After annealing at 600°C, the decolorization effect of ZrO2 nanotubes on methyl orange was better than that post-annealing at 400 and 800°C. ZrO2 nanotubes demonstrated higher microshear bond strength.ConclusionsZirconium nanotubes were successfully synthesized and demonstrated good structural characteristics, which can be applied to transplanting and treating caries.

Mononuclear High‐spin Octahedral Cobalt(II) Complex with Positive Axial Magnetic Anisotropy: Synthesis, Crystal Structure, and DFT Studies

This article outlines the magnetic features of a new six–coordinate high‐spin cobalt(II) complex cis‐[CoII(tmphen)2(NCS)2] (1) achieved via the reactions of cobalt(II) thiocyanate with 3,4,7,8‐tetramethyl‐1,10‐phenanthroline. The complex 1 was thoroughly characterized by different analytical and spectroscopic techniques and further confirmed by single X‐ray crystal diffraction pattern. Complex 1 is a neutral molecule and adopt highly distorted six‐coordinate CoN6 octahedral coordination sphere surrounded by two thiocyanate N atoms in cis locations and the equatorial plane is occupied by two imine N atoms from the two tmphen ligand while the remaining two imine N atoms reside in the axial positions. Magnetic susceptibility data of complex 1 revealed that the χΜT values decrease significantly to a value of 1.49 cm3·K·mol–1 at 2.0 K on decreasing temperatures below 100 K, mainly ascribed to the significant spin–orbit coupling (SOC) of six‐coordinate CoII ions. Furthermore, a field‐dependence measurement was performed at 2 K, which shows a positive curvature up to 27 kOe, while it becomes linear up to 2.01 NμB, which authenticated the fact that only the lowest Kramers doublet of ground state is appreciably populated.