Isotropic Atomic Displacement Parameters Research Articles

Using graphlet degree vectors to predict atomic displacement parameters in protein structures.

In structural biology, atomic displacement parameters, commonly used in the form of B values, describe uncertainties in atomic positions. Their distribution over the structure can provide hints on local structural reliability and mobility. A spatial macromolecular model can be represented by a graph whose nodes are atoms and whose edges correspond to all interatomic contacts within a certain distance. Small connected subgraphs, called graphlets, provide information about the wiring of a particular atom. The multiple linear regression approach based on this information aims to predict a distribution of values of isotropic atomic displacement parameters (B values) within a protein structure, given the atomic coordinates and molecular packing. By modeling the dynamic component of atomic uncertainties, this method allows the B values obtained from experimental crystallographic or cryo-electron microscopy studies to be reproduced relatively well.

Anharmonicity effects and thermal expansion of thermoelectric (M,M’,M”)NiSn (M,M’,M”=Ti, Zr, Hf) half-Heusler alloys

High-resolution synchrotron radiation X-ray powder diffraction was used for the structural characterization of half-Heusler alloys with compositions MNiSn, M0.5M′0.5NiSn, and M0.5M′0.25M”0.25NiSn ((M, M′, M”) = Ti, Zr, Hf). These alloys were synthesized by arc melting and subsequent thermal annealing. Rietveld refinements of the room temperature patterns revealed that the unit cell parameter is larger for ZrNiSn and smaller for TiNiSn, in accordance with the respective atomic radii. The site occupation of each atomic species exhibited similar trends to those reported in the literature. The values of the linear coefficient of thermal expansion (α) for all the investigated phases within the alloys are < 10−5 K−1. In addition, the value of the Debye temperature (θD) is estimated by analyzing the temperature dependence of the isotropic atomic displacement parameters. In the case of these half-Heusler alloys, it is observed that a lower θD corresponds to a lower α. The good agreement between the temperature dependence of the Debye temperature and the calculated values using the Thirring-Stern expansion enables us to demonstrate the significant role of anharmonicity: the lighter the compound, the lower the anharmonicity. Furthermore, we also discuss the implications of anharmonicity on the thermal conductivity of this family of half-Heusler compounds at room temperature.

Crystal structure, absolute configuration and characteristic temperatures of SmFe3(BO3)4 in the temperature range 11-400 K.

The crystal structure of samarium iron borate was analyzed with regard to growth conditions and temperature. The inclusion of about 7% Bi atoms in the crystals grown using the Bi2Mo3O12-based flux was discovered and there were no impurities in the crystals grown using the Li2WO4-based flux. No pronounced structural features associated with Bi inclusion were observed. The different absolute configurations of the samples grown using both fluxes were demonstrated. Below 80 K, a negative thermal expansion of the c unit-cell parameter was found. The structure of (Sm0.93Bi0.07)Fe3(BO3)4 belongs to the trigonal space group R32 in the temperature range 90-400 K. A decrease in the (Sm,Bi)-O, Sm-B, Sm-Fe, Fe-O, Fe-B and Fe-Fe distances is observed with a lowering of the temperature, B1-O does not change, B2-O increases slightly and the B2O3 triangles deviate from the ab plane. The strongest decrease in the equivalent isotropic atomic displacement parameters (Ueq) with decreasing temperature is observed for atoms Sm and O2, and the weakest is observed for B1. The O2 atoms have the highest Ueq values, the most elongated atomic displacement ellipsoids of all the atoms and the smallest number of allowed vibrational modes of all the O atoms. The largest number of allowed vibrational modes and the strongest interactions with neighbouring atoms is seen for the B atoms, and the opposite is seen for the Sm atoms. The quadrupole splitting Δ(T) of the paramagnetic Mössbauer spectra increases linearly with cooling. The Néel temperature [TN= 31.93 (5) K] was determined from the temperature dependence of the hyperfine magnetic field Bhf(T), which has a non-Brillouin character. The easy-plane long-range magnetic ordering below TN was confirmed.

Investigation of the Anisotropic Thermal Expansion Mechanism of AgxGaxGe1-xSe2 Crystals.

Quaternary nonlinear optical single crystals AgxGaxGe1-xSe2 (x = 0.250, 0.167) were grown by the Bridgman method in a four-zone furnace. The thermal expansion behavior of AgxGaxGe1-xSe2 (x = 0.25, 0.167) was studied by the method of single-crystal X-ray diffraction from 150 to 295 K and powder X-ray diffraction in the range of 298-773 K. Both results show the crystals have positive linear thermal expansion coefficients in different directions and a positive volume thermal expansion coefficient, and it is observed that they satisfy the relationship of αa > αc > αb and αV ≈ αa + αb + αc for the orthorhombic structure. It is found that the AgxGaxGe1-xSe2 (x = 0.25, 0.167) unit cells varying with temperature were mainly dominated by variations in framework geometry (AgSe4 tetrahedron), and the thermal motion of Ag atoms in the AgSe4 tetrahedron. As it was revealed, according to the powder X-ray diffraction, it is found that the isotropic thermal atomic displacement parameter of the Ag atoms is much larger than those of the Se and Ga(Ge) atoms in the AgSe4 tetrahedron. Furthermore, anisotropic atomic displacement parameters (ADPs) of Ag atoms are extracted from the single-crystal diffraction; the ADPs along the a axis, b axis, and c axis have a significant difference, which means the thermal vibration of Ag atoms is anisotropic. It is of great significance for improving crystal growth technology and understanding the thermal properties of this kind of crystals.

Improvement of precision in refinements of structure factors using convergent-beam electron diffraction patterns taken at Bragg-excited conditions

A local structure analysis method based on convergent-beam electron diffraction (CBED) has been used for refining isotropic atomic displacement parameters and five low-order structure factors with sin θ/λ ≤ 0.28 Å-1 of potassium tantalate (KTaO3). Comparison between structure factors determined from CBED patterns taken at the zone-axis (ZA) and Bragg-excited conditions is made in order to discuss their precision and sensitivities. Bragg-excited CBED patterns showed higher precision in the refinement of structure factors than ZA patterns. Consistency between higher precision and sensitivity of the Bragg-excited CBED patterns has been found only for structure factors of the outer zeroth-order Laue-zone reflections with larger reciprocal-lattice vectors. Correlation coefficients among the refined structure factors in the refinement of Bragg-excited patterns are smaller than those of the ZA ones. Such smaller correlation coefficients lead to higher precision in the refinement of structure factors.

Crystallographic and superconducting properties of filled skutterudite SrOs4P12

The crystallographic and physical properties of the recently discovered filled skutterudite superconductor ${\mathrm{SrOs}}_{4}{\mathrm{P}}_{12}$, synthesized by a high-pressure and -temperature technique, are studied by measuring electrical resistivity, specific heat, and magnetization, and by performing electronic band calculations. X-ray powder diffraction with Rietveld refinement indicates that the lattice parameter of ${\mathrm{SrOs}}_{4}{\mathrm{P}}_{12}$ is 8.093(2) \AA{} and that fractional coordinates of the P site are [0, 0.3607(9), 0.1450(9)], which is also confirmed by calculations based on density functional theory. The electrical resistivity indicates a metallic nature of ${\mathrm{SrOs}}_{4}{\mathrm{P}}_{12}$, which is consistent with the density of states at Fermi energy with 7.5 (states/eV)/f.u. deduced from the electronic band calculations. The Sommerfeld coefficient $\ensuremath{\gamma}$ and Einstein temperature $\ensuremath{\theta}{}_{\mathrm{E}}$ of ${\mathrm{SrOs}}_{4}{\mathrm{P}}_{12}$ are deduced as $\ensuremath{\gamma}\ensuremath{\sim}26\phantom{\rule{4pt}{0ex}}\mathrm{mJ}/{\mathrm{mol}\phantom{\rule{0.16em}{0ex}}\mathrm{K}}^{2}$ and $\ensuremath{\theta}{}_{\mathrm{E}}\ensuremath{\sim}150$ K, respectively. A larger isotropic atomic displacement parameter ${U}_{\mathrm{eq}}$ of Sr compared to other atomic species as obtained from a Rietveld analysis and a specific heat anomaly around 30 K refers to anharmonic lattice vibrations of Sr in ${\mathrm{SrOs}}_{4}{\mathrm{P}}_{12}$. ${\mathrm{SrOs}}_{4}{\mathrm{P}}_{12}$ exhibits two superconducting transitions at ${T}_{\mathrm{c}1}=1.6$ K and ${T}_{\mathrm{c}2}=1.0$ K. Specific-heat data indicate that the observed superconductivity is of bulk nature with approximate volume fractions of $27%$ and $38%$ for superconductivity at ${T}_{\mathrm{c}1}$ and ${T}_{\mathrm{c}2}$, respectively. The electrical resistivity under field and pressure as well as the specific heat under field indicate that ${T}_{\mathrm{c}1}$ is sensitive to the magnetic field and ${T}_{\mathrm{c}2}$ is sensitive to pressure. The results show that ${\mathrm{SrOs}}_{4}{\mathrm{P}}_{12}$ is an $s$-wave weakly coupled superconductor with an electron-phonon mass enhancement ${\ensuremath{\lambda}}_{\text{ep}}\ensuremath{\sim}0.47$.

A positive to negative uniaxial thermal expansion crossover in an organic benzothienobenzothiophene structure.

Compound 6,6'-([1]benzothieno[3,2-b][1]benzothiophene-2,7-diyl)bis(butan-1-ol) (BTBT-C4OH) displays a continuous type 0 first-order isosymmetric phase transition at 200 K which is accompanied by a continuous change of the thermal expansion along the b axis from positive to negative. The equivalent isotropic atomic displacement parameters for all non-hydrogen atoms as well as all the eigenvalues of the anisotropic atomic displacement tensor show discontinuous behavior at the phase transition. The eigenvalues of the translational tensor in a rigid-body description of the molecule are all discontinuous at the phase transition, but the librational eigenvalues are discontinuous only in their temperature derivative. BTBT-C4OH displays a similar type of quasi-supercritical phase transition as bis(hydroxyhexyl)[1]benzothieno[3,2-b][1]benzothiophene (BTBT-C6OH), despite the difference in molecular packing and the very large difference in thermal expansion magnitudes.

Redetermination of the crystal structure of R 5Si4 (R = Pr, Nd) from single-crystal X-ray diffraction data

The crystal structures of praseodymium silicide (5/4), Pr5Si4, and neodymium silicide (5/4), Nd5Si4, were redetermined using high-quality single-crystal X-ray diffraction data. The previous structure reports of Pr5Si4 were only based on powder X-ray diffraction data [Smith et al. (1967 ▸). Acta Cryst. 22 940-943; Yang et al. (2002b ▸). J. Alloys Compd. 339, 189-194; Yang et al., (2003 ▸). J. Alloys Compd. 263, 146-153]. On the other hand, the structure of Nd5Si4 has been determined from powder data [neutron; Cadogan et al., (2002 ▸). J. Phys. Condens. Matter, 14, 7191-7200] and X-ray [Smith et al. (1967 ▸). Acta Cryst. 22 940-943; Yang et al. (2002b ▸). J. Alloys Compd. 339, 189-194; Yang et al., (2003 ▸). J. Alloys Compd. 263, 146-153] and single-crystal data with isotropic atomic displacement parameters [Roger et al., (2006 ▸). J. Alloys Compd. 415, 73-84]. In addition, the anisotropic atomic displacement parameters for all atomic sites have been determined for the first time. These compounds are confirmed to have the tetra-gonal Zr5Si4-type structure (space group: P41212), as reported previously (Smith et al., 1967 ▸). The structure is built up by distorted body-centered cubes consisting of Pr(Nd) atoms, which are linked to each other by edge-sharing to form a three-dimensional framework. This framework delimits zigzag channels in which the silicon dimers are situated.

Using Complementary Methods of Synchrotron Radiation Powder Diffraction and Pair Distribution Function to Refine Crystal Structures with High Quality Parameters—A Review

Determination of the atomic-scale structures of certain fine-grained minerals using single-crystal X-ray diffraction (XRD) has been challenging because they commonly occur as submicron and nanocrystals in the geological environment. Synchrotron powder diffraction and scattering techniques are useful complementary methods for studying this type of minerals. In this review, we discussed three example studies investigated by combined methods of synchrotron radiation XRD and pair distribution function (PDF) techniques: (1) low-temperature cristobalite; (2) kaolinite; and (3) vernadite. Powder XRD is useful to determine the average structure including unit-cell parameters, fractional atomic coordinates, occupancies and isotropic atomic displacement parameters. X-ray/Neutron PDF methods are sensitive to study the local structure with anisotropic atomic displacement parameters (ADP). The results and case studies suggest that the crystal structure and high-quality ADP values can be obtained using the combined methods. The method can be useful to characterize crystals and minerals that are not suitable for single-crystal XRD.

First Principles Study of the Vibrational and Thermal Properties of Sn-Based Type II Clathrates, CsxSn136 (0 ≤ x ≤ 24) and Rb24Ga24Sn112

After performing first-principles calculations of structural and vibrational properties of the semiconducting clathrates Rb24Ga24Sn112 along with binary CsxSn136 (0 ≤ x ≤ 24), we obtained equilibrium geometries and harmonic phonon modes. For the filled clathrate Rb24Ga24Sn112, the phonon dispersion relation predicts an upshift of the low-lying rattling modes (~25 cm−1) for the Rb (“rattler”) compared to Cs vibration in CsxSn136. It is also found that the large isotropic atomic displacement parameter (Uiso) exists when Rb occupies the “over-sized” cage (28 atom cage) rather than the 20 atom counterpart. These guest modes are expected to contribute significantly to minimizing the lattice’s thermal conductivity (κL). Our calculation of the vibrational contribution to the specific heat and our evaluation on κL are quantitatively presented and discussed. Specifically, the heat capacity diagram regarding CV/T3 vs. T exhibits the Einstein-peak-like hump that is mainly attributable to the guest oscillator in a 28 atom cage, with a characteristic temperature 36.82 K for Rb24Ga24Sn112. Our calculated rattling modes are around 25 cm−1 for the Rb trapped in a 28 atom cage, and 65.4 cm−1 for the Rb encapsulated in a 20 atom cage. These results are utilized to predict the lattice’s thermal conductivity (approximately 0.62 W/m/K) in Rb24Ga24Sn112 within the kinetic theory approximation.

Using powder XRD and pair distribution function to determine anisotropic atomic displacement parameters of orthorhombic tridymite and tetragonal cristobalite.

Determination of the crystal structures of low-temperature tridymite and cristobalite using single-crystal XRD has been challenging because they generally occur as metastable fine-grained crystals in the geological environment. Therefore, using powder diffraction and scattering techniques is critical to study the low-temperature crystals. Synchrotron powder X-ray diffraction (XRD), pair distribution function (PDF) and transmission electron microscopy were used to investigate the structure of orthorhombic tridymite with C2221 symmetry and tetragonal cristobalite with P41212 symmetry, including their anisotropic atomic displacement parameters (ADPs). Rietveld refinement was used to determine the unit-cell parameters, fractional coordinates and isotropic atomic displacement parameters (Uiso) of the tridymite and cristobalite. The PDF method was used to determine ADPs for each atom. The results suggest that the crystal structure with high quality ADP values can be obtained using the combined methods of XRD and PDF analyses. The method can be used for characterizing crystals that are not suitable for single-crystal XRD.

First-Principles Study of the Electronic, Vibrational Properties and Anharmonic Effects of Some Si-Based Type-II Binary Clathrates.

Electronic, vibrational, and anharmonic studies on some binary clathrate AxSi136 (A = Na, K, Rb, Cs; 0 < x ≤ 24) are theoretically presented. The Fermi energy lies in the range of 1.1 eV to 1.4 eV for NaxSi136 and increases as stoichiometry (x) is tuned from 8 to 12 to 16. The determined isotropic “Mexican-hat” shape of the guest-host potential describing Na motion in the Si28 cage indicates the “off-center” position when the temperature is elevated beyond zero. Accordingly, the calculated Na “off-center” displacements correlate well with the X-Ray Diffraction (XRD) data (0.4 Å–0.5 Å) for a similar composition range (0 < x < 24). The lack of first-principles analysis on quartic anharmonicity motivates us to initiate a self-consistent model to examine the temperature-dependent rattling frequency Ω(T) of the guest (Na, Rb). The predicted values of Ω(T) for Na24Si136 at 300 K are significantly higher (approximately six times larger) than the value at absolute zero, which contrasts with the case of Rb8Si136. Moreover, underestimation of the isotropic atomic displacement parameter Uiso is caused by the temperature-dependent quartic anharmonicity of Na, and this discrepancy might be offset by the square of the “off-center” displacement.

Development and Characterisation of New Biocompatible Sn-Mg Lead-Free Solder

This work is focused on a development and research of a new lead-free Sn-Mg solder, alloy compatible with the human body. Tin and magnesium are biocompatible elements which do not cause an inflammation or allergic reactions with living tissues. We have prepared the Sn97Mg3 solder (wt. %) by a rapid solidification of its melt on a copper wheel (melt-spinning technique). This solder may find applications in electronic devices for intracorporeal utilisation. The microstructure of the prepared solder exhibits a heterogeneous distribution of the SnMg2 intermetallic particles within the β-Sn matrix. Structure of the solder was studied by an in-situ high energy X-ray diffraction experiment (energy of an X-ray photon: 60 keV) where 2D XRD patterns were collected from the sample in the temperature range from 298 K to 566 K. The experiment was performed at a high brilliance 3rd generation synchrotron source of radiation (PETRA III storage ring, DESY, Hamburg, Germany) at the P02 undulator beamline. From the measured X-ray diffraction data by applying the Rietveld refinement technique we have obtained thermal volume expansion data, mean positions of atoms as well as isotropic atomic displacement parameters of the constituent SnMg2 and the β-Sn crystalline phases. Thermal behaviour was studied by differential scanning calorimetry at heating rates of 5, 15, 30 and 60 K.min-1 and compared with the measured X-ray data. Our main goal lies in a preparation of a lead-free solder with fine grain structure made exclusively of biocompatible elements. We demonstrated that the rapid melt solidification technique leads to in an improvement and better thermal stability of this alloy.

Thermal properties of 2:1 bismuth borate: Temperature‐dependent characterizations of lone electron pairs

AbstractApplications of bismuth borate ceramics require understanding of the microscopic features, leading to macroscopic behaviors such as thermal expansion. We report the structural and spectroscopic features of Bi4B2O9 between 4 K and 900 K using a combination of temperature‐dependent neutron and X‐ray powder diffractions and Raman spectroscopy. Lattice thermal expansion was modeled using the Debye‐Einstein‐Anharmonicity (DEA) fit. The model also follows four independent thermal expansion tensors of the monoclinic system. Phonon density of states obtained from the density functional theory (DFT) calculations helps to understand the low Debye temperature calculated from the metric expansion as well as from the isotropic atomic displacement parameters. Both Wang‐Liebau eccentricity (WLE) parameter and Liebau density vector (LDV) are calculated from the structural data and from the DFT calculation, respectively. Whereas, the dimensionless absolute value of WLE measures the degree of deformation of the electronic deformation density of the 6s2 lone electron pairs (LEPs) of the Bi3+ cations, LDV additionally shows the changes of the orientation of the LEP‐lobes as function of temperature. Analyses of the temperature‐dependent frequencies of some selected Raman modes support the choice of the elastic model of the Debye approach.

Incommensurate phase of the stuffed tridymite derivative BaSrFe4O8

We demonstrate a new modulation for a high-temperature polymorph of BaSrFe4O8 via synchrotron powder X-ray diffraction and transmission electron microscopy (TEM) experiments. Although the powder X-ray diffraction pattern was successfully analyzed using a structure model of space group Pnna, an unusually large isotropic atomic displacement parameter (Uiso) was observed for the O1 atom. A split atom model that was applied to the O1 site and the adjacent Ba/Sr site, both of which are on the two-fold axis along the c-axis, indicated that positional disorder occurred in these atoms along the c-axis. The electron diffraction pattern and high-resolution TEM observations combined with the structure refinements revealed an incommensurate structure with a modulation vector q=0.4270(1)a* and a displacement vector perpendicular to the a-axis, which gave rise to the large Uiso value of the O1 atom. The modulation observed in this study may be a signature of structural instability, which has commonly been discussed in the stuffed tridymite-type oxides.

Thermal Expansion Behaviors of Li3AsW7O25: A Case Study for Comparative Debye Temperature for a Large Polyatomic Unit Cell

The thermal expansion behavior of Li3AsW7O25 has been studied. The temperature‐dependent development of crystal structural parameters was obtained from Rietveld refinement using neutron time of flight powder diffraction data. Modeling of the lattice thermal expansion was carried out using a Grüneisen first‐order approximation for the zero‐pressure equation of state, where the temperature‐dependent vibrational energy was calculated taking the Debye‐Einstein‐Anharmonicity approach. Temperature‐dependent Raman spectra shed light on some selective modes with unusual anharmonicity. Debye temperatures were calculated using three different theoretical approaches, namely, thermal expansion, mean‐squared isotropic atomic displacement parameter and heat capacity. Similarities as well as discrepancies between the numerical values obtained from different theoretical approaches are discussed.

Single-crystal growth, structure refinement and the properties of Bis(glycine) Strontium Chloride

Single crystals of Bis (glycine) Strontium Chloride (BGSC) were grown by means of slow evaporation process by using analar grade Glycine and Strontium Chloride Hexahydrate as a parent compound from its aqueous solution at room temperature. The final chemical composition, formed were metallic light colorless block, about the size of 28 mm × 9 mm × 8 mm. A single-crystal x-ray diffraction study revealed an ordered superstructure with orthorhombic symmetry that could be assigned to the space group Pbcn. The structure in BGSC, revealed in the electron density distribution was analyzed by the direct methods (SHELXS-2014) and refined by least squares full matrix method (SHELXL-2014). The crystal structure, including anisotropic atomic displacement parameters for each atom and isotropic atomic displacement parameters for hydrogen atom, was refined to R1 = 0.0395, wR2 = 0.0776 using 1097 independent reflections. The FTIR spectrum of BGSC confirms the protonation of amino groups and the different molecular groups present in BGSC vibrate in different modes. Reverse Indentation Size Effect (RISE) was revealed in BGSC in the micro-hardness analysis using Vicker’s micro-hardness analysis. DTA and DSC results ruled out the possibility of structural change independent of mass change. The AFM studies shows fine nano size fiber like structure of the grown crystals.

A shallow origin of so-called ultrahigh-pressure chromitites, based on single-crystal X-ray structure analysis of the high-pressure Mg2Cr2O5phase, with modified ludwigite-type structure

The crystal structure of the high-pressure Mg 2 Cr 2 O 5 phase was studied by single-crystal X-ray diffraction (XRD) analysis for the recovered samples. The 61 parameters including anisotropic displacement parameters of each atom and site occupancies of Mg and Cr in cation sites were refined with R 1 = 1.26%, wR 2 = 4.33%, and S fit = 1.265 for 470 unique reflections. The results show that the structure of the recovered Mg 2 Cr 2 O 5 phase is the same as modified ludwigite (mLd)-type Mg 2 Al 2 O 5 [space group: Pbam (no. 55)], and the lattice parameters are a = 9.6091(2), b = 12.4324(2), c = 2.8498(1) A ( Z = 4). The refined structure of the Mg 2 Cr 2 O 5 phase has four (Mg,Cr)O 6 octahedral sites and a MgO 6 trigonal prism site, and is similar to but distinct from that of CaFe 3 O 5 -type Mg 2 Fe 2 O 5 phase, which has two octahedral sites and a bicapped trigonal prism site with two longer cation-oxygen bonds. The isotropic atomic displacement parameter of the trigonal prism site cation in mLd-type Mg 2 Cr 2 O 5 is relatively small compared with that of CaFe 3 O 5 -type Mg 2 Fe 2 O 5 , suggesting that the trigonal prism site is less flexible for cation substitution than that of CaFe 3 O 5 -type structure. To stabilize mLd-type A 2 2+ B 2 3+ O 5 phase, it would be an important factor for the B 3+ cation to have high octahedral-site preference, resulting in only A 2+ cation being accommodated in the tight trigonal prism site. Our study also suggests that mLd-type phase with (Mg,Fe 2+ ) 2 Cr 2 O 5 composition would crystallize as one of decomposed phases of chromitites, when the chromitites were possibly subducted into the mantle transition zone.

Anomalous behavior of displacement correlation function and strain in lanthanum cobalt oxide analyzed both from X-ray powder diffraction and EXAFS data

A combined X-ray powder diffraction (XPD) and high-resolution extended X-ray absorption fine structure (EXAFS) at the Co and Ga K-edges study has been performed for LaCoO3 and LaGaO3 ceramics, the latter sample was used as a reference without spin transitions. Based on the X-ray diffraction data, we have found that isotropic atomic displacement parameters (ADP) or mean-squared displacement of the Co–O bond exhibit gradual growth below ~50 K, wherein the strain dependencies testify rapid increase below 150 K for the LaCoO3 having rhombohedral structure. No similar features could be observed for LaGaO3 sample. Above ~100 K the isotropic ADP of the Co–O bond indicate a gradual growth, whereas strain curves show distinct bend near the spin-state transition temperature at about 150 K. According to the EXAFS data, the correlated parallel mean squared relative displacement (MSRD||) of Co–O and Ga–O bonds exhibit a gradual growth above 150 K; however, in the LaCoO3 this parameter is notably bigger. It is supposed that at low temperature the cobalt ions are dominantly in low-spin (LS) state, while certain amount of Co3+ ions located within the surface layer of the crystallines have high-spin state (HS). Temperature growth leads to a gradual transformation of the HS state of the cobalt ions into the highly-hybridized intermediate-spin (IS) state, while the cobalt ions located in the inner part of the crystallines remain LS configuration up to 150 K. Further temperature increase leads to a spin transition of the Co3+ ions located within the crystallines from the LS state into the IS one.

Atomic displacement in the CrMnFeCoNi high-entropy alloy – A scaling factor to predict solid solution strengthening

Although metals strengthened by alloying have been used for millennia, models to quantify solid solution strengthening (SSS) were first proposed scarcely seventy years ago. Early models could predict the strengths of only simple alloys such as dilute binaries and not those of compositionally complex alloys because of the difficulty of calculating dislocation-solute interaction energies. Recently, models and theories of SSS have been proposed to tackle complex high-entropy alloys (HEAs). Here we show that the strength at 0 K of a prototypical HEA, CrMnFeCoNi, can be scaled and predicted using the root-mean-square atomic displacement, which can be deduced from X-ray diffraction and first-principles calculations as the isotropic atomic displacement parameter, that is, the average displacements of the constituent atoms from regular lattice positions. We show that our approach can be applied successfully to rationalize SSS in FeCoNi, MnFeCoNi, MnCoNi, MnFeNi, CrCoNi, CrFeCoNi, and CrMnCoNi, which are all medium-entropy subsets of the CrMnFeCoNi HEA.