Lattice Parameter Measurements Research Articles

Structure of a Novel Spinel Li0.5Zn5/3Sb2.5/3O4 by Neutron and Synchrotron Diffraction Analysis

Zn7/3Sb2/3O4 is a secondary phase in ZnO-based varistors. Acceptor impurities, such as Li+, increase the resistivity. This effect is produced by a modification of the grain boundary barriers. The role of the cationic distribution in the mentioned events is worth clarifying. The Li0.5Zn5/3Sb2.5/3O4 room-temperature structure was determined by means of a neutron diffraction and synchrotron X-ray diffraction investigation. The title compound was prepared by conventional ceramic process. The elemental composition of the investigated sample was verified by means of electron microscopy—energy dispersive X-ray spectroscopy and X-ray photoelectron spectroscopy. The neutron experiment was performed at the high-intensity neutron diffractometer with position-sensitive detector at the D1B beamline of the Laue-Langevin Institute, Grenoble. The high resolution synchrotron measurement was carried out at MCX beamline of Elettra Sincrotrone Trieste. Rietveld analysis was performed with the FullProf program. Li0.5Zn5/3Sb2.5/3O4 belongs to the spinel family, space group F d 3 ¯ m (227). The measured lattice parameter is a = 8.5567(1) Å. The Li+1 and Zn+2 ions are randomly distributed among the tetrahedral and octahedral sites as opposed to Sb+5 ions which have preference for octahedral sites. Fractional coordinate of oxygen, u = 0.2596(1), indicates a slight deformation of the tetrahedral and octahedral sites. The data given in this paper provide structural support for further studies on measurements and microscopic explanations of the interesting properties of this family of compounds.

A new analysis for diffraction correction in optical interferometry

Dimensional measurements by laser interferometry require a correction because of diffraction, which makes the fringe period different from the wavelength of a plane wave. The fractional correction—from parts in 10−7 to parts in 10−9, depending on the beam collimation—is half the central second moment of the angular power-spectrum of the beam, a generalization of the divergence concept. We report new insights into the second moment measurement and their consequences on the measurement of the silicon lattice parameter by combined x-ray and optical interferometry.

Microstructural characterization of boron-rich boron carbide

Boron carbide has a wide range of solubility, but the effects of stoichiometry on its microstructure and mechanical response are not well understood. In this study, detailed microstructural characterization was carried out on three hot-pressed B-rich boron carbide samples. Lattice parameter measurements from XRD identified the compositions to be B4.2C, B5.6C and B7.6C. Local substitutional disorder was observed by Raman spectroscopy, particularly for more B-rich samples. Electron energy loss spectroscopy observations suggest that excess boron preferentially substitutes for carbon atoms in the B11C icosahedra; after which additional boron modifies the CBC chains. Moreover, the boron content has salient effects on boron carbide densification and microstructure. Improved densification was observed in the more B-rich samples (B5.6C and B7.6C), and there is a transition from few or no intragranular planar defects (B4.2C), to numerous stacking faults (B5.6C), to copious twins (B7.6C). Nanoindentation experiments revealed that the highest value for B4.2C is statistically larger than that for B5.6C or B7.6C, suggesting that the hardness of boron carbide is reduced by boron substitution.

Crystallographic and optical study of PbHfO3 crystals.

The symmetry of the intermediate high-temperature phase of PbHfO3 has been determined unambiguously to be orthorhombic using a combination of high-resolution X-ray diffraction and birefringence imaging microscopy measurements of crystal plates. While lattice parameter measurements as a function of temperature in the intermediate phase are consistent with either orthorhombic or tetragonal symmetry, domain orientations observed in birefringence imaging microscopy measurements utilizing the Metripol system are only consistent with orthorhombic symmetry with the unit cell in the rhombic orientation of the pseudocubic unit cell.

Neutron diffraction of Cu–Zn–Sn ternary alloys: non-invasive assessment of the compositions of historical bronze/brass copper ternary alloys

Neutron diffraction can be used as a tool for the characterization of metal materials in a totally non-invasive mode. In binary alloys with two elements in solid solution, crystallographic structure analysis provides information on the overall element compositions of the metal, based on the linear relationship between elemental fractions and lattice parameters known as Vegard's rule. However, for ternary solid-solution alloys the derivation of the overall metal composition is not straightforward because the problem is mathematically underdetermined. A number of artificially produced samples in the ternary system Cu–Zn–Sn, widely used in antiquity for gunmetal, were investigated by time-of-flight neutron diffraction, inductively coupled plasma mass spectroscopy, scanning electron microscopy with energy-dispersive X-ray spectroscopy and electron microprobe analysis. The multi-analysis approach allows definition of the limits and capabilities of neutron diffraction for obtaining the overall composition of a small sample set of ternary alloys, and thus moves the methodical approach a step forward even though it is applicable to the present sample set only. A relation showing an increasing Cu and Sn fraction counterbalanced by decreasing Zn content is presented, which allows the determination of the δ-phase composition from a lattice parameter measurement. Furthermore, the observed Zn loss up to 1.8 wt% for each melting step is of significance for the reconstruction of ancient technologies.

Rapid hydrothermal synthesis of SrMo1−xWxO4 powders: Structure and luminescence characterization

Strontium molybdate, strontium tungstate particles and their solid solutions (SrMo1−xWxO4) with 0⩽x⩽1.0, were synthesised by means of a hydrothermal process. Crystallisation of SrMo1−xWxO4 particles took place rapidly using SrSO4 as the Sr precursor under hydrothermal conditions involving stirring (130rpm) at 150 or 200°C for 2h. Structural analyses of the powders were conducted by XRD with Rietveld refinement and FT-Raman spectroscopy, and the particle shape was observed by FE-SEM. Lattice parameter measurements indicated a linear dependence of both “a0” and “c0” in the scheelite structured SrMo1−xWxO4 with a changing W content following Vegard’s law. These analyses also provided evidence of the structural variation localised in the tetrahedral site as a result of the simultaneous incorporation of MoO4 and WO4 in the solid solutions formed in the compositional range of 9⩽x⩽60mol%. The SrMo1−xWxO4 particles exhibited a predominantly euhedral shuttle-shaped morphology and particle sizes varying between 0.75 and 1.5μm. The particle growth was affected by increasing the reaction temperature and the tungsten concentration. Photoluminescence analysis (PL) revealed a marked attenuation of the blue and green emissions preferentially for the powder containing 48.5mol% of W, which makes it potentially useful for optoelectronic applications.

Composition dependent order-disorder transition in NdxZr1−xO2−0.5x pyrochlores: A combined structural, calorimetric and ab initio modeling study

The order-disorder phase transition in the NdxZr1−xO2−0.5x system is studied by complementary techniques which include wet chemical synthesis of a series of compositions with various Nd/Zr ratios with the final annealing at 1873 K, X-ray diffraction, oxide melt solution calorimetry and ab initio thermodynamic modeling. Our structural data indicate the transition from ordered to disordered pyrochlore at x ∼0.31 at a temperature of 1873 K. Our calorimetric data show a transition enthalpy of ∼30 kJ/mol, which corresponds to an entropy of disordering of ∼16 J/K/mol. The latter value is significantly smaller than the configurational entropy of transition computed under the assumption of complete disorder in a fluorite phase, indicating a substantial degree of order remaining in the fluorite phase at the temperature of synthesis. The considered phases are computed ab initio using a series of special quasi-random structures that emulate the complete or partial disorder. The results of our calculations and thermodynamic modeling are in good agreement with the measured lattice parameters, the Nd content at the order-disorder transition, and the measured formation and transformation enthalpies. Thus our combined experimental and modeling results provide valuable insight into the disordering of this pyrochlore phase and of other pyrochlore materials.

Study of the structure and composition of the strained epitaxial layer in the InAlAs/GaAs(100) heterostructure by transmission electron microscopy

The results of electron microscopy studies of an epitaxial InAlAs layer on a GaAs(100) substrate are reported. It is established that there exist misfit dislocations at the interface between the materials and there are residual strains distorting the lattice in the layer. From the measurements of lattice parameters in the directions parallel and orthogonal to the growth direction away from misfit dislocations, the local nominal lattice parameter of the layer is calculated and the relative content of indium is determined.

Quantitative Phase Analysis of Aluminium-Lithium Alloys

A quantitative approach to the determination of the phase composition in the Al-Mg (Cu)-Li alloys has been developed on the basis of the balance equations of chemical and phase compositions as well as the lattice parameter measurement of the α solid solution. It is shown that, for the Al-Mg (Cu)-Li alloys, the ratio between the fractions of the δ' (Al3Li) and S1 (T1) phases is determined by the ratio between the molar fractions of Li and Mg (Cu). By means of this technique it is shown that in Al-Cu-Li alloys the proportion of δ'-phase is much higher than ternary T1-phase, and the proportion of δ'-phase and a ternary phase (S1) are approximately equal in alloys of Al-Mg-Li system. The equations for the calculation of the contents of the S1 (Al2MgLi), T1 (Al2CuLi) and δ' (Al3Li) phases in the 1420, 1424, 5090 alloys (Al-Mg-Li alloys) and in the 1440, 1441, 1450, 1460, 1461, 1464, 1469, 2050, 2090, 2091, 2094, 2098, 2099, 2195, 2198, 2199, 2297, 8090 (alloys (Al-Cu-Li alloys) are given.

Size dependent spinodal decomposition in Cu-Ag nanoparticles

Nanoparticles are of considerable interest, owing to their size-dependent properties, different from those of bulk materials. For revealing internal atomic processes in them, individual nanoparticles of Cu-Ag alloys were grown by direct current (DC) magnetron sputtering. Phase-separation during growth in Cu-Ag particles was found to be size- and composition-dependent. Particles below 5 nm in diameter grow as a solid solution of the components for all compositions (15–80 at.% Ag). In the low Ag content range (15 and 30 at.% Ag) phase-separation occurs only for particles above 5 nm in diameter. The separation into Cu-rich and Ag-rich domains, when observed, takes place by spinodal decomposition for all particle sizes. In particles undergoing incomplete coalescence, phase-separation occurs even if the diameter of the colliding particles is below 5 nm. In the higher Ag content range (60–80 at.%), however, no phase-separation is observed until coalescence sets in. Lattice parameter measurements in alloy particles of 30 at.% Ag revealed that the miscibility gap in individual particles varies between 70 and 90 at.%. Calculation of the composition dependence of the critical length for spinodal decomposition provided quantitative explanation for the observed phenomena.

Preparation of Mo-Re-C samples containing Mo7Re13C with the β-Mn-type structure by solid state reaction of planetary-ball-milled powder mixtures of Mo, Re and C, and their crystal structures and superconductivity

Mo-Re-C compounds containing Mo7Re13C with the β-Mn structure were synthesized with high-melting-temperature metals Mo, Re, and C powders using a conventional solid state method with a planetary ball milling machine instead of the arc melting method. Use of the ball milling machine was necessary to obtain Mo7Re13C with the β-Mn structure using the solid state method. Almost single-phase Mo7Re13C with a trace of impurity were obtained using the synthesis method. By XRF and lattice parameter measurements on the samples, Fe element existed in the compound synthesized using the planetary ball milling machine with a pot and balls made of steel, though Fe element was not detected in the compound synthesized using a pot and balls made of tungsten carbide. The former compound containg the Fe atom did not show superconductivity but the latter compound without the Fe atom showed superconductivity at 6.1K.

Structural and mechanical properties of nitrogen-deficient cubic Cr–Mo–N and Cr–W–N systems

Our computational and experimental results reveal the inherent driving force of cubic Cr–TM–N (TM=Mo, W) solid solutions for nitrogen deficiency, expressed chemically as Cr1-xTMxN1–0.5x. Their computationally predicted large positive mixing enthalpies indicate a high driving force for isostructural decomposition into B1-structured CrN and γ-TM2N. The calculations further predict an improved ductility with increasing TM-content and significant anisotropy of elastic constants and Young's modulus in the entire compositional range. The experimentally measured lattice parameters, nitrogen content in Cr-Mo-N, and elastic properties of Cr1-xTMxN1–0.5x corroborated our theoretical predictions. Our combined theoretical and experimental study provides new understanding and insights into these complex material systems.

Vibrational properties ofLiNb1−xTaxO3mixed crystals

Congruent lithium niobate and lithium tantalate mixed crystals have been grown over the complete compositional range with the Czochralski method. The structural and vibrational properties of the mixed crystals are studied extensively by x-ray diffraction measurements, Raman spectroscopy, and density functional theory. The measured lattice parameters and vibrational frequencies are in good agreement with our theoretical predictions. The observed dependence of the Raman frequencies on the crystal composition is discussed on the basis of the calculated phonon displacement patterns. The phononic contribution to the static dielectric tensor is calculated by means of the generalized Lyddane-Sachs-Teller relation. Due to the pronounced dependence of the optical response on the Ta concentration, lithium niobate tantalate mixed crystals represent a perfect model system to study the properties of uniaxial mixed ferroelectric materials for application in integrated optics.

Composition measurement of epitaxial ScxGa1−xN films

Four different methods for measuring the compositions of epitaxial ScxGa1−xN films were assessed and compared to determine which was the most reliable and accurate. The compositions of epitaxial ScxGa1−xN films with 0 ≤ x ≤ 0.26 were measured directly using Rutherford backscattering (RBS) and x-ray photoelectron spectroscopy (XPS), and indirectly using c lattice parameter measurements from x-ray diffraction and c/a ratio measurements from electron diffraction patterns. RBS measurements were taken as a standard reference. XPS was found to underestimate the Sc content, whereas c lattice parameter and c/a ratio were not reliable for composition determination due to the unknown degree of strain relaxation in the film. However, the Sc flux used during growth was found to relate linearly with x and could be used to estimate the Sc content.

MoNbTaV Medium-Entropy Alloy

Guided by CALPHAD (Calculation of Phase Diagrams) modeling, the refractory medium-entropy alloy MoNbTaV was synthesized by vacuum arc melting under a high-purity argon atmosphere. A body-centered cubic solid solution phase was experimentally confirmed in the as-cast ingot using X-ray diffraction and scanning electron microscopy. The measured lattice parameter of the alloy (3.208 Å) obeys the rule of mixtures (ROM), but the Vickers microhardness (4.95 GPa) and the yield strength (1.5 GPa) are about 4.5 and 4.6 times those estimated from the ROM, respectively. Using a simple model on solid solution strengthening predicts a yield strength of approximately 1.5 GPa. Thermodynamic analysis shows that the total entropy of the alloy is more than three times the configurational entropy at room temperature, and the entropy of mixing exhibits a small negative departure from ideal mixing.

A New XRD Method to Quantify Plate and Lath Martensites of Hardened Medium-Carbon Steel

This paper introduces a new technique to separately measure the volume fraction and tetragonal ratio of co-existing lath and plate martensites in ultrahigh strength steel, and to calculate their different carbon contents. First, the two martensites are assumed to have body-centered tetragonal lattice structures of different tetragonal ratios. X-ray diffraction is then applied to obtain the overlapping {200} diffraction peak, which is subsequently separated as four sub-peaks using a self-made multiple Gaussian peak-fitting method to allow the measurement of the individual lattice parameters c and a. Finally, a modified equation is applied to calculate the carbon contents from the obtained tetragonal ratios. The new technique is then applied to investigate the effect of subsequent tempering on the decarbonization of the as-quenched martensites.

Determination of the stretch tensor for structural transformations

Structural transformations in crystalline solids are increasingly the basis of the functional behavior of materials. Recently, in diverse alloy systems, both low hysteresis and reversibility of phase transformations have been linked to the satisfaction of the nongeneric conditions of compatibility between phases. According to the Cauchy–Born rule, these conditions are expressed as properties of transformation stretch tensor. The transformation stretch tensor is difficult to measure directly due to the lack of knowledge about the exact transforming pathway during the structural change, and the complicating effects of microstructure. In this paper we give a rigorous algorithmic approach for determining the transformation stretch tensor from X-ray measurements of structure and lattice parameters. For some traditional and emerging phase transformations, the results given by the algorithm suggest unexpected transformation mechanisms.

Influence of Martensite Fraction on Tensile Properties of Quenched and Partitioned (Q&P) Martensitic Stainless Steels

By means of a simplified quenching and partitioning (Q&P) processing with quench temperature equal to room temperature, austenite fractions of 56, 43, and 24 vol% are stabilized in the microstructures of Q&P‐processed Fe–Cr–C, Fe–Cr–C–Co, and Fe–Cr–C–N stainless steels, respectively. The mechanical stability of austenite is quantified by tensile tests at temperatures between 20 and 200 °C. In agreement with the Q&P concept, the stability of austenite is found to be highest for the steel with the highest martensite fraction. The carbon enrichment of austenite in a specimen of the Fe–Cr–C steel processed to have 82 vol% martensite is estimated by X‐ray diffraction measurement of the austenite lattice parameter. The results indicate that only about 12% of the carbon contained in the martensite has partitioned into the austenite. The formation of tempering carbides is one of the mechanisms behind the significant deviation of the carbon enrichments from the full partitioning assumption.

Sintering behaviour, solid solution formation and characterisation of TaC, HfC and TaC–HfC fabricated by spark plasma sintering

Solid solution formation and sintering behaviour of TaC–HfC ceramics made from commercial TaC and HfC powders prepared using spark plasma sintering (SPS) at temperatures up to 2450°C was investigated. Phase analysis and lattice parameter measurements using X-ray Diffraction (XRD) showed mutual diffusion of Hf and Ta with increasing sintering temperature. High Resolution Transmission Electron Microscopy (HRTEM) confirmed that solid solution formation and densification were achieved by a solid-state mechanism. Solid solutions were achieved for 4TaC–1HfC, 1TaC–1HfC and 1TaC–4HfC powders after sintering at temperatures of at least 2350°C. Fracture toughness (KIC) values were in the range of 2.7–3.4MPam1/2 for all ceramics measured using Vickers indentation. Thermal conductivity of TaC was 55.8W/mK at 1400°C. Coefficients of thermal expansion (CTE) varied from 7.08–7.66×10−6/K (in the range of 25–2000°C), with TaC at the lower end.

Neutron Diffraction Measurements and Micromechanical Modelling of Temperature‐Dependent Variations in TATB Lattice Parameters

AbstractTriaminotrinitrobenzene (TATB) is a highly anisotropic molecular crystal used in several plastic‐bonded explosive (PBX) formulations. TATB‐based explosives exhibit irreversible volume expansion (“ratchet growth”) when thermally cycled. A theoretical understanding of the relationship between anisotropy of the crystal, crystal orientation distribution (texture) of polycrystalline aggregates, and the intergranular interactions leading to this irreversible growth is necessary to accurately develop physics‐based predictive models for TATB‐based PBXs under various thermal environments. In this work, TATB lattice parameters were measured using neutron diffraction during thermal cycling of loose powder and a pressed pellet. The measured lattice parameters help clarify conflicting reports in the literature as these new results are more consistent with one set of previous results than another. The lattice parameters of pressed TATB were also measured as a function of temperature, showing some differences from the powder. This data is used along with anisotropic single‐crystal stiffness moduli reported in the literature to model the nominal stresses associated with intergranular constraints during thermal expansion. The texture of both specimens were characterized and the pressed pellet exhibits preferential orientation of (001) poles along the pressing direction, whereas no preferred orientation was found for the loose powder. Finally, thermal strains for single‐crystal TATB computed from lattice parameter data for the powder is input to a self‐consistent micromechanical model, which predicts the lattice parameters of the constrained TATB crystals within the pellet. The agreement of these model results with the diffraction data obtained from the pellet is discussed along with future directions of research.