Static Atomic Displacements Research Articles

Investigations on the structural disordering of neutron-irradiated highly oriented pyrolytic graphite by X-ray diffraction and electron microscopy

Light and heavy neutron-irradiation damage of highly oriented pyrolytic graphite (HOPG) crystals was examined by means of X-ray diffraction and high-resolution high-voltage transmission electron microscopy (TEM). From the X-ray data analysis, it was found that there is an average increase of about 3% in thec-axis lattice parameter of the unit cell of graphite for lightly neutron-irradiated HOPG. However, thec-axis lattice parameter could not be estimated from the HOPG sample having the highest dose of neutron irradiation under the present investigation, because the X-ray profile was highly asymmetrical. This increase in thec-axis lattice parameter is attributed to lattice expansion due to the static displacement of atoms after neutron irradiation. Local structure analysis by TEM shows that the 0002 lattice spacing for the above-mentioned HOPG samples has been increased by up to 10% as a result of the neutron irradiation. This increase inc-axis lattice spacing can be ascribed to the fragmentation of the crystal lattice into nanocrystallites, breaking and bending of the 0002 straight lattice fringes, appearance of dislocation loops, and extra interstitial planes within the fragmented nanocrystallites. All these changes are a result of the static displacement of atoms after neutron irradiation.

Long-wavelength static atomic displacements in γ-FeNi alloys

The temperature dependences of the intensity of elastic diffuse neutron scattering from γ-FexNi100−x (x=57 and 68 at. %) alloy single crystals near basic reciprocal-lattice sites in the (110) plane are measured using a triaxial neutron spectrometer. New effects of instability of the γ-phase lattice with respect to long-wavelength (transverse and longitudinal) static atomic displacements have been detected. The displacements are found to depend on the iron concentration in the alloys and on temperature. The relations of these structural distortions to premartensitic phenomena and the invar effect in γ-FeNi alloys are discussed

Amorphisation compositional limits and atomic displacement in fcc solid solutions

Although amorphisation and melting processes are characterised by different thermodynamic and kinetic features, it appears that intimate connections exist between the two topological order–disorder transitions. Experimental and theoretical findings suggest that both static and thermal atomic displacements from crystalline lattice equilibrium positions are able to induce the loss of long-range order. In this paper, the relationship between the critical volume expansion at amorphisation compositional limits and the static atomic displacement is investigated. The volume expansion associated with the substitutional dissolution of B atoms into a given fcc crystalline matrix A is evaluated according to the simplified model of Egami and Waseda and compared with the volume reached by the pure matrix A at the melting temperature. The resulting volumes are used to calculate the average static atomic displacement induced by local elastic distortions of crystalline lattice. The static atomic displacement is then connected with the size ratio between solute and matrix atoms.

Amorphisation compositional limits and atomic displacement in fcc solid solutions

Although amorphisation and melting processes are characterised by different thermodynamic and kinetic features, it appears that intimate connections exist between the two topological order–disorder transitions. Experimental and theoretical findings suggest that both static and thermal atomic displacements from crystalline lattice equilibrium positions are able to induce the loss of long-range order. In this paper, the relationship between the critical volume expansion at amorphisation compositional limits and the static atomic displacement is investigated. The volume expansion associated with the substitutional dissolution of B atoms into a given fcc crystalline matrix A is evaluated according to the simplified model of Egami and Waseda and compared with the volume reached by the pure matrix A at the melting temperature. The resulting volumes are used to calculate the average static atomic displacement induced by local elastic distortions of crystalline lattice. The static atomic displacement is then connected with the size ratio between solute and matrix atoms.

Multiscale studies and modeling of SPD materials

Abstract Recent results of experimental studies and computer modeling of bulk pure metals, subjected to severe plastic deformation (SPD) are presented. Experimental investigations and computer modeling were conducted on different scale levels. Influence of the processing parameters on the flow character of the deformed material and elastic stresses’ fields appearing in the die-set is studied on the macrolevel. Conformities of grain and subgrain size evolution, as well as the texture development at SPD were revealed on the mesolevel. On the microlevel as a result of computer simulation there were evaluated densities of the extrinsic grain boundary dislocations; there was analyzed the influence of SPD on the values of static and dynamic atomic displacements and the Debye temperature in the materials under investigation. The obtained results make it possible to explain novel properties, such as simultaneous appearance of high strength and ductility (the SPD paradox), enhanced diffusion properties, low-temperature and/or high-rate superplasticity of bulk SPD nanomaterials.

The effect of the static atomic displacements on the structure factors of weak reflections in cubic semiconductor alloys

We show that the static atomic displacements (SDs) from the average crystal sites, which exist in all III–V and II–VI semiconductor alloys where atoms having different covalent radii share a mixed sublattice, have a large effect on the structure factors (SFs) of the weak reflections (h + k + l = 4n + 2) of the cubic crystals of such alloys. Using atomistic simulations, this effect is studied quantitatively for 25 ternary alloys. Parameters describing the variations in the SFs with alloy composition for both electrons and X-rays are given. The sign of the difference between SFs calculated with and without SDs is the same for most alloys with a type-III or type-II mixed sublattice and reverses for a type-V mixed sublattice. Non-zero imaginary parts appear for reflections with all indices non-zero. We use a simple approximation to explain these results, to provide general rules for the effect of the SDs and to estimate its magnitude. We also study quantitatively the large effect of the SDs in quaternary Ga1− x In x As1− y N y alloys with y ≪ 1. Our calculations explain part of the difference between the experiments and the standardly calculated SFs of Ga 1−x In x As alloys. They show that the SDs must be taken into account, particularly when such ‘quasiforbidden’ reflections are used to measure alloy composition by electron microscopy.

Static displacements of Pd in the solid solution PdBy (0 <y < 0.2) as determined by neutron diffraction

The mean square atomic displacement parameter of Pd in the fcc interstitial solid solution PdB y , (u 2 Pd (y)), was determined for atomic ratios of y = 0.050, 0.100, and 0.184 using neutron powder diffraction data obtained at 15 K and 300 K. The values determined are significantly larger than those determined for pure Pd, (u 2 Pd (0)), at the same temperatures. Assuming that the dynamic (thermal) contribution to (u 2 Pd (y)) equals (u 2 Pd (0)), the static mean square atomic displacement parameter (u 2 Pd (y))) st = (u 2 Pd (y)) - (u 2 Pd (0)) was obtained as 0.0020(1) A 2 to 0.0027(1) A 2 . (u 2 Pd (y)) st showed no systematic variation with y or the sample temperature. This contrasts with an expected y(1 - y) concentration dependence for (u 2 Pd (y)) st . Comparison of (u 2 Pd (y)) st with values for the static mean square displacements of the metal atoms in different defect-NaCl type transition metal nitrides and carbides indicates that the current values for Pd in PdB y are exceptionally small.

The role of volume expansion in the formation of metallic glasses

Amorphisation and melting processes are generally regarded as topological order–disorder phase transitions characterised by basically different thermodynamic and kinetic features. Experimental and theoretical findings suggest, however, the existence of intimate connections between them. In particular, it seems that both the static and dynamic atomic displacements from the equilibrium positions characteristic of the ideal crystalline lattice play a fundamental role in driving the necessary instabilities for the loss of crystalline order. If the melting of a pure element and the amorphisation of a binary mixture with solute atoms larger than the matrix atoms are considered, the static and dynamic atomic displacements are simply related to the volume expansion. In this study, the volume expansions associated with the occurrence of amorphisation and melting are compared. The critical volume required in a binary system for the metallic glass to form is found to be approximately coincident with the volume reached by one of the two metals at the melting temperature. Theoretical estimates of the critical volume are obtained through the application of the criterion of Egami and Waseda and compared with experimental values. Significant connections are established between the so-called Born's shear instability and the loss of crystalline order.

Understanding Precursor Phenomena for the R-Phase Transformation in Ti-Ni-Based Alloys

AbstractPrecursor phenomena are critical issues for martensitic transformations. In this article, we show recent progress in understanding precursor phenomena to the R-phase transformation, which is important for both fundamentals and applications. Structural modulation in the parent phase was intensively studied by means of detailed analyses of the weak diffuse scattering of electrons with the aid of recently developed energy-filtered transmission electron microscopy coupled with x-ray diffraction. A peculiar domain-like structure, which originates from static transverse atomic displacements in the parent phase, was discovered by virtue of these advanced methods. The characteristics of this structure (e.g., size, shape, and temperature-dependence), as well as its role in the subsequent R-phase transformation, are discussed.

Wall-related Raman scattering in ferroelastic lead phosphate Pb3(PO4)2

Micro-Raman spectroscopy is applied to study structural changes in the vicinity of the domain walls in ferroelastic lead phosphate Pb3(PO4)2. The Raman spectra measured in untwinned and in heavily twinned regions of monoclinic Pb3(PO4)2 are studied and the observed differences are analysed on the basis of calculated vibrational modes of monoclinic structural units with different atomic arrangements. The wall-related Raman signals observed near 537, 65 and 51 cm−1 result from static displacements of the Pb2 atoms along the monoclinic binary axis. PO4 tetrahedra of rhombohedral geometry can also contribute to the extra Raman scattering near 537 cm−1. The deviations of the Pb2 atoms from their monoclinic positions couple preferably within the Pb2–O sheets parallel to the cleavage plane. Rearrangements of the Pb2 atoms occurring across the domain walls affect the intensity ratios between out-of-plane and in-plane components of ν4(PO4) bending, PO4 rotational and PO4 translational modes.

X-ray study of antiphase boundaries in the quadruple-period ordered GaAs0.87Sb0.13 alloy

The x-ray diffraction intensity from antiphase boundaries (APBs) in a quadruple-period ordered GaAsSb alloy is derived introducing statistical probabilities for these APBs and their associated phase shifts. Through experimental fits, we obtain an average distance between the neighboring APBs of approximately 130, 400, and 5 nm along [110], [−110], and [001] directions, respectively. The short distance along the [001] growth direction leads to a narrow streak along [001] in an intensity contour map. In addition, we find that the APBs broaden the ordering peaks, while their effect on the intensity ratio between the ordering peaks is negligible. Static atomic displacements, associated with bond length disparities are also included in the calculations.

Renormalization of the phase transition in lead phosphate, Pb3(PO4)2, by high pressure: structure

The structure of the high-pressure phase of lead phosphate, Pb3(PO4)2, has been determined from neutron powder time-of-flight diffraction data. Rietveld refinement to data collected at a pressure of 1.93(1) GPa and room temperature yielded unit-cell parameters a = 5.4613(3) Å, c = 20.069(1) Å, V = 518.41(4) Å3. The space group is R3̄m. The structure consists of PO4 tetrahedra together with Pb atoms in two symmetrically distinct sites. Analysis of the anisotropic displacement parameters of the Pb and O atoms indicates that they are spatially disordered within the structure. A structural model including split sites for these atoms suggests that the local environments around the Pb atoms in the high-pressure phase are very similar to those found in the low-pressure phase. We conclude that the phase transition from C2/c to R3̄m symmetry occurs as a result of the disordering of the static displacements of the Pb2 atoms and not, to pressures of 1.93 GPa, as the result of the elimination of these displacements. The evolution of the structure of the monoclinic phase of lead phosphate with pressure was also followed. With increasing pressure there is an apparent decrease in the displacements of the Pb atoms from the symmetry points of the high-pressure phase, but that of Pb2 does not extrapolate to zero at the phase transition pressure.

Effect of static displacements of the host atoms on short-range order in the hydrogen subsystem of Ni-H solution

Effect of static displacements of the host atoms on short-range order in the hydrogen subsystem of Ni-H solution

Effect of static displacements of the host atoms on short-range order in the hydrogen subsystem of Ni-H solution

Abstract The temperature and concentration dependences of the short-range order (SRO) parameters and their Fourier transform in H subsystem distributed on the octahedral interstices of fcc Ni are analysed, taking into account both direct (electrochemical) and indirect (strain-induced) contributions into the H-H interaction. The parameters of the electrochemical H-H interaction are estimated within the framework of the semiempirical approximation for atom-atom potentials. In order to calculate the energy parameters of the H-H strain-induced intraction, the Matsubara-Kanzaki-Krivoglaz lattice-statics method is applied. We demonstrate that, in the framework of the considered model, the strain-induced part mainly contributes to the total H-H interatomic mixing potential. For a description of the H-H SRO, the high-accuracy analytical (so-called ring) approximation is used. It is revealed that, for all considered values of the H concentration c = 0.10. 0.25 and 0.50. the H-H SRO Fourier transform is characteriz...

X-ray and neutron scattering study of Si-rich Si-Ge single crystals

The local atomic environments of homogeneous Si-rich Si-Ge single crystals were studied using x-ray and neutron diffuse scattering. No evidence of either chemical short-range order or clustering was observed. Static atomic displacements, however, were clearly present and are consistent with an expansion of the lattice in the vicinity of the Ge atoms. The dispersion of the acoustic phonons was also measured using inelastic neutron scattering. The acoustic modes of the Si-Ge alloy were found to lie nearer those of pure Si than expected from the homologous relationship found between pure Si and pure Ge.

The hydrogen diffusion in disordered systems

This paper analyzes the experimental data and presents a critical review of the existing approaches to the description of hydrogen diffusion in disordered amorphous alloys. It is noted that the available theories ignore the role of the short-range order in hydrogen diffusion. A diffusion model, which is based on the approach developed by us earlier, has been proposed for disordered crystalline alloys. In terms of this model specific features of the amorphous state are allowed for by homogeneous local distortions of voids, i.e. a kind of frozen fluctuations of the free volume. General expressions for the chemical diffusion coefficient of hydrogen in amorphous metals and binary alloys having FCC-like short-range crystalline order have been derived. It was shown that the diffusion coefficient may depend on a structural characteristic of disordered systems—the mean square of static displacement of atoms in the vicinity of a void—and also on the paired radial distribution function of atoms. The analysis of the proposed model suggests that the crystalline disorder causes an increase in the diffusion coefficient, which grows (unlike in crystals) linearly with the hydrogen concentration.

Effect of nonstoichiometry and ordering on the period of the basis structure of cubic titanium carbide

We have examined the influence of nonstoichiometry and order-disorder phase transformations on the basis period (of type B1) of the structure of titanium carbide TiCy (0.5<y<1.0). We found that ordering of titanium carbide TiCy with formation of superstructures of the type Ti Ti2C and Ti3C2 leads to growth of the period of the basis crystal lattice in comparison with the disordered carbide. Taking the change in the lattice period into account, we discuss the question of the directions of the static displacements of atoms near a vacancy.

Static displacements of atoms near isotopic impurities and residual resistivity

The question of the residual resistivity of chemically pure metals which are mixtures of atoms of different isotopes is discussed. The question of the static displacements appearing near isotopic impurities due to differences in the zero-point vibrations is analyzed in a microscopic approach. It is shown that such static displacements have a significant influence on the residual resistivity ρr. Their contribution to ρr is far greater than the contribution due to differences in the dynamic elastic electron scattering amplitudes.

A Displacive Structural Transformation in theCuO2Planes ofYBa2Cu3Oxat the Underdoped-Overdoped Phase Separation Line

A structural phase transformation in the CuO_2 planes of YBa_2Cu_3O_x has been observed at the onset of the overdoped regime, x=6.95. We have measured as a function of x the dimpling in the CuO_2 planes by EXAFS, and the O2,3 in-phase (A_1g) mode by Raman scattering. The data show for x>6.95 anomalously large static displacements of the Cu2 atoms off the O2,3 layer, and a gap in the distribution of the O2,3 in-phase Raman shifts. We conclude the structure of overdoped YBa_2Cu_3O_x to be a martensitic form of the structure most favourable for the superconductivity, and possibly at the origin of the split superconducting transition in the overdoped regime.

Grain-size dependence of thermal properties of nanocrystalline elemental selenium studied by x-ray diffraction

Quantitative x-ray-diffraction measurements in a temperature range 88-325 K were performed on porosity-free nanocrystalline (nc) elemental Se samples with a hcp structure. The nc-Se samples with different grain sizes were synthesized by crystallizing a melt-quenched amorphous-Se solid. Thermal-expansion coefficients (TECs) for the nc-Se samples were determined according to the temperature dependence of the lattice parameters (a and c) and the unit-cell volume (V). It was found that at higher temperatures the lattice expands along a axis but contracts along c axis. With a reduction of grain size, the linear TECs (both along a axis and c axis) increase significantly, resulting in an evident increase in the volume TEC that follows the D-1 rule. The temperature dependence of the mean Debye-Waller parameter (DWP) was measured, from which the static and thermal components of the DWP, as well as the Debye characteristic temperature for the nc-Sz samples were obtained, The observed enhancement in the mean DWP can be attributed mainly to the increase of static atomic displacement with a reduction of grain size that follows the D-1 rule. The characteristic temperature for the nc-Se specimens was found to decrease significantly with a refinement of grains. These results suggest larger displacements of the atoms from their ideal lattice locations and more defects in the nc-Se samples with smaller grains.