Microscopic strain,local structural heterogeneity and the energetics of silicate solid solutions

Abstract

Evidence for the existence and scale of local microscopic strains in silicate minerals is reviewed. From the compositional limit of the plateau for the monoclinic ? triclinic phase transition in alkali feldspars, the microscopic strain fields around impurity atoms in framework silicates can be ～20–40 Å in diameter. This dimension fails within the characteristic length scale of phonons in these materials, and phonon spectra should therefore be particularly sensitive to the extent and magnitude of local elastic strain effects. The most prominent feature is expected to be broadening of absorption peaks, which can now be followed quantitatively in complex spectra by autocorrelation analysis. Such strain fields contribute elastic energy to the enthalpy of a crystal and might be expected to be largely responsible for enthalpy changes accompanying cation ordering processes and solid solution formation. Comparisons of line broadening data from powder IR absorption spectra with calorimetric determinations of enthalpy for selected mineral systems confirm a close relationship between local structural heterogeneity and enthalpy variations.     

Compositional fluctuations in isotopic solid solutions

The effect of compositional fluctuations in isotopic solid solutions on the frequency shift and broadening of Raman lines is investigated. The broadening of the optical phonon line depends on the composition throughout the concentration range of the binary solid solution. It is shown that the line broadening is caused by elastic phonon scattering from compositional fluctuations. The type, size, and number of fluctuations responsible for the scattering are determined, and the dependences of these quantities on the concentration of solid solution components are established.     

Potential industrial applications of inhomogeneous broadening imaging.

Variations in magnetic susceptibility at air-water interfaces can result in inhomogeneous broadening of the NMR line. By special asymmetrical imaging techniques, originally developed for lung imaging, images can be formed of only those molecules that experience this inhomogeneous broadening. The basic concepts and latest developments in inhomogeneous-broadening-imaging techniques are described. Potential industrial applications are also discussed.     

Stable isotope composition of daily and monthly precipitation in Zagreb

Stable isotopic compositions (delta2H and delta18O) of daily precipitation collected in the period from October 2002 to March 2003 and monthly precipitation in the period from 2001 to 2003, as well as the corresponding meteorological data (temperature, amount of precipitation), all collected in Zagreb, Croatia, are presented. delta2H and delta18O values, both daily and monthly, show large variations due to large temperature variations and the different origin of the air masses. Variations are larger for daily samples than for composite monthly samples. Good correlation of delta18O with temperature is obtained for both types of samples. On the basis of the correlation between delta2H and delta18O, the local meteoric water line is close to the global meteoric water line. Deuterium excess of both daily and monthly precipitation indicates that in the Zagreb area, the influence of air masses from the Mediterranean area prevails in the autumn period.     

Thermodynamics of molybdenum-niobium-hydrogen ternary solid solutions

The enthalpy of solution of hydrogen has been measured in a series of Mo-Nb solid solutions in the composition range 0–77 at.% Nb. In the solid solutions of Mo and Nb there is good evidence that the enthalpy of solution of H will not be influenced by strain energy factors or by a change in the electronic work function of the metal surface with composition. No correlation between the measured enthalpies and the density of electron states at the Fermi surface was found. The binary Mo-Nb system was chosen because the density of states varies drastically across the system, exhibiting an extremum.     

Raman spectroscopy of solid nitrogen up to 374 kbar

We measured the Raman spectrum of room-temperature solid nitrogen in a diamond cell at pressures up to 374 kbar. Only the molecular stretching mode was observed. The frequency of this mode appears to increase smoothly from 2340 cm^-1 at 39 kbar to 2394 cm^-1 at 374 kbar. Between about 50 and 120 kbar, the Raman line is split into a second, higher-frequency peak, which may be associated with molecular ordering in the solid. Measurements of broadening and splitting in fluorescence lines from the ruby pressure gauge indicate that solid nitrogen is reasonably plastic up to 130 kbar. We suggest that nitrogen might serve as a useful pressure medium.     

Effect of alkali-earth ions on the local structure of LaAlO3-La0.67A0.33MnO3 (A = Ca, Sr, Ba) diluted solid solutions: 27Al NMR studies

²⁷Al magic angle spinning (MAS) nuclear magnetic resonance (NMR) was studied for diluted alkali earth metal-doped lanthanum manganite solid solutions in the lanthanum aluminate (1 − y)LaAlO₃-yLa_0.67 A _0.33MnO₃ (A = Ca, Sr, Ba) with y =0, 2, 3, and 5 mol %. The spectra depended on the dopant species and showed higher substitutional ordering for the Ba-containing mixed crystals. Magnetically shifted lines were observed in all solid solutions and were attributed to Al in the octahedral oxygen environment near manganese trivalent ions. Nonlinear dependences of their intensity were referred to the manganese-rich cluster formation. An additional MAS NMR line corresponding to aluminum at sites different from the octahedral site in pure LaAlO₃ was observed only in solutions doped with Ba. 3Q MAS NMR revealed that the broadening of this line is governed mainly by quadrupole coupling and made it possible to calculate the isotropic chemical shift. The article was submitted by the authors in English.     

The diffusion of hydrogen in b.c.c. VTi solid solutions

Recent data for the variation of the diffusivity of hydrogen in b.c.c. VTi solid solutions with Ti-concentration and temperature have been analyzed in terms of the cell model for such ternary solid solutions. The data have been shown to be compatible with this model and a simple cell energy spectrum involving H-metal interactions which are linearly dependent upon the Ti-concentration.It is shown that the interaction energies deduced from the kinetic behavior of the system are in good accord with thermodynamic data for the VH and TiH terminal solid solutions.     

Solid state broadening in Auger spectra

Some Auger spectra in the gas phase show extremely sharp lines and a great deal of fine structure while the Auger spectra of solids, even at high resolution, lack this detailed fine structure and generally have much broader peaks. In an effort to understand the broadening processes which occur on condensation of a gas or vapour to the solid phase, several solids for which high resolution gas phase data exists have been studied. The result of measurements of the M₄₅N₄₅N₄₅ Auger spectrum of cadmium are reported and comparison is made with the vapour phase data. Although the solid data contains considerable quasi-atomic fine structure the lines are broader than the vapour phase and by matching computer broadened vapour phase data to the experimental data an estimate of the individual line widths may be made. The relative intensities of the lines in the simulation agree closely with the solid data if loss processes are considered. Measurements have also been made on the same Cd transition in CdS and in this material the Auger lines are much broader than in Cd metal and the fine structure has almost disappeared. Results are also reported of measurements of the Auger spectra of solid rare gases made with the aid of a UHV cryostat capable of operating at temperatures down to 10 K. The gases studied were Xe, Ar and Kr and again comparison with computer broadened gas data enable the broadening of individual Auger lines to be estimated. Measurements of the line breadths have been made at various temperatures and the results of these experiments will be discussed in terms of lifetime and lattice vibrational broadening.     

Microscopic theory of vitrification of metallic solutions

A Green's function technique is developed for describing compositional ordering and vitrification of solid solutions with arbitrary composition. It is shown that the proposed approach is related with the standard theory of ordering of regular solid solutions. Peculiarities of the diagrammatic technique are studied. Explicit expressions are derived for the spectrum of solitary excitations, which are responsible for the ordering. Equations are derived for determining the temperature-concentration dependences of the compositional order parameter, the vitrification parameter, and the chemical potential.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 60–65, May, 1991.     

Laser array beam propagation through liver tissue

Laser array beam propagating through mouse liver tissue is investigated. The turbulence power spectrum of the liver tissue is employed in the extended Huygens–Fresnel method to obtain an optical intensity profile and beam broadening at the observation point in biological liver tissue. Variations of the beam profile and the beam broadening are simulated based on the number of beamlets, source size, wavelength and the ring radius of the array. A biological tissue, illuminated by the laser array beam, exhibits different beam profiles and beam spot radius variations when the number of beamlets, source size, wavelength and the ring radius of the laser array beam are varied. Examining these variations observed in the propagated optical beam and comparing them with the test cases, abnormalities such as cancer and tumor in a biological liver tissue can be diagnosed.     

面心立方固溶体合金的团簇加连接原子几何模型及典型工业合金成分解析

工业合金牌号的成分选择体现了固溶体合金的化学短程有序结构,满足由最近邻两层原子组成的"团簇加连接原子"模型,例如对于置换型面心立方固溶体Cu-Zn,其合金牌号成分可以表述为[Zn-Cu_(12)]Zn_(1-6)和[Zn-Cu_(12)](Cu,Zn)_6,其中方括号内为第一近邻配位多面体团簇.基于此,本文赋予团簇式以具体原子结构的含义,对置换型面心立方固溶体结构中团簇的可能存在形式进行了穷尽,得出团簇式所对应的所有"团簇加连接原子"结构单元模型,给出团簇和连接原子之间的比例和空间排列的所有可能,并对Cu-Zn和Cu-Ni合金常用牌号对应的团簇式给出了三维结构模型,进一步验证了前期关于合金团簇式解析的正确性.用这些模型中原子化学序描述合金的成分,赋予团簇式以具体的原子结构意义,为进一步开发新的合金提供了理论依据.     

原子光谱线增宽的原因

本文从理论上给出了原子光谱线增宽的几种原因 ,即 :①自然线宽 ,它是原子的内禀特性 (即在跃迁中所涉及到的能级的特性 ) ;②多普勒增宽 ,它是原子无规则热运动的结果 ;③碰撞增宽 ,它是原子间相互作用的结果。并对这几种原因分别给出了数量级上的估算。对原子光谱的测定具有参考意义。     

On the effect of time-ordering for Lyman-α

Numerical calculations of the wings of the hydrogen Lyman-α line due to Stark broadening by electrons have been performed including time ordering effects. It is concluded that two recent calculations, which apparently disagree, are numerically correct within their respective approximations and their differences are explained.     

First-principles investigations of ordering in binary α-Ti solid solutions

The ordering tendency in binary f-Ti solid solution containing 3sp or 4sp simple-metal (SM) or 3d transition-metal (TM) solute is investigated systematically by the linear muffin-tin orbital (LMTO) method within the atomic sphere approximation (ASA). We demonstrated that the effective pairwise interaction (EPI) energy in a solid solution is equal to half the solute-solute interaction energies and can be evaluated by a supercell total energy approach. The calculations of EPI energy both with and without volume relaxation of the supercells and local density of states (LDOS) show that the EPI energies of Ti-SM and Ti-TM solutions are dominated by different factors. For Ti-SM solutions, the EPI energies are of large absolute values with a negative sign, indicating strong ordering tendency in these solutions. The volume relaxation does not alter the EPI energy substantially. The calculated LDOS shows that the ordering tendency in Ti-SM solutions may be related to the hybridization between the electrons of the SM atoms when they are close to each other. For most Ti-TM solutions, if calculated without relaxation, the absolute EPI energies are very small; however, if calculated with relaxation, they are of relatively large positive values, indicating a clustering tendency in these solutions. By combining the calculated EPI energy and Flinn's model for short-range order (SRO) strengthening, the increase in critical shear stress sro due to SRO is estimated for Ti-SM alloys, and the results qualitatively agree with experiment.     

Modelling in relation to cation ordering

We review the methodology of using computer models to obtain quantitative information about cation ordering. Empirical interatomic potentials or ab initio electronic structure calculations are used to generate the energies for many configurations containing disordered arrangements of cations, and the parameters in model Hamiltonians can be determined from these energies. Monte Carlo simulations are then used to generate ensemble averages as functions of temperature or chemical composition. Analysis of the Monte Carlo ensembles directly yields the temperature dependence of long-range and short-range order, and thermodynamic quantities such as energy and heat capacity. Use of thermodynamic integration allows for the calculation of entropy and free energy. The methods are illustrated by examples showing long-range order/disorder phase transitions (feldspars), short-range order in solid solutions (pyrope-grossular), and non-convergent ordering (magnesium aluminate spinel); where comparisons with experimental data are possible, the model calculations are seen to give results that are reasonably accurate. The example in which ab initio electronic structure calculations are used show that it is now possible to extract accurate thermodynamic data for ordering processes using models that require no prior experimental data.     

The optical spectroscopy of chromium in ed-2 silicate glass

The technique of fluorescence line narrowing is used to probe the inhomogeneously broadened ²E-⁴A₂ transition of Cr³⁺ in a silicate glass. The resultant sharp zero-phonon line is accompanied by a vibrational sideband which carries information about the range of vibrational modes in the glass and about the strength of the orbit-lattice interaction. The homogeneous broadening of the zero-phonon line is measured as a function of temperature and compared with the analogous broadening in Cr-doped crystals. The broadening of the zero-phonon line in the glass at high temperatures is attributed to a Raman relaxation mechanism such as is observed in crystals. At low temperatures, however, there is an additional broadening mechanism which has an approximately linear dependence on temperature and which has no analogue in crystalline materials.     

Proton NMR study of α-MnH0.06

Proton nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rates for the solid solution α-MnH_0.06 have been measured over the temperature range 11-297 K and the resonance frequency range 20-90 MHz. A considerable shift and broadening of the proton NMR line and a sharp peak of the spin-lattice relaxation rate are observed near 130 K. These effects are attributed to the onset of antiferromagnetic ordering below the Néel temperature T_N≈130 K. The proton NMR line does not disappear in the antiferromagnetic phase; this suggests a small magnitude of the local magnetic fields at H-sites in α-MnH_0.06. The spin-lattice relaxation rate in the paramagnetic phase is dominated by the effects of spin fluctuations.     

Long-range spatial correlations in the exciton energy distribution in GaAs/AlGaAs quantum wells

Variations in the width of a quantum well (QW) are known to be a source of broadening of the exciton line. Using low temperature near-field optical microscopy, we have exploited the dependence of exciton energy on well width to show that in GaAs QWs, these seemingly random well-width fluctuations actually exhibit well-defined order-strong long-range correlations appearing laterally, in the plane of the QW, as well as vertically, between QWs grown one on top of the other. We show that these fluctuations are correlated with the commonly found mound structure on the surface. This is an intrinsic property of molecular beam epitaxial growth.     

Evaluation of Mössbauer line diffusion broadening by exponential fit

The Mössbauer line broadening measured by R.Lindsey in -iron stabilized with vanadium is evaluated by an exponential fit described in the APPENDIX of this paper. By this procedure the low temperature Mössbauer line width _m ⁰ , the diffusion frequency factorD ₀ and the activation enthalpyH are computed.Knauer's andSørensen-Trumpy's definitions of the time correlation factorf _t , necessary for theD ₀ calculation from Mössbauer line broadening, are applied to the Fe-V diluted BCC solid solutions.