The effect of clamped and free boundaries on long range strain coupling in structural phase transitions

In ferroelastic structural phase transitions, the atomic ordering in one cell creates a local strain field which is propagated elastically throughout the material, resulting in an effective or indirect coupling J(R _ij ) between the ordering in cells i and j. With free boundaries on the sample, the J(R _ij ) contains a Zener-Eshelby term J _Z of infinite range, which largely determines the transition temperature T _c. The present paper shows what happens when the boundaries are clamped. On cooling from a high temperature an anomaly takes place at more or less the same temperature as the phase transition for free boundaries. Cooling results in an irregular pattern of domains with positive and negative order parameter whose long range strains cancel. Two cases are distinguished. In the “tweed” case coherent domain boundaries form easily and result in fine lamellar domains. When coherent domain boundaries are not possible (the “non-Sapriel”) case, larger less regular domains are formed. In either case the macroscopic net strain adds up to zero.     

Investigation of domain behaviour in 0.7Pb(Mg1/3Nb2/3) O3-0.3PbTiO3 single crystals at different temperatures in the transmission electron microscope

Using transmission electron microscopy, in-situ changes in ferroelastic domains in 0.7Pb(Mg_1/3Nb_2/3)O₃-0.3PbTiO₃ single crystals were observed at 60 to -163°C. At -163°C, the microscopic tweed morphology of the ferroelastic domains rotated by 90°, and certain orientation changes in the mesoscopic sawtooth domains took place. At this temperature, the ferroelastic domains became coarsened and certain S-shaped mesoscopic domains were reshaped. The disappearance and/or changes in the orientations of both the sawtooth and the ferroelastic domains were reversible upon return to room temperature. On heating to 60°C, both the mesoscopic sawtooth and the microscopic tweed domains were stable below 53°C. Above 53°C, the mesoscopic walls disappeared and the contrast of the tweed domains became blurred. Upon return to room temperature from 60°C, the mesoscopic domain patterns could not be retrieved, indicating that the transformation was irreversible. The morphology of the tweeds at this temperature indicated a structural transition from a two-variant domain state to a multivariant state, eliminating mesoscopic boundaries.     

Energy level scheme and the effect of magnetic order on the optical transitions in europium chalcogenides

The optical constants of Eu-chalcogenide single crystals have been determined at room temperature for photon energies from 1 to 6 eV. In the same energy range the transmission of thin evaporated films (except for EuO) has been measured with polarized light above and below the magnetic ordering temperature. The observed polarization-dependent splittings of the two main absorption maxima in the region of magnetic order suggest transitions from the 4f⁷-level into the crystal field split 5dt_2g- and 5de_g-states. An attempt has been made to relate the maxima of the absorption coefficient to interband transitions and transitions from the localized 4f-states. With this assumption we derived a consistent energy level scheme of the four Eu-chalcogenides. From the scheme we gained useful information about the width of the 5d-states, the crystal field splitting and the possible type of conductivity. Finally we tried to explain theoretically the splittings observed in the region of magnetic order. For this purpose a one-particle model has been used to calculate the transition probabilities for the 4f⁷?4f⁶(⁷F _J ) 5dt_2g and the 4f⁷?4f⁶(⁷F _J ) 5de_g transition, taking into account an exchange interaction as well as a spin-orbit coupling. Although this simple model can explain the splittings of the excited 4f⁶(⁷F _J ) 5de_g-state, a complete explanation of the effect of magnetic order on the 4f⁶(⁷F _J ) 5dt_2g-state fails up to now.     

The anisotropic 3D Ising model

An expression for the free energy of an (001) oriented domain wall of the anisotropic 3D Ising model is derived. The order--disorder transition takes place when the domain wall free energy vanishes. In the anisotropic limit, where two of the three exchange energies (e.g. J_x and J_y ) are small compared to the third exchange energy (J_z ), the following asymptotically exact equation for the critical temperature is derived, sinh(2J_z /k _B T _c)sinh(2(J_x ?+?J_y )/k _B T _c))?=?1. This expression is in perfect agreement with a mathematically rigorous result (k _B T _c/J_z ?=?2[ln(J_z /(J_x ?+?J_y ))?ln(ln(J_z /(J_x ?+?J_y ))?+?O(1)]^?1) derived earlier by Weng, Griffiths and Fisher (Phys. Rev. 162, 475 (1967)) using an approach that relies on a refinement of the Peierls argument. The constant that was left undetermined in the Weng et al. result is estimated to vary from ～0.84 at ((H_x ?+?H_y )/H_z )?=?10^?2 to ～0.76 at ((H_x ?+?H_y )/H_z )?=?10^?20.     

Analyzing power measurements for p-3He elastic scattering from 1.75 to 4.50 MeV

Analyzing powers for p-³He elastic scattering have been measured at 12 energies between 1.75 and 4.50 MeV for θ_c.m. = 40° to 150°. A comparison of our results with earlier data of Drigo et al. shows substantial differences at all energies. The R-matrix fits to our data that were included in the global search calculations of Hale and Dodder are shown. These calculations established the ordering of the lowest-lying T = 1 levels of ⁴He as J^π = 2^?, 1^? (triplet), 0^?, and 1^? (singlet), which is the WMI (MHI) ordering.     

NMR 1 J(HD) coupling in HD as a function of interatomic distance in the presence of an external magnetic field

A theoretical study has been made of the dependence of the ¹ J(HD) coupling in HD on the interatomic distance R in the presence of a static uniform magnetic field B ₀. The behaviour of all coupling terms arising from Ramsey's magnetic electron-nucleus interactions, Fermicontact (FC), spin-dipolar (SD) and paramagnetic (PSO) and diamagnetic (DSO) spin-orbital interactions is analysed qualitatively for large R. It is concluded that the PSO, DSO and SD terms become negligibly small as R increases. Detailed calculations were carried out for the FC term following two different approaches: detailed full CI calculations within a non-perturbative approach; and explicit diagonalization of the Hamiltonian operator restricted to the subspace spanned by the ¹Σ⁺;_g and the ³Σ⁺;_u states. Within the approximations considered, the FC term of ¹ J(HD) is found to be independent of B ₀ and to increase by several orders of magnitude, in agreement with previous results by Bacskay, G. B., 1995, Chem. Phys. Lett., 242, 507, until a critical distance R(B ₀) is reached, beyond which it almost vanishes. The quenching of the coupling at R(B ₀) is due to the splitting of the ³Σ⁺;_u state in the presence of the field B ₀. The stronger the field the shorter is R(B ₀).     

On the structural phase transitions in the incommensurate Cs2CdBr4

Abstract

In the series of incommensurate A₂BX₄ halides with the β-K₂SO₄ type structure, Cs₂CdBr₄ exhibits an unusual behaviour since the “lock-in” phase transition occurs at the centre of the Brillouin zone. The observed phase sequence is the following: Pnma (Z = 4)?INC(k₀ ≈ 1/6a*)?P2_1/n(Z = 4)?P1 (Z = 4). These phase transitions have been studied by means of Raman scattering and ultrasonic measurements. It is shown that the Pnma?INC?P2_1/n sequence is governed by order-disorder processes due to CdB2-₄ tetrahedra reorientations coupled with translations of the Cs⁺ cations, and that the low-temperature P2_1/n?P1 transition is of a displacive nature, governed by a soft optical mode. The “pseudo-proper” ferroelastic character of these transformations is clearly established. A model potential developed in the framework of Landau theory is proposed; this model is able to reproduce the general trends observed in the temperature dependence of the soft-modes and of the elastic constants in the different phases.     

High-resolution infrared spectrum and analysis of the ν2 band of CF3Cl

The rotational structure of the ν₂ band of CF₃Cl, with natural isotopic abundance, has been investigated using a tunable diode laser spectrometer. The spectra have been obtained for a low-temperature (200 K) sample, to reduce the interfering contributions of hot-band transitions. Due to the very small value of the (ΔA − ΔB) constant for both isotopic species, the K structure of most P(J) and R(J) multiplets is generally not resolvable. Only for CF₃³⁵Cl, the K structure could be resolved for P(J) multiplets with J≥55. Molecular constants for the ν₂ fundamental of both isotopic species have been obtained using least-squares fitting routines in combination with band contour simulations for unresolved K structure.     

Optical studies of the ferroelastic phase transitions in KFe(MoO4)2

ABSTRACT

The ferroelastic phase transitions in KFe(MoO₄)₂ have been studied by means of polarized light microscopy. The crystal undergoes a sequence of ferroelastic phase transitions. It has been found that the second transition consists of two transitions separated by the temperature interval of about 0.4 K. Both these transitions are of the first order and are evidenced through a phase front passing, without the domain structure rebuilding. The disposition of optical indicatrix axes n_g, n_m has been established, and the birefringence has been measured in the plane (0001) in the temperature range covering all ferroelastic phases. From temperature studies of the morphic birefringence, a critical exponent of the order parameter has been estimated.     

Analysis of the 2ν3 band of 12CD3F at 5.06 μm recorded under high resolution

The 2ν₃(A₁) band of ¹²CD₃F near 5.06 μm has been recorded with a resolution of 20–24 × 10^?3 cm^?1. The value of the parameter (α^B ? α^A) for this band was found to be very small and, therefore, the K structure of the R(J) and P(J) manifolds was unresolved for J < 15 and only partially resolved for larger J values. The band was analyzed using standard techniques and values for the following constants determined: ν₀ = 1977.178(3) cm^?1, B″ = 0.68216(9) cm^?1, D″_J = 1.10(30) × 10^?6 cm^?1, α^B = (B″ ? B′) = 3.086(7) × 10^?3 cm^?1, and β^J = (D″_J ? D′_J) = ?3.24(11) × 10^?7 cm^?1. A value of α^A = (A″ ? A′) = 2.90(5) × 10^?3 cm^?1 has been obtained through band contour simulations of the R(J) and P(J) multiplets.     

The ν1 + ν3 combination band of 238UF6

The ν₁ + ν₃ band of ²³⁸UF₆ has been observed at Doppler-limited resolution between 1291.5 and 1297.2 cm^?1 in a statically cooled longpath cell at 226 K. The frequencies of 21 transitions belonging to P(22, 28, 30), 14 belonging to R(12, 30, 31), and 28 belonging to the Q branch with 41 ≤ J ≤ 71, were measured with an accuracy of ±0.002 cm^?1. In addition, 53 frequency differences were measured in the Q branch between lines having different J assignments from Q(14) to Q(76). Five spectroscopic constants were fitted to these 116 data points with a standard deviation of 0.0006 cm^?1. The rotational constants have nearly the values expected from a consideration of ν₁ and ν₃ themselves, and there is little evidence for interaction of ν₁ + ν₃ with other levels.     

Analyses of 4f11 Energy Levels and Transition Intensities Between Stark Levels of Er3+ in Y3Al5O12

ABSTRACT

Absorption and fluorescence spectra obtained at temperatures as low as 4 K were investigated between 200 and 1550 nm on samples containing approximately 1.2 at. wt. % Er in Y₃Al₅O₁₂ (YAG). Within this wavelength range 125 experimental energy (Stark) levels were analyzed, representing data that span 29 ^2S+1 L _J multiplet manifolds of Er³⁺(4f¹¹) in D₂ sites up to an energy of 44,000 cm^?1. Agreement between calculated and observed Stark levels was achieved with an r.m.s. deviation of 11.2 cm^?1. These transitions originate from the ground-state Stark level in the ⁴I_15/2 manifold to J + 1/2 Stark levels associated with each of the 28 excited-state manifolds. A total of 88 ground-state absorption transition line strengths were measured for 19 ^2S+1 L _J multiplet manifolds between 280 and 1550 nm. For line strength measurements, the Er³⁺ ion is assumed to be distributed homogeneously throughout the D₂ cation sites of Y³⁺ in the lattice. The line strengths were analyzed with a weighted (E _i  ? C _i )/E _i , with an r.m.s. error of 0.25. Use of a “vector crystal field” parametrization resolves ambiguities in the transition intensity parameters and allows for the definition of polarization-resolved Judd-Ofelt parameters, which may have wide-ranging applicability for future Judd-Ofelt-type intensity calculations.     

Measurement of multiplet intensities and noble gas-broadened line widths in the V3-fundamental of methane

Integrated intensity data at 300°K for J-multiplets between P(11)and R(11) in the _{V3-fundamental of ¹²CH4} are presented, along with the intensity of the entire Q-branch, which also encompasses the Q-branch of the _{V3-fundamental of ¹³CH4}. These data, together with theoretical estimates for the intensities of J-multiplets of J > 11, sum up to a value of S_band= 284±14cm^?2atm^?1 at 300°K. This results is in excellent agreement with most of the previously published values for this parameter. Within experimental error, the intensities of the J-multiplets in the _{V3-fundamental do not seem to exhibit the strong anamolies that were characteristic of lines in the 2V3}-band.Line widths have been measured at 100°K, 130°K, 190°K, 250°K, and 300°K for R(0), R(1), and R(2) broadened by He, Ne and Ar. The temperature dependence of the line width is discussed for the three cases of broadening. In neon broadening at 300°K, the ‘effective mean line widths’ for multiplets R(3) through R(11) have also been obtained experimentally; their J-dependence is interpreted using Gordon's theory of line shapes in multiplet spectra.     

Contact terms in E.M. decays of mesons

The ratios R_J(P)Γ(J)→P⁺P^?), P = π or K, have been evaluated ad due to contact interactions genrated by gauge invariance, for mesons with natural J^P. R_J increases rapidly with J. This provides unambigous tests for the model and indicates that contact terms are prolific sources of photons and leptons in hadron collisions.     

Anisotropic impurity scattering in palladium silver alloys

Measurements have been made of the Hall coefficientR of some alloys of silver in palladium over the temperature range 1°K to 120°K. The alloys contain between ∼1 and ∼10 at.-% silver. Values ofR were also obtained at room temperature and these were in good agreement with earlier published work. The values ofR are negative in all the alloys, and |R| increases both on reducing the temperature and increasing the silver concentration,c. Below ∼10°K, |R| becomes independent of temperature but shows a linear dependence onc, increasing by a factor of 2.5 over the concentration range measured. This increase is too great to be accounted for in terms of band structure changes alone, so we have examined the effects of anisotropic impurity scattering. To a first approximation it can be shown thatR is proportional to an anisotropy parameterA, defined asA=〈τ ²(k)〉/〈τ(k)〉², whereτ(k) represents the relaxation time of an electron in a statek, and 〈〉 is an average over the Fermi surface. In palladium we assume that the majority of the current is carried by the s-electrons. In the presence of silver impurities these electrons can be scattered into s-states or d-states with relaxation times given byτ _ss α1/c(1−c) andτ _sd α1/c ²(1−c) respectively. FollowingPlate we have assumed thatτ _ss is isotropic and thatτ _sd is anisotropic, leading to an overall anisotropic relaxation time for impurity scattering. We then find the parameterA increases approximately linearly with silver content, in accordance with our experimental results.     

Computational study of linear and nonlinear optical properties of substituted thiophene imino dyes using long-range corrected hybrid DFT methods

The molecular structures, linear and nonlinear optical properties of a series constituted by four R-substituted thiophene imino dyes, namely A(R?=?SO₂Me), B(R?=?SO₂Ph), C(R?=?NO₂), and D(R?=?C₂(CN)₃) were analysed using CAM-B3LYP, ωB97XD and LC-ωPBE hybrid DFT functionals in combination of the 6-311++G(d,p) standard basis set. The dipole moments, polarisabilities, HOMO-LUMO energy gaps, maximum absorption wavelengths and first hyperpolarisabilities were calculated in the gas phase and the obtained results are in good agreement with experimental NLO activity order A?<?B?<?C. Compared to synthesised dyes A-C, the designed dye D presents a longer maximum absorption wavelength and a lower HOMO-LUMO gap because of the appreciable stabilisation of its LUMO energy. These results were confirmed by the calculation of the total second-order stabilisation energy E⁽²⁾ defined in the context of the NBO population analysis. Consequently, dye D is predicted to exhibit a higher first hyperpolarisability in comparison with dyes A-C. This result can be justified by the enhanced intramolecular charge transfer in dye D due to the stronger electron-withdrawing ability and the cumulative action of the long π-conjugation of the tricyanovinyl moiety. The very high total hyperpolarisability (27 times greater than that of para-nitroaniline) of the designed dye D suggests its promising use in organic NLO devices.     

DNA Duplex Dynamics: NMR Relaxation Studies of a Decamer with UniformlyC-Labeled Purine Nucleotides

Dynamics in a DNA decamer duplex,d(CATTTGCATC) ·d(GATGCAAATG), were investigated via a detailed¹³C NMR relaxation study. Every 2′-deoxyadenosine and 2′-deoxyguanidine was chemically enriched with 15%¹³C and 98%¹⁵N isotopes. Six nuclear relaxation parameters [R(¹³C_z),R(¹H_z),R(2¹H_z¹³C_z),R(¹³C_x),R(2¹H_z¹³C_x) and steady-state¹³C{¹H} NOE] were measured at 600 MHz and three were measured at 500 MHz (¹H frequency) for the CH spin systems of sugar 1′, 3′, and 4′ as well as base 8 and 2 positions. A dependence of relaxation parameter values on chemical position was clearly observed; however, no sequence-specific variation was readily evident within our experimental error of ∼5–10%, except for 3′ and 5′ termini. It was demonstrated that the random 15%¹³C enrichment effectively suppressed both scalar and dipolar contributions of the neighboring carbons and protons on the relaxation parameters. To analyze dynamics via all observed relaxation parameters, full spectral density mapping (1992, J. W. Peng and G. Wagner,J. Magn. Reson.98, 308) and the “model-free” approach (1982, Lipari and Szabo,J. Am. Chem. Soc.104, 4546) were applied complementarily. A linear correlation between three spectral density values,J(ω_C),J(ω_H− ω_C), andJ(ω_H+ ω_C) was observed in plots containing all measured values, but not for the other spectral density terms includingJ(0). These linear correlations reflect the effect of overall motion and similar internal motions for each CH vector in the decamer. The correlations yielded two correlation times, 3–4 ns and 10–200 ps. One value, 3–4 ns, corresponds to the value of 3.3 ns obtained for the overall isotropic tumbling correlation time determined from analysis of¹³C T1/T2 ratios. The possibility of overall anisotropic tumbling was examined, but statistical analysis showed no advantage over the assumption of simple isotropic tumbling. Lack of correlations entailingJ(0) implies that a relatively slow chemical exchange contributes to yielding of effectiveJ_eff(0) values. Based on spectral density mapping and the T1/T2 ratio analysis, three basic assumptions were initially employed (and subsequently justified) for the model-free calculation: isotropic overall tumbling, one internal motion, and the presence of chemical exchange terms. Except for terminal residues, the order parameterS²and the corresponding fast internal motion correlation time were determined to be about 0.8 ± 0.1 and 20 ± 20 ps, respectively, for the various CH vectors. Only a few differences were observed between or within sugars and bases. The internal motion is very fast (ps–ns time scale) and its amplitude restricted; e.g., assuming a simple wobble-in-a-cone model, the internal motion is restricted to an angular amplitude of ±22.5° for each of the 1′, 3′, 4′, 2, and 8 positions in the purine nucleotides in the entire duplex.     

Infinitesimal loops and tweed structure

Some results are collected for phase transitions in which the elastic strain plays a decisive role. Both ferroelastic and antiferroelastic behaviour results in patterning which has a tweed-like appearance. The infinitesimal loop approximation first used by Kroupa in 1962 is used to try to sort out the possible effects. Transformations resulting in pure shear produce ferroelastic tweed, whereas transformations based on the nucleation and growth of platelike precipitates seem likely to produce antiferroelastic tweed.Dedicated to Dr. Frantiek Kroupa in honour of his 70^th birthday.It is of course a pleasure to recall the interaction with Franta Kroupa, who taught me about infinitesimal loops 35 years ago, and to express gratitude for the hospitality of Prof. David R. Clarke at the Department of Materials, University of California at Santa Barbara, where this paper was written.     

Monte Carlo study of entropy for face-centered cubic Ising antiferromagnets

A face-centered cubic Ising model with nearest neighbor antiferromagnetic exchangeJ _nn in the presence of a magnetic fieldH is investigated by Monte Carlo methods. Free energy and entropy of the model are obtained by integrating the equation of state along various paths, starting at suitable reference states. It is shown that at low temperatures first-order phase transitions can be located with very good precision. At the two critical fieldsH _c1/|J _nn |=4,H _c2/|J _nn |=12 a residual ground-state entropyS(0) is found, which is estimated as aboutS(0)/k _B (ln 2)/3 in both cases.In the presence of a ferromagnetic next-nearest neighbor exchange there is no longer a nonzero entropy at the critical fields, however. ForR+J _nnn /J _nn +–1 we find the same structure of the phase diagram as qualitatively predicted by Domany et al., where lines of 3-state and 4-state Potts model-like transitions meet at a multicritical point atH=0. Some consequences of our results for interpreting the ordering of face-centered cubic binary alloys are also discussed.     

Amino wagging and inversion in hydrazine: K′ = 1 levels in the first excited state of the antisymmetric wagging vibration

The infrared absorption spectrum of NH₂NH₂ vapor has been observed in the region 899–1077 cm^?1, where the antisymmetric wagging band (v_a = 1 ← 0) appears, by the use of a Fourier transform spectrometer with a practical resolution of 0.003 cm^?1. In the region 925.0–925.6 cm^?1, the spectrum was also observed with a tunable diode laser, and a component, β, of the ^pQ₂ cluster has been further resolved. Most of the absorption lines assignable to β-^pP₂(J″), γ-^pP₂(J″), β-^pQ₂(J″), γ-^rQ₀(J″), β-^rR₀(J″), and γ-^rR₀(J″), where J″ = 2 ～ 15, have been identified. From these observed transition frequencies, in combination with the ground state energy levels given by microwave spectroscopy, the energy level structure of the K′ = 1 rotational states was determined. From this, the following molecular parameters for the v_a = 1 state were determined: molecular asymmetry, B′-C″ = 0.00017 cm^?1; a parameter q₅ describing an umbrella motion Coriolis interaction (q₅K) about the a axis, q₅ = ?0.0030 cm^?1; its J(J + 1) variation, q_5j = 0.00014 cm^?1; and a parameter describing an umbrella-motion K-type doubling g₅J(J + 1), g₅ = 0.000021 cm^?1.