Relativistic calculation of atomic X-ray transition rates

The fully relativistic transition probabilities in atomic X-ray emission are calculated for a wide range of selected elements of the periodic table, fromZ=21 toZ=93. The treatment includes the effect of the retardation of the radiation field. The atomic model used is the self-consistent relativistic Hartree-Fock, with the Slater approximation for the exchange term. The formulas for EL and ML multipole transition rates are derived, and transition rates are calculated for all transitions to theK-shell,L-subshells, andM-subshells. The contributions of all multipoles, as determined by the angular momentum and parity selection rules, are included in the present work. The calculated values of (Kα ₂/Kα ₁), (Kβ ₁/Kα ₁), (Kβ ₃/Kβ ₁) and (Kβ ₂ Kβ ₁) transition rates are in good agreement with the available experimental data. Rates for the forbidden (M1) 2s _1/2→1s _1/2 transitions are also presented.     

Spin gap, phase separation and d-wave pairing as revealed by electron spin-lattice relaxation in 123 and 124 YBaCuO systems doped with Gd3+

With an original modulation technique, the Gd³⁺ electron spin-lattice relaxation has been investigated in normal and superconducting states of YBa₂Cu₃O_6+x (123) and YBa₂Cu₄O₈ (124) compounds doped with 1% Gd. In the 123 sample withx = 0.9T _c = 90 K), theT ₁ behavior within 50 <T< 200 K reveals the [1 ? tanh²(Δ/2kT)]/T dependence typical of a spin gap opening with Δ ≈ 240 K. Below 50 K, the exponential slowing down ofT ₁ is limited by the Korringa-like behaviorT ₁ T = const); the same Korringa-like law is found in the 123 sample withx = 0.59 (T _c = 56 K) within the total 4.2–200 K temperature range. This is interpreted in terms of microscopic separation of the normal and superconducting phases allowing for the electron spin cross-relaxation between them. In the 124 sample (T _c = 82 K), the Gd³⁺ relaxation rate below 60 K is found to obey a power lawT _n with an exponentn ≈ 3. Such a behavior (previously reported for nuclear spin relaxation) is indicative of the d-wave superconducting pairing. Additional paramagnetic centers characterized by relatively slow spin-lattice relaxation are found in both 123 and 124 systems. A well-pronounced change in theT ₁ temperature dependence atTT* ≈ 180–200 K is observed for these slowly relaxing centers as well as for the conventional, fast-relaxing Gd³⁺ ions, suggesting microscopic phase separation and a change in the relaxation mechanism due to electronic crossover related with the opening of the spin gap. This hypothesis is supported by some “180 K anomalies” previously reported by other authors.     

The properties of the (H2O)6 water cluster that depend on its density during temperature transitions

Water clusters (H₂O)₆ are simulated by the Monte Carlo method with the Metropolis function at various temperatures (T ₁ = 273 K, T ₂ = 298 K, and T′₁= 373 K) and densities (ρ₁ = 0.9998 g/cm³, ρ₂ = 0.9167 g/cm³, and ρ₃ = 0.00059 g/cm³) of the system. It is established that the number of retained most probable configuration types at ρ₁ = 0.9998 g/cm³ during temperature transitions from T ₁ = 273 K to T ₂ = 298 K and from T′₁ = 373 K to T ₂ = 298 K is smaller than at ρ₃ = 0.00059 g/cm³. This result was acquired on the background of the following invariable parameters of the system with the same temperature transitions for each of three values of density: (i) the average number of retained most probable configuration types, (ii) the average fraction of weight coefficients of the most probable configuration types, and (iii) the average potential energy. The configuration type that was retained among the most probable configuration types of the system for all values of density (ρ₁ = 0.9998 g/cm², ρ₂ = 0.9167 g/cm³, and ρ₃ = 0.00059 g/cm³) of the system for temperature transitions from T ₁ = 273 K to T ₂ = 298 K and from T′₁ = 373 K to T ₂ = 298 K was also revealed.     

Critical behavior of heat capacity in the vicinity of phase transitions in [NH2(CH3)2]5Cd3Cl11

The heat capacity of a [NH₂(CH₃)₂]₅Cd₃Cl₁₁ crystal was studied calorimetrically in the temperature interval 100–300 K. The C _p (T) dependence indicates that, as the temperature is lowered, phase transitions occur at temperatures T ₁ = 176.5 K and T ₂ = 123.5 K. The thermodynamic characteristics of this crystal were determined. It is shown that the transition at T ₂ = 123.5 K is an incommensurate-commensurate phase transformation and that the transition at T ₁ = 176.5 K is a normal-incommensurate phase transition.     

Electron spin-lattice relaxation of Yb3+ and Gd3+ ions in glasses

The electron spin-lattice relaxation rate (T ₁ ^?1) was measured in two glass samples: (i) a phosphate glass doped with 1 wt% Yb₂O₃ and (ii) a Li₂Si₄O₉ glass sample doped with 0.2 wt% Gd₂O₃. In the Yb³⁺-doped glass sample,T ₁ was measured by an electron-spin-echo technique from 4.2 to 6 K, by the modulation method from 10 to 26 K and by the EPR linewidth from 30 to 100 K. It was found thatT ₁ ^?1 αT ⁿ withn=9 in the range 4.2–6 K.n decreased gradually as the temperature was increased and tended towards 2 above 40 K. Over the entire temperature range 4.2–100 K,T ₁ ^?1 was fitted toAT+BT ⁹ J ₈ (Θ _D/T) (whereA andB are two temperature-independent constants,J ₈ is the well-known Van Vleck integral andΘ _D is the Debye temperature). The value ofΘ _D (=46.3±0.9 K) so determined is in good agreement with that of Stevens and Stapleton from theirT ₁ measurements in the range 1.5 to 7 K. In the Gd³⁺-doped glass, it was observed thatT ₁ ^?1 αT over the range 50–150 K. The data for Ye³⁺-doped glass sample were accounted for by assuming that the phonon modulation of the ligand field is the dominant mechanism, associated with a low Debye temperature in accordance with the published data obtained by using other techniques to study lattice dynamics. On the other hand, the data on the Gd³⁺-doped glass sample were explained to be predominantly due to a mechanism involving Two-Level-Systems (TLS)     

Nuclear magnetic resonance study of the heavy-fermion system URu2Si2

Nuclear magnetic resonance (NMR) and relaxation studies on ²⁹Si have been carried out on the heavy Fermion system URu₂Si₂. Above the Kondo temperature of about 60 K, the nuclear relaxation time T₁ is nearly temperature independent, which is consistent with the occurrence of fluctuations of localized U moments. Below about 60 K T₁ is inversely proportional to temperature suggesting that the system behaves like a Fermi liquid. A sharp increase in T₁ occurs below 17 K which is probably associated with the opening of an energy gap at the Fermi surface due to the formation of a spin density wave state. Below about 10 K, T₁ reacquires the inverse temperature dependence observed in the 17 K ∼ 60 K temperature range.     

Intensity and half-width measurements in the 1·525 μm band of acetylene

Line intensities at 150°K and 295°K, self-broadened half-widths at 171°K, 200°K, 250°K and 295°K, and hydrogen-broadened half-widths at 171°K, 200°K and 295°K have been measured in the ν₁+v₃ band of C₂H₂ at 1·525 μm. The absolute intensity of the band has been determined independently by employing the Wilson-Wells-Penner-Weber technique. Our best estimate for the absolute intensity of the band is S_v=7·82 ± 0·07 cm^?2 atm^?1 at 295°K. Line intensities calculated using this value of S_v are in good agreement with the measured intensities at the two extreme temperatures of 150°K and 295°K considered in the present study, thereby not suggesting any significant intensity anomalies. Line positions have been measured for the first time for this band for R(29)?P(25).     

Thermal evidences for successive CDW phase transitions in 1T-TaS2

The heat capacity of 1T-TaS₂ has been measured over the temperature range including the successive phase transitions (140 K–370 K) by an adiabatic calorimeter. There are three transitions in the measured temperature range, two first-order transitions (at about 226 K (T₁) and about 353.5 K (T₃)) and one small anomaly at about 283 K (T₂) with a broad peak. The transition enthalpies are as follows; ΔH₁=52±5 cal·mol^-1, ΔH₂=7.5±2 cal· mol^-1 and ΔH₃=122±8cal·mol^-1.     

1H NMR study of the α phase of Mg2NiHx system

Hydrogen behavior in the α phase of Mg₂NiH_x system was studied by ¹H NMR. ¹H NMR spectra and spin-lattice relaxation times, T₁ and T_1ρ, of Mg₂NiH_0.22 were measured in the temperature range between 100 and 480 K. The drastic change in the linewidth is observed between 170 and 340 K, and ¹H rigid lattice is observed below 170 K, from which it is deduced that the hydrogen atoms are randomly distributed in α-Mg₂NiH_x. The relaxation mechanism for t₁ is the paramagnetic one, while the T_1ρ value is determined partially by hydrogen diffusion. The hydrogen diffusion rate has been determined from the linewidth and the T_1ρ value. The paramagnetic relaxations observed in T₁ and T_1ρ have been discussed relating to the hydrogen diffusion.     

Evidence for the fröhlich collective mode in the one-dimensional conductor K2[Pt(CN)4] Br0.3 · 3H2O from far infrared reflection

Far infrared and infrared reflection measurements on single crystals of the one dimensional conductor K₂[Pt(CN)₄] Br_0.3 · 3H₂O have been performed at 4.2K, 62K and 300K for light polarized parallel (E6z) and perpendicular (E ? z) to the platinum chains. At 4.2K and 62K a strong structure is observed in the E6z spectrum near 40 cm^-1 which is not observable at 300K. This structure is interpreted as due to the Fröhlich collective 2q_F-phonon mode.     

Spin relaxation of conduction electrons in GaAs

We have used optical spin orientation techniques to measure T₁ of conduction electrons in GaAs (NinA ≈ 10¹⁷ cm^-3) for 4.7 K ? T ? 200 K. From Hall effect measurements we estimated the electron momentum relaxation time τ_p. For 50 K ? T ? 200 K, the product T₁τ_p agrees with our earlier order of magnitude estimate of the D'yakonov-Perel' mechanism, in which band structure induced precession is strongly narrowed by momentum relaxation. The Elliott mechanism is one to two orders of magnitude weaker.     

Isotope effect on the Peierls transition temperature of TTF-TCNQ

Conductivity measurements on isotopically substituted single crystals of TTF-TCNQ show a relatively large shift in the phase transition temperatures at 52.5 K (T₁) and 37.7 K (T₃). Deuteration of both TTF and TCNQ chains increases T₁ by 0.75 ± 0.15 K, N¹⁵ substitution increases T₁ by 0.6±0.1 K while deuteration of the TTF chains apparently has no significant effect. Different possible interpretations of these results are briefly discussed.     

Effect of γ-irradiation on the heat capacity of an [NH2(CH3)2]2 · CuCl4 crystal in the temperature range 80–300 K

The heat capacity of [NH₂(CH₃)₂]₂ · CuCl₄ crystals prior to and after γ-irradiation with doses of 1, 5, 10, and 50 MR is measured by the calorimetric method in the temperature range 80–300 K. It is found that, as the temperature decreases, the temperature dependence C _p (T) exhibits two anomalies which correspond to phase transitions from the incommensurate to the ferroelectric phase at T _c =281 K and from the ferroelectric to the ferroelastic phase at T ₁=255 K. The nature of the anomalies is typical of a first-order phase transition. In addition, a smeared anomaly in the form of a small increase in the heat capacity of the ferroelectric phase is observed at T≈275 K. It is demonstrated that when the dose of γ-irradiation increases, the anomalies decrease in magnitude and the phase transition temperatures are displaced: T _c increases and T ₁ decreases.     

Vacancy-induced low-energy excitations in the one-dimensional ionic conductor β-eucryptite

We have measured the specific heat C of β-Li_xAl_xSi_2?xO₄ (β-eucryptite) for x = 1 and 0.93 between 0.1 and 2.5 K. Below 1 K, an anomaly is observed in C which exhibits a maximum at 0.6 K. This anomaly is enhanced by a factor of 10 in the substoichiometric sample. These results are interpreted in the Frenkel-Kontorova model of configurational excitations which arise in this material because of vacancies in the ion channels. Below 0.5 K a time dependence of the specific heat is observed which hints at rather slow dynamics of the configurational excitations.     

Pulsed NMR study of hydronium β-alumina

Pulsed ¹H NMR measurements are reported for hydronium β-alumina powder in the temperature range 77 K < T < 440 K at 16 MHz. Motional narrowing due to translation (E_A = 21 kJ mol^-1 occurs at T > 260 K. Spin-lattice relaxation is non-exponential in both the laboratory and rotating frames. The observed M₂ suggests that reorientation of H₃O⁺ may also occur, but there are no indications of reorientational minima in T₁ or T_1?.     

Charge density waves in layer structures: A NMR study on a 2HNbSe2 single crystal

We have studied by pulsed NMR a single crystal of 2HNbSe₂ at ambient pressure and under hydrostatic pressure of 21 kbar in the temperature range 4.2–273 K. Our results are consistent with the onset of incommensurate charge density waves (ICDW) at T_CDW = 33 K atP = 1 bar and 26 K at P = 21 kbar. Below T_CDW, the lineshapes of the (m → m ? 1) transitions agree with a local distribution of Knight shift and electric field gradients respecting the symmetry of a triple ICDW, while above T_CDW, pre-transitional broadening is observed. The product T₁T = 500 ± 100 msk was found constant in the temperature range 4.2–77 K and pressure independant.     

Isotope effect on the Peierls transition temperature of TTF-TCNQ

Conductivity measurements on isotopically substituted single crystals of TTF-TCNQ show a relatively large shift in the phase transition temperatures at 52.5 K (T₁) and 37.7 K (T₃). Deuteration of both TTF and TCNQ chains increases T₁ by 0.75 ± 0.15 K, N¹⁵ substitution increases T₁ by 0.6 ± 0.1 K while deuteration of the TTF chains apparently has no significant effect. Different possible interpretations of these results are briefly discussed.     

Magnetic and related properties of GdCu5.1In6.9

Magnetic measurements performed between 1.7 and 300K show that GdCu_5.1In_6.9 is an antiferromagnet below T _N = 13.4(1) K. At temperatures 17–300K the Curie-Weiss law is followed with p _eff = 7.57 μ _B and θ = -33.8K. Electrical resistivity measurements do not show any pronounced anomaly, but the resistivity is rather low with RRR ≈ 59. The EPR experiment shows that the resonance exists between 10 and 300 K. A temperature independent g-shift (Δg = -0.036(10)) and a Korringa.type linewidth broadening of 2.6 G/K was observed at temperatures higher than 55 K. The linewith increase found at high temperature well above T _N can suggest a significant amount of short. range order. ¹⁵⁵Gd Mössbauer effect examinations show that H _hf is perpendicular to the c-axis and therefore magnetic moments of Gd are located within the ab-plane.