Z variations in yields of multicharged ions scattered and recoiled from a silicon surface

The doubly charged and triply charged ion yields from keV ion-silicon surface scattering are found to have a strong dependence on the atomic number Z₁ of the incident ion. For Z₁ < Z₂ the yield of scattered multicharged ions increases with Z₁, so that these ions dominate the recoiling Si²⁺ and Si³⁺ ions by Z₁ = 9. In contrast, when Z₁ > Z₂, there are large yields of Si²⁺ and Si³⁺ ions, and the multicharged scattered ion yields are too small to detect. The interaction radius at which shell vacancies are produced is also found to change, suggesting that electron promotion occurs at a different level crossing on either side of Z₁ = Z₂.     

Mass spectrometric investigation of the vaporization of li2tio3(s)

The vaporization of Li₂TiO₃(s) has been investigated by the mass spectrometric Knudsen effusion method. Partial pressures of Li(g), LiO(g), Li₂O(g), Li₃O(g) and O₂(g) over Li₂TiO₃(s) have been obtained in the temperature range 1180–1628 K. When the vaporization of Li₂TiO₃(s) proceeds, the content of Li₂O in the Li₂TiO₃(s) sample decreases. The phase of the sample is a disordered Li₂TiO₃ solid solution above 1486 K. The enthalpies of formation and the atomization energies for LiO(g) and Li₃O(g) have been evaluated from the partial pressures to be ΔH^o_f0(LiO, g) = 65.4 ± 17.4 kJ/mol, ΔH^o_f0(Li₃O, g) = − 207.5 ± 56.6 kJ/mol, D^o₀(LiO) = 340.5 ± 17.4 kJ/mol and D^o₀(Li₃O) = 931.6 ± 56.6 kJ/mol, respectively.     

Neutron noise and random trees links between past and present Special Lecture SMORTH VIII — Göteborg, 27–31 May 2002

After reviewing personal reminiscences about the history of reactor noise research, the generalized notion of neutron importance is discussed and advantages of the backward generating function equation are shown by calculating the space-time fluctuations of the neutron density in a simple virtual (one-dimensional) reactor. Similarities between chain reactions and randomly evolving trees are used to study the special properties of branching processes. It is assumed that at t = 0 the tree consists of a single living node called root which, after a certain time τ ≥ 0, may produce η ≥ 0 new living nodes and then becomes dead. τ and η are random variables with known distribution functions. Each new living node evolves further independently of the others as does the root. The time dependence of the expectation value of the living nodes number is determined by the average number q₁ of the new nodes produced by one dying node. Depending on whether q₁ < 1 or q₁ = 1 or q₁ > 1 the randomly evolving tree is called subcritical, critical, and supercritical, respectively. The probability distributions of the tree lifetime and the tree size are determined in two exactly solvable models, and it is proven that a supercritical tree may be finite even at t = ∞ with non-zero probability.     

Dynamic response of target electrons upon low and medium energy ion impact

We found that differential scattering cross sections for medium and low energy He⁺ and Ne⁺ impact on high Z-atoms were significantly enhanced compared with those calculated from the inter-atomic potential based on the Hartree–Fock–Slater atomic model coupled with the bare nuclear charge of a projectile. The enhanced scattering cross sections determined experimentally are reproduced well by a simple model that the center of gravity of target electrons is shifted toward the projectile during a large-angle collision. The shift from the target nucleus is expressed as a function of inter-nuclear distance in terms of a dipole moment (Z₁ and Z₂: atomic numbers of projectile and target, : polarizability, e: electron charge). The effective polarizability β (≡Z₁/Z₂) is expressed as a function of ion velocity v [10⁷ cm/s], in the form β = 0.079 exp[−0.46v].     

Thermodynamic studies on Cs4U5O17(s) and Cs2U2O7(s) by emf and calorimetric measurements

The oxygen potentials over the phase field: Cs₄U₅O₁₇(s)+Cs₂U₂O₇(s)+Cs₂U₄O₁₂(s) was determined by measuring the emf values between 1048 and 1206 K using a solid oxide electrolyte galvanic cell. The oxygen potential existing over the phase field for a given temperature can be represented by: Δμ(O₂) (kJ/mol) (±0.5)=−272.0+0.207T (K). The differential thermal analysis showed that Cs₄U₅O₁₇(s) is stable in air up to 1273 K. The molar Gibbs energy formation of Cs₄U₅O₁₇(s) was calculated from the above oxygen potentials and can be given by, Δ_fG⁰ (kJ/mol)±6=−7729+1.681T (K). The enthalpy measurements on Cs₄U₅O₁₇(s) and Cs₂U₂O₇(s) were carried out from 368.3 to 905 K and 430 to 852 K respectively, using a high temperature Calvet calorimeter. The enthalpy increments, (H⁰_T−H⁰₂₉₈), in J/mol for Cs₄U₅O₁₇(s) and Cs₂U₂O₇(s) can be represented by, H⁰_T−H⁰_298.15 (Cs₄U₅O₁₇) kJ/mol±0.9=−188.221+0.518T (K)+0.433×10⁻³T² (K)−2.052×10⁻⁵T³ (K) (368 to 905 K) and H⁰_T−H⁰_298.15 (Cs₂U₂O₇) kJ/mol±0.5=−164.210+0.390T (K)+0.104×10⁻⁴T² (K)+0.140×10⁵(1/T (K)) (411 to 860 K). The thermal properties of Cs₄U₅O₁₇(s) and Cs₂U₂O₇(s) were derived from the experimental values. The enthalpy of formation of (Cs₄U₅O₁₇, s) at 298.15 K was calculated by the second law method and is: Δ_fH⁰_298.15=−7645.0±4.2 kJ/mol.     

L-shell ionization of Cd, Sb, Te, Ba, La, Eu, Tb and Yb by O ions in the energy range from 0.19 to 0.75 MeV u

L_1,2, Lβ_1,3,4, Lβ_2,15, Lγ₁₍₅₎ and Lγ_2,3(4,4′) X-ray production cross-sections have been measured on selected medium-Z elements using ¹⁶O ions with energies from 0.19 to 0.75 MeV u⁻¹. Calculated L-subshell ionization cross-sections were compared with the predictions of the direct ionization theories: the ECPSSR theory, the semiclassical approximation (SCA) in the united atom limit (SCA-UA) and SCA coupled-channel calculations (SCA-CC) involving a few lowest lying states. For the ECPSSR theory, large discrepancies were found for all three subshells. Better overall agreement between the experiment and theory was found for the SCA-UA theory. SCA-CC calculations improved the agreement between experiment and theory for the L₂-subshell in the very adiabatic region. By measuring the L X-ray production cross-sections on W targets of different thickness, possible contribution of electron capture (EC) to the X-ray production cross-section was estimated to be less than 20%. The degree of multiple ionization of outer shells caused by heavy ion bombardment was estimated from the X-ray line energy shifts and by comparing the X-ray intensity ratios for heavy ions and protons.     

M-shell X-ray production cross sections for PIXE applications

M-shell X-ray production cross sections by protons of energies 0.1–4.0 MeV are reported for the most intense M_β(M_4,5N_6,7), M_γ(M₃N_4,5) and M₃O_4,5 M-X ray transitions appearing in PIXE spectra. The cross sections have been measured systematically for selected heavy elements between Ta and Th (Z₂=73–90). Measured M-X-ray production cross sections were found to be universal with respect of M-shell scaled velocity ξ_M. The data are compared with available theoretical calculations of M-shell ionization by charged particles based on the plane-wave Born approximation (PWBA) and the semiclassical approximation (SCA), as well as the ECPSSR theory and relativistic RPWBA-BC which are going beyond the first order treatment. Simple parameterization of experimental proton induced M-X-ray cross sections is proposed for PIXE applications. This parameterization, being accurate within ±5%, can be used for precise determination of heavy metal concentrations by PIXE technique.     

Empirical K-shell ionization cross-sections of elements from 4Be to 92U by proton impact

A large database containing about 5400 experimental K-shell ionization cross-sections by protons for elements from Be to U is collected from various sources and compilations available in the literature from 1953 to 1999. The data are divided into groups corresponding to their atomic numbers and fitted separately by analytical functions to deduce empirical K-shell ionization cross-sections. The deduced empirical K-shell ionization cross-sections are presented together with the reference ones obtained by Paul and Sacher for selected elements [H. Paul, J. Sacher, At. Data Nucl. Data Tables 42 (1989) 105]. The two sets of results are compared to the calculations within the ECPSSR theory and discussed.     

Electron Capture in M-Shell X-Ray Production from Heavy Elements by 25- and 35-MeV Fluorine Ions

M-shell x-ray production cross sections have been measured for thin solid targets (~2 ?g/cm2) of Au, Pb, Bi, and U for 25 and 35 MeV incident 199Fq+ ions (q = 4, 5, 6, 8, 9). The target M-shell x-ray production cross sections by projectiles with one or two K-shell vacancies are found to be enhanced over those by projectiles without K-shell vacancies. The cross sections averaged over target thickness were measured as a function of target thicknesses. Electron capture (EC) to the L-, M-, ...shells and EC to the K-shell of the projectile, have been extracted from the data. These are compared with the predictions of first Born theories, i.e., OBK of Nikolaev for EC. The data are also compared with the theory by Brandt and Lapicki that goes beyond the first Born approximation, i.e., the ECPSSR approach which accounts for the Energy loss, Coulomb deflection and Relativistic effects in the Perturbed Stationary State theory.     

Thermochemical study of vaporization of LiTiO by a mass spectrometric Knudsen effusion method

The vaporization of Li₄TiO₄ has been studied by a mass spectrometric Knudsen effusion method in the temperature range 1082–1582 K. Identified vapors are Li(g), LiO(g), Li₂O(g) and Li₃O(g). When the vaporization proceeds, the content of Li₂O in the Li₄TiO₄ sample decreases and the condensed phase of the sample changes to β-Li₄TiO₄ plus l-Li₂TiO₃ below 1323 K, to β-Li₄TiO₄ plus h-Li₂TiO₃ in the range 1323–1473 K and to h-Li₂TiO₃ plus liquid above 1473 K. On the basis of the partial pressure data, the enthalpies of formation for β-Li₄TiO₄ from elements and from constituent oxides have been determined to be ΔH_f,298^°(β-Li₄TiO₄,s) = −2247.8 ± 14.3 kJ mol⁻¹ and Δ_fox,298^°(β-Li₄TiO₄, s) = −107.3 ± 14.3 kJ mol⁻¹, respectively.     

Standard Gibbs energy of formation of Mo3Te4 by emf measurements

The emf of the galvanic cells Pt, Mo, MoO₂¦8 YSZ¦‘FeO’, Fe, Pt (I) and Pt, Fe,‘FeO’ ¦8 YSZ¦MoO₂, Mo₃Te₄, MoTe₂(), C, Pt (II) were measured over the temperature ranges 837 to 1151 K and 775 to 1196 K, respectively, using 8 mass% yttria-stabilized zirconia (8 YSZ) as the solid electrolyte. From the emf values, the partial molar Gibbs energy of solution of molybdenum in Mo₃Te₄/MoTe₂(), was found to be

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. Using the literature data for the Gibbs energy of formation of MoTe₂(). the expression ΔG°_f(Mo₃Te_4,s) ± 5.97 (kj/mol) = −253.58 + 0.09214T(K) was derived for the range 775 to 1196 K. A third-law analysis yielded a value of −209 ± 10 kJ/mol for ΔH°_f.298^o of Mo₃Te₄(s).     

Response of Si p-i-n diode and Au/n-Si surface barrier detector to heavy ions

Pulse height versus energy calibrations of a Si p-i-n diode and a Au-/n-Si surface barrier detector have been studied for heavy ions with atomic number (Z₁) from 3 to 79 in a range from 0.1 to 0.8 MeV per nucleon as a function of bias voltage and detector tilting angle. The detector response is simultaneously measured using a time of flight-energy elastic recoil detection analysis set-up with recoils produced over a wide energy range from a thick target of each element. Prior to impinging on the Si detector, the individual recoil is tagged by its energy determined from the time of flight and tabulated isotopic mass. For both detectors, the pulse height-energy calibration for recoils with a given Z₁ is described well by a linear relationship with small systematic deviations. The linear-fit parameters show similar, but not identical dependence on both Z₁ and bias voltage (collecting field strength) for the surface barrier detectors and the p-i-n diode. These results suggest that the efficiency of electron–hole pair collection is markedly dependent on the different electric field configurations for the two detector structures.     

Fundamental effects and non-linear Si detector response

Non-linearity in the energy response of a Si p-i-n charged particle detector has been studied for incident particles with Z₁ between 3 and 26, and energies between 0.1 and 0.7 MeV per nucleon. Although the data closely followed a straight line relations, fitting of the data to a third order polynomial revealed that the response exhibited a persistent curvature that acted to reduce the energy interval spanned by a channel as the energy increased. The curvature increased as Z₁ increased from 4 to 8 and then systematically decreased. The curvature is larger and has the opposite energy dependence to the stopping in a dead entrance window and the energy deposited in non-ionising processes within the active layer. The plasma recombination dependence on the average stopping along the plasma column may account for the reduction in curvature as Z₁ increases from 9 to 25 but cannot explain the net effect. The low-energy increase in energy channel span, which has also been reported by others, might be associated with electron excitation in resonant and direct classical quasi-elastic collisions for low-energy ions, or less likely, electronic non-linearity's associated with Z₁ and energy dependent time structure in the current pulse from the detector. Simple interpolation of the window-loss corrected polynomial coefficients is the best approach if the calibration for Z₁ cannot be established directly.     

Deviations of the Kβ/Kα intensity ratio of Ti upon impact with low velocity ions

Deviations of the branching ratio of the decay of K-vacancies in Ti have been observed during bombardment with low velocity ions of H, He and N. Beams of these ions have been used for various applications in which resonant nuclear reactions were used as the main analytical technique, whereas the X-ray signal could conveniently be used for monitoring the accumulated charge. During the evaluation of this monitoring signal, it was observed that the commonly made assumption that the K_β/K_α intensity ratio is a constant can easily be off by 30% or more. Also a few data of L-shell ionisation cross sections has been measured on Au to establish if the onset of deviations in the branching ratio parallels the onset of deviations from the ECPSSR theory for inner shell ionisation.     

Standard Gibbs energy of formation of Cs2CdI4

The vapor pressures of CdI₂ and Cs₂CdI₄ were measured below and above their melting points, employing the transpiration technique. The standard Gibbs energy of formation Δ_fG° of Cs₂CdI₄, derived from the partial pressure of CdI₂ in the vapor phase above and below the melting point of the compound could be represented by the equations Δ_fG°Cs₂CdI₄ (±6.7) kJ mol⁻¹=−1026.9+0.270 T (643 K≤T≤693 K) and Δ_fG°{Cs₂CdI₄} (±6.6) kJ mol⁻¹=−1001.8+0.233 T (713 K≤T≤749 K) respectively. The enthalpy of fusion of the title compound derived from these equations was found to be 25.1±10.0 kJ mol⁻¹ compared to 36.7 kJ mol⁻¹ reported in the literature from differential scanning calorimetry (DSC). The standard enthalpy of formation Δ_fH°_298.15 for Cs₂CdI₄ evaluated from these measurements was found to be −918.0±11.7 kJ mol⁻¹, in good agreement with the values −920.3±1.4 and −917.7±1.5 kJ mol⁻¹ reported in the literature from two independent calorimetric studies.     

Analysis of the desorption of clusters of intact amino acid valine molecules induced by energetic monoatomic and cluster ions

The experiments on the desorption of intact valine molecules and (nM + H)⁺ clusters are analyzed and a ln(Y/S_e) − 1/S_e scaling is found where Y, and S_e are the sputtering yield and the electronic stopping power, respectively. The scaling can be derived with the assumption of a thermal activation mechanism. In the plots the desorption is a uniform process without threshold value of S_e, having different activation energies U in various charge states. The desorption of (nM + H)⁺ clusters proceeds in n steps with varying Coulomb contributions. Irradiation with C₁₀ and C₆₀ ions leads to higher Y, however, the increment is reduced with the increase of S_e.     

Status of delayed-neutron precursor data: half-lives and neutron emission probabilities

We present in this paper a compilation of the present status of experimental delayed-neutron precursor data; i.e. β-decay half-lives (T_1/2) and neutron emission probabilities (P_n) in the fission-product region (27 ≤ Z ≤ 57). These data are compared to two model predictions of substantially different sophistication: (i) an update of the empirical Kratz-Herrmann formula (KHF), and (ii) a unified macroscopic-microscopic model within the quasi-particle random-phase approximation (QRPA). Both models are also used to calculate so far unknown T_1/2 and P_n values up to Z = 63. A number of possible refinements in the microscopic calculations are suggested to further improve the nuclear-physics foundation of these data for reactor and astrophysical applications.     

Determination des proprietes elastiques dynamiques du systeme UO2-SiO2 dans la gamme de temperatures 0–300°C

The complex elastic modulus E*(=E₁ + iE₂) of UO₂-SiO₂ with 64 mol% UO₂ in the range 0–300°C was measured by means of the resonant constrained bar technique. The modulus was found to be constant in the range investigated. Using the elastic moduli of UO₂ and SiO₂, the modulus of the sample were estimated theoretically and found to be close to the measured values; the theoretical model used can thus justifiably be adopted for other volume fractions.     

Phase transitions in U3O8−z: I, heat capacity measurements

The heat capacity of U₃O_8−z with various O/U ratios was measured in the range from 250 to 750 K, and λ-type heat capacity anomalies were found in each sample. The transition temperatures were 487 and 573 K for UO_2.663, 490 and 576 K for UO_2.656 and 508, 562 and 618 K for UO_2.640. The entropy changes of the transitions were 0.44 and 0.39 J K⁻¹mol⁻¹ for UO_2.663, 0.58 and 0.47 J K⁻¹mol⁻¹ for UO_2.656 and 0.62, 0.51 and 0.25 J K⁻¹mol⁻¹ for UO_2.640, increasing as O/U decreases. The enthalpy change due to the transition varied linearly with the transition temperature except for UO_2.640, showing the presence of the same mechanism of phase transition among the samples with various O/U ratios. The mechanism of the phase transition was discussed on the assumption that the transition is originated from the order-disorder rearrangement of U⁵⁺ and U⁶⁺ with a consequent displacement of atoms, similarly to the case of U₄O_9−y.     

Investigation of in-reactor creep and irradiation growth of zirconium-2.5 wt% niobium channel tubes

We summarize the diametral creep results obtained in the MR reactor of the Kurchatov Institute of Atomic Energy on zirconium-2.5 wt% niobium pressure tubes of the type used in RBMK-1000 power reactors. The experiments that lasted up to 30 000 h cover a temperature range of 270 to 350°C, neutron fluxes between 0.6 and 4.0 ×10¹³ n/cm² · s (E > 1 MeV) and stresses of up to 16 kgf/mm². Diametral strains of up to 4.8% have been measured. In-reactor creep results have been analyzed in terms of thermal and irradiation creep components assuming them to be additive. The thermal creep rate is given by a relationship of the type ε_th = A₁ exp [(A₂ + A _3σt) T] and the irradiation component by ε_rad = A_4σtø(T − A₅), where T = temperature, σ_t = hoop stress, ø = neutron flux and a₁ to A₅ are constants. Irradiation growth experiments carried out at 280° C on specimens machined from pressure tubes showed a non-linear dependence of growth strain on neutron fluence up to neutron fluences of 5 × 10²⁰ n/cm². The significance of these results to the elongation of RBMK reactor pressure tubes is discussed.