Softening during and after the hot deformation of the AISI 321 steel with respect to practical applications

The softening processes during and after the hot deformation (850–1180 C) in AISI 321 stainless steel were studied with respect to true strains _D and true strain rates . The analysis of deformation curves indicates the occurrence of dynamic recrystallization for values of Zener-Hollomon parameterZ10¹⁵ s^–1. The retardation of static recrystallization by fine Ti(N, C) precipitates is documented by microstructure studies and by variations of annealing conditions.     

Microstructure changes in high-speed hot rolling of steel rods

Transmission electron microscopy (TEM), quantitative texture analysis by means of neutron diffraction (QTA) and X-ray diffraction profile analysis (XDPA) were used to study the microstructure changes occurring in high-speed hot rolling ( 1500 s^–1;T=1073 K) of high-alloy stainless steel X8CrTi17 (ferrite) and X8CrNiTi18.10 (austenite). The investigations indicate that at higher deformation rates recrystallization due to adiabatic overheating becomes an important process of microstructure formation.     

Superplasticity in A Zn-1·1 wt. % Al alloy

In the paper the results of the deformation behaviour study in a fine-grained Zn-1·1 wt. % Al alloy are presented. The influence of strain rate ranging from 4·2×10^–5 to 4·2×10^–2 s^–1 on the true stress — true strain curves, ductility and strain rate sensitivity was investigated at temperatures 295 K and 375 K. At both temperatures the superplastic behaviour was observed. The increase in temperature improved the superplastic properties and shifted the region of the superplastic behaviour to higher strain rates. The maximum values of ductilityA=700% and strain rate sensitivity parameter m=0·48 were established at 375 K at strain rates . The true stress — true strain curves were found to be influenced by a grain growth taking place during the deformation. The grain growth was also found to be responsible for significant differences in the parameterm values obtained from the log plots and from the strain rat-changes.     

A New Integrable Hierarchy,Parametric Solutions and Traveling Wave Solutions

In this paper we give a new integrable hierarchy. In the hierarchy there are the following representatives:

RareB-decays and heavy to light semileptonic transitions in the Isgur and Wise limit

From the experimental braching ratios for and one finds, in the heavy quark limit of HQET, |V _bu|=(8.1±1.7)×10^–3, larger but consistent with the actual quoted range (2–7)×10^–3. In the same framework one predicts forR(BK ^*)=(2±2)10^–2.     

Quantized IR properties reconfirmed in the CO and SiO surface oscillators present in the surface layer of A bamboo stem

From analysis of diffusion diagrams of CO stretching band (25002180 cm^–1), bending band (800200 cm^–1) and SiO stretching band (1100700 cm^–1) measured in a skin surface layer of a bamboo stem (silicate cellulose), azimuthal directions where oscillators oriented were shown as ('=-90) _N=a·N-b, with a=28.3, 2×28, 22.7, b=25, 47.5, 10. And N=1,2.....14, N=1, .....6. N=1,2.....16. The optical activity (reflection integral) was shown for the CO stret. band as M_i(N)=a·N+b, with a=21.8, b=42 and N =1,2.....9. And for the bending band as M_i(N)=a·N² +b·N–c, with a=1.87×10¹, b=3.73×10³, c=7.06×10² with N=1,2.....9. Six stepnized fine series in CO weak reflection bands were confirmed as, and with N=1,2.....22. Mean values of the vibrational quantized states of the A, B and C-series in the SiO stretching weak band with R1.0% were shown as, (meV) with .     

Transient creep during transformation in Cd-Zn alloys

Transient creep of Cd-2 wt. % Zn and Cd-17·4 wt. % Zn alloys has been studied under different constant stresses ranging from 6·4 MPa to 12·7 MPa near the transformation temperature. The results of both compositions showed two transient deformation regions, the low temperature region (below 483 K) and the high temperature region (above 483 K). From the transient creep described by the equation _tr=Bt ⁿ, where _tr andt are the transient creep strain and time. The parametersB andn were calculated. The parameterB was found to change with the applied stress from 0·3×10^–4 to 3×10^–4 and from 0·6×10^–4 to 18×10^–4 for Cd-2 wt. % Zn and Cd-17·4 wt. % Zn, respectively. The exponentn was found to change from 0·8 to 0·95 for both alloys. The parameterB was related to the steady state creep rate through the equation , the exponent was found to be 0·5 for Cd-2 wt. % Zn and 0·6 for the eutectic composition. The activation energies of transient creep in the vicinity of the transformation regions (above 483 K) were found to be 50·2 kJ/mole for Cd-2 wt. % Zn and 104·7 kJ/mole for the eutectic composition characterizing the mechanisms of grain boundary diffusion and volume diffusion in Cd, respectively.     

Solubility of Na2Co3 in NaCl:CaCl2 crystals

Measurements of electrical conductivity of NaCl 10^–5 molar fr. CaCl2 (1–80)×10^–5 molar fr. Na₂CO₃ crystals have been used to determine the temperature dependence of the solubility of CO₃-ions over the temperature range from 75 to 530 °C. The total solubility of CO₃-ions and that of [CO ₃ ^2– -vacancy] complexes may be expressed by simple relationships andc _ka=3·19× 10^–2 exp (–0·25 eV/kT), resp. The heat of solution of complexes is equal to 0·25 eV and that of free CO ₃ ^2– ions is higher than 1·2 eV. Under conditions of the thermal equilibrium between the solid solution and precipitate, the ratio of Na₂CO₃ and CaCO₃ components in the precipitate has been calculated at various temperatures and CO₃ concentrations.     

Generalization of the $$\mathcal{U} $$ q (gl(N)) Algebra and Staggered Models

We develop a technique for the construction of integrable models with a ₂ grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang–Baxter equations are written down and their solution for the gl(N) case is found. We analyze in details the N = 2 case and find the corresponding quantum group behind this solution. It can be regarded as the quantum group , with a matrix deformation parameter q such that (q )² = q ². The symmetry behind these models can also be interpreted as the tensor product of the (–1)-Weyl algebra by an extension of _q (gl(N)) with a Cartan generator related to deformation parameter –1.     

Instability of the molecular structure of monobenzoporphin to the alternation of the macrocycle bond lengths and its manifestation in the electronic spectra

Quantum-chemical calculations of the geometric structure of the molecules of monobenzoporphin (H₂ MBP) and monobenzoporphin with methyl and ethyl substituents in the five-member rings (H₂MBPm) have been carried out by the restricted and unrestricted Hartree-Fock methods with the AM1 Hamiltonian (AM1 RHF and AM1 UHF methods). The calculation of the above-indicated molecules by the AM1 RHF method without restrictions on their symmetry has given, for them, a planar structure with an alternation of the lengths of the bonds along the 18-member azacyclopolyene and the symmetry C _1h for their aromatic part. The calculation of the transitions to the excited electron Q states in such a structure by the CNDO/S method has shown that these states are characterized by large hypsochromic shifts (~3000–4000 cm^–1 ) relative to the Q levels of porphin (H₂P), which is in contradiction with the experimental data, according to which these shifts are bathochromic and comprise = –330 cm ^–1 and = –750 cm^–1. Optimization of the geometry of the H₂ MBP and H₂MBPm molecules by the AM1 UHF method gives, for them, a structure with equal lengths of the bonds along the 18-member azacyclopolyene with a symmetry differing insignificantly from the D _2h symmetry; elements of the structure with a lower symmetry and an alternation of the lengths of the bonds are retained in the condensed pyrrolenine and benzene rings. The calculation of the shifts of the Q levels in the H₂MBPm molecule of this geometry relative to the analogous levels in H₂P has shown that they are bathochromic and equal to = –520 cm^–1, and the RHF calculation with optimization of the geometry of the molecule and restrictions on the effective symmetry D _2h of the 18-member azacyclopolyene has given = –350 cm^–1 and = –430 cm^–1. The restrictions imposed on the C ₂ symmetry of the H₂MBP molecules by the RHF method are inadequate to equalize the lengths of the bonds along the 18-member azacyclopolyene. The calculations of the energy of the B levels of the monobenzoporphyrins considered also lend credence to their geometric structure with equal lengths of the bonds along the 18-member azacyclopolyene.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 712–721, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Some Remarks on the Smoluchowski–Kramers Approximation

According to the Smoluchowski–Kramers approximation, solution q _t of the equation , where is the White noise, converges to the solution of equation as µ 0. Many asymptotic problems for the last equation were studied in recent years. We consider relations between asymptotics for the first order equation and the original second order equation. Homogenization, large deviations and stochastic resonance, approximation of Brownian motion W _t by a smooth stochastic process, stationary distributions are considered.     

Zero magnetic field splitting and anomalies of intensities in the Zeeman spectra of La(Pr)Cl3-crystals

Optical absorption and Zeeman effect measurements on La(Pr)Cl₃ show a zero magnetic field splitting of the degenerate Pr³⁺ levels and . The site symmetry of the Pr³⁺ ions is lowered fromC _3h toC _s . The resultant splittings of the doublet levels are:I ³ H ₄:2|T _ak |=(0.12±0.05)cm^–1;a ³ P ₁:2|T _al |=(0.10±0.05)cm^–1.The intensities of the optical transitions induced by the deformation decrease with increasing magnetic field. All observations are described by a first order perturbation calculation using a low symmetric part of the crystal field and Zeeman energy as simultaneous perturbations on a Pr³⁺ ion in a crystal field with site symmetryC _3h .Project of the Sonderforschungsbereich Festkörperspektroskopie SFB65, Darmstadt—Frankfurt, supported by the Deutsche Forschungsgemeinschaft.     

Crystal field of Dy implanted in Cu single crystals obtained by Mössbauer spectroscopy

The field dependence of the hyperfine interaction of¹⁶¹Dy impurities in Cu has been studied in external magnetic fields up to 3.21 T by means of Mössbauer spectroscopy. ¹⁶¹Dy was introduced into a single crystal of Cu by means of low temperature ion implantation. From the measurements we determine the parameters of the cubic crystalline electric field acting on the Dy nuclei:A ₄<r⁴>=–28±58 K and . The ground state is a doublet, separated well from a excited quartet by .     

Dynamic recrystallization of austenite during hot plastic deformation

The kinetics of dynamic recrystallization is dependent on the thermomechanical conditions in which plastic deformation is taking place. To determine the timet _p needed for the onset of dynamic recrystallization, experimental work was performed on low-carbon austenite to check the validity of the equationW= 2·1 × 10^–1 Z ^–0.94, whereW= t_pexp(–Q/RT),Z represents the Zener-Hollomon parameter, and Q=276 kJ mol^–1.     

Accurate determination of wavenumbers for iodine molecular lines in the red spectral region

The hyperfine structure of various absorption lines of molecular iodine with wavenumbers between 12980 and 13890 cm^–1 has been resolved using Doppler-free polarization spectroscopy. The wavenumbers of theo-component of 17 rovibrational lines of I₂ due to the transitionB ³ _ou ⁺ –X¹ _g ⁺ with even rotational quantum numbers have been determined with an accuracy of 0.001 cm^–1. A comparison of the centers of gravity of these 17 lines with the values of the iodine atlas of Gerstenkorn et al. yields a difference of thus corroborating the data of the iodine atlas in the red region within limits of error.     

Conte Truncated Expansion and Applications

In the special Conte truncated expansion approach one obtains different solutions of the Prigogine–Lefever equation by use of various solutions of a type of Riccati equation, including the periodic soliton solutions and singular soliton solutions. In order to acquire conveniently the soliton solutions of the Boussinesq equation, a proper transformation is applied. Using the special Conte truncated expansion approach yields the known bell-shape solutions and some new soliton solutions like cot² × sec², tan² × c sec², tanh² × sech², etc. We also study the soliton solutions of the modified Burgers equation (MBE). Using leading term analysis, we find the exponent is a fraction, i.e., – . Therefore, the special Conte truncated expansion approach cannot be used directly. A transformation is first made to them another form of the MBE. Various soliton solutions of MBE are then presented, including the periodic solutions and singular soliton solutions.     

Levinson's Theorem for the Nonlocal Interaction in One Dimension

The Levinson theorem for the one-dimensional Schrödinger equation with both local and the nonlocal symmetric potentials is established by the Sturm–Liouville theorem. The critical case where the Schro;audinger equation has a finite zero-energy solution is also analyzed. It is shown that the number n ₊ (n _–) of bound states with even (odd) parity is related to the phase shift ₊(0)[_–(0)] of the scattering states with the same parity at zero momentum as

Existence of Resonances for Metric Scattering in Even Dimensions

Suppose _g is the (negative) Laplace–Beltrami operator of a Riemannian metric g on ⁿ which is Euclidean outside some compact set. It is known that the resolvent R()=(– _g –²)^–1, as the operator from L ² _comp( ⁿ ) to H ² _loc( ⁿ ), has a meromorphic extension from the lower half plane to the complex plane or the logarithmic plane when n is odd or even, respectively. Resonances are defined to be the poles of this meromorphic extension. We prove that when n is 4 or 6, there always exist infinitely many resonances provided that g is not flat. When n is greater than 6 and even, we prove the same result under the condition that the metric is conformally Euclidean or is close to the Euclidean metric.