Asymptotic time behavior of correlation functions. III. Local equilibrium and mode-coupling theory

The decay to equilibrium is discussed from a general point of view based on the assumed rapid approach to local equilibrium for well-chosen initial states. The assumption is applied to the problem of time correlation functions and it is shown that the mode-coupling formula describes the asymptotics of the so-called projected wavenumber-dependent correlation functions. The local equilibrium assumption thus provides a general basis for thet ^–3/2 behavior of correlation functions derived in previous papers in this series, as well as for the infinite series of correction termst ^–(2–Pn (n 2), withPn=2^–n, and for the corresponding series of corrections of orderk ^3–Pn (n1) to Navier-Stokes hydrodynamics.     

Nonlinear refraction and nonlinear absorption of As2S3 aqueous solution

We report for the first time to our knowledge on the preparation of colloidal solution of chalcogenide semiconductor As₂S₃ by laser ablation and the measurements of its nonlinear-optical characteristics using Z-scan method at the wavelength of Nd:YAG laser radiation ( = 1064 nm, = 25 ns). The nonlinear refractive index was measured to be –7.5 × 10^–18 m² W^–1. Nonlinear absorption coefficient of chalcogenide solution was measured to be 1 cm GW^–1.     

Untersuchungen im Anfangsbereich der Verformungskurve von Eisen-Einkristallen

The stress-strain curves of iron single crystals at room temperature and at –78°C (strain rate =5·5.10^–5 sec^–1) are characterized by a dynamical yield point followed by a strong work-hardening. The plastic deformation starts by the movement ofa/2111 dislocations from several places of the specimen. Macroscopically, the dislocations move approximately along the planes with maximum resolved shear stress. Slip bands are formed by multiplication of the moving dislocations. They broaden and fill the whole specimen at a strain smaller than 0·1% or 0·2% for the deformation at room temperature and –78°C respectively. The corresponding dislocation densities are <4.10⁶ cm^–2 and 2.10⁷ cm^–2 respectively. At these strains a strong work-hardening begins. The mosaic structure causes an increase of the yield stress and of the difference between the upper and lower yield stress. Differences between iron and iron-3% Si alloy single crystals at the beginning of the plastic deformation have only a quantitative character and can be explained by the fact that the lattice friction stress in iron is approximately 15 times smaller than in iron-3% Si alloy.

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Vorgetragen auf der Diskussionstagung der Arbeitsgemeinschaft Metallphysik über Die Plastizität und Strahlenschädigung von Metallen und Legierungen, 10.–13. Oktober 1967; (diese Tagung wurde mit Unterstützung des Wirtschaftsministeriums Baden-Würtemberg durchgeführt).

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Herrn Dr. F. Kroupa möchten wir für die wertvollen Ratschläge zur Diskussion der experimentellen Ergebnisse und Frau Dipl. Phys. N. Zárubová für ihre Bemerkungen zum Manuskript danken. Frau I. Velartová sei für ihre Hilfe bei den Berg-Barrett-Aufnahmen gedankt.     

Trace norm convergence of exponential product formula

LetH andK be lower-bounded self-adjoint operators whose form sum is denoted byH K. We show the norm inequality (e^–rH/2 e^–rK e^–rH/2)^1/r forr > 0 and any symmetric norm . WhenH +K is essentially self-adjoint and e^–K is of trace class, we prove that (e^–rH/2e^–rK e^–rH/2)^1/r converges asr 0 to e^–(H+K) in the trace norm.     

Theoretical characterisation of a superlattice avalanche photodiode

A superlattice avalanche photodiode using III–V materials is expected to be used in long-distance fiberoptic communication systems in the 1.3 to 1.55 m wavelength range. Theoretical studies have been made on the effective ionization rates of electrons and holes of the device, I–V characteristic and the frequency response characteristic of the Al _x Ga_1–x As/GaAs superlattice p⁺-i-n⁺ structure. It is observed that the/ ratio of the device increases with the field and the bandwidth of the response curve increases with decrease in the dc multiplication gain.     

Pitfalls in the Use of Common Luminescent Probes for Oxidative and Nitrosative Stress

Lucigenin (LC²⁺, bis-N-methylacridinium) and 2,7-dichlorofluorescin (DCFH₂) are widely used as chemiluminescent or fluorescent probes for cellular oxidative stress, to reflect levels of superoxide (O₂ ^·–) and hydrogen peroxide, respectively. We report mechanistic studies that add to the growing evidence for the unsuitability of either probe except in very well-defined circumstances. The ability for lucigenin to generate superoxide via reduction of LC²⁺ to LC^·+ and redox cycling with oxygen depends on the reduction potential of the LC²⁺/LC^·+ couple. Redox equilibrium between LC^·+ and the redox indicator benzyl viologen is established in microseconds after generation of the radicals by pulse radiolysis and indicated E(LC²⁺/LC^·+) –0.28 V vs. NHE. Reaction of LC^·+ with O₂ to generate O₂ ^·– was also observed directly similarly, occurring in milliseconds, with a rate constant k 3 × 10⁶ M ^–1 s^–1. Quinones act as redox mediators in LC^·+/O₂ redox cycling. Oxidation of DCFH₂ to fluorescent DCF is not achieved by O₂ ^·– or H₂O₂, but NO₂ ^·) reacts rapidly: k 1 × 10⁷ M ^–1 s^–1. Oxidation by H₂O₂ requires a catalyst: cytochrome c (released into the cytosol in apoptosis) is very effective (even 10 nM). Fluorescence reflects catalyst level as much as O₂ ^·–) production.     

Avalanche multiplication of charge carriers in isotype GaAs-Ga1−xAlxAs n+-v-n heterojunctions

The current-voltage characteristics of n⁺-v-n structure based on GaAs and Ga_1–xAl_xAs with x=0.2–0.8 were investigated. Voltages of 7–30 V lead to avalanche multiplication of charge carriers in the high-resistance layer. Depending on the C-band discontinuity _o on the n⁺-GaAs--Ga_1–xAl_xAs junction, the prebreakdown current is limited either by the probability of electron tunneling (_o > 0.3 eV) or by space charge in the v layer (_o < 0.2 eV). An expression for the multiplication coefficient in the case of space-charge limitation of the prebreakdown current is obtained. It is shown that in the structures in question the effect of external factors on the multiplication of electrons and holes can be investigated separately.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 80–84, June, 1978.     

Current transport in Pd2Si/n-Si(100) Schottky barrier diodes at low temperatures

The forward current-voltage (I–V) characteristics of Pd₂Si/n-Si(100) Schottky barrier diodes are shown to follow the Thermionic Emission-Diffusion (TED) mechanism in the temperature range of 52-295 K. The evaluation of the experimentalI–V data reveals a decrease of the zero-bias barrier height ( _b0) and an increase of the ideality factor () with decreasing temperature. Further, the changes in _b0 and become quite significant below 148 K. It is demonstrated that the findings cannot be explained on the basis of tunneling, generation-recombination and/or image force lowering. Also, the concepts of flat band barrier height and T ₀-effect fail to account for the temperature dependence of the barrier parameters. The 1n(I _s /T ²) vs 1/T plot exhibits nonlinearity below 185 K with the linear portion corresponding to an activat ion energy of 0.64 eV, a value smaller than the zero-bias barrier height energy (0.735 eV) of Pd₂Si/n-Si Schottky diodes. Similarly, the value of the effective Richardson constant A** turns out to be 1.17 × 10⁴ A m^–2 K^–2 against the theoretical value of 1.12 × 10⁶ A m^–2 K^–2. Finally, it is demonstrated that the observed trends result due to barrier height inhomogeneities prevailing at the interface which, in turn, cause extra current such that theI–V characteristics continue to remain consistent with the TED process even at low temperatures. The inhomogeneities are believed to have a Gaussian distribution with a mean barrier height of 0.80 V and a standard deviation of 0.05 V at zero-bias. Also, the effect of bias is shown to homogenize barrier heights at a slightly higher mean value.     

Influence of the overall pressure on electrical conductivity of the amorphous semiconductor Ge15Te81S2As2

The experimental results obtained with the chalcogenide glass Ge₁₅Te₈₁S₂As₂ with imposed overall pressure up to 700 MPa are presented. The material exhibits the switching effect and the memory effect. It is shown that the overall pressure changes remarkably d.c. electrical conductivity of the amorphous semiconductor. It is assumed that the changes in conductivity are caused by changes in activation energy. The changes in activation energy within the range of considered pressures are, as follows from our measurements, E/p–10·95×10^–5 eV/MPa +p × 10·41 W 10^–7 eV/MPa². The assumption of the activation energy dependence on pressurep are confirmed also by measurements of dependence In vs. 1/T at various pressures.     

Charge Exchange of the Centers in Electron–Irradiated Zinc Selenide

The optical absorption induced by the photosensitive centers formed upon electron irradiation (E = 5 MeV, = 1.7·10¹⁸ cm^–2) of polycrystalline ZnSe has been studied. A comparison of the optical properties of the irradiated crystals with the known data for ZnS has allowed the assumption that the 496–, 563–, and 652–nm bands in ZnSe are associated with the anion vacancies being in different charge states. The ratio between the concentrations of the optical absorption centers in the crystals photoexcited at 80 K is determined by the electron traps participating in the processes of charge exchange of the vacancies.     

Space- and time-resolved investigation of gain lines in Na-like copper

We report space- and time-resolved measurements of the gain coefficient for four gain lines in sodium-like copper. The lines investigated include the twon = 1 transitions 5g–4f and 5f–4d at 11.1 nm and 10.3nm and the twon = 2 transitions 6g–4f and 6f–4d at 7.2 nm, and 6.9 nm. The investigations were carried out for four irradiation intensities from 4 × 10¹² W/cm² to 3 × 10¹³ W/cm² using the Asterix IV high-power iodine laser at Garching (wavelength 1.315 µm, pulse duration 450 ps).The main results may be summarized as follows: On varying the laser intensity it was found that the highest values of the gain could be seen at an irradiation of 8 × 10¹² W/cm². For then = 1 lines the spatial maximum of the gain occurred at a distance of 300 µm from the target, and for then = 2 lines at 200 µm. The temporal gain maximum occurred at a time of 1.8 ns after the pulse maximum. The gain values range up to 2.6 cm^–1.Dedicated to the memory of the late Prof. Shi-shen Chen, who contributed to the early phase of this work     

Creep of cadmium single crystals

The creep of cadmium single crystals has been investigated in the temperature range of 78 to 297 K. It has been shown that the transient creep of Cd single crystals is described by a time dependence of the creep strain rateå t ^–m wherem is a function of the resolved shear stress and temperature. The activation areaA* depends on the resolved shear stress,, A ^{* –r} wherer=1 for room temperature andr 1·4 for 204 and 78 K. The activation enthalpy does not practically depend on the resolved shear stress in the whole region of the resolved shear stress measured and with increasing temperature it increases roughly withT ². For temperatures above 200 K the nonconservative jog motion is proposed to be the dominant thermally activated process.The authors are very grateful to Dr. P.Kratochvíl for valuable discussions.     

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.     

Ensemble average of an arbitrary number of pairs of different eigenvalues using Grassmann integration

An identity satisfied by the eigenvalues of a real-symmetric matrix and an integral representation of a determinant using Grassmann variables are used to show that the ensemble average ofS different pairs of eigenvalues of a GOE is given by (–1) ^S 2^{–S –1/2}(S+1/2).     

Supertransferred hyperfine interaction in magnetic insulators (II)

The important mechanisms of supertransferred hyperfine (STHF) interactions in N–O–M chains are briefly discussed: (i) spin polarization ofns states in the N-ion due to the s-d exchange interaction,H _STHF ^sd ; (ii) contributions of spin-polarized states of the intervening O-ion,H _STHF ^II ; (iii) transfer of d-electrons of the M-ion to emptyns states in the N-ion,H _STHF ^III . The dependence ofH _STHF upon the N–O–M bond configuration, electronic structure, and orbital state of the M-ion is presented in a convenient form. The STHF interactions in the chains Sn⁴⁺–O^2––Fe³⁺, Cr³⁺ in compounds with slightly distorted Perovskite structure are considered. The STHF field in the chain Sn⁴⁺–O^2––Cr³⁺ is shown to change the sign within the range of angles near 170°. This conclusion is in line with published data on the isoelectronic chain Sn⁴⁺–O²–Mn⁴⁺ in the compounds Ca_1–x Sr _x MnO₃. The results obtained for the N–O–Fe³⁺ chain are rationalized by the predicted angular dependence ofH _STHF=+ cos + cos². Features of the STHF interactions in N–O–M chains with an M-ion in an orbital degenerate state are examplified by a preliminary analysis of N–O^2––V³⁺ chains in orthovanadites.     

Infrared absorption of silane,ammonia, acetylene and diborane in the range of the CO2 laser emission lines: Measurements and modelling

Absorption spectra of the gases SiH₄, NH₃, C₂H₂ and of SiH₄/Ar and SiH₄/B₂H₆ mixtures have been measured in the spectral range of the CO₂ laser from 9.2 to 10.8 µm. In agreement with literature, silane shows the highest absorption (absorption coefficient = 3.3 × 10^–2 Pa^–1 m^–1). The deviation of the measured absorption behaviour of silane from literature, as far as the pressure dependence is concerned, can be explained by the enhanced spectral energy density in our experiment. This is confirmed by a rate-equation model involving the basic mechanisms of V-V and V-T energy transfer between vibrationally excited silane molecules. In contrast to silane, the absorption coefficient of NH₃ at the 10P(20) laser line is 4.5 × 10^–4 Pa^–1 m^–1 atp = 20 kPa and has its maximum of 4.5 × 10^–3 Pa^–1 m^–1 at the 10R(6) laser line. For C₂H₂ and B₂H₆, is even less ( 2.1 Ò 10^–5 Pa^–1 m^–1 for C₂H₂).     

The hall effect in PdSi-based amorphous alloys containing Co.

The Hall effect in amorphous Pd₈₀Si₂₀ and Pd_80–x Si₂₀Co _x , wherex=2, 4, 6 (at.% are implied throughout) alloys was investigated. Measurements were carried out at r.t. in fields up to 17·5 kG. Also the electrical conductivity was measured. The Hall effect was found negative in all alloys of the above composition. Observedx-dependence of the Hall constantR _H tends to change the sign of the effect and is interpreted on the assumption that an extraordinary Hall effect manifests itself besides the ordinary one in Co-containing alloys. The value ofR _H for the basal alloy should be looked upon as an evidence of electron transfer from glass-former (Si) to transition metal (Pd) empty d-states. The values ofR _H obtained for the alloys withx=0, 2, 4, 6 are respectively, –7·8; –8·7; –8·3; –5·2 (×10^–5 cm³/A. sec throughout).     

Excess capacitance of ZnO-Au varactors

Doped ZnO single crystals were deposited with gold and indium in 1×10^–8 Torr vacuum. The lithium-doped ZnO single crystals and the gold interface revealed not only a Schottky diode but also varactor characteristics. TheI-V andC-V characteristics of ZnO:Li-Au devices were determined in the 0–140 mV and 0–1.5 V ranges.The frequency dependence of ZnO:Li-Au varactors was investigated in the 6–550 kHz range and the value of the most efficient varactor frequency was found to be 50 kHz for the lithium-doped samples prepared.To bring further insight into the matter the concept of excess capacitance was introduced and 1/C ²=f(–V) curves were rearranged between 0–150 mV where Schottky characteristics are non-linear. The excess capacitance values of lithium-doped varactors were determined at four different frequencies and ranged from 26 pF at 50 kHz to 70 pF at 6kHz.Finally, the bulk donor concentrations of the single crystals were calculated from the modifiedC-V curves to beN _D= 3×10²⁰ m^–3. On the other hand, the bulk donor concentration determined from the non-modifiedC-V curves wasN _D=1.02×10²² m^–3.     

Sensitivity of approximate formulas for determining optical constants of thin films

The sensitivity of approximate formulas for determining the optical constants of thin films using measurement of reflectancesR and transmittancesT at normal incidence have been investigated theoretically. The ranges of refractive indexn, absorption indexk,2nk (=₂) andn ²–k ²(=₁) within relative errors of 5%, 10%, and 20% may be obtained. Selected signs of (₁)⁺ or (₁)^– have been determined. Validity of the condition n₀ A=n _s A has been also evaluated (A=1–R –T andA=1–R–T).     

119Sn-mössbauer,IR, and DSC study of tin oxyfluoride glasses

The¹¹⁹Sn-Mössbauer spectra ofxSnO·(70–x)SnF₂·30P₂O₅ glasses (0 x70) measured at 78 K comprised a doublet due to Sn²⁺ (=3.30–3.36 mm s^–1, = 1.70–1.72 mm s^–1) and a weak singlet due to Sn⁴⁺ located at –0.23 mm s^–1 with respect to BaSnO₃. The and of Sn²⁺ were comparable to those of Sn₂P₂O₇. Small Debye temperatures (146 and 155 K) were obtained from the low-temperature measurements. These results indicate that Sn²⁺ and Sn₄₊ occupied interstitial sites, being loosely and ionically bonded to distorted PO_4–x F _x tetrahedra.