Properties of single vacancies and of divacancies in copper

The electrical resistivity change at high temperatures due to vacancies was determined as a function of temperature. From the data E^F_1V=1.00 eV, E^B_2V=0.45 eV and about C^tot_V=4 × 10^-4 at the melting point results.     

M-Zentrenbildung in röntgenbestrahlten KCl-Kristallen

The production of F- and M-centres in KCl by X-irradiation has been studied at temperatures between ?20 °C and 50 °C. The optical absorption measurements could be conducted without interrupting the X-irradiation. The results can be summarized as follows: 1. In Harshaw KCl crystals the number of F-centres created by the so-called fast coloration process was proportional to the height of the absorption band at 204 mμ prior to the irradiation. 2. The F-centres formed by the fast process did not contribute to the formation of M-centres. 3. In crystals with a strong absorption band at 204 mμ unstable M-centres were observed, which decayed rapidly after the cessation of the X-irradiation. Their concentration was found to be independent of the F-centre concentration. 4. At temperatures below 0 °C the relation between the concentration of the stable M-centres and the F-centre concentration could not any longer be represented by [M]=k ₁₂·[F₁]·[F₂]+k ₂₂·[F₂]², F₁ and F₂ referring to the F-centres created respectively by the fast and the slow coloration process. Except at very low F₂-centre concentrations however the relationship [M]=k ₀+k ₂·[F₂]² represented the experimental data at all temperatures between ?20 °C and 50 °C. At constant temperaturek ₂ varied withL, the X-ray energy absorbed per unit time and unit volume, according to 1/k ₂=a+bL+cL ². The temperature dependence ofa ^?1 b ^?1 andc ^?1 could be approximated by Boltzmann factors. The corresponding activation energies wereE _a=0.12 eV,E _b=0.53 eV,E _c=0.97 eV.     

The loss of single vacancies in metals during quenching

The Lomer equation, describing the rate of change of single vacancy concentration in a metal specimen during exponential quenching, was numerically solved for different quenching temperatures and different quenching rates. A relation has been found between the constantb, which characterizes the initial quenching rate, and the quenching temperature leading to the same percentual loss of vacancies. This relation enables us to determine the conditions of quenching, yielding the predetermined percentage of retained vacancies.The possibility is discussed of applying the above results in measurements of the formation energyEf^F, to estimate the migration energyE ^M and to determine the change of the mean number of jumps during quenching.The author would like to express his gratitude to Dr. K. Míek, head of the Metal Physics Department, for his interest and useful comments.     

Temperature dependence of spin-hamiltonian parameters for chromium doped rutile

The temperature dependence of the spin-Hamiltonian parameters for substitutional Cr³⁺-ions in single crystal rutile (TiO₂) has been studied. The measurements were performed at about 9·2 GHz and 35 GHz on a fine powder of single crystalline Cr-TiO₂ for three temperatures, 95, 200, and 295°K. It was found that the spin-Hamiltonian parameter D diminishes with decreasing temperature in the temperature interval studied. The behaviour of g and E is more complex. A tentative extrapolation of the data towards 0°K has been made.     

Helium defectoscopy of cerium gadolinium ceramics Ce0.8Gd0.2O1.9 with a submicrocrystalline structure in the impurity disorder region

The concentration of impurity anion vacancies formed upon the dissociation of gadolinium-vacancy complexes has been determined using helium defectoscopy of the cerium gadolinium ceramics Ce_0.8Gd_0.2O_1.9 with a submicrocrystalline structure in the temperature range T = 740–1123 K and at saturation pressures ranging from 0.05 to 15 MPa. It has been found that the energy of dissociation of gadoliniumvacancy complexes is E _eff ^D = 0.26 ± 0.06 eV, and the energy of dissolution of helium in anion vacancies in the impurity disorder region is E ^P = ?0.31 ± 0.09 eV. The proposed mechanism of dissolution has been confirmed by the investigation of the electrical conductivity of the cerium gadolinium ceramics, as well as by the high-speed molecular dynamics simulation of the dissociation of gadolinium-vacancy complexes. It has been assumed that a decrease in the effective dissolution energy in comparison with the results of the previously performed low-temperature investigations is caused by the mutual repulsion of vacancies formed upon the dissociation of gadolinium-vacancy complexes in highly concentrated solutions of gadolinium in CeO₂ with increasing temperature.     

Study of cation tracer diffusion in NaF

Cation tracer diffusion coefficients were measured in pure NaF crystals in the intrinsic ionic conductivity range (876–970 °C). The results can be rationalized satisfactorily in terms of contributions to the observed Na tracer diffusivities arising from both free vacancies and neutral vacancy pairs, the latter contribution amounting to about 53 per cent of the total Na diffusion at the highest measuring temperature. The best-fit defect parameters derived in an earlier conductivity study [21] from this laboratory on similar NaF crystals give for the free vacancy contribution D_v^*(Na) = 4·25 exp (?2·21 eV/kT) cm²s^?1. A combination of these D_v^*(Na) values with the present diffusion data yields for the vacancy-pair contribution D_p^*(Na) = 1·15 × 10⁸exp (?4·04 eV/kT) cm²s^?1. Comparison of the present findings with published values of the anion tracer diffusion coefficient in NaF showed that D_p^* (F) is 2·3 to 4·4 times larger than D_p^*(Na) over the temperature range of our observations, the difference between the two contributions increasing with decreasing temperature. When approximate account is taken of the temperature-dependence of the two pair correlation factors, this last result indicates that the anion jumps into the vacancy pair occur with a higher frequency, and increasingly so at lower temperatures, than do those involving the cations.     

Dielectric relaxation and ac conductivity of sodium tungsten phosphate glasses

Studies of dielectric relaxation and ac conductivity have been made on three samples of sodium tungsten phosphate glasses over a temperature range of 77–420 K. Complex relative permitivity data have been analyzed using dielectric modulus approach. Conductivity relaxation frequency increases with the increase of temperature. Activation energy for conductivity relaxation has also been evaluated. Measured ac conductivity (σ_m(ω)) has been found to be higher than σ_dc at low temperatures whereas at high temperature σ_m(ω) becomes equal to σ_dc at all frequencies. The ac conductivity obeys the relation σ_ac(ω)=Aω ^S over a considerable range of low temperatures. Values of exponent S are nearly equal to unity at about 78 K and the values decrease non-linearly with the increase of temperature. Values of the number density of states at Fermi level (N(E _F)) have been evaluated at 80 K assuming values of electron wave function decay constant α to be 0.5 (Å)^?1. Values of N(E _F) have the order 10²⁰ which are well within the range suggested for localized states. Present values of N(E _F) are smaller than those for tungsten phosphate glasses.     

Simulation of the thermal fragmentation of fullerene C60

Defect formation and annealing processes in fullerene C₆₀ at T = (4000–6000) K are studied using molecular dynamics with a tight-binding potential. The cluster lifetime until fragmentation, which proceeds, as a rule, through the loss of a C₂ dimer, has been found as a function of temperature. The activation energy and the frequency factor in the Arrhenius equation for the fragmentation rate have been found to be E _a = (9.2 ± 0.4) eV and A = (8 ± 1) × 10¹⁹s^?1. It is shown that fragmentation can occur already after the C₆₀ cluster loses its spherical shape. This fact must be taken into account in theoretical calculations of E _a.     

Contraction par autoirradiation a 4,2°k de la phase δ cubique a faces centrees du plutonium

Measurements have been made of the initial rates of contraction due to self-irradiation damage at 4·2°K in PuSc f.c.c. alloys containing 5, 12 and 18 at % scandium. The measured values were respectively ?7·3 × 10^?6/hr, ?3·8 × 10^?6/hr and ?0·6 × 10^?6/hr.From these values, we deduced the formation volume of Frenkel pairs in each alloy. Then, we tried to explain the high negative values, with the help of the elastic theory, assuming that the radius of the interstitial atoms has been decreased by a 5f → 6d electronic promotion. Afterwards the basic hypothesis of the calculation of the formation volume of Frenkel pairs have been investigated. On the existing grounds of the elastic theory, our results cannot be understood quantitatively. However the negative formation volumes of interstitials and vacancies, therefore the weak volume of the former and the large relaxation of the latter, are not doubtful.     

On the study of fluid structure of tetrahydrofuran-n-butyric acid mixture by dielectric studies

The Kirkwood correlation factors g^eff and g_f, excess permittivity ε^E and excess free energy F^E of mixing for the binary mixture of n-butyric acid with tetrahydrofuran (THF) were calculated from the experimental dielectric data obtained at temperatures 303, 308, 313 and 318 K over the entire composition range. The value of g^eff decreases with increase in acid concentration and g_f is found to be greater than unity. At higher temperature, two maxima and two minima have been obtained for ε^E and F^E, respectively. These parameters are analyzed to obtain information about the complex formation through H-bond and dipolar orientation.     

Study of complex impedance spectroscopic properties of the KFeP2O7 compound

The KFeP₂O₇ compound was prepared by the conventional solid-state reaction. The sample was characterized by X-ray powder diffraction. The AC electrical conductivity and the dielectric relaxation properties of this compound have been investigated by means of impedance spectroscopy measurements over a wide range of frequencies and temperatures, 200 Hz–5 MHz and 553–699 K, respectively. Both impedance and modulus analysis exhibit the grain and grain boundary contribution to the electrical response of the sample. The temperature dependence of the bulk and grain boundary conductivity were found to obey the Arrhenius law with activation energies Eg?=?0.94 (3)?eV and Egb?=?0.89 (1)?eV. The grain-and-grain boundary conductivities at 573 K are 1.07?×?10^?4 and 1.16?×?10^?5 (Ω^?1 cm^?1). The scaling behavior of the imaginary part of the complex impedance suggests that the relaxation describes the same mechanism at various temperatures. The near value of the activation energies obtained from the equivalent circuit, conductivity data, and analysis of M″ confirms that the transport is through ion hopping mechanism.     

On the mechanism of diffusion in sodium beta alumina

A microscopic interstitialcy-type diffusion mechanism for sodium beta-alumina involving three crystallographically different types of cation sites but only two equilibrium configurations of interstitialcy pairs is proposed. The resulting cation-site occupation probabilities are shown to agree with the experimental neutron-diffraction data of Roth et al. For various sizes of the associated regions around the charge-compensating oxygen interstitials (in which Na⁺ ions are not freely mobile), the ratio of the radiotracer diffusivity with respect to the charge diffusivity (the so-called Haven ratio, H_R)is determined. In agreement with the measurements of Kim et al.,H_R is found to increase with increasing temperature as a result of the decrease in the average size of the associated regions. It is concluded that, while at lower temperatures all excess Na⁺ ions are found in the associated regions around the oxygen interstitials, with increasing temperature more and more of them are freely mobile in the unassociated regions of the conduction plane. The formation enthalpy associated with the thermally activated creation of mobile “interstitials” is determined to be about 0.05 eV. The slope of the slightly curved Arrhenius plot associated with the proposed mechanism therefore consists of the sum of the energy of formation of freely mobile interstitials and the energies of migration of two types of interstitialcy pairs. The Raman and IR-conductivity results are found to be compatible with this emerging picture for the microscopic diffusion process in sodium β-alumina. Spectroscopic diffusion techniques (NMR, internal friction, dielectric loss) show more than one apparent activation energy E^A while, in the same temperature region, the d.c. ionic conductivity yields a unique value of E^A; reasons for this discrepancy are discussed.     

Monovacancy formation energy in copper,silver, and gold by positron annihilation

Monovacancy formation energies in copper, silver, and gold have been deduced from the temperature variation of the peak counting rate in the angular correlation curve of positron annihilation radiation from these metals. The counting rate was temperature dependent over the entire temperature range, including temperatures so low that no trapping of positrons at vacancies is effective. At these temperatures the increase in counting rate results from thermal expansion of the lattice. By separating this thermal expansion effect from the vacancy trapping effect at higher temperatures, we obtained values for the monovacancy formation energyE _1v for copper, silver, and gold to 1.29±0.02 eV, 1.16±0.02 eV, and 0.97±0.01 eV, respectively.     

Intermediate electronic relaxation betweenS=3/2 andS=1/2 states in Fe(J-mph)NO with a jäger-type ligand J-mph

The incomplete spin transition between the low-spin (LS) (S=1/2) and the intermediate-spin (IS) (S=3/2) states in the iron (III) complex Fe(J-mph)NO (mph=4-methyl-o-phenylene), centered atT _c≈212 K, has been studied with⁵⁷Fe Mössbauer spectroscopy and magnetic susceptibility measurements between 80 K and 320 K. The lineshape of the Mössbauer spectra is well reproduced by a two state stochastic relaxation model resulting in values of about 2·10⁶ s^?1 to 7·10⁶ s^?1 for the IS→LS transition rate constantk _IL. The kinetics of this spin transition can be described by an Arrhenius equation yielding activation energiesE _IL=1.1 (2) kJ/mol andE _LI=6.1 (2) kJ/mol for the IS→LS and LS→IS conversion, respectively.     

Magneto-acoustic attenuation in AuSb2

Quantum oscillations in the ultrasonic attenuation in AuSb₂ were studied as a function of temperature, magnetic field and crystal orientation. The effective masses of the carriers associated with the F₅ and F₆ oscillations were measured in a (110) plane. For the F₅ oscillations, the Dingle temperature and apparent magnetic breakdown field appear to depend strongly upon orientation. For the F₆ oscillations, however, there were no signs of magnetic breakdown up to the highest magnetic fields available (70 kOe) and the Dingle temperature was roughly independent of orientation. From the acoustic velocities, the elastic constants were determined at 77 K: C₁₁ = (14·7 ± 0·9) × 10¹¹ dyne/cm², C₁₂ = (6·0 ± 0·9) × 10¹¹ dyne/cm², and C₄₄ = (2·59 ± 0·06) × 10¹¹ dyne/cm². These elastic constants give an adiabatic compressibility K_s = (1·13 ± 0·12) × 10^?12 cm²/dyne and a Debye temperature ?_D = (203 ± 15) K.     

Nuclear orientation of156Tb in gadolinium matrix

The anisotropy of the angular distribution of gamma-rays from the decay of¹⁵⁶Tb, oriented in a gadolinium matrix at low temperatures, has been measured at the angles of 0 and π/2 with respect to the applied magnetic field direction in the range of temperatures from 14·6 to 68·4 mK. The temperature dependence of anisotropy was measured for the first time. The parameters of hyperfine magnetic dipole and electric quadrupole splittings have been determined and the values of the magnetic dipole moment ¦Μ¹⁵⁶¦=(9·6±1·3)×10^?27 J/T and the electric quadrupole momentQ ¹⁵⁶=(2·9±0·9)×10^?28 m² of the¹⁵⁶Tb ground state have been calculated. Multipole mixing ratios andB(E2) branching ratios of many gamma-ray transitions occurring in¹⁵⁶Gd have been found and the results have been discussed in terms of the rotational-vibration and pairing-plus-quadrupole models.     

Dielectric dispersion and its temperature variation in calcite single crystals

The variation of dielectric constant and loss of calcite single crystals with frequency and temperature over wide ranges (10² to 2.4×10¹⁰c/s and ?193 to 450 °C) in two orientations of the crystal, namely, the electric field (i) parallel to the optic axis and (ii) perpendicular to the optic axis, has been studied and the results reported. The dielectric constant at 25 °C in both orientations (E‖, 7.8 andE⊥, 8.2) is frequency-independent. The dielectric loss shows a minimum in the 10⁵ to 10⁸ c/s region. Dielectric constant as a function of temperature exhibits two distinct regions: frequency-independent (?193 to 50 °C) and frequency-dependent (50 to 450 °C). The temperature variation of specific conductivity can be represented by a sum of two exponentials, e.g., \(\sigma = Ae^{ - E_1 /kT} + Be^{ - E_2 /kT}\) with the usual notation; the constants have different values in the two orientations. The intrinsic conductivity with larger activation energy (E‖ 0.91 eV andE⊥ 1.05 eV) is attributed to the movement of lattice vacancies in the crystal. The 15% larger value for the intrinsic activation energy alongE⊥ optic axis over the other orientation may be due to a probably large electrostatic interaction between the charge carriers and the lattice ions in this orientation.     

Zero-bias tunneling anomaly in a two-dimensional electron system with disorder

The temperature dependence of a zero-bias anomaly in the tunneling conductance of an Al/δ-GaAs tunneling structure with a two-dimensional electron density in the δ-layer of 3.5 × 10¹² cm^?2 has been investigated. It has been shown that the respective drop Δρ(?, T) in the tunneling density of states ρ near the Fermi level E _F of the two-dimensional electron system depends logarithmically on the energy ? within the range of 2.7kT < |?| < ?/τ, where ? is measured with respect to E _F and τ is the momentum relaxation time of two-dimensional electrons. It has been found that the drop depth Δρ(0, T)/ρ is also proportional to ln(kT/?₀) in the temperature range T = 0.1–20 K and saturates below 0.1 K.     

Iodine as a donor in CdS

Iodine doped single crystals of CdS were grown from the vapor phase. High temperature Hall effect measurements for the crystals equilibrated with Cd and S₂ vapors at temperatures between 700 and 1000°C gave the free electron concentration as a function of p_Cd or p_S2 and temperature. The results can be explained on the basis of a model in which the CdS is saturated with iodine at low p_Cd (=high p_S2) but unsaturated at high p_Cd.The solubility of iodine in CdS is given by c_t=1·73×10²²p_S2^?1/8 exp (?1·045 eV/kT) cm^?3 atm^?1/8=4·62×10¹⁹p_Cd^1/4 exp (?0·195 eV/kT) cm^?3 atm^1/4The formation of pairs (I_SV_Cd)′ from I_S^· and V_Cd″ is governed by the equilibrium constant K_{P(I, V)}=4 exp (≤1·1 eV/kT)If Cd diffusion occurs primarily by free vacancies, the Cd^* tracer self diffusion leads to a vacancy mobility of (1·2±0·5)×10^?5 cm² sec^?1 at 900°C, in agreement with results reported by Woodbury [12], but (7±3) times larger than reported by Kumar and Kroger [10].     

Pulsed nuclear magnetic resonance and molecular reorientation in solid 1,3,5-trifluorobenzene

Single and double-pulse transient experiments have been used for the direct measurement of the resonant and non-resonant spin contributions to the ¹H and ¹⁹F second moments in polycrystalline 1,3,5,-C₆H₃F₃. The applicability of these experiments to molecular solids is examined. The temperature dependence of the experimental proton second moment has been investigated between 130 K and the melting point at 267·7 K; a transition centred on 200 K is observed. It is shown that the molecules have an ordered arrangement in the crystal at all temperatures and that this transition is due to thermally activated reorientational jumps of the molecules through 120° about their triad axes. The activation energy for this motion is 42·7 ± 2·9 kJ mol^-1 as determined from the temperature dependence of the ‘apparent’ second moment in the transition region.