Vacancy formation energy related to liquid structure in a nonlinear scaled potential theory

Summary A scaling relation is derived for the vacancy formation energyE _v in a family of homologous systems at their melting temperatureT _m, using a pair potential theory which relatesE _v atT _m to liquid structure under the assumption that atomic relaxation round the vacancy can be neglected.

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Riassunto Il lavoro deriva una relazione di scala per l’energiaE _v di formazione di un posto vacante in una famiglia di sistemi omologhi alla loro temperatureT _m di fusione, nell’ambito di una teoria a potenziale di coppia che legaE _v aT _m alla struttura della fase liquida nell’ipotesi che rilassamenti atomici attorno al posto vacante possano essere trascurati.

     

Polycrystalline semiconductors

Generally substances are more stable in a crystalline than in a glassy state. Therefore, to form a glass, crystallization must be bypassed. Under certain conditions, the melts of many substances can be cooled to the glass state. Whether or not the melt of a given material forms a glass is determined principally by a set of factors which can be specified to some extent in the laboratory, namely, the cooling rate, - T, the liquid volume, v], and the seed density, ps and upon a set of materials constants: the reduced crystal–liquid interfacial tension, α the fraction, f, of acceptor sites in the crystal surface, and the reduced glass temperature, T_rg . The glass-forming tendency will be greater the larger are - T and T_rg and the smaller are v]. ps, and f. The number and variety of substances which have been prepared in a glassy or ‘amorphous solid’ form have been greatly increased with techniques in which the material is condensed from solution on to a surface held well below its glass temperature. There are at least some glass formers in every category of material, according to bond type, i.e. covalent, ionic, metallic, van der Waals or hydrogen. However, it is not established whether or not every substance can be put into a glass form.     

Diffusion activation energy versus the favourable energy in two-order-parameter model:A molecular dynamics study of liquid Al

In the present work, we find that both diffusion activation energy E_a(D) and E_a(S^ex) increase linearly with pressure and have the same slope (0.022±0.001 eV/GPa) for liquid Al. The temperature and pressure dependence of excess entropy is well fitted by the expression -S^ex(T,P)/k_B=a(P)+b(P)T+c(P)exp(E_f/k_BT), which together with the small ratio of E_f/k_BT leads to the relationship of excess entropy to temperature and pressure, i.e. S^ex≈-cE_f/T, where c is about 12 and E_f (=Δ E-PΔV) is the favourable energy. Therefore, there exists a simple relation between E_a(S^ex) and E_f, i.e. E_a(S^ex)≈cE_f.     

Isothermal Melt Crystallization Kinetics for Poly(Trimethylene Terephthalate)/Poly(Butylene Terephthalate) Blends

The kinetics of isothermal melt crystallization of poly(trimethylene terephthalate) (PTT)/poly(butylene terephthalate) (PBT) blends were investigated using differential scanning calorimetry (DSC) over the crystallization temperature range of 184–192°C. Analysis of the data was carried out based on the Avrami equation. The values of the exponent found for all samples were between 2.0 and 3.0. The results indicated that the crystallization process tends to be two‐dimensional growth, which was consistent with the result of polarizing light microscopy (PLM). The activation energies were also determined by the Arrhenius equation for isothermal crystallization. The values of ΔE of PTT/PBT blends were greater than those for PTT and PBT. Lastly, using values of transport parameters common to many polymers (U*=6280 J/mol, T _∞=T _g – 30), together with experimentally determined values of T _m ⁰ and T _g, the nucleation parameter, K _g, for PTT, PBT, and PTT/PBT blends was estimated based on the Lauritzen–Hoffman theory.     

A model for viscosity coefficients of gases with potentials differing in form

A recent theory of non-conformal interactions has been very succesful in providing effective spherical potentials for the pressure of more than 40 real gases and many of their binary mixtures. Here, this theory is applied to deal with low-density viscosity coefficients. In its simplest form, the approximate non-conformal (ANC) theory introduces, besides the usual corresponding states parameters-energy ? and distance r_m-a softness parameter s to account for the form of a particular potential function. We investigate the effects of the potential form on the temperature behaviour of the viscosisty coefficient η. It is shown that the softer potentials, with wider attractive wells, have larger viscosities and an explicit expression for η (T, ?, r_m, s) is obtained. The ANC potentials are tested in their capacity to reproduce the temperature dependence of η for the heavier noble gases (Ar, Kr and Xe), diatomics (H₂, N₂, O₂ and CI₂) and a dozen small polyatomics. It is found that the ANC model η (T, ?, r_m, s), with only three substance-dependent parameters, reproduces experimental 7 data within their estimated error.     

Thermal behavior of gamma-irradiated low-density polyethylene/paraffin wax blend

The thermal properties of low-density polyethylene (LDPE)/paraffin wax blends were studied using differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and melt flow index (MFI). Blends of LDPE/wax in ratios of 100/0, 98/2, 96/4, 94/6, 92/8, 90/10 and 85/15 (w/w) were prepared by melt-mixing at the temperature of 150°C. It was found that increasing the wax content more than 15% leads to phase separation. DSC results showed that for all blends both the melting temperature (T_m) and the melting enthalpy (ΔH_m) decrease linearly with an increase in wax content. TGA analysis showed that the thermal stability of all blends decreases linearly with increasing wax content. No clear correlation was observed between the melting point and thermal stability. Horowitz and Metzger method was used to determine the thermal activation energy (E_a). MFI increased exponentially by increasing the wax content. The effect of gamma irradiation on the thermal behavior of the blends was also investigated at different gamma irradiation doses. Significant correlations were found between the thermal parameters (T_m, ΔH_m, T₅%, E_a and MFI) and the amount of wax content and gamma irradiation.     

Effect of Alkyl Side Chain Length on Relaxation Behaviors in Poly(n-alkyl Acrylates) and Poly(n-alkyl Methacrylates)

Dynamic mechanical analysis (DMA) is used to investigate the effect of alkyl side chain length on the relaxation behavior of poly(n-alkyl acrylates) (PnAA) and poly(n-alkyl methacrylates) (PnAMA) above the glass transition temperature (T_g). Master curves and shift factors (log a_T) were obtained using the time–temperature superposition (TTS) principle. The log a_T curves of PnAA and PnAMA exhibit a dynamic crossover from one Vogel–Fulcher–Tammann–Hesse (VFTH) equation to another above T_g. The corresponding temperature was designated as the dynamic crossover temperature (T_c). It is found that T_c/T_g and the apparent activation energy (E_g) increases, e whereas the fragility index (m) decreases with increasing alkyl side chain length. Further analysis shows that m ∝ T_g, E_g∝ , and E_g∝ m² for both PnAA and PnAMA.     

Infrared transitions of C2D6 from v 4 to the interacting system v 4+ v 6, v 4+ v8, v 3+ 2v 4: rotational analysis,and torsional splitting in the v 3+ 2v 4 and v 3+ v 4 states

The hot infrared transitions of C₂D₆ from the υ₄(A_1u ) to the υ₄ + υ₆(A_2g ) and υ₄ + υ₈(E _g ) vibrational states, observed from 960 to 1180 cm^?1, have been rotationally analysed on a high-resolution Fourier transform spectrum (full width at half-maximum about 0·0030 cm^?1). The vibration-rotation interactions affecting the upper vibrational states are very similar to those of the corresponding cold system. A strong x,y Coriolis interaction between υ₄ + υ₆ and υ₄ + υ₈, with K-level crossing, generates large displacements of the rotational components of both vibrational states, tuning them to additional local resonances in several spectral regions. Thus l resonances with Δl = ±2, Δk = ±1 occur within υ₄ + υ₈. A x,y Coriolis-type resonance between υ₄ + υ₈(?l,K ? 1) and υ₃ + 2υ₄(K) occurs at K = 11,12,13, and a further coupling of υ₄ + υ₈(+l,K + 1) and υ₃ + 2υ₄(K + 3) is most effective at K = 11 and 12. These resonances induce torsional splittings on the perturbed levels of υ₄ + υ₈ and allow us to determine the torsional splittings in the υ₃ + 2υ₄ state. The vibration-rotation constants of υ₄ + υ₆, υ₄ + υ₈ and υ₃ + 2υ₄, several interaction parameters and the torsional splitting of υ₃ + 2υ₄ have been determined by least-squares fit of 1391 observed transition wavenumbers, with an overall standard deviation σ = 0·75 × 10^?3 cm^?1. The vibrational wavenumbers found for the four torsional components of (υ₃ + 2υ₄)? υ₄ are υ(E_3d) = 1040·961 82(809)cm^?1, υ(A_3d) = 1041·218 27(865)cm^?1, υ(E_3s) = 1041·225 23(662)cm^?1 and υ(A_1s) = 1041·407 77(633)cm^?1. These are anomalous for both the order of the torsional components and the magnitudes of their separations. We believe that this is mainly due to the interactions of υ₃ + 2υ₄ with the torsional manifolds with υ₃ = 0 and υ₃ = 2, through the vibration-torsion Hamiltonian term (?V ₆/?q ₃)q ₃cos (6γ)]/2. The further observation of a few doublets of υ₈ and υ₃ + υ₄ at resonance provides information on the torsional splitting of the latter state.     

Low-temperature x-ray diffraction studies of the crystallographic parameters and thermal expansion of (CH3)2NH2Al(SO4)2 · 6H2O crystals

The a, b, c, and β crystallographic parameters of the (CH₃)₂NH₂Al(SO₄)₂ · 6H₂O crystal (DMAAS) have been measured by x-ray diffraction in the 90–300-K temperature range. The thermal expansion coefficients along the principal crystallographic axes α_a, α_b, and α_c have been determined. It was shown that, as the temperature is increased, the parameter α decreases and b increases, whereas c decreases for T<T _c (where T _c is the transition temperature) and increases for T>T _c, so that one observes a minimum in the c=f(T) curve in the region of the phase transition (PT) temperature T _c ～ 152 K. The thermal expansion coefficients α_a, α_b, and α_c vary in a complicated manner with increasing temperature, more specifically, α_a and α_c assume negative values at low temperatures, and the α_a=f(T), α_b=f(T), and α_c=f(T) curves exhibit anomalies at the PT point. The crystal has been found to be substantially anisotropic in thermal expansion.     

| m | Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

The symmetry and |m| partial-wave analysis for two-dimensional (2D) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef _|m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off _|m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f _|m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off _|m|(θ) on the positive real |m| axis.     

Evaluation of Effect of Plastic Injection Molding Process Parameters on Shrinkage Based on Neural Network Simulation

The effects of process parameters, mold temperature (T _mo), melt temperature (T _me), cooling time (t_c ), fill pressure (P_f ), packing pressure (P_p ), and packing time (t_p ) on the shrinkage of injection molded polypropylene were investigated by utilizing a combination of the Artificial Neural Network (ANN) method and Moldflow software. An ANN model is developed to understand the relationship between plastic injection molding process parameters and shrinkage. The test results on the performance of the ANN model show that it can predict the shrinkage with reasonable accuracy. The simulation results show that the most important process parameter affecting shrinkage is P_p , followed by T _me and T _mo, with t_c , P_f , and t_p having the least effect. Shrinkage increases with the elevated T _mo and t_c . In contrast, the increases in P_p , T_me , t_p , and P_f cause shrinkage to decrease. The strongest effect on the shrinkage is the amount of material forced into the mold, followed by the crystallinity and orientation of the material.     

U-perturbation treatment of heavy fermion systems

Heavy fermion systems are described by the periodic Anderson Model (PAM), i.e. a lattice of localized, highly correlatedf-electron states hybridized with the delocalized states of a conduction band. We treat the PAM within the second orderU perturbation theory around the non-magnetic Hartree-Fock solution (U on site Coulomb correlation between thef-electrons). This treatment has the advantage that Fermi liquid relations (Luttinger theorem) are automatically fulfilled. Thef-electron selfenergy and spectral function are calculated for different temperatures, and, for the symmetric PAM, we obtain single-particle peaks near toE _f andE _f +U and in addition many-particle (Kondo) resonance peaks near to the chemical potential (E _f baref-electron energy). The resonance peaks are strongly temperature dependent and vanish on a characteristic temperature scaleT _K. For the symmetric PAM and a constant on-site hybridization the Fermi energy falls into a hybridization gap. A second, smaller characteristic temperature scaleT _coh (coherence temperature), on which the hybridization gap vanishes, is observed within this approach. For the non-symmetric PAM (i.e.E _f andE _f +U not symmetric around the chemical potential) we obtain a similar behaviour, but the single-particle peaks are no longer at the correct positionsE _f andE _f +U. The proper behaviour for the symmetric PAM but less satisfactory behaviour for the non-symmetric PAM can be understood from the fact that only for the symmetric PAM the exactly solvable limit of a vanishing hybridization is reproduced within this approach.     

A study of radiative properties of fractal soot aggregates using the superposition T-matrix method

We employ the numerically exact superposition T-matrix method to perform extensive computations of scattering and absorption properties of soot aggregates with varying state of compactness and size. The fractal dimension, D_f, is used to quantify the geometrical mass dispersion of the clusters. The optical properties of soot aggregates for a given fractal dimension are complex functions of the refractive index of the material m, the number of monomers N_S, and the monomer radius a. It is shown that for smaller values of a, the absorption cross section tends to be relatively constant when D_f<2 but increases rapidly when D_f>2. However, a systematic reduction in light absorption with D_f is observed for clusters with sufficiently large N_S, m, and a. The scattering cross section and single-scattering albedo increase monotonically as fractals evolve from chain-like to more densely packed morphologies, which is a strong manifestation of the increasing importance of scattering interaction among spherules. Overall, the results for soot fractals differ profoundly from those calculated for the respective volume-equivalent soot spheres as well as for the respective external mixtures of soot monomers under the assumption that there are no electromagnetic interactions between the monomers. The climate-research implications of our results are discussed.     

Properties of (Bi1/9Na2/3)(Mn1/3Nb2/3)O3 analysed within dielectric permittivity,conductivity, electric modulus and derivative techniques approach

The (Bi_1/9Na_2/3)(Mn_1/3Nb_2/3)O₃ ceramics with perovskite structure were sintered. The XRD test proved that the samples are cubic (a?=?3.920?±?0.001?Å). Microstructure and atomic composition were determined with a SEM (JSM-5410) equipped with energy dispersion X-ray analyser (ISIS-300). The fluctuation in the chemical composition was found indicating on local disorder. Broadband dielectric spectroscopy in the range 10^?1–3?·?10⁷?Hz was applied within the range of 100–650?K. The real, ?′(f,?T), and imaginary, ?″(f,?T), parts of complex dielectric permitivity characteristics, both in the temperature and frequency domain, show relaxation processes partially covered by electric conductivity. At high temperatures the electric conductivity exhibits a thermally activated behaviour σ(f,?T)?∝?exp(?E _a/kT) but the variable range hopping (VRH) dependence σ?∝?exp[?(T ₀/T)^1/4] is manifested at low temperatures. The derivatives technique in the frequency (??log??/??log?ω) and temperature (??log??/?T) domain enabled various relaxation processes to be distinguished. The data converted to electric modulus representation, M*(f,?T)?=?1/?*, exhibited clearly resolved relaxation peaks. The relaxation times obtained from the peaks position show a slightly non-Arrhenius temperature behaviour with the activation energy varying in 0.4–0.6?eV range and characteristic time of the electric conductivity relaxation of the order of 10^?12?s. The relaxation times can be fitted at better accuracy with the VRH dependence where T ₀ are of the order of 10⁸?K. It is shown that the low frequency ac-conductivity converges to dc-conductivity and the relation σ(0)?～?ω_m?～?τ_m ^?1 typical for the disordered solids applies. The conduction current relaxation relationship behaves in accord with the VRH system: σ_dc?∝?(T/T ₀)^q (e ²/kT) ω_c, where ω_c?=?ν_ph exp[?(T ₀/T)^1/4] is valid for the locally disordered (Bi_1/9Na_2/3)(Mn_1/3Nb_2/3)O₃ compound.     

NMR self-diffusion study of organic glasses: COANP,MBANP, PNP,NPP

A pulsed field gradient proton spin-echo NMR self-diffusion study of organic glasses COANP, MBANP, PNP and NPP in their liquid and weakly supercooled states was performed. The NMR phase diagrams, based on the proton NMR transverse relaxation time (T ₂) temperature hysteresis data of these materials, clearly give evidence of the onset of a glass phase on cooling the isotropic liquids below their respective melting temperatures. The self-diffusion data exhibit in the supercooled glassy state a non-Arrhenius behaviour and can be described in terms of the Vogel-Fulcher modification of the Arrhenius law,D=D exp{–E _a /[k _B (T–T _VF )]}. The activation energiesE _a and Vogel-Fulcher temperaturesT _VF are 83.2 meV and 239 K for COANP, 66 meV and 249 K for MBANP, and 85 meV and 245 K for PNP, respectively. The flow viscosity data obtained for COANP in the same temperature region as well conform to the Vogel-Fulcher behaviour, exp{E _a ⁽⁾ /[k _B (T–T _VF )]}, withE _a ⁽⁾ =80.4 meV andT _VF =239 K. In case of COANPD was found to increase with decreasing diffusion time in the supercooled (glassy) melt just belowT _M whereas no such behaviour was found aboveT _M .     

Diffuse phase transition of BaTi0.6Zr0.4O3 relaxor ferroelectric ceramics

BaTi_0.6Zr_0.4O₃ ceramic was prepared through solid state reaction route. X-ray diffraction showed that the composition has cubic perovskite structure with space group Pm-3m at room temperature. Temperature dependency dielectric study of the ceramic has been investigated. Bulk density was determined using Archimedes principle and found to be ～97% of X-ray density. The average grain size in the pallet is measured by an optical microscope and found to be 22.23?µm. The dielectric measurement revealed diffuse phase transition of second-order, where dielectric peak temperature (T _m) is dependent of frequency showing relaxor-type behaviour. A clear deviation from Curie–Weiss law is observed in the paraelectric region. The dielectric relaxation rate follows the Vogel–Fulcher relation with E _a?=?0.1020?eV, T _f?=?106?K, ν₀?=?8.5?×?10¹¹?Hz.     

Electronic spectra of mono-substituted chromates

The electronic spectra of monosubstituted chromate ion derivatives, CrO₃X^-, where X^-=F^-, Cl^-, Br^- and IO₃ ^-, have been measured at liquid helium temperature, employing a variety of sample forms. The observed electronic transitions correlate simply and directly with those of CrO₄ ^2-, the lowest-lying transitions being only very weakly perturbed. Of particular interest is that the lowest excited state ¹ E^a retains the peculiarities of the ¹ T ₁ parent state of CrO₄ ^2-. The sharp line spectrum observed in Cr₂O₇ ^2- between 18 000 and 19 000 cm^-1 is identified as ¹ E^a (¹ T ₁ in T _d) ←¹ A ₁ in a single O₃CrO⁼ chromophore. It is suggested that the observed features of the low-lying absorption bands can be explained by assuming that two spin-triplet states [³ E, ³ A ₂] are located a few hundred wave numbers above the sharp 0-0 line of ¹ E^a ←¹ A ₁.     

Dielectric response of the relaxor ferroelectric Pb(Mg1/3Nb2/3)O3 in the nonergodic state after a DC electric field is turned off

The Pb(Mg_1/3Nb_2/3)O₃ (PMN) relaxor system is used as an example to analyze the temperature dependences of the low-frequency dielectric permitivity (?′(T)) measured during zero-field heating (ZFH) from T = 10 K to T = 300 K after using different field cooling (FC) conditions. No changes in the temperature dependences of the permittivity have been detected during the transition from a nonergodic relaxor state (NERS) into an ergodic relaxor state (ERS) (at T _f ≈ 216 K). However, the difference Δ?′(T) between the curves corresponding to different field cooling conditions in the same electric field has different shapes and different values below and above T → (T _f + 9 K)^? (for E _dc = 1.52 kV/cm). The reduced permittivities ?′_r(T, f) recorded under different cooling conditions are shown to change their behavior when passing through T = T _f + 9 K. In NERS, these curves diverge: the stronger the field (0 ≤ E _dc ≤ 3 kV/cm), the larger the divergence. In ERS, however, the ?′_r(T, f) curves coincide under different cooling conditions irrespective of the field. The character of the changes in Δ?′(T) and ?′_r (T, f) during the NERS-ERS transition is frequency-independent. The difference in the behavior of the dielectric response during ZFH after cooling in different (ZFC, FC) modes (even in a weak field), for both transition through T _f and cooling down to T = 10 K, indicates different NERSs forming under these conditions. The contribution to ?′(T) from slowly relaxing regions (ω ～ 0.1 mHz), whose polarization is reoriented after the field is turned off, is responsible for the fact that, during the NERS-ERS transition, the ?′_r(T, f) curves coincide at a temperature that is higher than T = T _f.     

Tunable optical limiting of gold nanorod thin films

Permalloy (Py) films were deposited on Si(111) or Corning 0211 glass substrates. There were two deposition temperatures: T _s=room temperature (RT) and T _s=270°C. The film thickness (t _f) ranges from 10 to 130 nm. The crystal structure properties of the films were studied by X-ray diffraction and transmission electron microscopy. Mechanical properties (including Young’s modulus E _f and hardness H _f) of each film were measured by the nanoindentation (NI) technique. E _f of the Py/Si(111) films was checked again by the laser induced surface acoustic wave (LA-SAW) technique. It was found that the NI technique is best suited for the measurements of E _f and H _f, but only when the sample belongs to the (soft film)/(soft substrate) system, such as the Py/glass film. For the (soft film)/(hard substrate) system, such as the Py/Si(111) film, the NI technique often provides higher values of E _f and H _f than expected. The anomalous phenomenon, associated with the NI technique may be related to the anisotropic crystal structures in the Py films on different kinds of substrates. From this study, we conclude that [E _f of Py/Si(111)]>[E _f of Py/glass] and [H _f of Py/Si(111)]>[H _f of Py/glass]. The good mechanical properties of the Py/Si(111) film make it a better candidate for recording head applications.