The order parameter model for structural relaxation in glass

The order parameter model assumes that the state of a glass or liquid depends on T, P and a number of order parameters Z_i. Structural relaxation is due to the kinetically impeded evolution of the order parameters following a rapid change in T or P. The linear relaxation function for the evolution of property Q (V or H) in response to a change in X (T or P) is of the form φ_QX = Σ_igⁱ_QX exp(?tτ_i). Expressions are derived for the qeighting coefficients gⁱ_QX in terms of the dependences of V and H on the various order parameters. It is shown that gⁱ_VT = gⁱ_HP and that gⁱ_VTgⁱ_HP/gⁱ_VPgⁱ_HT = II, where II is the Prigogine-Defay ratio. The corresponding relations among the relaxation functions are φ_VT = φ_HP and φ_VTφ_HP/φ_VPφ_HT ? II. The predictions of the order parameter model for structural relaxation are compared with and found generally to agree with existing literature data. A number of suggestions for future investigations to test this model are made.     

Raman line shape analysis as a mean characterizing molecular glass-forming liquids

Raman scattering spectra in glass forming toluene were studied in the temperature range 50–323 K with the goal of extracting information about homogeneous, inhomogeneous and orientational broadening. It was found that the temperature dependence of inhomogeneous line width allows one to depict two peculiar temperatures: T_A and T_g, where T_g is the glass transition temperature and T_A is the temperature of transition from an Arrhenius-like to a non-Arrhenius behavior for the α-relaxation time dependence on temperature, τ_α(T). Temperature dependence of the orientational phase loss time τ_OPL was found to correspond well to τ_α at T > T_A and continues approximately Arrhenius behavior for lower temperature in contrast to τ_α(T). Also, a comparative analysis of homogeneous broadening of polarized and depolarized lines was done, which provided an estimation of the orientational broadening γ_NL(T). The found γ_NL(T) decreases linearly as the temperature decreases and goes to zero at T ~ T_c, where T_c is the critical temperature in framework of the mode-coupling theory (note that T_c is close to other peculiar temperatures T_B and T_β, but we did not intent to distinguish among them in the present work). Thus, it was shown that the Raman line shape analysis in molecular glass forming materials allows one to extract peculiar temperatures: T_A, T_g, and, probably, T_c.The test of the possibility to use a probe molecule for the Raman line shape analysis has revealed that the extracted data for probe molecule lines do not characterize the host matrices, at least in the low-viscous state (T > T_A).     

Growth of Nd-doped YVO4 single crystals along 〈1 0 0〉tetra by the anisotropic heating floating zone method

Nd-doped YVO₄ single crystals were grown along 〈1 0 0〉_tetra by the anisotropic heating floating zone (AHFZ) method. The relationship between the lamp power ratio (P_C/P_A) and the aspect ratio (c/a-axis diameter, D_C/D_A) of the grown crystals was investigated. D_C/D_A increased from 1.01 to 1.52 with increasing P_C/P_A from 0.7 to 1.5. The crystals grown by the AHFZ method developed a cylindrical shape with decreasing P_C/P_A, whereas those grown by a conventional FZ method developed an elliptical cylinder shape.     

Young's modulus sound velocity and Young's modulus of Ti-, Zr- and Hf-based amorphous alloys

The Young's modulus sound velocity (V_E) and the Young's modulus of amorphous ribbons for (Ti, Zr, Hf)_100?x (Si, Ge)_x binary and (Ti, Zr, Hf)_85?xM_x(Si, Ge)₁₅ (M = V ? VIII group transition metal) ternary systems were measured as a function of alloy composition. V_E increases with increasing silicon or germanium content and with the replacement of titanium, zirconium or hafnium by M elements except tantalum or hafnium, and tends to increase with the Debye temperature of the constituent elements themselves. E increases linearly with increasing σ_f and H_v, and ratios of σ_f/E and H_v/3E show a nearly constant value (? 0.018) for Zr_100?xSi_x and Zr_85?xM_xSi₁₅(M = Ti, V, Nb, Ta or Mo) amorphous alloys. Considering the compositional dependence of these mechanical properties (E, σ_f and H_v) and the strong correlation among them, it is suggested that (1) the short-range ordering due to the strong interaction among constituent atoms causes an increase in E, σ_f and H_v, and (2) all the early transition metal-based amorphous alloys possess a common mechanism for plastic flow.     

Properties and structure of cesium phosphate glasses

A series of Cs-phosphate glasses, xCs₂O(1−x)P₂O₅, where 0?x?0.60, were prepared. The glass transition temperature (T_g) decreases with the initial addition of Cs₂O to P₂O₅, from 637 K at x=0 to 472 K at x=0.16. There is little change in T_g with further additions of Cs₂O up to x=0.60. The ³¹P magic angle spinning nuclear magnetic resonance (MAS NMR) spectra show that Cs₂O additions systematically convert the cross-linked ultraphosphate network of ν-P₂O₅ to a chain-like metaphosphate structure as x approaches 0.50. The ¹³³Cs MAS NMR spectra show a 90 ppm increase in isotropic chemical shift (δ_iso) with increasing Cs₂O content, which indicates a decrease in the average electron density around the Cs⁺ ions, more covalent Cs-O bonding, and a shorter average Cs-O bond length. The physical properties and spectroscopic results are interpreted using a structural model that considers the effects of composition on the average coordination environment of Cs⁺ ions.     

Characterization of vapor grown (001) GaAs1−xPx layers by selective photo-etching

The technique of selective photo-etching known for GaAs was successfully applied to (001)GaAs_0.6P_0.4 and it can also be used for the characterization of phosphorus-rich GaAs_1?xP_x layers and for GaP. Using this technique misfit dislocations in GaAs_1?xP_x up to now mainly examined with the transmission electron microscope (TEM) in the GaAs_1?xP_x transition layer could be examined in a density range which is hardly accessible for observation with the TEM. Misfit dislocations are also observed in GaP and GaAs_1?xP_x layers when these are heavily doped with nitrogen. The dislocation density of GaAs_1?xP_x layers of constant composition is compared with predictions from a model of Abrahams et al. for the dislocation density of GaAs_1?xP_x as a function of the rate of grading. Within this model our results can only be explained when the asymmetry factor m between the length to distance ratio of misfit dislocations in the transition layer is about two orders of magnitude greater than the value previously derived from TEM studies of GaAs_1?xP_x layers.     

Thermal diffusivity measurements on As-Te-Ga glasses by photo-thermal deflection technique: Composition dependence and topological thresholds

The thermal diffusivity (α) of As₂₀Te_80−xGa_x glasses (7.5 ? x ? 18.5) has been measured using photo-thermal deflection (PTD) technique. It is found that the thermal diffusivity is comparatively lower for As₂₀Te_80−xGa_x glasses, which is consistent with the memory type of electrical switching exhibited by these samples. Further, the thermal diffusivity of As₂₀Te_80−xGa_x glasses is found to increase with the incorporation of gallium initially (for x ? 9), which is consistent with the metallicity of the additive. This increase in α results in a maximum at the composition x = 9; beyond x = 9, a decrease is seen in α leading to a minimum at the composition x = 15. The observed composition dependence of thermal diffusivity of As₂₀Te_80−xGa_x glasses has been found to be similar to that of Al₂₀As_xTe_100−x glasses, based on which it is proposed that As₂₀Te_80−xGa_x glasses exhibit an extended stiffness transition with compositions x = 9 and x = 15 being its onset and completion, respectively. Also, the composition x = 17.5 at which a second maximum is seen in the thermal diffusivity has been identified to be the chemical threshold (CT) of the As₂₀Te_80−xGa_x glassy system, as at CT, the glass is configurationally closest to the crystalline state and the scattering of the diffusing thermal waves is minimal for the chemically ordered phase.     

Transformation behavior of PdAuSi metallic glasses

The transformation behavior of roller-quenched amorphous Pd_0.82?xAu_xSi_0.18 and Pd_0.835?xAu_xSi_0.165 alloys, where x ? 0.10, after rapid heating to temperatures near to or above T_g, is reported. The calorimetrically determined glass (T_g) and kinetic crystallization (T_c) temperatures both increased with x up to x ≈ 0.04. With increasing x, at x ? 0.04, T_c decreased rapidly while T_g varied little. Binary Pd_0.82Si_0.18 alloys crystallized to an fcc phase without apparent composition segregation. The tendency to phase separate at T near T_g, as manifested by small- (SAXS) and large-angle X-ray scattering and calorimetry, increased with increasing Au substitution. Pd_0.8Au_0.035Si_0.165 alloy apparently phase separated by a nucleation and growth mechanism, with a growth rate limited by the melt viscosity, to form an fcc phase dispersed in an amorphous phase which later crystallized. Pd_0.74Au_0.08Si_0.18 alloy phase separated initially to two melts, each of which later crystallized in turn. The initial separation behavior was generally consistent with the predictions of the spinodal theory but with some deviation from Cahn's linear relation.     

Characterization of the optical properties of LPE InxGa1−xAsyP1−y thin layers grown on InP

A series of In_xGa_1?xAs_yP_1?y single-crystal thin layers have been grown on an InP substrate in a vertical liquid phase epitaxy furnace with a rotating slide boat system. The optical properties of these LPE quaternary alloys lattice-matched to InP have been investigated mainly by photoluminescence and electroreflectance measurements. Photoluminescence spectra of In_xGa_1?xAs_y P_1?y epitaxial layers are dominated by a strong luminescence line due to band-edge emission. At low temperatures, around 4.2 K, we have observed complicated luminescence bands with many fine structures. Electroreflectance spectra for the LPE In_xGa_1?xAs_yP_1?y layers are sufficiently broad to fulfil the low-field condition, and the analysis enabled us to determine precisely the band gap energy.     

Cluster self-organization of germanate systems: Suprapolyhedral nanocluster precursors and self-assembly of the Li8GeO6, Li4GeO4, and Li6Ge2O7 crystal structures

Nanoparticles (An clusters of atoms or Kn polyhedra, where n is the number of atoms or polyhedra) corresponding to the initial stage of evolution of a chemical system have been modeled. Four series of cluster isomers K3 and K4 formed by different T tetrahedra are selected. The clusters are topologically represented by two-colored graphs. A change in their symmetry, depending on the composition and mutual arrangement of L and G tetrahedra in the chemical isomers, is established. Our model is used to search for cluster precursors in Li germanates Li₈GeO₆ (P6₃ mc, hP30), Li₄GeO₄(Cmcm, mC36), and Li₆Ge₂O₇ (P2₁/n, mP60). Three types of nanocluster precursors are identified: (A) polycyclic, with a tetrahedral arrangement of 3L + GG polyhedra (L and G are LiO₄ and GeO₄, respectively) in the Li₈GeO₆ structure; (B) monocyclic, with a sequence of L-G-L-G polyhedra in the Li₄GeO₄ structure; and (C) polycyclic, in the form of two bound monocyclic clusters with a sequence of L-L-G-G polyhedra in the Li₆Ge₂O₇ structure. Lithium atoms are found to play three different roles during structural self-assembly: they participate in the formation of nanocluster precursors, they serve as templates stabilizing the local structure of nanocluster precursors, and they act like spacers filling the voids between nanocluster precursors.     

High-temperature relaxation mechanisms in inorganic glasses

At temperatures below T_g two relaxation processes are observed in sheet glass (200–500°C) and low-alkali glass (300–600°C): the fast R₁ and the slow R₂ processes which are not connected with the viscous flow, and the structural relaxation occurring R₃ above T_g. The processes R₁ and R₂ proceed at an invariable structure and are characterized by activation energies as high as 5 kcal mol^?1 and 13–15 kcal mol^?1, respectively. The contribution of R₂ amounts to 70–80%. The process R₃, observed near and above T_g, is accompanied with structural variations and, therefore, its activation energy depends on temperature; at T_g it is equal to 60 kcal mol^?1.The processes R₁ and R₂ are due to the mobility and rearrangement of large kinetic units. On the contrary, R₃ is characterized by a low volume of kinetic units. This shows that the ions of silicon and oxygen are involved in this process. The relaxation process R₁ is assumed to be connected with the local fluctuation deformationsof the glass network as in the case of reverse glass deformation under high pressures, and the process R₂ with the mobility of microscopic areas of the glass micro-inhomogeneous structure (structural complexes, microblocks). The continuous spectra corroborate the existence of several high-temperature relaxation processes in silicate glasses.Thus, three relaxation processes are observed in alkali-silicate glasses in the temperature range 200–600°C: the processes R₁ and R₂ are mechanical relaxations, whereas the process R₃ is a structural relaxation determining the viscous flow of glass. The contribution of R₃ to stress relaxation amounts to 5%.There exists a temperature T_k (20–30° below T_g) which is the upper limit of the process R₂. At higher temperatures beginning from T_k the stress relaxation is first determined by the two processes R₁ and R₃, and then by one process R₃. At temperatures below T_k all three processes determine the stress relaxation, but with the decreasing temperature the rate of R₃ becomes negligible and, therefore, in the glass annealing range (below T_k) the mechanical relaxation R₂ and R₁ are mainly responsible; their contribution to the whole relaxation process is as high as 95%.     

Evaluation for photo-induced changes of photoluminescence and optical energy gap in amorphous Se100−xGex (x=5, 25 and 33) thin films

We have investigated photo-induced changes of photoluminescence (PL) and optical energy gap (E_OP) in amorphous Se_100−xGe_x (x=5, 25 and 33) thin films from illumination by HeCd laser light (hν=3.81 eV). The E_OP is obtained by a linear extrapolation of (αhν)^1/2 vs. hν to the energy axis. The optical absorption coefficient (α) is calculated from the extinction coefficient k measured in the wavelength range of 290-900 nm. Although the values of ΔE_OP are very different, all films exhibit a photo-induced photodarkening (PD) effect that is a red shift of E_OP. In particular, ΔE_OP in a-Se₇₅Ge₂₅ thin film exhibits the largest value (i.e., ΔE_OP∼40 meV for a-Se₉₅Ge₅, ΔE_OP∼200 meV for a-Se₇₅Ge₂₅, ΔE_OP∼130 meV for a-Se₆₇Ge₃₃). PL spectra in a-SeGe by hν_HeCd have no Stokes shift (SS). Although the PL intensity in the Se_100−xGe_x system is very small, the PL spectra (three-trial average) show a dependence on both composition and illumination time. The intensities of five band peaks (I₁-I₅) observed in the range of 1-2 eV increase with an increase of Ge content. The intensity of I₂ peak (the strongest intensity) increases with increasing illumination time, while the peak-energy position decreases. This is evidence of PD. A decrease in PL peak-energy position with Ge contents shows a similar tendency to that in E_OP. That is, the ΔE(I₂) is 25.2, 45.0 and 44.5 meV for a-Se₉₅Ge₅, a-Se₇₅Ge₂₅ and a-Se₆₇Ge₃₃, respectively. We propose in this paper a triple-well potential model that can universally explain the energy-induced phenomena in the a-SeGe, such as the PD and thermal bleaching, the native charged-defect generation and the no-SS PL, etc.     

Studies on the AsSbSe glass system

Results are reported of measurements of the glass transition temperature (T_g), conductivity and density (d) for glasses of the AsSbSe system, with compositions (As, Sb)₄₀Se₆₀ and As_xSb₁₅Se_85?x. The results are compared with glasses of similar compositions of the As_xSe_100?x about compositions in the Ge_xSb₁₅Se_85?x and As_xSe_100?x glasses, in the case of As_xSb₁₅Se_85?x glasses, the As-rich compositions exhibit higher values of T_g and d compared to the stoichiometric composition As₂₅Sb₁₅Se₆₀. These results are discussed in the light of a chemically ordered structural arrangement in these glasses.     

Crystal structure of α‴-(Zn1−x Cd x )3As2 (x = 0.26)

Single crystals of the α?-phase of (Zn_{1 ? x} Cd _x )₃As₂ solid solution (x = 0.26) have been prepared and investigated by X-ray diffraction analysis. The tetragonal unit-cell parameters are found to be a = b = 8.5377(2) Å, c = 24.0666(9) Å, sp. gr. I4₁/amd, Z = 16. Zn and Cd atoms in the crystal statistically occupy three symmetrically independent positions in the mirror planes and are tetrahedrally coordinated by arsenic atoms. (Zn,Cd) tetrahedra share edges to form a three-dimensional structure framework. The α?-phase is geometrically related to the fluorite structure. The character of arrangement of tetrahedral vacancies in fluorite-like unit cells is revealed. Chains of tetrahedral vacancies form microchannels oriented parallel the a and b axes, which pierce the three-dimensional structure framework at different levels along the c axis. The structure of α″-Cd₃As₂ crystals is found to be similar to that of α?-(Zn_0.74Cd_0.26)₃As₂.     

Effect of antimony addition on the thermal and electrical-switching behavior of bulk Se-Te glasses

The thermal properties and electrical-switching behavior of semiconducting chalcogenide Sb_xSe_55−xTe₄₅ (2 ? x ? 9) glasses have been investigated by alternating differential scanning calorimetry and electrical-switching experiments, respectively. The addition of Sb is found to enhance the glass forming tendency and stability as revealed by the decrease in non-reversing enthalpy ΔH_nr, and an increase in the glass-transition width ΔT_g. Further, the glass-transition temperature of Sb_xSe_55−xTe₄₅ glasses, which is a measure of network connectivity, exhibits a subtle increase, suggesting a meager network growth with the addition of Sb. The crystallization temperature is also observed to increase with Sb content. The Sb_xSe_55−xTe₄₅ glasses (2 ? x ? 9) are found to exhibit memory type of electrical switching, which can be attributed to the polymeric nature of network and high devitrifying ability. The metallicity factor has been found to dominate over the network connectivity and rigidity in the compositional dependence of switching voltage, which shows a profound decrease with the addition of Sb.     

The presence of a thermally reversing window in Al-Te-Si glasses revealed by alternating differential scanning calorimetry and electrical switching studies

Alternating differential scanning calorimetric (ADSC) studies and electrical switching experiments have been undertaken on Al₁₅Te_85−xSi_x (2 ? x ? 12) system of glasses. These glasses are found to exhibit two crystallization reactions (T_c1 and T_c2), for compositions with x < 8. Above x = 8, a single-stage crystallization is seen. Further, a trough is seen in the composition dependence of non-reversing enthalpy (ΔH^NR), based on which it is proposed that there is a thermally reversing window in Al₁₅Te_85−xSi_x glasses, in the composition range 4 ? x ? 8. Electrical switching studies indicate that Al₁₅Te_85−xSi_x glasses exhibit a threshold type electrical switching at ON state currents less than 2 mA. Further, the switching voltages are found to increase with the increase in silicon content. It is interesting to note that the start (x = 4) and the end (x = 8) of the thermally reversing window are exemplified by a kink and a saturation in the composition dependence of switching voltages, respectively.     

Network topological thresholds in gallium doped As–Te glasses – Electrical and thermal investigations

Electrical switching and differential scanning calorimetric studies are undertaken on bulk As₂₀Te_80−xGa_x glasses, to elucidate the network topological thresholds. It is found that these glasses exhibit a single glass transition (T_g) and two crystallization reactions (T_c1 & T_c2) upon heating. It is also found that there is only a marginal change in T_g with the addition of up to about 10% of Ga; around this composition an increase is seen in T_g which culminates in a local maximum around x = 15. The decrease exhibited in T_g beyond this composition, leads to a local minimum at x = 17.5. Further, the As₂₀Te_80−xGa_x glasses are found to exhibit memory type electrical switching. The switching voltages (V_T) increase with the increase in gallium content and a local maximum is seen in V_T around x = 15. V_T is found to decrease with x thereafter, exhibiting a local minimum around x = 17.5. The composition dependence of T_c1 is found to be very similar to that of V_T of As₂₀Te_80−xGa_x glasses. Based on the present results, it is proposed that the composition x = 15 and x = 17.5 correspond to the rigidity percolation and chemical thresholds, respectively, of As₂₀Te_80−xGa_x glasses.     

An analysis of the radial distribution function of SIOx

A theory is presented for the short-range order (sro) in the SiO_x alloy system for 0?x?2. The parameters of the sro are taken to be fixed by the properties of amorphous Si and SiO₂, except that the probability of an Si atom having (i?1) oxygen neighbors is left as a free parameter, C_i(x), for i=1 through 5. The areas of the first three peaks in the radial distribution function (RDF) of SiO_x are calculated as a function of x and C_i(x). It is shown that the RDF can be used to differentiate between the two models proposed for the sro in SiO_x namely the SiSiO₂ mixture model and the random bonding model. In the case of SiO powder, a mixture model at the atomic level is found to be consistent with the RDF. It is suggested that accurate RDF's of SiO_x films, which are not currently available, would be useful in determining the sro of the alloy system. The present theory may be extended to analyze the GeO_x and SnO_x alloy systems.     

Ionic conductivity of cold-pressed ceramics from grinding of R0.95M0.05F2.95 solid electrolytes (R = La,Nd; M = Ca,Sr, Ba) synthesized by reaction in melt

Cold-pressed ceramics of fluorine-conducting solid electrolytes La_{1 ? y} M _y F_{3 ? y} (M = Ca, Sr, Ba) and Nd_{1 ? y} Ca _y F_{3 ? y} with y = 0.95 have been synthesized in a melt of RF₃ (R = La, Nd) and MF₂ components in a fluorinating atmosphere and ground in a ball mill. The as-prepared ceramics require annealing, during which their porosity decreases and the conductivity is stably increased (by a factor of 250 for the R _{1 ? y} M _y F_{3 ? y} composition at 293 K). The Nd_0.95Ca_0.05F_2.95 and Nd_0.95Ca_0.05F_2.95 compositions have a maximum ionic conductivity σ(293 K) ～ 5 × 10^?6 Sm/cm. This value is larger (by a factor of about 10) than σ (293 K) for the R _{1 ? y} M _y F_{3 ? y} ceramics of tysonite phases prepared by mechanochemical synthesis with the cold pressing of reaction products.     

Reverse metal-non-metal transition in semiconducting melts

Electrical conductivity, σ(T), and thermopower, α(T), measurements were performed for liquid TlAsSe₂, CuTlSe₂, Cu_0.2(CuAsSe₂)_0.8, Cu_0.4(CuAsSe₂)_0.6, and Cu_0.6(CuAsSe₂)_0.4 alloys in a wide temperature range (700<T<1800 K) under ambient pressures of argon gas (up to 25 MPa). A reverse metal-non-metal high temperature transition is observed when temperature increases to about 1500 K. A mechanism involving the opening of a pseudogap is proposed. The mechanism suggests formation of both a mobility edge responsible for the electrical conductivity behavior, and a density of states edge that is responsible for the thermopower behavior.