Fractal geometry modeling with applications in surface characterisation and wear prediction

Manufactured surfaces such as those produced by electrical discharge machining, waterjet cutting and ion-nitriding coating can be characterized by fractal geometry. A modified Gaussian random fractal model coupled with structure functions is used to relate surface topography with fractal geometry via fractal geometry via fractal dimension (D) and topothesy (L). This fractal characterization of surface topography complements and improves conventional statistical and random process methods of surface characterization, Our fractal model for surface topography is shown to predict a primary relationship between D and the bearing area curve, while L affects this curve to a smaller degree.A fractal geometry model for wear prediction is proposed, which predicts the wear rate in terms of these two fractal parameters. Using this model we show that the wear rate V_r and the true contact area A_r have the relationship V_rα (A_r)^m(D), where m(D) is a function of D and has a value between 0.5 and 1. We next study the optimum (ie the lowest wear rate) fractal diemsnsion in a wear process. It is found that the optimum fractal dimension is affected by the contact area, material properties, and scale amplitude. Experimental results of bearing area curves and wear testing show good agreement with the two models.     

Thermodynamic properties of the ternary system InSb–NiSb–Sb in the temperature range 640–860 K

The ternary InSb–NiSb–Sb system has been studied by X-ray diffraction and by potentiometry. The electromotive forces (EMF) have been measured in the temperature range 640<T/K<860 by using the following galvanic cell:

with x (0.075<x<0.498) and y (0<y<0.359). The investigated samples are located on the following lines of the Gibbs triangle: InSb–Ni_0.33Sb_0.66, InSb–Ni_0.48Sb_0.52, InSb–NiSb, Sb–(InSb)_0.75(NiSb)_0.25, Sb–(InSb)_{0. 5}(NiSb)_0.5, Sb–(InSb)_0.25(NiSb)_0.75. From these measurements, the values of the partial molar thermodynamic functions (Δμ°_m,In, ΔH°_m,In, ΔS°_m,In) (data at reference pressure p⁰=10⁵ Pa), for the liquid InSb alloy, for the three solid heterogeneous regions InSb–NiSb₂–Sb, InSb–NiSb_1±δ?–NiSb₂, InSb–NiSb_1±δ, for six ternary liquid–solid alloys, have been calculated.     

Multilayer planar rectangular coils for eddy current testing: Design considerations

Planar rectangular coils provide some interesting features different from those of pancake coils, such as good performance in conductivity measurement at high frequencies, high sensitivity to scratches and other shallow imperfections and the possibility of inspecting complex surfaces. The impedance of these coils has been modeled by different authors. A brief discussion of some analytical approaches in the literature is presented and calculations using the second-order vector potential approximation are introduced, aimed at the study of the influence of coil shape and size on the sensitivity to electrical conductivity of the substrate. Three cases were modeled, (A) coil in free space—inductance L₀ as a function of number of turns (n) and width of the spiral conductive lanes (c) for different coil inner shape factor (rr_i); (B) coil on a conductive substrate (Zircaloy-4)—impedance change, ΔZ, as a function of f·σ, the product of the test frequency (f) and the substrate electrical conductivity (σ) for different rr_i and (C) coil sensitivity to small changes in σ(Δσ).L₀=L₀(c, n) increased as expected with n and/or coil area and decreased with shape factor. Normalized ΔZ depends strongly on inner rr_i, the curves (or surfaces) for smaller values of rr_i enclosing those for larger values. Another shape factor, the outer shape factor (rr_o), was introduced. Strong dependence of the sensitivity to Δσ on n was observed, as well as the existence of an optimal theoretical frequency. Because the sensitivity to surface conditions also increases with coil size, it could be established that for conductivity assessment it is better to use coils with the smallest n and c, compatible with the particular application, and that the resolving power for this type of measurements is not greatly affected by the shape factor.     

Role of thermal stability and vapor pressure of bis(2,2,6,6-tetramethyl-3,5-heptanedionato)magnesium(II) and its triamine adduct in producing magnesium oxide thin film using a plasma-assisted LICVD process

Thin films of magnesia were deposited on various substrates using plasma-assisted liquid injection chemical vapor deposition with volatile Mg(tmhd)₂·2H₂O (1) (tmhd = 2,2,6,6-tetramethyl-3,5-heptanedione). The precursor complexes, Mg₂(tmhd)₄·(2), and Mg(tmhd)₂·pmdien (3) (pmdien; N,N,N′,N″,N″-pentamethyldiethylenetriamine) were prepared from Mg(tmhd)₂·2H₂O (1). The temperature dependence equilibrium vapor pressure (p_e)_T data yielded a straight line when log p_e was plotted against reciprocal temperature in the range of 360–475 K, leading to standard enthalpy of vaporization (Δ_vapH°) values of 59 ± 1 and 67 ± 2 kJ mol^− 1 for (2) and (3) respectively. Thin films of magnesium oxide were grown at 773 K using complex (1) on various substrate materials. These films were characterized by X-ray diffraction, scanning electron microscopy and energy dispersive X-ray for their composition and morphology.     

Synthesis, photophysical and photochemical properties of crown ether substituted zinc phthalocyanines

The photophysical and photochemical properties of the tetra- and octa-12-crown-4-substituted zinc (II) phthalocyanines are reported for the first time in the scope of this work. The new compounds have been characterized by elemental analysis, IR, ¹H and ¹³C NMR spectroscopy, electronic spectroscopy and mass spectra. General trends are described for photodegradation, singlet oxygen and fluorescence quantum yields, and fluorescence lifetimes of these compounds in dimethylsulphoxide (DMSO). Photophysical and photochemical properties of phthalocyanine complexes are very useful for photodynamic therapy (PDT) applications. The effects of the substituents on the photophysical and photochemical parameters of the zinc (II) phthalocyanines (5, 6 and 7) are also reported. The singlet oxygen quantum yields (Φ_Δ) ranged from 0.48 to 0.78 are indicating the potential of the complexes as photosensitizers in applications of PDT. The fluorescences of the substituted ZnPc complexes are effectively quenched by benzoquinone (BQ).     

Conductive molecular solids: partial iodine oxidation of octaethylporphyrins

We report e.p.r. and resonance Raman spectra, and electrical conductivity for polycrystalline samples of the M(OEP)(I)_x, where M = “H₂”, Ni, Cu; OEP = 1,2,3,4,5,6,7,8-octaethylporphinato; x 5.8. These materials are shown by resonance Raman spectrometry to be properly formulated as . The electrical conductivities depend strongly on ρ = x/5 and M. In some cases (e.g., Ni(OEP)(I)_x, x > 1.4) the ambient temperature polycrystalline conductivities (0.03 S cm⁻¹) and the activation energies (0.10 eV) are comparable with those of polycrystalline samples of materials whose single crystal conductivities are 500 Sm⁻¹ with a metal-like temperature dependence (dσ/dt < 0).     

Synthesis and characterization of a series of bis(dimethyl-n-octylsilyl)oligothiophenes for organic thin film transistor applications

A series of bis-dimethyl-n-octylsilyl end-capped oligothiophenes consisting of two to six thiophene units has been synthesized and characterized to develop novel organic semiconductor materials. The UV–vis spectral data indicate that these silyl end-capped oligothiophenes have longer conjugation lengths as evidenced by the higher λ_max values than the corresponding unsubstituted thiophene oligomers. The thermal analyses indicate that the bis-silylated oligothiophenes show lower melting point (DSi-4T = 80 °C; DSi-5T = 115 °C; DSi-6T = 182 °C) than the corresponding dialkylated thiophene oligomers by 100 °C and hexamer DSi-6T exhibits a liquid crystalline mesophase at 143 °C. The α,ω-bis(dimethyl-n-octylsilyl)oligothiophenes (DSi-6T) have a remarkably high solubility in chloroform which are comparable to the corresponding α,ω-dihexyloligothiophenes. The remarkably increased solubility by these silyl end groups leads bis-silylated oligothiophenes to be applicable to solution processable devices for thin film transisitor (TFT) by utilizing a spin-coating technique. α,ω-Bis(dimethyl-n-octylsilyl)sexithiophene can be deposited as active semiconducting layer in thin film transistors, either by vacuum evaporation or by spin-coating. A high charge-carrier mobility has been obtained for both deposition techniques, μ = 4.6 × 10⁻² and 1.4 × 10⁻² cm² V⁻¹ s⁻¹, respectively.     

Nano metrology of cylinder bore wear

Cylinder bores are multi-process surfaces whose roughness is difficult to characterise for tribological purposes by conventional methods. Statistical approaches may be used to compute asperity densities, summit curvatures and so on, but suffer from the usual disadvantage of tending to infinite values in the absence of a short-wavelength cutoff. A useful advance in tribological roughness assessment would be to find a means of establishing an appropriate scale of measurement. Using a form of the plasticity index corrected for anisotropy, a short-wavelength limit λ_p is derived below which asperities will not take part in long-term tribological interactions. A general relationship is obtained between three dimensionless numbers, the short-wavelength limit λ_p normalised by the topothesy Λ, the fractal dimension D and the material ratio (the ratio of the Hertzian elastic modulus E′ to the hardness H). From this relationship, presented as a carpet plot, the appropriate scale of roughness measurement for any tribological investigation of a fractal surface may be determined. With a stylus instrument and an atomic force microscope, a number of cylinder bores were measured at locations of both high and medium wear before and after running in. By inspection of an ensemble of structure functions, it is shown that cylinder bore surfaces are multifractal, with a transition point (the so-called “corner frequency”) at about 20 μn, corresponding to the average size of a honing grit. Below this length the surfaces are self-similar fractals down to the limits of AFM resolution. The short wavelength limit using the above formulation appears to be about 40 nm, weI1 below the range of instruments usually employed to measure tribological surface roughness.     

Experimental investigation of the effect of solidification processing parameters on the rod spacings in the Sn–1.2 wt.% Cu alloy

Sn–1.2 wt.% Cu alloy was prepared in a graphite crucible under the vacuum atmosphere. The samples were directionally solidified upwards under argon atmosphere with different temperature gradients (G = 2.69–8.88 K/mm) at a constant growth rate (V = 6.80 μm/s) and with different growth rates (V = 2.78–136.36 μm/s) at a constant temperature gradient (G = 2.69 K/mm) by using a Bridgman-type directional solidification apparatus. The microstructure of Sn–1.2 wt.% Cu alloy seems to be rod eutectic structure. The rod spacings (λ) were measured from both transverse and longitudinal sections of the samples. The influence of the growth rate (V) and temperature gradient (G) on the rod spacings (λ) and undercoolings (ΔT) was analysed. The values of λ²V, λ²G, ΔTλ, ΔTV^−0.5 and ΔTG^0.5 were determined by using the Jackson–Hunt eutectic theory. The results obtained in the present work have been compared with the similar experimental results obtained in the previous works for binary alloys.     

Fabrication and performance of La0.8Sr0.2MnO3/YSZ graded composite cathodes for SOFC

The performance of multi-layer (1 − x) La_0.8Sr_0.2MnO₃/x YSZ graded composite cathodes was studied as electrode materials for intermediate solid oxide fuel cells (SOFC). The thermal expansion coefficient, electrical conductivity, and electrochemical performance of multi-layer composite cathodes were investigated. The thermal expansion coefficient and electrical conductivity decreased with the increase in YSZ content. The (1 -x)La_0.8Sr_0.2MnO₃/x YSZ composite cathode greatly increased the length of the active triple phase boundary line (TPBL) among electrode, electrolyte, and gas phase, leading to a decrease in polarization resistance and an increase in polarization current density. The polarization current density of the triple-layer graded composite cathode (0.77 A/cm²) was the highest and that of the monolayer cathode (0.13 A/cm²) was the lowest. The polarization resistance (R_p) of the triple-layer graded composite cathode was only 0.182 ω·cm² and that of the monolayer composite cathode was 0.323 ω·cm². The power density of the triple-layer graded composite cathode was the highest and that of the monolayer composite cathode was the lowest. The triple-layer graded composite cathode had superior performance.     

Predicting the thermal stability of RE-based bulk metallic glasses

The Gibbs free energy of formation of amorphous alloy, ΔG^a has been calculated, for some typical bulk metallic glasses (BMGs). The strong negative linear relationship between crystallization temperature T_x and ΔG^a has been found, and hence ΔG^a can be used as an efficient parameter to evaluate and predict the thermal stability of rare earth (RE)-based BMGs, in a narrow composition region of the same alloy system. The origin of the strong linear relationship has also been discussed.     

Copper(I) coordination ability of the outer S-position isomer of EDT-DMT-TTF (D1): crystal structure of (D1)2Cu2Br4,2CH2Cl2; structural correlation with the (D1)2Cu2Br6 copper(II) salt

The (D1)₂Cu₂Br₄,2CH₂Cl₂ (1) and (D1)₂Cu₂Br₆ (2) radical cation salts, where D1 is the outer S-position isomer of ethylenedithiodimethylthiotetrathiafulvalene (EDT-DMT-TTF), have been synthesized and their X-ray crystal structures have been solved. The molecular structure of 1 is built up from (D1–Cu₂Br₄–D1) metal complexes. Each copper(I) atom is coordinated to a sulfur atom of the D1 disulfide bridge through a σ-type dative bond. Consequently, Cu₂Br₄ part is located between two organic molecules which are approximately plane and parallel to each other. In compound 2, (Cu₂Br₆)²⁻ anions, in which copper atoms are at the +2 oxidation state, also lie between two oxidized donors. In both resulting structures, the D1–Cu₂Br_x–D1 parts (x=4 for 1, x=6 for 2) are stacking in order to form columns containing dimerized (D1⁺)₂ units.     

Effects of Nd on the microstructure and magnetic properties of Ni-Zn ferrites

Ni_0.4Zn_0.6Fe_2−xNd_xO₄(x = 0-0.07) ferrites doped with different amounts of Nd₂O₃ were prepared using standard ceramic technique. The samples were uniaxially pressed and sintered at 1250°C for 4 h in air. The phase structure and microstructure of the samples were investigated using X-ray diffraction and scanning electron microscope, respectively. The complex permeability was measured using the impedance analyzer in the range of 1-100 MHz. The results indicate that with increasing Nd³⁺ content, the relative density and lattice parameter a of the sintered samples increase, whereas the real part of permeability (μ′) and the magnetic loss tangent (tan δ) decrease. The substitution of Nd³⁺ for Fe³⁺ forms a secondary phase on the grain boundary of the matrix, which strongly restrains the grain growth of the matrix.     

Separation of form from orientation in 3D measurements of aspheric surfaces with no datum

Measurement and characterisation of 3D form to maintain manufacturing quality has particular problems in cases such as lenses which do not generally have a clear measurement datum. A 3D-form measurement includes information about the form, the orientation and the position of the surface under test. Orientation and position can be design parameters or may result from misalignment of the test specimen on a measurement table. In either case, it is necessary to separate form from orientation and position if the data-set is to be fitted and compared with an “ideal” surface. In this paper two pre-processing algorithms are presented and examples given of the separation of form from orientation and position. The algorithm is applied to simulated data-sets consisting of up to 26,000 discrete points on a square grid, simulating the measurement of an aspheric lens in 3D. The rotationally symmetric data-set is translated for a distance x₀, y₀ and z₀ and rotated about two axes, x and y, to simulate misalignment. To simulate inaccuracies from a manufacturing process, normally distributed random noise is superimposed on the ideal surface. An application of pre-processing using a real data-set is also shown. Furthermore, form fitting is addressed and the interpretation of form by decomposition of the data into error types is discussed.     

EPR and photoluminescence studies on lithium-potassium borophosphate glasses doped with Mn ions

The mixed alkali borophosphate xLi₂O–(30 − x)K₂O–35B₂O₃–34.5P₂O₅ (5 ≤ x ≤ 25) glasses doped with 0.5 mol% of manganese ions have been studied using EPR and photoluminescence techniques. The EPR spectra of all the investigated samples exhibit resonance signals which are characteristic of Mn²⁺ ions. The resonance signal with effective g value at g = 2.02 exhibits a six line hyperfine structure. The zero-field splitting parameter (D) at room temperature has been evaluated from the intensities of allowed hyperfine lines. The EPR spectra at different temperatures (123–295 K) have also been studied. It is found that the spin concentration (N) exhibits non-linear behaviour with composition showing the mixed alkali effect (MAE). From the EPR data, the paramagnetic susceptibility (χ) has been calculated at various temperatures. The Curie constant (C) and paramagnetic Curie temperature (θ_p) have been evaluated from the 1/χ versus T graph. The photoluminescence (PL) spectrum exhibits a green emission band at 582 nm and this band has been assigned to a transition from the upper ⁴T_1g → ⁶A_1g ground state of Mn²⁺ ions.     

Kinetics and formation mechanism of amorphous Fe52Nb48 alloy powder fabricated by mechanical alloying

A single phase amorphous Fe₅₂Nb₄₈ alloy has been synthesized through a solid state interdiffusion of pure polycrystalline Fe and Nb powders at room temperature, using a high-energy ball-milling technique. The mechanisms of metallic glass formation and competing crystallization processes in the mechanically deformed composite powders have been investigated by means of X-ray diffraction, Mössbauer spectroscopy, differential thermal analysis, scanning electron microscopy and transmission electron microscopy. The numerous intimate layered composite particles of the diffusion couples that formed during the first and intermediate stages of milling time (0–56 ks), are intermixed to form amorphous phase(s) upon heating to about 625 K by so-called thermally assisted solid state amorphization, TASSA. The amorphization heat of formation for binary system via the TASSA, ΔH_a, was measured directly as a function of the milling time. Comparable with the TASSA, homogeneous amorphous alloys were fabricated directly without heating the composite multilayered particles upon milling these particles for longer milling time (86 ks–144 ks). The amorphization reaction here is attributed to the mechanical driven solid state amorphization. This single amorphous phase transforms into an order phase (μ phase) upon heating at 1088 K (crystallization temperature, T_x) with enthalpy change of crystallization, ΔH_x, of −8.3 kJ mol⁻¹.     

Electrical anisotropy of α-(BEDT-TTF)2KHg(SCN)4

The transverse magnetoresistance of α-(BEDT-TTF)₂KHg(SCN)₄ was investigated with the magnetic field rotated within a conducting ac-plane. It was found that the magnetic-field-orientation dependence of the magnetoresistance in the weak-field limit, ΔR(B,θ), has the form ΔR(B,θ) = B²(psin²(θ − θ_min) + qcos²(θ − θ_min), where θ is the angle betweeen a-axis and magnetic field direction and (p, q, θ_min) are temperature-dependent parameters. By examining the results based on the classical theory of magnetoresistance, it was concluded that the electrical anisotropy within be-plane is 3.5 4.5 and 2.5 3.0 above and below the phase transition at 10 K, respectively.     

Luminance materials containing carbazole and triphenylamine exhibiting high hole-transporting properties

Two novel 2-substitutd-8-hydroxyquinoline derivatives were designed and synthesized. Their luminance properties and carrier transporting abilities were studied when integrated in four different organic light-emitting device structures. The four devices are structured as following—device A: indium tin oxide glass substrate (ITO)/2-TNATA/NPB/(2-[2-(9-ethyl-9H-carbazol-2-yl)-vinyl]-quinolato zinc (1) and 2-[2-(4-diphenylamino-phenyl)-vinyl]-quinolato zinc (2))/Alq₃/LiF/aluminum (Al); device B: ITO/2-TNATA/NPB/1 or 2/LiF/Al; device C: ITO/2-TNATA/1 or 2/Alq₃/LiF/Al; device D: ITO/2-TNATA/1 or 2/Alq₃/LiF/Al. In the device A, the maximum brightness of compound 1 is 5857 cd m⁻² at 11 V with the luminance efficiency 1.84 cd A⁻¹. For 2 it is 6047 cd m⁻² at 10 V with an efficiency of 2.22 cd A⁻¹. In the device B, the maximum brightness of 1 is 745 cd m⁻² at 11 V and efficiency is 0.32 cd A⁻¹. These values are 1748 cd m⁻² at 10 V and 0.42 cd A⁻¹ for 2, respectively. In the device C, the maximum brightness of 1 and 2 are 8729 and 5838 cd m⁻² at 10 V, respectively, with an efficiency of 1.99 and 1.71 cd A⁻¹. In the device D, the maximum brightness and efficiency of 1 are 8512 cd m⁻² at 13 V and 3.10 cd A⁻¹, and they are 9818 cd m⁻² at 13 V and 0.42 cd A⁻¹, for 2. Our results also show that both 1 and 2 are good bipolar and bifunctional molecules with high hole-transporting and luminance properties.     

The preparation and thermodynamic properties of Fe(II)---Fe(III) hydroxide-carbonate (green rust 1); Pourbaix diagram of iron in carbonate-containing aqueous media

Carbonate-containing green rust 1, GR1(CO₃²⁻), is prepared by oxidation of Fe(OH)₂ in aqueous solution. Ferrous hydroxide is precipitated from NaOH and FeSO₄·7H₂O solutions and carbonate ions are added as a Na₂CO₃ solution. For sufficiently large concentrations of sodium carbonate, SO₄²⁻ ions do not play any role during the oxidation process and, at the end of the first stage of reaction, Fe(OH)₂ oxidizes into GR1(CO₃²⁻). In the second stage of reaction, GR1(CO₃²⁻) oxidizes into α-FeOOH goethite except when the transformation of ferrous hydroxide is partial, which leads to the formation of magnetite. From the X-ray diffraction analysis of GR1(CO₃²⁻), lattice parameters of its hexagonal cell are found to be a = 3.160 ± 0.005 Å and C = 22.45 ± 0.05 Å. From the Mössbauer analysis of the stoichiometric GR1(CO₃²⁻), which leads to a Fe²⁺:Fe³⁺ ratio of 2:1, the chemical formula is established to be: [Fe₄^(II)Fe₂^(III)(OH)₁₂][CO₃·2H₂O]. The 78 K Mössbauer spectrum of the compound can be fitted with three quadrupole doublets, two Fe²⁺ doublets d₁ and D₂ corresponding to isomer shifts (IS) of 1.27 and 1.28 mm s⁻¹ and quadrupole splittings (QS) of 2.93 and 2.67 mm s⁻¹, respectively, and one Fe³⁺ doublet D₃ with an IS of 0.47 mm s⁻¹ and QS of 0.43 mm s⁻¹. These three doublets were already used to fit the Mössbauer spectrum of chloride-containing GR1(Cl⁻) [see J.M.R. Génin et al., Mat. Sci. Forum8, 477 (1986) and J.M.R. Génin et al., Hyp. Int. 29, 1355 (1986)]and therefore are characteristic of GR1 compounds. From the recording of electrode potential E and the pH of the suspension versus time during the oxidation, the standard free enthalpy of formation of stoichiometric GR1(CO₃²⁻) is estimated to be ΔG °_f = − 966.250 cal mol⁻¹. Knowing the chemical formula and ΔG °_f of GR1(CO₃²⁻) the Pourbaix diagram of iron in carbonate-containing aqueous solutions is drawn.     

Some considerations on the polarization resistance method

A new mathematical approach aimed at giving light on the polarization resistance method is developed and its basic ideas are discussed to establish a suitable criterion to be used to compute the left bound ΔE₁ and the right bound ΔE₂ of the ΔE interval where the linear approximation works properly with reference to a prefixed degree of accuracy. Examination of the results relating to the theoretical cases, characterized by the Tafel slope values (40, 120) and (80, 100) mV, stresses that the width L() of the interval, where the linear approximation can be considered valid for a given value of , depends on B_a and B_c, their values determining the position of the inflection point ΔE_i of i(ΔE) where G(ΔE)=(αe^αΔE+βe^−βΔE)/(α+β)−1 exhibits a maximum. The maximum per cent value of the relative error μ, that is less than 10, for values ranging from 1 to 15 indicates that it is reasonable to replace i′(0) with the incremental ratio computed at ΔE₁ or ΔE₂. Furthermore, the Newton method was always successful in determining the values of ΔE₁ and ΔE₂. Applications to experimental polarization data refer to the behaviour of iron in 1 N H₂SO₄ solutions containing KCl at various concentrations. All the experimental polarization curves of the current transient type were best-fitted with a polynomial of the fourth degree over the [−50, 50] mV interval to determine the analytical expression of G(ΔE). The good agreement of the values of R_p, R_pa and R_pc, which are computed at ΔE₂ and ΔE₁ respectively for the case =10, underlines the validity of the present approach in providing accurate information on the resistance to corrosion of iron.