Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.

The Larger Grain and (111)-Orientation Planes of Poly-Ge Thin Film Grown on SiO₂Substrate by Al-Induced Crystallization

Al-induced crystallization yields the larger grain and (111)-orientation planes of poly-Ge thin film grown on SiO2 substrate, the (111)-orientation planes of poly-Ge thin film grown on SiO2 substrate are very important for the superior performance electronics and solar cells. We discussed the 50 nm thickness poly-Ge thin film grown on SiO2 substrate by Alinduced crystallization focusing on the lower annealing temperature and the diffusion control interlayer between Ge and Al thin film. The (111)-orientation planes ratio of poly-Ge thin film achieve as high as 90% by merging the lower annealing temperature (325℃) and the GeOx diffusion control interlayer. Moreover, we find the lack of defects on poly-Ge thin film surface and the larger average grains size of poly-Ge thin film over 12 μm were demonstrated by electron backscatter diffraction measurement. Our results turn on the feasibility of fabricating electronic and optical device with poly-Ge thin film grown on SiO2 substrate.

The space time CE/SE method for solving one-dimensional batch crystallization model with fines dissolution

This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution.In batch crystallization,dissolution of smaller unwanted nuclei below some critical size is of vital importance as it improves the quality of product.The crystal growth rates for both size-independent and size-dependent cases are considered.A delay in recycle pipe is also included in the model.The space–time conservation element and solution element method,originally derived for non-reacting flows,is used to solve the model.This scheme has already been applied to a range of PDEs,mainly in the area of fluid mechanics.The numerical results are compared with those obtained from the Koren scheme,showing that the proposed scheme is more efficient.

Problem and Improvement of Kissinger Method──New Method on Measuring Crystallization Activation Energy of Amorphous Alloy

By measuring and analyzing the crystallization activation energy (CAE) of Fe-based amorphous alloy Fe79B16Si5 and Fe78B13Si9, it is reconfirmed and further analyzed that the conventional Kissinger method does not conform with the premise of Kissinger equation, namely, samples with different heating rates should keep a constant fraction of transformation at the exothermal peak temperature Tp of DSC thermogram. The XRD equal first peak height (EFPH) method is applied to CAE measurement of Fe-based amorphous alloy for the first time. It is shown again that the EFPH method coincides with the premise of Kissinger equation. The procedure of EFPH method is introduced in detail in this paper. The accuracy in determining CAE of amorphous alloy may be improved by applying the EFPH method. As a result, the mechanism of embrittlement of amorphous alloy may be better elucidated.

Organic Melt Crystallization as a Method for Synthesis of Supramolecular Complexes

The most simple method for solventless synthesis of supramolecular complex of CMCR·2BPY·BZP, [CMCR = C-methylcalix[4]resorcinarene, BPY = 4,4'-bipyridine, BZP = benzophenone], is proposed. Although CMCR by itself is high melting point compound (above 300°C), CMCR was found to be dissolved in melt mixture of BPY and BZPeven below 120°C. In the mixture of the three components, the reaction occurs to form CMCR·2BPY·BZP supramolecular complex.

A Novel Method of Fabricating a Well-Faceted Large-Crystal Diamond Through MPCVD

A novel method was developed to deposit a large crystal diamond with good facets up to 1000 μm on a tungsten substrate using a microwave plasma enhanced chemical vapor deposition （MPCVD）. This method consists of two steps, namely single-crystal nucleation and growth. Prior to the fabrication of the well-faceted, large crystal diamond, an investigation was made into the nucleation and growth of the diamond which were affected by the O2 concentration and substrate temperature. Deposited diamond crystals were characterized by scanning electron microscopy and micro-Raman spectroscopy. The results showed that the conditions of single-crystal nucleation were appropriate when the ratio of H2/CH4/O2 was about 200/7.0/2.0, while the sub- strate temperature Ts of 1000℃ to 1050℃ was the appropriate range for single-crystal diamond growth. Under the optimum parameters, a well-faeeted large crystal diamond was obtained.

Texture evolution and inhomogeneous deformation of polycrystalline Cu based on crystal plasticity finite element method and particle swarm optimization algorithm

Texture evolution and inhomogeneous deformation of polycrystalline Cu during uniaxial compression are investigated at the grain scale by combining crystal plasticity finite element method(CPFEM) with particle swarm optimization(PSO) algorithm. The texture-based representative volume element(TBRVE) is used in the crystal plasticity finite element model, where a given number of crystallographic orientations are obtained by means of discretizing the orientation distribution function(ODF) based on electron backscattered diffraction(EBSD) experiment data. Three-dimensional grains with different morphologies are generated on the basis of Voronoi tessellation. The PSO algorithm plays a significant role in identifying the material parameters and saving computational time. The macroscopic stress–strain curve is predicted based on CPFEM, where the simulation results are in good agreement with the experimental ones. Therefore, CPFEM is a powerful candidate for capturing the texture evolution and clarifying the inhomogeneous plastic deformation of polycrystalline Cu. The simulation results indicate that the <110> fiber texture is generated finally with the progression of plastic deformation. The inhomogeneous distribution of rotation angles lays the foundation for the inhomogeneous deformation of polycrystalline Cu in terms of grain scale.

Study on Inclusions in Large Sapphire Optical Crystal Grown by SAPMAC Method

The sapphire （Al2O3） single crystal is a kind of excellent infrared transmission window materials. A large-sized sapphire （Ф225 mm×205 mm, 27.5 kg） was grown by SAPMAC method （sapphire growth technique with micro-pulling and shoulder-expanding at cooled center）. Several kinds of inclusion in the large sapphire crystal were investigated by means of an optical microscopy （OM）, scanning electron microscopy （SEM） and electron probe microanalysis （EPMA）. The experimental results show that most inclusions are consisted of solid metallic and non-metallic particles as well as gas pores caused by the impurity of alumina as the raw material, the thermal dissociation of aluminum oxide melt and the reaction of the melt to the crucible material （Mo） at high temperatures. It is also found that in different crystal regions the inclusions are of varied sizes, morphology and chemical compositions. Finally, the measures to reduce and eliminate the inclusions are proposed to improve the crystal quality.

Optimization of Polishing Parameters with Taguchi Method for LBO Crystal in CMP

Chemical mechanical polishing （CMP） was used to polish Lithium triborate （LiB3O5 or LBO） crystal. Taguchi method was applied for optimization of the polishing parameters. Material removal rate （MRR） and surface roughness are considered as criteria for the optimization. The polishing pressure, the abrasive concentration and the table velocity are important parameters which influence MRR and surface roughness in CMP of LBO crystal. Experiment results indicate that for MRR the polishing pressure is the most significant polishing parameter followed by table velocity; while for the surface roughness, the abrasive concentration is the most important one. For high MRR in CMP of LBO ctystal the optimal conditions are： pressure 620 g/cm^2, concentration 5.0 wt pct, and velocity 60 r/min, respectively. For the best surface roughness the optimal conditions are： pressure 416 g/cm^2, concentration 5.0 wt pct, and velocity 40 r/min, respectively. The contributions of individual parameters for MRR and surface roughness were obtained.

Adaptive split-step Fourier method for simulating ultrashort laser pulse propagation in photonic crystal fibres

In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.

Analysis of the special hollow-core photonic crystal fibre by finite element method

Two kinds of fabricated hollow-core photonic crystal fibres （HC-PCFs） arc studied using finite element method （FEM） because the structures of the fibres are special, Normalized transmission spectra and transverse intensity distribution of the modes are calculated and measured. And the dispersion characteristics of these two kinds of HC- PCFs were analysed from 400 nm to 800 nm. Simulated and measured results show that the special structure could affect the properties of HC-PCFs, By comparing the simulated values with the measured results, it can be clarified that FEM is feasible and accurate for analysing photonic crystal fibres whose structures are irregular and complex.

A novel method of rapidly modeling optical properties of actual photonic crystal fibres

The flexible structure of photonic crystal fibre not only offers novel optical properties but also brings some difficulties in keeping the fibre structure in the fabrication process which inevitably cause the optical properties of the resulting fibre to deviate from the designed properties. Therefore, a method of evaluating the optical properties of the actual fibre is necessary for the purpose of application. Up to now, the methods employed to measure the properties of the actual photonic crystal fibre often require long fibre samples or complex expensive equipments. To our knowledge, there are few studies of modeling an actual photonic crystal fibre and evaluating its properties rapidly. In this paper, a novel method, based on the combination model of digital image processing and the finite element method, is proposed to rapidly model the optical properties of the actual photonic crystal fibre. Two kinds of photonic crystal fibres made by Crystal Fiber A/S are modeled. It is confirmed from numerical results that the proposed method is simple, rapid and accurate for evaluating the optical properties of the actual photonic crystal fibre without requiring complex equipment.

Prediction of grain scale plasticity of NiTi shape memory alloy based on crystal plasticity finite element method

Grain scale plasticity of NiTi shape memory alloy(SMA)during uniaxial compression deformation at 400℃was investigated through two-dimensional crystal plasticity finite element simulation and corresponding analysis based on the obtained orientation data.Stress and strain distributions of the deformed NiTi SMA samples confirm that there exhibits a heterogeneous plastic deformation at grain scale.Statistically stored dislocation(SSD)density and geometrically necessary dislocation(GND)density were further used in order to illuminate the microstructure evolution during uniaxial compression.SSD is responsible for sustaining plastic deformation and it increases along with the increase of plastic strain.GND plays an important role in accommodating compatible deformation between individual grains and thus it is correlated with the misorientation between neighboring grains,namely,a high GND density corresponds to large misorientation between grains and a low GND density corresponds to small misorientation between grains.

Growth and characterization of superconducting Ca_(1-x)Na_(x)Fe_(2)As_(2) single crystals by NaAs-flux method

High-quality superconducting Ca_(1-x)Na_(x)Fe_(2)As_(2)single crystals have been successfully grown by the NaAs-flux method,with sodium doping level x=0.4–0.64.The typical sizes of these crystals are more than 10 mm in ab-plane and~0.1 mm along c-axis in thickness.X-ray diffraction,resistance and magnetization measurements are carried out to characterize the quality of these crystals.While no signature of magnetic phase transitions is detected in the normal state,bulk superconductivity is found for these samples,with a sharp transition at T_(c) ranging from 19.8 K(x=0.4)to 34.8 K(x=0.64).The doping dependences of the c-axis parameter and T_(c) are consistent with previous reports,suggesting a possible connection between the lattice parameters and superconductivity.

Numerical simulation and experimental verification of axial-directional crystallization purification process for high-purity gallium

A transient numerical model was applied to simulating the axial-directional crystallization purification(ADCP) process of gallium(Ga) raw material at different coolant temperatures(Tc), and the evolutions of melt/crystal(m/c) interface shape, temperature distribution and thermal stresses were simulated and analyzed. The results showed that the m/c interface shape, temperature distribution, and thermal stress in the Ga material were determined by the Tc in the crystallizer during the ADCP process. The temperature gradient and thermal stress in the grown Ga crystal increased with decreasing Tc. At Tc=15 ℃, the m/c interface shape was flat, and the temperature gradient was ideal. Therefore, the Ga materials with lower thermal stresses and suitable m/c interface shape, and an ideal efficiency of impurity removal were obtained. The purity of Ga reached 6 N standard by using ADCP process repeated 6 times at Tc of 15 ℃. The results of the simulation showed good agreement with the experimental results.

Synthesis of large diamond crystals containing high-nitrogen concentration at high pressure and high temperature using Ni-based solvent by temperature gradient method

This paper reprots that with Ni-based catalyst/solvent and with a dopant of NAN3, large green single crystal diamonds with perfect shape are successfully synthesized by temperature gradient method under high pressure and high temperature in a China-type cubic anvil high-pressure apparatus （SPD-6 × 1200）, and the highest nitrogen concentration reaches approximately 121-1257 ppm calculated by infrared absorption spectra. The synthesis conditions are about 5.5 CPa and 1240-1300 ℃. The growth behaviour of diamond with high-nitrogen concentration is investigated in detail. The results show that, with increasing the content of NaN3 added in synthesis system, the width of synthesis temperature region for growth high-quality diamonds becomes narrower, and the morphology of diamond crystal is changed from cube-octahedral to octahedral at same temperature and pressure, the crystal growth rate is slowed down, nevertheless, the nitrogen concentration doped in synthetic diamond increases.

Machine Learning to Instruct Single Crystal Growth by Flux Method

Growth of high-quality single crystals is of great significance for research of condensed matter physics. The exploration of suitable growing conditions for single crystals is expensive and time-consuming, especially for ternary compounds because of the lack of ternary phase diagram. Here we use machine learning(ML) trained on our experimental data to predict and instruct the growth. Four kinds of ML methods, including support vector machine(SVM), decision tree, random forest and gradient boosting decision tree, are adopted. The SVM method is relatively stable and works well, with an accuracy of 81% in predicting experimental results. By comparison,the accuracy of laboratory reaches 36%. The decision tree model is also used to reveal which features will take critical roles in growing processes.

Application of quartz crystal nanobalance in conjunction with a net analyte signal based method for simultaneous determination of leucine, isoleucine and valine

The aim of the present investigation was to develop a biosensor for the detection of amino acids, Leucine, Isoleucine and Valine based on a quartz crystal nanobalance. leucine (Leu), isoleucine (Ile), and valine (Val) were selectively determined by quartz crystal nanobalance (QCN) sensor in conjunction with net analyte signal (NAS)-based method called HLA/GO. An orthogonal design was applied for the formation of calibration and prediction sets including Leu, Ile and Val compounds. The selection of the optimal time range involved the calculation of the net analyte sig-nal regression plot in any considered time window for each test sample. The searching of a region with maximum linearity of NAS regression plot (minimum error indicator) and minimum of PRESS value was carried out by applying a moving window strategy. On the base of obtained results, the differences on the adsorption profiles in the time range between 1 and 300 s were used to determine mixtures of compounds by HLA/GO method. The results showed that the method was successfully applied for the determina-tion of Leu, Ile and Val.

Optical simulation of in-plane-switching blue phase liquid crystal display using the finite-difference time-domain method

The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.

Simulation of polycrystalline aluminum tensile test with crystal plasticity finite element method

The crystal plasticity was implemented in the finite element method(FEM) software ABAQUS through the user subroutine UMAT. By means of discretizing the space at the grain level with the Voronoi diagram method, a polycrystal model was built and used in the FEM analysis. The initial orientation of each grain was generated based on the orientation distribution function(ODF). The developed model was successfully applied in simulation of polycrystalline aluminium samples deformed by the tensile tests. The theoretical strain—stress relation was in good agreement with the experimental result. The simulation results show that the grain size has significant effect on the deformation behavior. The initial plastic deformation usually occurs at grain boundaries, and multiple slip often results in an enhanced local hardening at grain boundaries.