Onset of chaotic dynamics in a ball mill: Attractors merging and crisis induced intermittency

In mechanical treatment carried out by ball milling, powder particles are subjected to repeated high-energy mechanical loads which induce heavy plastic deformations together with fracturing and cold-welding events. Owing to the continuous defect accumulation and interface renewal, both structural and chemical transformations occur. The nature and the rate of such transformations have been shown to depend on variables, such as impact velocity and collision frequency that depend, in turn, on the whole dynamics of the system. The characterization of the ball dynamics under different impact conditions is then to be considered a necessary step in order to gain a satisfactory control of the experimental set up. In this paper we investigate the motion of a ball in a milling device. Since the ball motion is governed by impulsive forces acting during each collision, no analytical expression for the complete ball trajectory can be obtained. In addition, mechanical systems exhibiting impacts are strongly nonlinear due to sudden changes of velocities at the instant of impact. Many different types of periodic and chaotic impact motions exist indeed even for simple systems with external periodic excitation forces. We present results of the analysis on the ball trajectory, obtained from a suitable numerical model, under growing degree of impact elasticity. A route to high dimensional chaos is obtained. Crisis and attractors merging are also found. (c) 2002 American Institute of Physics.     

Magnetoresistivity and microstructure of YBa2Cu3Oy prepared using planetary ball milling

We have studied the microstructure and the magnetoresistivity of polycrystalline YBa₂Cu₃O_y (YBCO or Y-123 for brevity) embedded with nanoparticles of Y-deficient YBCO, generated by the planetary ball milling technique. Bulk samples were synthesized from a precursor YBCO powder, which was prepared from commercial high purity Y₂O₃, Ba₂CO₃ and CuO via a one-step annealing process in air at 950 °C. After planetary ball milling of the precursor, the powder was uniaxially pressed and subsequently annealed at 950 °C in air. Phase analysis by X-ray diffraction (XRD), granular structure examination by scanning electron microscopy (SEM), microstructure investigation by transmission electron microscopy (TEM) coupled with energy dispersive X-ray spectroscopy (EDXS) were carried out. TEM analyses show that nanoparticles of Y-deficient YBCO, generated by ball milling, are embedded in the superconducting matrix. Electrical resistance as a function of temperature, ρ(T), revealed that the zero resistance temperature, T_co, is 84.5 and 90 K for the milled and unmilled samples respectively. The milled ceramics exhibit a large magnetoresistance in weak magnetic fields at liquid nitrogen temperature. This attractive effect is of high significance as it makes these materials promising candidates for practical application in magnetic field sensor devices.     

The Principles of Developing the Ball Lightning Theory

Criteria for developing the ball lightning theory based on the results of observations are analyzed. It is assumed that the key features of ball lightning are a large energy (more than 10⁶ J) and long lifetime (more than 1 s). We exclude from consideration theories which do not explain these features and concentrate our attention on the analysis of three models where the large energy of the autonomous ball lightning and the forces providing the compression of the ball lightning substance are taken into account. The first considered model was developed by Geert Dijkhuis, in which the appearance of a force directed towards the system center is attributed to the Bose condensation of vortices of degenerated electrons as well as to gradient forces arising due to a nonuniform distribution of the electron density over the ball lightning volume. The second model proposed by Vladimir Bychkov assumed that the energy reservoir of ball lightning is polymer threads carrying a big electric charge. Our model assumes that the energy is stored in the form of kinetic energy of ions which the positively charged core of ball lightning is thought to consist of. The core is compressed by a dielectric shell which, in turn, is shrunk by the force created due to the nonuniform electric field of the core. The merits and limitations of these and other models are discussed.     

Removal of Congo red dye from aqueous solution with nickel-based metal-organic framework/graphene oxide composites prepared by ultrasonic wave-assisted ball milling

Metal-organic frameworks (MOFs) were successfully synthesized by ultrasonic wave-assisted ball milling. In the absence of organic solvent, the coupling effect of ultrasonic wave and mechanical force played an significant role in the synthesis of MOFs. Adsorption of Congo red (CR) was studied in view of adsorption kinetic, isotherm and thermodynamics. The adsorbent was carried out using X-ray diffraction (XRD), thermogravimetric analysis (TGA), N₂ adsorption-desorption isotherms, Raman spectroscopy and scanning electron microscope (SEM) methods. It was found that pseudo-second-order kinetic model and Freundlich adsorption isotherm matched well for the adsorption of CR onto nickel-based metal-organic framework/graphene oxide composites (Ni-MOF/GO). The results of the adsorption thermodynamics indicated that the adsorption process was a spontaneous and endothermic process. The adsorption capacity of graphene oxide/metal-organic frameworks (GO/MOFs) for CR reached 2489 mg/g, much higher than previous reports. It was demonstrated that an increase in the number of active metal sites can dramatically improve the adsorption capacity of dye. A suitable dry temperature is beneficial for the improvement of adsorption capacity for dye. In this paper, the adsorption results indicated that ultrasonic wave-assisted ball milling has a good prospect for synthesis of MOFs with excellent adsorption performance.     

Production of pyrite nanoparticles using high energy planetary ball milling for sonocatalytic degradation of sulfasalazine

Sonocatalytic performance of pyrite nanoparticles was evaluated by the degradation of sulfasalazine (SSZ). Pyrite nanoparticles were produced via a high energy mechanical ball milling (MBM) in different processing time from 2 h to 6 h, in the constant milling speed of 320 rpm. X-ray diffraction (XRD), scanning electron microscopy (SEM) coupled with energy dispersive X-ray (EDX), Fourier transform infrared spectroscopy (FT-IR) analysis and Brunauer–Emmett–Teller (BET) confirmed the production of pyrite nanoparticles during 6 h of ball milling with the average size distribution of 20–80 nm. The effects of various operational parameters including pH value, catalyst amount (mg/L), SSZ concentration (mg/L), ultrasonic frequency (kHz) and reaction time on the SSZ removal efficiency were examined. The obtained results showed that the maximum removal efficiency of 97.00% was obtained at pH value of 4, catalyst dosage of 0.5 g/L, SSZ concentration of 10 mg/L and reaction time of 30 min. Experimental results demonstrated that the kinetic of the degradation process can be demonstrated using Langmuir–Hinshelwood (L-H) kinetic model. The effect of different inorganic ions such as Cl⁻, CO₃²⁻ and SO₄²⁻ was investigated on the L-H reaction rate (k_r) and adsorption (K_s) constants. Results showed that the presence of the mentioned ions significantly influenced the L-H constants. The impact of ethanol as a OH radical scavenger and some enhancers including H₂O₂ and K₂S₂O₈ was investigated on the SSZ removal efficiency. Accordingly, the presence of ethanol suppressed SSZ degradation due to the quenching of OH radicals and the addition of K₂S₂O₈ and H₂O₂ increased the SSZ removal efficiency, due to the formation of SO₄⁻ and additional OH radicals, respectively. Under the identical conditions of operating parameters, pyrite nanoparticles maintained their catalytic activity during four consecutive runs.     

梯度折射率球透镜的制备及其光线轨迹测试

自麦克斯韦鱼眼透镜理论模型提出后,长期以来学术界一直以为它只是一种绝对光学仪器,在实践中并没有应用的可能。但通过对麦克斯韦鱼眼微球透镜的理论研究表明,在一定条件下,它具有良好的成像性能和耦合效率。根据菲克定律推导出梯度折射率球透镜的折射率分布函数。并且熔制了含Li+硅酸盐玻璃和采用槽沉法以及Na+/Li+离子交换法制备直径为0.3—3.0mm的梯度折射率球透镜。通过干涉法测得了梯度折射率球透镜的折射率分布曲线,并研究了光线通过梯度折射率球透镜的轨迹。研究结果表明:在590℃,离子扩散系数为3.07×10-6mm2/s;所制备的梯度折射率球透镜的折射率分布是抛物线分布,并且和理论分析相吻合;梯度折射率球透镜的光线轨迹满足椭圆方程。     

Preparation of magnesium ferrite nanoparticles by ultrasonic wave-assisted aqueous solution ball milling

Magnesium ferrite, MgFe₂O₄ nanoparticles with high saturation magnetization were successfully synthesized using ultrasonic wave-assisted ball milling. In this study, the raw materials were 4MgCO₃·Mg(OH)₂·5H₂O and Fe₂O₃ powders and the grinding media was stainless steel ball. The average particle diameter of the product MgFe₂O₄ powders was 20 nm and the saturation magnetization of them reached 54.8 emu/g. The different results of aqueous solution ball milling with and without ultrasonic wave revealed that it was the coupling effect of ultrasonic wave and mechanical force that played an important role during the synthesis of MgFe₂O₄. In addition, the effect of the frequency of the ultrasonic wave on the ball milling process was investigated.     

钡铁氧体前驱体高能球磨过程的红外拟合光谱分析

高能球磨法是材料制备过程中常用的方法,通过物料在高速运转的过程中进行磨合而产生晶体空位缺陷,实现元素的掺杂,进而发生化学吸附或化学反应,合成产生新的物相,对于后续合成材料的性能有很大影响。钡铁氧体具有良好的磁性能,被用于功能材料制备的诸多领域。采用高能球磨法制备钡铁氧体前驱体,利用XRD,SEM和FTIR检测方法考察不同高能球磨时间下钡铁氧体前驱体物相、微观形貌及官能团的变化规律,并通过红外二阶导数光谱、拟合平滑光谱计算法,定量分析高能球磨过程中物相的变化规律。XRD及SEM检测结果表明,随球磨时间增加,钡铁氧体前驱体各物相的衍射峰宽度变宽,粉末细化,晶格逐渐发生畸变,产生晶体空位缺陷,从而使Ba溶入Fe₂O₃晶格中生成Ba_xFe_2-xO₃的固溶体,且产生吸附“团聚”现象;当球磨时间大于40 h时,发生“纳米尺寸效应”,生成有磁性的Fe₃O₄及Ba_xFe_3-xO₄固溶体。红外光谱分析结果显示,随着球磨时间的增加,BaCO₃和α-Fe₂O₃的特征峰均存在峰强减小、峰位发生明显移动的规律,表明随着球磨时间增加,BaCO₃和α-Fe₂O₃颗粒粒度变小,且发生化学吸附。通过红外光谱的平滑拟合光谱和二阶导数光谱计算可知,随球磨时间的增加,各吸收峰面积均明显减小。相对于球磨0 h,在球磨10,20和40 h后,波数473 cm-1的Fe—O键振动吸收峰的峰面积分别减少48.84%,65.97%和93.54%;而在波数540 cm-1处的Fe—O键吸收峰的峰面积则分别减少37.11%,51.76%和82.85%;同理,在波数856 cm-1处的O—C—O键的面内弯曲振动吸收峰的峰面积分别减少30.62%,44.71%和67.10%;在波数1 446 cm-1处的C—O键不对称伸缩振动峰的峰面积则分别减少0.03%,27.63%和57.90%。从定量分析的角度考察了钡铁氧体前驱体高能球磨过程中物相的变化规律并精准确定反应产物含量变化的百分比,对于后续材料的合成与性能随钡铁氧体前驱体物相不同而发生变化的研究有重要的指导意义。     

Heterogeneous sono-Fenton-like process using martite nanocatalyst prepared by high energy planetary ball milling for treatment of a textile dye

High energy planetary ball milling was applied to prepare sono-Fenton nanocatalyst from natural martite (NM). The NM samples were milled for 2–6 h at the speed of 320 rpm for production of various ball milled martite (BMM) samples. The catalytic performance of the BMMs was greater than the NM for treatment of Acid Blue 92 (AB92) in heterogeneous sono-Fenton-like process. The NM and the BMM samples were characterized by XRD, FT-IR, SEM, EDX and BET analyses. The particle size distribution of the 6 h-milled martite (BMM₃) was in the range of 10–90 nm, which had the highest surface area compared to the other samples. Then, the impact of main operational parameters was investigated on the process. Complete removal of the dye was obtained at the desired conditions including initial pH 7, 2.5 g/L BMM₃ dosage, 10 mg/L AB92 concentration, and 150 W ultrasonic power after 30 min of treatment. The treatment process followed pseudo-first order kinetic. Environmentally-friendly modification of the NM, low leached iron amount and repeated application at milder pH were the significant benefits of the BMM₃. The GC–MS was successfully used to identify the generated intermediates. Eventually, an artificial neural network (ANN) was applied to predict the AB92 removal efficiency based upon the experimental data with a proper correlation coefficient (R² = 0.9836).     

Surface coating of Al nanoparticles by using a wet ball milling method: A facile synthesis and characterization of colloidal stability

A facile surface coating of aluminum (Al) nanoparticles with various dispersants by using a wet ball milling method is reported. Various mixtures of Al nanoparticles (d = 30–130 nm) and dispersants in solvent were ball milled. The excellent surface coating was observed with coating thickness ranging from 10 to 13 nm. The resulting good colloidal stability confirmed by both visual inspection of colloidal precipitation and Turbiscan backscattering was attributed to a stable dispersant organic layer formed on Al nanoparticle surfaces after ball milling as observed in HRTEM images. This method can be extended to the synthesis of a variety of any other metallic nano-colloidal solutions.     

Short-range order of quasicrystals after ball milling

Thermodynamically stable icosahedral Al₆₅Cu₂₀Fe₁₅ alloy is studied using⁵⁷Fe Mössbauer experiments. Its quasicrystalline structure is subjected to a low energy process of mechanical grinding up to 800 hours. The influence of ball milling on the electric field gradient magnitudes is discussed using an analysis of the Mössbauer spectra to different fitting models. The presence of an amorphous phase which co-exists with the quasicrystalline one is revealed in the early stage of mechanical grinding.     

Synthesis and characterization of magnetite-maghemite nanoparticles obtained by the high-energy ball milling method

We present the process of synthesis and characterization of magnetite-maghemite nanoparticles by the ball milling method. The particles were synthesized in a planetary ball mill equipped with vials and balls of tempered steel, employing dry and wet conditions. For dry milling, we employed microstructured analytical-grade hematite (α-Fe₂O₃), while for wet milling, we mixed hematite and deionized water. Milling products were characterized by X-ray diffraction, transmission electron microscopy, room temperature Mössbauer spectroscopy, vibrating sample magnetometry, and atomic absorption spectroscopy. The Mössbauer spectrum of the dry milling product was well fitted with two sextets of hematite, while the spectrum of the wet milling product was well fitted with three sextets of spinel phase. X-ray measurements confirmed the phases identified by Mössbauer spectroscopy in both milling conditions and a reduction in the crystallinity of the dry milling product. TEM measurements showed that the products of dry milling for 100 h and wet milling for 24 h consist of aggregates of nanoparticles distributed in size, with mean particle size of 10 and 15 nm, respectively. Magnetization measurements of the wet milling product showed little coercivity and a saturation magnetization around 69 emu g^?1, characteristic of a nano-spinel system. Atomic absorption measurements showed that the chromium contamination in the wet milling product is approximately two orders of magnitude greater than that found in the dry milling product for 24 h, indicating that the material of the milling bodies, liberated more widely in wet conditions, plays an important role in the conversion hematite-spinel phase.     

Characterization of nanocrystalline FeSiCr powders prepared by ball milling

FeSi₁₀Cr₁₀ powder was mechanically alloyed by high energy planetary ball milling, starting from elemental powders. The microstructural and magnetic properties of the milled powders were characterized by scanning electron microscopy, X-ray diffraction, ⁵⁷Fe Mössbauer spectrometry and a vibratory sample magnetometer.After 3 h of milling, the formation of two bcc solid solutions α-Fe₁ (Si, Cr) and α-Fe₂ (Si, Cr) is observed. Their grain sizes decrease with increase in milling time attaining, at 15 h of milling, 23 and 11 nm, respectively. Mössbauer spectra of the milled powder show the presence of two components. One is a ferromagnetic type with a broad sextuplet. Its distribution of hyperfine field is characterized by high and low hyperfine field’s peaks and a mean value of 26.5 T. The other is a single paramagnetic peak. Its low concentration increases to ∼4% at 15 h of milling. These results can be explained by different atomic environments affected by Si or/and Cr elements, as well as the increased disordered grain boundaries.Magnetic measurements of the milled FeSi₁₀Cr₁₀ alloy powder exhibit a soft ferromagnetic character with a decrease of both magnetization at saturation (Ms) and coercive force (Hc) with milling time attaining values of Ms=151 emu/g and Hc=2500 A/m at 30 h of milling time.     

Microstructural evolution characterization of Fe–Nb–B ternary systems processed by ball milling

Fe–Nb–B alloys prepared by ball milling can undergo a complex microstructural evolution during milling. In order to overcome the limitations imposed by traditional X-ray bulk analysis, a comprehensive multi-technique approach was devised to systematically characterize samples with the required resolution. A combination of in situ FIB (focused ion beam) lift-out and high-resolution ATEM (analytical transmission electron microscopy) has allowed the characterization of the phase evolution during milling. In particular, boron inclusions, not detected by X-ray diffraction, have been found to remain undissolved in the Fe matrix.     

Iron nanoparticles produced by high-energy ball milling

In this investigation, the chemical and structural characteristics of Fe nanoparticles synthesized by high-energy ball milling have been explored. After the milling process the nanoparticles were collected using a magnetic field. The structure, morphology and composition of the powders were obtained using high-resolution electron microscopy. HREM images confirmed the nanoparticles’ presence with approximately 2–4 nm in size. It was found that using this method allowed the formation of nanoparticles in a smaller size range than other synthesis methods. Also, it was confirmed by HREM images that the obtained nanoparticles were mainly of the fcc nature and some of them of the MTP type.     

Anisotropy models in precise crystallite size determination of mechanically alloyed powders

Nanocrystalline AA 4032 alloy powder was synthesized by high-energy ball milling from elemental powders for 30 h duration. XRD and TEM results reveal that the powder is cubic and nanocrystalline in nature. X-ray peak broadening analysis was used to evaluate the lattice strain and the crystallite size using the Williamson-Hall analysis with three different models viz., uniform deformation, uniform deformation stress and uniform deformation energy density. The root mean square (RMS) strain was calculated from the interplanar spacing and the strain estimated from the three models. The three models yield different strain values due to the anisotropic nature of the material. The energy density model is proposed to be the best fit model among the three as severe lattice strain is associated with ball milled powders.     

Structural,thermal and optical study of nanocrystalline silicon produced by ball milling

The ball milling process was used to obtain nanocrystalline cubic silicon. Between 5 and 10 h of milling, amorphous silicon was also formed. The differential scanning calorimetry (DSC) spectrum of a powder milled for 10 h showed that the amorphous–crystalline phase transition occurs at about 450 °C. According to Raman spectroscopy and X‐ray diffraction results, volume fractions of the crystalline, interfacial and amorphous phases were about 30, 39 and 31%, respectively. Copyright © 2010 John Wiley & Sons, Ltd.     

Hyperchaotic qualities of the ball motion in a ball milling device

Ball collisions in milling devices are governed by complex dynamics ruled by impredictable impulsive forces. In this paper, nonlinear dynamics techniques are employed to analyze the time series describing the trajectory of a milling ball in an empty container obtained from a numerical model. The attractor underlying the system dynamics was reconstructed by the time delay method. In order to characterize the system dynamics the calculation of the spectrum of Lyapunov exponents was performed. Six Lyapunov exponents, divided into two terns with opposite sign, were obtained. The detection of the positive tern demonstrates the occurrence of the hyperchaotic qualities of the ball motion. A fractal Lyapunov dimension, equal to 5.62, was also obtained confirming the strange features of the attractor. (c) 1999 American Institute of Physics.     

Characterization of nanostructured ceramics prepared by both high energy ball milling and fast firing sintering processes

High-energy ball milling technique was successfully applied to calcinated lead zirconate titanate (PZT 60/40) powders. After 20?h of ball milling, large PZT particles were completely broken down, reducing its initial size in three orders of magnitude. Experimental results show a huge sinterability enhancement of the PZT powders by using this technique, achieving its maximum sintering rate at ～800°C. Relatively low densities (～91%) were achieved in stoichiometric samples, while in 3% lead excess samples sintered at 950°C for 30, 45, 60, 90 and 120?min using a fast firing process and a post-annealing treatment at 800°C for 4 h, densities of ～97% of the theoretical were achieved. PZT nanostructured ceramics prepared under optimized processing conditions (60?h of powder milling, 950°C of sintering temperature, 60?min of sintering time and a post-annealing process at 800°C during 4?h) show high dielectric constant (ε′) values (900) and low dielectric loss (tan?δ) at room temperature and a ferroelectric-paraelectric transition temperature at 375°C.     

Structural phase transitions during high-energy ball milling of BaTiO3

Microstructural characterization of ball milled perovskite BaTiO₃ powders has been done by the modeling of X-ray diffraction profiles. The study reveals that on size reduction, BaTiO₃ powders undergo a continuous, displacive, and diffusionless dynamic phase transitions involving tetragonal (T), monoclinic (M), and orthorhombic (O) symmetry via the second-order type [T?→?(T?+?M)?→?(M?+?O)?→?O] when stimulated by a high-power pulse of pressure in a planetary mill. The order parameter, a phenomenological quantity to describe the general behavior of a system going through phase transitions has been estimated using spontaneous strain calculated from lattice parameters or physical distortions derived from atomic coordinates or both. At room temperature, BaTiO₃ nanoparticle achieved an orthorhombic phase when a critical size (<15?nm) has been reached at later stage of milling (≥70?h). Raman's study reveals similar structural phase transitions sequence on size reduction and TEM study reveals the corresponding particle diameter.