Thermodynamics of Densification: I, Sintering of Simple Particle Arrays, Equilibrium Configurations, Pore Stability, and Shrinkage

Equilibrium configurations for linear and closed arrays (rings and regular polyhedra containing a single pore) of identical particles (cylinders or spheres) were determined by minimizing the array's surface and grain-boundary energies with the assumption that each particle conserves its mass. The change in free energy between the initial and equilibrium configuration increases with dihedral angle (i.e., the equilibrium angle). More significantly, it is shown that pores will shrink to an equilibrium size if the number ( n ) of coordinating particles is greater than a critical value. The critical pore coordination number ( n _c) increases with the dihedral angle. Only pores with n n _c are thermodynamically unstable during sintering. It is also shown that any mass-transport mechanism can lead to pore shrinkage while a connecting path to the pore surface remains open. The effective sintering "stress" (i.e., driving force) increases with the dihedral angle and decreases to zero as the equilibrium configuration is reached. Sintering stresses increase with decreasing coordination number. It is also shown that the shrinkage strain for closed arrays increases with the pore coordination number. Rearrangement phenomena within a powder compact are discussed with regard to resultant sintering forces on nonsymmetrically coordinated particles.     

Densification of Large Pores: II, Driving Potentials and Kinetics

A kinetic analysis of densification is presented for the case of isolated, identical pores separated by dense, polyerystal-line material where the grain size is a variable (smaller to larger, relative to the pore size). The analysis includes the influence of both grain growth and mass transport rates on the driving potential for mass transport to the pore. For the expected condition where the rate of grain growth is much greater than the rate of pore shrinkage, it is shown that the driving potential is relatively independent of pore surface curvature, and approaches (2γ_s/ R _po) sin (ψ_e/2) during grain growth, where γ_s is the surface energy per unit area of the material, ψ_e is the dihedral angle, and R _po is the initial pore radius. Using this driving potential, an expression is derived for the current densification rate. The proposed mechanism for mass transport is radial diffusion through a spherical polycrystalline unit cell containing a spherical pore, where diffusion is restricted to grain boundaries that intersect the pore. The expression includes the average separation distance between pores and the grain boundary area intersecting each pore. This expression is in qualitative agreement for data reported in Part I for a Zr(3Y)O₂ material where the grain size is always smaller than the pore size, and a Zr(8Y)O₂ material where the grain size is larger than the pore size.     

Useful Extensions of the statistical theory of sintering

The statistical theory of sintering is modified to account for the new concept of pore coordination number (after Lange) as well as other refinements of the original assumptions (after Kuczynski). When pores are located in the grain boundaries, the theory postulates that for a given dihedral angle, a critical pore coordination number, n_crmc, exists such that when n < n_c, pores shrink, whereas when n > n_c pores grow. A general morphological kinetic equation is developed for uniform microstructures with pores located at the grain boundaries. This equation provides for contributions of grain boundary and volume diffusion to densification and is unrestricted with respect to the type of firing schedule imposed. Using this modified model, one may evaluate the significant parameter x, a measure of ‘the path of microstructural evolution’. For reasonably uniform compacts, the equation also provides a quantitative estimate of the relative width of the pore size distribution, y, during the later stages of sintering.     

固相烧结—Ⅰ气孔显微结构模型及其热力学稳定性,致密化方程

讨论了二维及三维闭口气孔的稳定性，发现二维状态时气孔的稳定性问题可以用数学方法根据气孔的颗粒配位数和二面角的大小解析；而三维状态时气孔则可借助球形气孔模型近似地确定。在这一模型的基础上，建立了烧结中期和后期的气孔显微结构模型，并由此推导了因相烧结中，后期作用于气孔的烧结应力和固相烧结中斯和后期的致密化方程。     

Morphology and Stability of the Glass Phase in Glass Ceramic Systems

An explanation is given for the apparent stability of a minor phase in a two-phase system, such as a glass in a glass ceramic, even though normally the glass would be expected to dissolve completely into the crystalline phase. It is shown that the glass would be stable only if it is segregated to the triple-junction nodes and only if the dihedral angle is <π/3. The size and morphology of the glass pocket are obtained in terms of the interface energies, the undercooling below the solidus temperature, and the dihedral angle.     

Pore–Boundary Separation Behavior during Sintering of Pure and Bi2O3-Doped ZnO Ceramics

Pore–boundary separation in ZnO and 99.95ZnO·0.05Bi₂O₃ (in mol%) specimens during sintering at 1200°C was investigated. In pure ZnO specimens, pores were attached to the grain boundaries and disappeared during the final stage of sintering. In the Bi₂O₃-doped specimens, on the other hand, many pores were separated from the boundaries and trapped inside the grains. Observation using transmission electron microscopy showed that a thin layer of Bi₂O₃-rich phase existed at the boundaries in the Bi₂O₃-doped specimens. The pore separation in 99.95ZnO·0.05Bi₂O₃ specimens was explained in terms of the dihedral angle change and the high mobility of a liquid film boundary.     

Unstable Spreading of a Fluid Inclusion in a Grrain Boundary under Normal Stress

A fluid inclusion trapped in a stress-free grain boundary will assume an equilibrium lenslike shape. The dihedral angle at apex will be determined by the ratio of the (isotropic) solid-solid and solid-liquid interface energies. The radius of curvature of the lens surface will depend on the volume of the inclusion. If a normal stress is now applied across the interface, then the mechanical energy (equal to the sum of the external work and (he strain energy) and the interface energy will together determine the shape of the inclusion. In this paper it is shown that the inclusion can spread catastrophically if the applied stress is greater than a critical value. The magnitude of the critical stress depends on the equilibrium dihedral angle and the volume of the inclusion. A smaller angle and a larger volume lead to a smaller value of the critical stress. As an example a fluid inclusion which is ∼1 μm in size and forms a dihedral angle of 15° is unstable under an applied stress of 100 MPa. The results have slgniflciincc in the phenomenon of liquid-phase-enlianccd sintering and diffuslonal creep.     

固相烧结——Ⅲ 实验：超细氧化锆素坯烧结过程中的 晶粒与气孔生长及致密化行为

研究了超细Y-TZP和YSZ粉料成型体在烧结中期的晶粒生长、气孔生长和致密化行为.根据作者前文     

半经验分子轨道法优化枞酸结构

运用分子轨道理论中的半经验MINDO／3,MNDO与PM3量子化学计算方法分别对松香中的枞酸分子进行几何结构优化,结果表明,3种方法预测枞酸菲环骨架内的键长、键角、两面角结果与文献值基本一致,而菲环外羧基及异丙基的键长、键角和两面角计算值与文献值有较大偏差,这是由于枞酸分子之间氢键作用以及异丙基热运动比较强烈影响的缘故。在不考虑羧基及异丙基相关的键长、键角和两面角之后,发现PM3方法计算的键长、键角与两面角的结果与文献值比较吻合,计算值与文献值的相关系数R^2分别为0．96432、0．91989和0．99912,而MINDO／3和MNDO的计算值与文献值偏差稍为大些。     

Thermodynamics of densification of powder compact

This paper established a necessary condition for the sintering of powder compacts by examining the total free energy balance in terms of the particle size, neck size and contact number. The thermodynamic analysis of the proposed model clarifies the relation of shrinkage (q) of powder compact-contact angle ()-relative density at a given dihedral angle (_e) of a grain boundary. Faster densification proceeds in the region with a larger coordination number (n) of particles at a small q value. A large shrinkage is needed to eliminate the large pores formed in the structure of small n value. Full density can be achieved in the range of 117° < _e < _c, where _c is the critical dihedral angle allowing the shrinkage required for full densification. The derived concepts are effective to interpret the densification of hierarchical particle clusters. The relative density of ceria powder compact approached nonlinearly unity with decreasing ratio of pore size (r(P)) to grain size (r) and this tendency was well expressed by the present densification model. The influence of grain growth on the densification of powder compact and size of large pore isolated in a dense matrix are also quantitatively discussed.     

Effects of Cr2O3 additions on the sintering and mechanical properties of Al2O3

The effect of Cr₂O₃ additions on the penetration of the intergranular phase between alumina grains of 96 wt % alumina ceramics has been investigated by applying the principles of quantitative metallography. From microsections, values of the true dihedral angle have been measured. Cr₂O₃ additions increased the dihedral angle and decreased the density of alumina ceramics. As a result, distinct deterioration of the mechanical properties of alumina ceramics was observed.     

Creep-Sintering and Microstructure Development of Heterogeneous MgO Compacts

Simultaneous creep and densification and the microstructure development of magnesium oxide powder compacts were studied at 125°C and for applied stresses of up to 0.25 MPa. Die-pressing the powder into compacts with a relative green density of ∼0.40 led to an approximately bimodal distribution of pores, with one fraction having sizes of the order of 10 times the (initial) particle size and the other fraction having pore sizes of the order of the particle size. The presence of the large pores in turn gave rise to rather unusual sintering effects. After first decreasing with relative density (ρ), the densification rate (dρ/dt) and the creep rate (dɛ/dt) then increased dramatically for 0.6 < ρ < 0.75. This range of ρ corresponded to the stage of microstructure development when grain growth and coalescence of the smaller pores have created a more uniform pore distribution. Above ρ∼ 0.75, both dρ/dt and dɛ/dt again decreased with ρ. These trends in the densification behavior are discussed in terms of material parameters such as the equilibrium dihedral angle and the pore coordination number.     

半晶态聚乙烯变形机理的分子动力学模拟

采用相间蒙特卡罗方法,建立半晶态聚乙烯模型。在温度350 K,x、y方向压力为0.1 MPa下进行拉伸,探究聚乙烯的拉伸机理和拉伸过程中微观结构的变化。在拉伸过程中,在弹性变形阶段,键长随着应变的增加而增加,键角和二面角也有少量的增加,且键长率先增长。过了屈服极限后,键长、键角和二面角不再增加,有一定量的减小,然后逐渐趋于稳定。变形区域主要发生在非晶区,拉伸时,分子链会发生取向,随着拉伸的进行,分子链发生滑移,最后会出现空穴现象。     

The formation of smooth spalls in steel during the interaction of glancing detonation waves

A study is made of the formation of smooth spalls in steel specimens when their surfaces are blasted by explosive charges via a glancing detonation wave. When a steel specimen is blasted with an explosive, behind the front of glancing shock waves of compression two glancing shock waves of rarefaction, propagating toward each other, form, the interaction of which produces in the steel a smooth spall in the form of a dihedral angle. It is shown that a variation of the composition of the explosive (TNT, plastic explosive, TG 50/50 alloy) of a given thickness changes the distance from the vertex of the dihedral angle to the surface at which the charge was placed.VNIIÉF, Arzamas-16 607200. Translated from Fizika Goreniya i Vzryva, Vol. 30, No. 4, pp. 138–140, July–August, 1994.     

孔隙特性参数对排驱过程影响的实验研究

两相宏观排驱特性是由微观孔隙尺度排驱特性决定的,而微观孔隙尺度多孔介质又处处不均匀、各向不均匀。为了研究孔隙尺度孔隙结构特征对驱替特性的影响,采用了独特设计的微多孔实验段,固定骨架圆柱间距离而变动驱替流体可流通方向,在此基础上研究了孔隙结构特征对驱替特性的影响。对于孔隙特性的表征采取了孔隙方向、关键比率（最大孔隙尺度与最小孔喉尺度比值）、迂曲度和孔隙率四个参数。结果表明：同流量时,微多孔结构的孔隙角越大、迂曲度越小,则对应的非浸润相（十二烷和十六烷）的饱和度（驱替效率）越高;对于不同流量,所有的微多孔结构都按照流量越大,则非浸润相（十二烷和十六烷）饱和度越高的规律变化;关键比率和孔隙率影响必须结合孔隙结构来判断;孔隙角、流量相同时,两相黏度接近的驱替效率更高。     

Effect of Heat Treatments on the Wetting Behavior of Bismuth-Rich Intergranular Phases in ZnO:Bi:Co Varistors

The effect of annealing on the wetting behavior of Bi-rich intergranular phases in ZnO:Bi:Co varistors was studied. The intergranular phase exhibits temperature-dependent grain-boundary wetting, with an average equilibrium dihedral angle of 0° at 1140°C and over 55° at 610°C. The temperature-dependent wetting may be related to the temperature dependence of the ZnO concentration in the Bi₂O₃ liquid phase. The effect of the intergranular phase distribation on the electrical properties of ZnO varistors is discussed.     

Restrained Molecular Dynamics Procedure for Protein Tertiary Structure Determination from NMR Data: A Lac Repressor Headpiece Structure Based on Information on J-coupling and from Presence and Absence of NOE's

In recent years a procedure has been developed by which the three-dimensional (3D) structure of biomolecules can be derived from 2D NMR data. This procedure combines model building with restrained energy minimization (EM) and molecular dynamics (MD) techniques. Distance information from NOE's is incorporated in the form of an upper limit distance restraining term that is added to the interatomic potential function. Here, two improvements of the refinement procedure are introduced. First, the information that is contained in empty parts of 2D-NOE spectra is transformed into, so-called, non-NOE's which are modelled by adding a lower limit distance restraining term to the potential function for each non-NOE proton pair. Secondly, the information that is contained in the occurrence of large J-coupling constants for specific dihedrals is modelled by adding a sinusoidal dihedral angle restraining term to the potential function for each dihedral angle with a large J-value. The improved refinement procedure is tested by application of the lac repressor headpiece. Both the inclusion of non-NOE data and the inclusion of J-coupling information markedly improve the result of the restrained MD refinement of headpiece. In the refinement procedure MD simulation is used for searching configuration space. Energy barriers which are too high to be crossed by MD are surmounted by manually changing the model structures on a picture system. The resulting close non-bonded contacts are relaxed by EM. The final structure of headpiece satisfies essentially all 169 NOE and 9529 non-NOE distance constraints as well as the 6C_α – C_β dihedral angle values corresponding to the measured J-coupling values.     

ASTRO‐FOLD 2.0: An enhanced framework for protein structure prediction

The three‐dimensional (3‐D) structure prediction of proteins, given their amino acid sequence, is addressed using the first principles–based approach ASTRO‐FOLD 2.0. The key features presented are: (1) Secondary structure prediction using a novel optimization‐based consensus approach, (2) β‐sheet topology prediction using mixed‐integer linear optimization (MILP), (3) Residue‐to‐residue contact prediction using a high‐resolution distance‐dependent force field and MILP formulation, (4) Tight dihedral angle and distance bound generation for loop residues using dihedral angle clustering and non‐linear optimization (NLP), (5) 3‐D structure prediction using deterministic global optimization, stochastic conformational space annealing, and the full‐atomistic ECEPP/3 potential, (6) Near‐native structure selection using a traveling salesman problem‐based clustering approach, ICON, and (7) Improved bound generation using chemical shifts of subsets of heavy atoms, generated by SPARTA and CS23D. Computational results of ASTRO‐FOLD 2.0 on 47 blind targets of the recently concluded CASP9 experiment are presented. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

溶胀辊轧法PVDF膜表面的疏水强化：溶胀剂的影响

提出了一种简便、低成本的聚偏氟乙烯（PVDF）微孔膜表面疏水增强方法——溶胀辊轧法,以微结构辊筒对表面喷涂溶胀剂的PVDF成品微孔膜辊轧后,采用浸没凝胶法成膜。以N-甲基吡咯烷酮/水（非溶剂）为溶胀体系,采用扫描电子显微镜（SEM）、原子力显微镜（AFM）、水接触角（WCA）、最大孔径、平均孔径、N₂通量、耐磨性、液体穿透压（LEP）等表征手段,系统地研究了溶胀剂体系、溶胀剂容量对PVDF微孔膜结构与性能的影响。结果表明：辊轧膜表面呈现微米-亚微米层次特征,溶胀辊轧操作起到了疏水增强、透过能力提升的效果。溶胀剂中水（非溶剂）质量分数为6%、喷涂密度为0.03mL/cm²时,膜性能最优。连续运行30h的真空膜蒸馏（VMD）对比实验表明,辊轧膜较未辊轧膜具有更高的产水通量、脱盐率及更好的耐污染性能。该方法为低成本、连续化进行成品膜表面疏水强化提供了一种新选择。     

Effects of Chemical Inhomogeneities on Grain Growth and Microstructure in Al2O3

Effects of chemical inhomogeneities and single-crystal seeds on normal and discontinuous grain growth were investigated in both undoped and MgO-doped Al₂O₃. The chemical impurities in the samples were exsolved at a lower temperature than the sintering temperature and measured by SEM/EDS to determine the correlation between the distribution of impurities and the microstructure in Al₂O₃. A feature of this study was the use of clean-room processing and firing procedures to maintain sample composition at the levels initially present in the starting powders. As the local concentrations of chemical impurities (i.e., Si, Ca) increased, the grain boundary–grain boundary dihedral angle distribution widened, with many angles at 180°, the grain-size distribution widened, and pore–boundary separation was enhanced. Discontinuous grain growth was observed in regions of undoped Al₂O₃ containing the largest Ca and Si concentrations. It is suggested that doping with MgO solute reduces the effects of impurities on grain growth by increasing the bulk solubility and decreasing interfacial segregation of impurities, especially Si, and by narrowing the distribution of grain boundary–grain boundary dihedral angles.