The structure of fractal-like agglomerates (physically-bonded) and aggregates (chemically- or sinter-bonded) is important in aerosol synthesis of nanoparticles, and in monitoring combustion emissions and atmospheric particles. It influences also particle mobility, scattering, and eventually performance of nanocomposites, suspensions and devices made with such particles. Here, aggregate sintering by viscous flow of amorphous materials (silica, polymers) and grain boundary diffusion of crystalline ceramics (titania, alumina) or metals (Ni, Fe, Ag etc.) is investigated. A scaling law is found between average aggregate projected area and equivalent number of constituent primary particles during sintering: from fractal-like agglomerates to aggregates and eventually compact particles (e.g. spheres). This is essentially a relation independent of time, material properties and sintering mechanisms. It is used to estimate the equivalent primary particle diameter and number in aggregates. The evolution of aggregate morphology or structure is quantified by the effective fractal dimension (Df ) and mass-mobility exponent (Dfm ) and the corresponding prefactors. The Dfm increases monotonically during sintering converging to 3 for a compact particle. Therefore Dfm and its prefactor could be used to gauge the degree or extent of sintering of agglomerates made by a known collision mechanism. This analysis is exemplified by comparison to experiments of silver nanoparticle aggregates sintered at different temperatures in an electric tube furnace.

中文翻译：

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烧结的聚集体形态演变：初级粒子的数量和直径

分形状附聚物（物理结合）和聚集体（化学或烧结结合）的结构在纳米颗粒的气溶胶合成以及监测燃烧排放和大气颗粒中很重要。它还会影响粒子的迁移率、散射以及最终的性能，纳米复合材料、悬浮液和由此类粒子制成的装置。在这里，研究了由非晶材料（二氧化硅、聚合物）的粘性流动和结晶陶瓷（二氧化钛、氧化铝）或金属（Ni、Fe、Ag 等）的晶界扩散引起的聚集体烧结。在烧结过程中，平均聚集体投影面积与组成初级粒子的等效数量之间存在比例法则：从分形状附聚物到聚集体并最终压实颗粒（例如球体）。这本质上是一种独立于时间的关系，材料特性和烧结机制。它用于估计聚集体中的等效初级粒径和数量。聚集体形态或结构的演变通过有效分形维数 (Df ) 和质量迁移指数 (Dfm ) 以及相应的前因数进行量化。Dfm 在烧结过程中单调增加，对于致密颗粒收敛到 3。因此，Dfm 及其前因数可用于测量由已知碰撞机制制成的团块的烧结程度或程度。该分析通过与在管式电炉中在不同温度下烧结的银纳米颗粒聚集体的实验进行比较来举例说明。聚集体形态或结构的演变通过有效分形维数 (Df) 和质量迁移率指数 (Dfm) 以及相应的前因数进行量化。Dfm 在烧结过程中单调增加，对于致密颗粒收敛到 3。因此，Dfm 及其前因数可用于测量由已知碰撞机制制成的团块的烧结程度或程度。该分析通过与在管式电炉中在不同温度下烧结的银纳米颗粒聚集体的实验进行比较来举例说明。聚集体形态或结构的演变通过有效分形维数 (Df) 和质量迁移指数 (Dfm) 以及相应的前因数进行量化。Dfm 在烧结过程中单调增加，对于致密颗粒收敛到 3。因此，Dfm 及其前因数可用于测量由已知碰撞机制制成的团块的烧结程度或程度。该分析通过与在管式电炉中在不同温度下烧结的银纳米颗粒聚集体的实验进行比较来举例说明。因此，Dfm 及其前因数可用于测量由已知碰撞机制制成的团块的烧结程度或程度。该分析通过与在管式电炉中在不同温度下烧结的银纳米颗粒聚集体的实验进行比较来举例说明。因此，Dfm 及其前因数可用于衡量由已知碰撞机制制成的团块的烧结程度或程度。该分析通过与在管式电炉中在不同温度下烧结的银纳米颗粒聚集体的实验进行比较来举例说明。