探寻等差数列前n项和公式的“自然”之路

中学数学绝大多数内容是人类在长期实践与反思中经过千锤百炼的数学精华和基础,其中数学概念、思想、方法的起源与发展过程都是自然的.每一种数学概念、思想与方法,从它的产生背景、形成过程及应用看,都是水到渠成、浑然天成的,不仅合情合理,而且很有人情味.[1]若在教学中,教师照本宣科,直接抛出数学概念、思想方法,就像魔术师"从帽子中突然掏出一个兔子"似的,这将不利于学生感受到数学的存在及领悟到数学的     

极端条件下6Li2O的热力学性能与电子结构

 采用密度泛函理论与准谐振德拜模型研究了面心立方相的⁶Li₂O在极端条件下的热力学性质与电子结构。结果表明: ⁶Li₂O的热膨胀系数在任何温度下都随压强增加明显降低,但仅当压强较低(低于40 GPa)时,温度对6Li2O的热膨胀系数的影响才明显;O原子半径随压强增大而迅速降低,而随温度的变化并不明显;在低压条件下(低于40 GPa),带隙随温度的升高缓慢降低;而在高压条件下(高于40 GPa),温度对带隙宽度的影响几乎可以忽略;无论在什么温度条件下,带隙宽度均随压强的增大而迅速增加。     

基于有限元法的激光等离子体诱导玻璃 损伤特性研究

研究了熔石英玻璃元件在纳秒激光等离子体冲击波作用下的表面和横截面损伤形貌,利用有限元法模拟了冲击波在熔石英玻璃内部的传播规律,并基于冲击波在玻璃内部的应力分布规律分析了损伤形成机理.研究发现:在冲击波作用下,石英玻璃会受到沿波面方向的压应力和沿波面切方向的拉应力,在这两种力的作用下,造成以激光辐照中心的弧状层状断裂和沿径向的断裂;冲击波的反射叠加还会使局部拉应力增大,造成靠近后表面的损伤.有限元法能够直观地分析等离子体冲击波对光学元件的作用,并分析光学元件在等离子体冲击波下的损伤机理.     

First-principles investigation on the structural and elastic properties of cubic-Fe,TiAl under high pressures

The structural, elastic, and thermodynamic properties of cubic-Fe2TiA1 under high temperatures and pressures are investigated by performing ab initio calculation and using the quasi-harmonic Debye model. Some ground state properties such as lattice constant, bulk modulus, pressure derivative of the bulk modulus, and elastic constants are in good agreement with the available experimental results and theoretical data. The thermodynamic properties of Fe2TiA1 such as thermal expansion coefficient, Debye temperature, and heat capacity in ranges of 0 K-1200 K and 0 GPa-250 GPa are also obtained. The calculation results indicate that the heat capacities at different pressures all increase with temperature increasing and are close to the Dulong-Petit limit at higher temperatures, Debye temperature decreases with temperature increasing, and increases with pressure rising. The cubic-FezTiA1 is stable mechanically under 250 GPa. Moreover, under lower pressure, thermal expansion coefficient rises rapidly with temperature increasing, and the increasing rate becomes slow at higher pressure.     

密度泛函理论研究高温高压下UO2弹性与热力学性能

采用第一性原理与准谐德拜模型研究UO2在高温高压条件下的弹性与热力学性能。UO2在高温高压下仍属离子型晶体,并且弹性性能计算表明,四角方向剪切常数在高温与高压下均保持稳定。高温下弹性常数C44没有明显变化,而高压下C44迅速增大。体积模量、剪切模量与杨氏模量均随压强增加而增大;高温条件下,体积模量、剪切模量与杨氏模量也未出现明显的降低,表明UO2在高温度高压下均可保持良好的力学性能。不同压强下,UO2定容热容均随温度迅速增大,并在1000 K 附近趋近于杜隆-佩蒂特极限。德拜温度则随温度降低,随压强升高。在低于室温条件下,热膨胀系数随温度急剧增加;温度继续增加,系数的增加趋势则逐渐变缓。计算结果还表明,UO2的热膨胀系数在相同条件下,远小于其他核材料。     

First-principles investigation on the structural and elastic properties of cubic-Fe_2 TiAl under high pressures

The structural, elastic, and thermodynamic properties of cubic-Fe 2 TiAl under high temperatures and pressures are investigated by performing ab initio calculation and using the quasi-harmonic Debye model. Some ground state properties such as lattice constant, bulk modulus, pressure derivative of the bulk modulus, and elastic constants are in good agreement with the available experimental results and theoretical data. The thermodynamic properties of Fe 2 TiAl such as thermal expansion coefficient, Debye temperature, and heat capacity in ranges of 0 K-1200 K and 0 GPa-250 GPa are also obtained. The calculation results indicate that the heat capacities at different pressures all increase with temperature increasing and are close to the Dulong-Petit limit at higher temperatures, Debye temperature decreases with temperature increasing, and increases with pressure rising. The cubic-Fe 2 TiAl is stable mechanically under 250 GPa. Moreover, under lower pressure, thermal expansion coefficient rises rapidly with temperature increasing, and the increasing rate becomes slow at higher pressure.     

He原子掺杂铝材料的第一性原理研究

采用基于第一性原理的平面波超软赝势方法,结合广义梯度近似(GGA),计算了铝及铝晶胞间隙位置掺入He原子后体系的几何结构、电子结构、总体能量和电荷布居值.计算结果表明:随着氦在金属铝中逐渐形成,铝晶胞体系会发生晶格畸变,但总的趋势是He在铝体系的八面体位置的晶格畸变小于其在四面体位置的晶格畸变.He在铝晶胞八面体和四面体间隙的杂质形成能分别为1.3367 eV和2.4411 eV.由此可知,He在铝晶胞中最稳定位置是八面体间隙位置.同时,文中还从原子尺度层面分析了He原子在铝晶胞中的占位及其键合性质,讨论 关键词： 铝材料 第一性原理 形成能     

ZrV2结构、弹性和热力学性质的第一性原理计算

采用基于密度泛函理论的第一性原理平面波赝势方法研究ZrV₂的晶体结构和弹性,利用准谐Debye模型计算在不同温度(T=0~1200 K)和不同压强(P=0~20 GPa)下ZrV₂的热力学性质,包括弹性模量与压强,热熔与温度,以及热膨胀系数与温度和压力的关系.结果表明:计算的ZrV₂晶格常数与实验值符合较好,晶体材料的弹性常数随着压力增加而增加;在一定温度下,相对体积、热熔随着压强的增加而减小,德拜温度、弹性模量随着压强的增加而增加,且高压下温度对ZrV₂热膨胀系数的影响小于压强的影响.