【作者】 李贵发；

【导师】 韩绍昌； 彭平；

【作者基本信息】 湖南大学 ， 材料学， 2009， 博士

【摘要】 液态金属快速凝固过程的分子动力学（MD）模拟与跟踪分析发现:部分液态金属团簇结构具有遗传与选择遗传特性,但目前对其遗传与演变的电子机制却缺乏清楚认识。在教育部科技重点项目“液态金属快速凝固过程中团簇结构遗传与选择遗传的电子机制”（编号:104139）的资助下,本文选取Al_n团簇作为研究对象,采用第一原理计算结合过渡态搜索方法,对Al_n团簇结构稳定性及其结构演变、团簇生长合成与分裂特性等进行了比较系统的研究,以期初步回答:为什么有些液态金属团簇在快凝过程中能够遗传,而其它团簇却会发生转变。为此,本文开展了下面的工作:1.采用CASTEP程序,计算了Al_n（n=2²4, 55）团簇几何、能态与电子结构,通过结合能Eb、HOMO-LUMO能隙ΔEH-L与能量二阶差分Δ2E（n）表征和考察了团簇原子数n对Al_n团簇基态结构稳定性的影响。结果表明:Al_n团簇结构稳定性随n增加而增大,并在n=7, 11, 13, 19, 23等近幻数和高对称性结构处出现极值,相对其临近Al_n团簇,具有较高的结构稳定性。2.基于Al_n⁺团簇分离方式主要以离解出中性或带电单Al_原子为主的实验结果,采用线性同步转变（LST）和二次同步转变（QST）方法,考察了Al_n⁺ （n=2¹3）团簇在“双相分裂”模式下的不同分裂过程,并通过分裂吸收热ΔHR-P和分裂激活能ΔER-T的计算,在能态结构上分析了Al_n⁺（n=2¹3）团簇的分裂路径及其机理。结果表明:Al_n⁺ （n=2¹3）团簇以分裂出电中性或带电Al_原子模式中吸热和所需分裂激活能最少,而分裂成原子数相差较小的两个较大团簇所需裂解能量最多,因此,Al_n⁺团簇主要以Al_n⁺→Al_<sup>+Al_n-1⁺或Al_n⁺→Al_<sup>+⁺ Al_n-1路经裂解。3.采用CASTEP程序中的LST方法,考察了Al_n （n=3⁷, 13, 19）团簇不同结构形态间的演化与转变。结果表明:Al₃, Al₄, Al₅ , Al₆, Al₇, Al₁3, Al₁9团簇的稳定结构形态分别为三角形、菱形、梯形、八面体、十面体、二十面体、双二十面体,Al₃, Al₄, Al₅, Al₇与Al₁3团簇不存在亚稳结构,Al₆与Al₁9团簇存在亚稳结构,其结构形态分别为平行四边形与八面体。Al₆团簇亚稳结构与稳定结构的能级差大、转变能垒低,结构转变容易,亚稳结构稳定性差;而Al₁9团簇亚稳结构与稳定结构的能级差小、转变能垒高,结构演化不易,因而实验和理论模拟中可观察到其亚稳结构形态—正八面体的存在。4.采用DMol³程序中的LST和QST方法,考察了基态Al_n（n=2¹3）团簇在Al_n ⁺Al_m→Al_n⁺m“双合模式”下的生长合成特性。结果表明:在反应物上添加一个原子形成新团簇的生长模式一般为自动完成的放热反应,而通过团簇与团簇间彼此连接而形成新团簇的部分合并模式则需要克服能垒。比较其反应热ΔHR-P与生成激活能ΔER-T时发现:形成Al_n团簇时合并模式比生长模式有利,并且,在这些合并模式中,相对于具有非晶或准晶结构单元特征（五次对称轴或十次对称轴）的团簇Al_n（n=7, 10¹3）,具有晶体结构单元特征的团簇Al_n（n=2⁶, 8⁹）更容易形成,也比较容易从与非晶或准晶特征原子结构组态的合并中得到,而从晶体类团簇则很难合成非晶或准晶性团簇。5.基于CI-NEB理论发展的MEP方法,采用DMol3程序的线性同步转变与二次同步转变LST/QST方法,通过对生成物的结构微调设定反应物,发展完善了一种新的过渡态搜索方法,并成功预测了Al₁2C团簇一种比较稳定的结构形态。6.基于CI-NEB理论发展的MEP方法,结合DMol3程序LST/QST方法,计算并分析了不同结构形态Al₁3团簇在Al₆⁺Al₇→Al₁3下的形成过程。结果显示:团簇合成存在两个阶段:初始变形阶段与随后的结构演变阶段。在初始变形阶段,反应物中的亚稳组态会先转变成稳定结构（如C5v-Al₆→Oh-Al₆）。在结构演变阶段,对于具有晶体结构单元特征的团簇合成,若具有非晶结构单元特性的团簇参与合成时,则反应存在结构演变能垒,而参与合成的团簇都是晶体型结构时,则反应是一自动放热过程。对于含有五次对称元素的非晶团簇合成,在反应物中若存在具有非晶结构单元特征的Al₇团簇时,演变过程无能垒或能垒很小。由上可见:具有五次对称轴或十次对称轴的十面体D5h-Al₇和二十面体Ih-Al₁3在过冷液态金属非晶组态与晶态核间形核竞争中具有关键性的作用。D5h-Al₇和Ih-Al₁3因幻数特性呈现出高结构稳定性,且不存在亚稳结构,因此具有一定的遗传特性。结构上与非晶和准晶类似的液态金属,其原子结构组态因比较容易在冷却放热过程中合并成具有晶体结构特征的原子团,所以通常情况下液态凝固会结晶。非晶或准晶的形成则只有在快速凝固等非平衡凝固条件下、当液态金属中大量存在的二十面体原子团及其组合结构被冻结和遗传到了固体结构中才有可能。更多还原

【Abstract】 The heredity and selective heredity of configurations in some liquid metals or alloys during rapidly solidified processes have been found by molecular dynamics （MD） simulation, but the electronic machanism of the heredity and evolution of configurations has not been understood yet up to now. Supported by Foundation of Ministry of Science and Technology of China （104939）, the stability and evolution of Al_n clusters were investigated by frist-principle calculation with the aid of transition state searching method so as to make clear why some liquid metal clusters have structural heredity, whereas the others will be transformed. The work is divided into four parts: the stability of Al_n clusters, configuration evolution, decomposition and synthesis of Al_n±m clusters.1. The energetics and electronic structure of neutral Al_n （n=2²3, 55） clusters were calculated by CASTEP program. Several parameters such as the binding energy Eb, the HOMO-LUMO energy gapΔEH-L and the second difference of energiesΔ2E（n） were utilized to characterize and analyze the structure stability of Al_n cluster. The results show the structure stability of Al_n clusters increases with total atom number n addition. For Al₇, Al₁1, Al₁3, Al₁9, Al₂3 clusters with a nearly filled covalence electron shell and a high geometrical symmetry, a higher structure stability than that of their neighbor Al_n （n≠7, 11, 13, 19） clusters can be seen.2. Based on the experiments of Al_n+m+ clusters decomposed by means of a isolated Al atom or cation, the disassociation route and mechanism of Al_n+m+ （n+m≤13） clusters in the Al_n ++Al_m （n=1¹2, m=1¹2） mode were investigated by using Linear Synchronous Transit （LST） and Quadratic Synchronous Transit （QST） method. The ionization potential, the endothermic reaction heatΔHR-P and the dissociation barrier energyΔER-T of Al_n+m+ （n+m≤13） clusters were calculated. Comparison ofΔHR-P andΔER-T in the disassociation route reveals the least energy of a isolated Al atom or cation from the Al_n+m+ clusters is related to a biggerΔHR-P and a moreΔER-T must be provided, while a big cluster decomposites into two small clusters. The energetics difference between routes should be responsible for the preference of Al_n+ （n=2¹3） clusters dissociated by means of Al_n+→Al₊ Al_n-1+ or Al_n+→Al₊+ Al_n-1.3. The configuration evolution and transformation of Al_n （n=3⁷, 13, 19） clusters were examined by LST method in CASTEP program. It is demonstrated that the stable configurations of Al₃, Al₄, Al₅, Al₆, Al₇, Al₁3, Al₁9 clusters are triangle, rhombus, trapezia, octahedron, decahedron, icosahedron and double icosahedron, respectively. For Al₆ and Al₁9 clusters there are metastable structures of parallelogram and octahedron, respectively, whereas in the Al₃, Al₄, Al₅, Al₇ and Al₁3 clusters, no metastable configuration is validated. There exist a large energy gap and a low energy barrier between the octahedron and the parallelogram of Al₆ clusters, so the transformation from its metastable to stable structures is rather easy. By contrast, a small energy gap and a high energy barrier between the stable and metastable structures of Al₁9 clusters mean its configuration evolution from the octahedron to the double icosahedron hardly, therefore the metastable octahedron configuration of Al₁9 clusters can be extensively detected in experiments and simulations.4. The formation routes of stable Al_n （n=2¹3） clusters assembled by two small clusters were investigated in the framework of LST/QST method in DMol3 program. The results show the addition of one sole atom to a cluster, i.e., the growth process, is generally automatic exothermic reaction, except for the growth of non-crystal configurations on the basis of crystal clusters. For the association of one cluster with another, i.e., the coalescence process, usually, there exists reaction energy barrierΔER-T. Comparison of the reaction heatsΔHR-P and activation energyΔER-T suggests that the coalescence processes are more favorable than the growth processes for Al_n （n=2¹3） clusters. In the coalescence processes, the clusters with typical crystal symmetrical elements, i.e., the crystal clusters Al_n （n=2⁶, 8⁹）, have higher formation ability than those with fivefold or tenfold symmetrical axes, i.e., the non-crystal clusters Al_n （n=7, 10¹3）. The formation with non-crystal Al₇ cluster as a precursor, i.e., Al_m+Al₇→Al_m+7, is the most preferable in energetics for non-crystal clusters among the coalescence routes considered.5. By slightly displacing the atom position of product to set up the reactant, a new transition state searching method of LST/QST is improved in the molecular orbital DMol3 program, with the aid of the minimum energy path （MEP） in the climbing image nudged elastic band （CI-NEB） method. The energetics and electronic structures of several Al₁2C configurations as well as their configuration evolution were investigated. A new low symmetrical isomer of Al₁₂C clusters with high stability, i.e., Cs-Al₁₂C, at the energy valley in the MEPs has been successfully predicted. 6.Using LST/QST method in a molecular orbital DMol3 program based on density functional theory, with the aid of the MEP in the CI-NEB method, the preference of synthesis modes and routes of three characteristic Al₁3 clusters in the mode of Al₆+Al₇→Al₁₃ were calculated and analyzed. The results show the synthesis process may be divided into two steps: the distortion stage and the configuration evolution stage. In the first stage, the metastable clusters, e.g., C5v-Al₆, are forced to transform into stable structure. In the configuration evolution stage, two different cases exist. For the synthesis of crystal clusters it is an automatic exothermic reaction if all reactants being of typical crystal symmetrical elements, while an energy barrier must be overcomed if one of reactants having fivefold or tenfold symmetrical axes. For the formation of non-crystal clusters with fivefold symmetrical axes, generally it is an automatic exothermic process or an exothermic synthesis reaction with low energy barrier when synthesis reactants include non-crystal clusters such as D5h-Al₇ clusters.In conclusion, the Al₇ decahedron and the Al₁3 icosahedron with fivefold or tenfold symmetrical axes play a key role for the competition of the formation and evolution of non-crystal configurations in a supercooling liquid against the nucleation and growth of crystals. D5h-Al₇ and Ih-Al₁3 with magic number character have high stability and no isomer, so these clusters have heredity to some extent. Owing to liquid metals or alloys similar to amorphous structures being composed of small non-crystal configurations, the preference of the nucleation and growth of crystals during exothermic solidification process can be attributed to the high association and synthesis ability of crystal clusters on the basis of these small non-crystal configurations such as D5h-Al₇ and Ih-Al₁₃ clusters. A potential evolution among non-crystal clusters from a small D5h-Al₇ cluster to medium Al₁0^Al₁₃ clusters even to larger Al₁₉ and Al₅₅ clusters as well as their defective structures should be responsible for the formation of the glassy state. Therefore the non-crystal or qusicrystal solids can’t be obtained unless the icosahedron clusters in liquid are freezed and passed down to solid structures during non-equilibrium conditions.更多还原