摘要
金属玻璃具有长程无序短程有序的特殊结构,研究其结构特征对于金属玻璃成分和性能的设计具有重大意义。在前期,我们课题组提出了团簇加连接原子结构模型,从局域团簇角度描述金属玻璃的结构,把任何结构分成团簇和连接原子两部分,对于理想金属玻璃,可表示成团簇式[团簇](连接原子)1,3,团簇来自于相应晶化相中的主团簇,进而通过引入电子共振效应,提出团簇共振模型,指出单位团簇式包含固定数目的电子数,构成理想金属玻璃的基本结构单元。本论文在此基础上,拓展了团簇加连接原子模型的结构内涵和应用范围,提出团簇共振修正模型,构建了块体二元体系和典型三元体系中块体金属玻璃的理想团簇式,解析了二元金属玻璃形成体系的共晶点成分规律,从而解释了共晶点集中出现于少数简单成分比例的现象,即‘'Stockdale/Hume-Rothery eutectic puzzle"。具体的工作内容涵盖如下四个方面：
1)针对团簇模型中的主团簇选择判据不够清晰和团簇式电子数非整数的问题,完善了主团簇的选择判据,提出团簇共振修正模型,指出单位团簇式包含整数的24个电子数。在本课题组的前期工作中,提出针对理想金属玻璃的团簇共振模型,单位团簇式包含恒定的接近于e/u=23.6的电子数,团簇来自相关晶化相中的具有近程有序结构代表性的主团簇。在本论文中,我们首先完善了主团簇的选择判据,在国外提出的团簇密堆几何判据基础上,获得了更加严格的适用于多组元团簇的团簇密堆准则,结合团簇在晶化相结构中的排布结构,提出了主团簇是具有最大空间孤立度(团簇共享后有效原子个数)且原子密堆(与理想密堆的接近程度)的团簇。我们进而修正了以前团簇共振模型中的团簇近邻关系,获得了理想金属玻璃的原子密度pa计算方法,最终得到团簇共振修正模型,给出理想金属玻璃的单位团簇式的价电子数e/u为固定且整数的24个。
2)将上述团簇加连接原子衍生出的团簇共振修正模型具体运用于二元块体金属玻璃的成分规律解析上,确定了所有已知二元块体金属玻璃的理想团簇式,包括Cu-(Zr,Hf), Ni-(Nb, Ta), Al-Ca和Pd-Si,并提出来成分解析的具体构建过程,即主团簇的选择和具有24电子数的理想团簇式[团簇](连接原子)1,3的构建。这些块体金属玻璃的团簇式为：[Cu8Zr5]Cu≈Cu64.3Zr35.7(e/u=23.7)、[Zr7Cu10]Zr≈Cu55.6Zr44.4(23.4)、[Zr7Cu8]Zr=Cu50Zr50(24.2)、[Cu8Hf5]Cu≈Cu64.3Hf35.7(23.7)、[Ni7Nb6]Ni3=Nb37.5Ni62.5(23.5)、[Ni-Ni6Ta6]Ni3=Ni62.5Ta37.5(23.1),[Ta-Ni6Ta6]Ni3=Ni56.25Ta43.75(23.8)、[Ca9Al6]Ca3≈Ca66.7Al33.3(23.8)和[Pd11Si3]Pd3≈Pd82.4Si17.6(24.0),其中括号内为实际电子数,与理论的24电子十分接近。
3)构建了三元理想金属玻璃团簇式,完美解释了实验成分统计规律。三元理想金属玻璃根据团簇式特征分为两类,第一类是基于二元基础体系团簇式的第三组元替换,多数三元金属玻璃属于这个类型,如Ca-Mg-(Cu, Zn), Cu-(Al,Ti)-Zr, La-Al-(Cu,Ni), Mg-Cu-Y, Ni-Nb-Zr, Pd-Cu-Si和Pd-Ni-P;第二类是主团簇直接来自三元晶化相,如Zr-Al-Co和Zr-Al-Ni。24电子规则同样在此得到证实。利用含有不同原子个数的团簇式,完美解释了经过统计大量实验成分得到的七个最稳定三元块体金属玻璃成分,分别为含有16个原子的A44B38C18≈A7B6C3、A44B43C13≈A7B7C2和A56B32C12≈A9B5C2;18个原子的A55B28C17≈A10B5C3;20个原子的A65B25C10=A13B5C2、A70B20C10=A14B4C2和A65B20C15=A13B4C3。
4)利用团簇式分析了二元金属玻璃形成体系中的共晶点成分特征,定量解释了Stockdale/Hume-Rothery共晶困惑。首先我们假设共晶体由两种稳定液态结构以等比例构成,我们证实,二元共晶点均可用源自两个共晶相中的主团簇式等比例混合解释,即两个主团簇分别匹配以1或者3个连接原子,共晶团簇式因此可以理解为两个主团簇加上2个、4个或6个连接原子,与之相关联的块体金属玻璃成分对应于其中一个24电子理想团簇式,主团簇与共晶相成分差越大,对应团簇式的玻璃形成能力越强。这些特点在二元块体玻璃形成体系Cu-(Hf,Zr)、Ni-(Nb,Ta)、Al-Ca和Pd-Si中得到证实。进而,我们把合金元素根据原子半径分为微小、小、中、大和超大的五组,金属玻璃和共晶体系均源自不同组的原子组合,而两组原子的平均半径比决定了密堆团簇的种类,这样就出现了少数密堆团簇以及相关联的共晶成分式,从而定量解释了Stockdale/Hume-Rothery共晶困惑,即共晶点成分集中出现在简单成分比例如8/1、5/1、3/1、2/1和3/2附近。
Metallic glasses are characterized by long-range disorders and short-range orders. Understanding their structures is of great significance to their composition and property design. In earlier works, our group proposed a cluster-plus-glue-atom model which described the structures of metallic glasses in terms of a local atomic cluster part and a glue atom part. Ideal metallic glasses can always be expressed by cluster formulas [cluster](glue atoms)1,3, where the cluster is the principal cluster in a relevant devitrification phase. After introducing the electronic resonance effect, this model was transformed into a cluster-resonance model that led to a constant number of valence electrons per unit cluster formula for all ideal metallic glasses, regardless of their chemical compositions. In this work, the contents and applications of the cluster-plus-glue-atom model are expanded and the issued cluster-resonance model is revised. The ideal cluster formulas of metallic glasses in bulk binary and typical ternary metallic glass forming systems are built using the revised model. The eutectic composition rule in binary glass forming systems is specially focused to answer "Stockdale/Hume-Rothery eutectic puzzle". Our contributions are summarized into the following four aspects:
1) To clarify the selection criteria for the principal clusters in the cluster-based models and to answer the doubt on non-integer constant of the electron number per unit cluster formula,the cluster criteria are first refined and the cluster-resonance model is revised. A unit cluster formula is shown to possess a constant24electrons, to amend the original cluster-resonance model that indicates a constant electron number being close to e/u=23.6. The principal cluster definition is further refined to better represent the short-range order structure in the relevant crystalline phase. A multi-component cluster close-packing criterion is established on the basis of cluster dense packing. The principal clusters have the largest cluster isolation (largest effective cluster size) and high atomic packing efficiencies (closeness to ideal dense packing). The calculation of atomic density pa in the model is then revised that leads to a revised cluster-resonance model. The universal cluster formulas for ideal metallic glasses are shown to possess a constant total electron number e/u=24.
2) The revised cluster-resonance model, issued from the cluster-plus-glue-atom model, is used to explain the glass-forming compositions of binary bulk metallic glasses, including Cu-(Zr,Hf), Ni-(Nb,Ta), Al-Ca and Pd-Si. The selection of the principal clusters and the establishment of24-electron cluster formulas [cluster](glue atoms)1,3are formalized. The ideal cluster formulas of all the known binary bulk metallic glasses are then:[Cu8Zr5]Cu≈Cu64.3Zr35.7(e/u=23.7),[Zr7Cu10]Zr≈Cu55.6Zr44.4(23.4),[Zr7Cu8]Zr=Cu50Zr50(24.2),[Cu8Hf5]Cu≈Cu64.3Hf35.7(23.7),[Ni7Nb6]Ni3=Nb37.5Ni62.5(23.5),[Ni-Ni6Ta6]Ni3=Ni62.5Ta37.5(23.1),[Ta-Ni6Ta6]Ni3=Ni56.25Ta43.75(23.8),[Ca9Al6]Ca3≈Ca66.7Al33.3(23.8) and [Pd11Si3]Pd3≈Pd82.4Si17.6(24.0), where the electron numbers of the real cluster formulas in the brakets are close to24.
3) The ideal cluster formulas of ternary metallic glasses are established, and the statistical results of experimental compositions are fully explained. Two kinds of ternary ideal cluster formulas are presented. In the first, ideal ternary cluster formulas are obtained by substitutions in binary cluster formulas by the third component, as in systems Ca-Mg-(Cu, Zn), Cu-(Al, Ti)-Zr, La-Al-(Cu, Ni), Mg-Cu-Y, Ni-Nb-Zr, Pd-Cu-Si and Pd-Ni-P. In the second, the principal clusters of ideal ternary cluster formulas are derived from ternary crystalline phases, as in Zr-Al-Co and Zr-Al-Ni systems. The24-electron rule is confirmed in these systems. The seven most stable ternary glass-forming compositions from the statistical experimental results are fully explained by cluster formulas with different total atoms, A44B38C18≈A7B6C3, A44B43C13≈A7B7C2and A56B32C12≈A9B5C2using16-atom formulas, A55B28C17≈A10B5C3using18, A65B25C10=A13B5C2, A70B20C10=A14B4C2and A65B20C15=A13B4C3using20.
4) Eutectic composition rules in binary systems are analysed by cluster formulas, and Stockdale/Hume-Rothery puzzle is quantitatively explained. It is assumed that a eutectic consists of two kinds of stable liquids in equal proportion. A binary eutectic is explained by the equal-proportion mixing of two principal cluster formulas where each principal cluster is matched with one or three glue atoms. A eutectic cluster formula is then composed of two principal clusters plus two, four or six glue atoms. The24-electron cluster formulas are correlated to glass formation:the principal cluster far away from the eutectic point has a high glass forming ability. This rule is verified in Cu-(Hf,Zr), Ni-(Nb,Ta), Al-Ca and Pd-Si systems. Alloying elements are classified into five types, tiny, small, middle, large and super, according to their atomic radii. The close-packed clusters are determined by the relative atomic radius ratio in the different eutectic systems formed by two types of these atoms, and then general eutectic formulas are obtained. The Stockdale/Hume-Rothery eutectic puzzle, that eutectic points are near the ratio8/1,5/1,3/1,2/1and3/2, is quantitatively explained.
引文
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