尚家香
论文题目：金属界面复合体电子结构和能量学研究
作者简介：尚家香，女，1963年08月出生，1997年09月师从于钢铁研究总院王崇愚教授，于2001年08月获博士学位。
摘 要
晶界是多晶材料特别是细晶粒材料最重要的缺陷类型之一，与材料的力学性能、化学行为以及光学特性密切相关。微量掺杂元素可以改变晶界的原子结构和电子结构，对材料的力学性能、化学性能以及电学性能有较大的影响。研究以能量为判据的偏聚效应以及研究脆性断裂的本质对于有效地防止晶界脆性断裂具有重要意义。
本文以基于密度泛函理论的离散变分方法(DV)和DMol方法为基础，研究合金化元素Nb，Ti，V在bcc铁晶界和fcc铁晶界中的作用以及晶界的脆性解理断裂中能量学和键合变化的问题，进行晶界电子结构和能量学研究，在电子及原子层次上探索微观与宏观物性的关联，进行第一原理热力学计算，直接给出物性判据；给出了金属铁晶界脆性解理断裂过程中的能量学和键合特征，为材料设计提供理论基础。本工作得到国家自然科学基金项目“59971041界面及位错成分设计与材料强度及材料特性”和国家重大基础项目“G2000067102材料设计中的跨尺度关联研究”的资助。
Rice-Wang热力学模型（计算所用的模型）：
界面的结合程度用材料的一个特征量2gint来表征，为界面分裂为两个相应自由表面的理想断裂功，表征材料阻止外力分裂界面结合的能力。按照Griffith弹性断裂理论，断裂功表示为
式中f为单位面积表面(s)或界面(b)的自由能，A、B为界面断开后分开的两侧的材料。2gint对于判断材料的韧脆性质是一个重要的参量。Rice和Wang提出了一个热力学模型（Rice-Wang 热力学模型），用此模型可以判定晶界溶质偏聚对2gint的影响，即
由上式可知，界面上的杂质元素是增强或减小界面的断裂功由(
)决定。如果(
)<0，则杂质原子使得晶界的断裂功增加，杂质原子增强晶界结合；如果(
)>0，则杂质原子使得晶界的断裂功减小，杂质原子减弱晶界结合。因此(
)可以作为杂质偏聚效应的热力学判据，关键是准确计算或测量溶质原子在界面和表面的偏聚能。
本文包括以下三部分的工作：
一、Nb、Ti和V对bcc Fe
晶界结合的影响
利用第一原理DMol 方法与分子动力学相结合，在Rice-Wang热力学模型的基础上，研究了合金化元素Nb、Ti和V对bcc Fe
晶界结合的影响。给出了合金化元素Nb、Ti和V的热力学判据，对合金设计具有实际意义；发现Nb、Ti和V的化学因素起主要作用，表现为较强的增强晶界结合的作用；力学因素也起着重要作用，表现为减弱晶界结合的作用。结果表明：合金化元素Nb、Ti和V在晶界和自由表面的偏聚能之差分别为-0.51eV、-0.37eV和-0.58eV均小于0，合金化元素Nb、Ti和V表现为增强晶界结合。在总的DEgb-DEs中，化学因素起主要作用，Nb、Ti和V的贡献分别为-0.95eV、-0.72eV和-0.75eV，表现为较强的增强晶界结合的作用；力学因素也起着重要作用，贡献分别为0.44eV、0.34eV和0.17eV，表现为减弱晶界结合的作用，力学效应即掺杂引起的局域畸变对韧脆作用的影响也不可忽略，因此DMol 优化是必要的。合金化元素Nb、Ti和V占据晶界时，合金化元素失去一部分电子，而它周围的基体原子得到一些电子，特别地，它们使得距它较近的跨越晶界的原子键加强，反映了Nb、Ti和V强化晶界的作用。
二、Nb、Ti和V在面心Fe
晶界中的作用
利用密度泛函理论框架下的的离散变分DV和DMol方法及分子动力学（MD）方法，研究了合金化元素Nb、Ti和V在面心Fe
晶界中的作用。给出了Nb、Ti、V在fcc Fe中的占位倾向和在其占位方式下的偏聚规律，发现Nb、Ti、V具有强化面心Fe
晶界的作用。结果表明：与在体内占位相比，晶界更适合Nb、Ti和V元素占据。Nb、Ti和V在晶界与在表面上的偏聚能之差分别为-0.39eV、-0.12eV和-0.46eV。根据Rice-Wang 热力学模型可以判定，Nb、Ti和V在面心铁中都可以增强晶界结合，表现为韧性合金化元素。原子间相互作用能和电荷分布计算表明，当Nb、Ti和V原子占据晶界位置时，电荷重新分布，它们失去电子，而距杂质原子较近的基体铁原子得到电子。Nb和Ti与周围的Fe原子相互作用有所减弱，而Nb和Ti原子两边的跨晶界的原子间的相互作用加强，反映了替位Nb、Ti原子强化Fe晶界的作用。而V与周围的基体原子的相互作用加强，V表现为强化晶界的作用。
三、Fe晶界脆性断裂的第一原理研究
晶界是材料中非常重要的缺陷类型之一，对材料的物理及力学性能影响很大，脆性断裂通常发生在晶界处，因此研究晶界脆性断裂对于弄清断裂的本质从而找出预防脆性断裂的方法具有重要意义。我们利用第一原理的离散变分方法(DV)计算, 研究了体心Fe
晶界和面心Fe
晶界沿晶界面或非晶界面脆性断裂过程中的能量变化和键合的变化, 发现了bcc Fe和fcc Fe晶界在脆性断裂过程中的能量学特征及键合的变化规律，给出了分离能与分离距离的简单表达式。结果如下：不同晶界在拉开不同距离时的分离能 Esep(d)与分开距离d的关系可用一函数形式表示：
Esep（d）=c0+c1/ {1+exp(d+c2)/c3}
其中c0, c1, c2 , c3 为拟合系数，他们随体系的不同及断裂面的不同而不同。c0为晶界的断裂能。在晶界被拉开的初始阶段，Esep随d增加很快，几乎是直线变化；d>3.0a.u.时，Esep随d增加变缓；在6.0<d<10.0a.u.区间，Esep随d增加很小；当d>10.0a.u.时，Esep不随d增加而增加。原子间相互作用能和电荷密度计算表明，当金属铁发生断裂形成新表面时，要断裂的键的强度随分离距离d 的增大而减弱，直至d =10.0a.u.时，减为0；与断裂平面的夹角小于45°且靠近断裂面的键的键强增加较大；与断裂平面的夹角大于45°且靠近断裂面的键的键强变化较小，结果使得断裂后表面键的强度要比其在晶界上的相应的键的强度要大。在脆性断裂过程中, 电荷的转移主要发生在断裂面附近, 电荷从要断裂的区域转移到新形成的表面区域, 而远离断裂面的区域变化很小。铁晶界在断裂时, 费密能级随d 的增加而升高, 费密能级从低能级向高能级移动, 断裂前后费密能级升高0.2eV左右。从态密度计算结果可以发现, 对不同的晶界沿不同的面断开时,费密能级附近能量约在-2.5~0.8eV范围的态密度随d 的增加而增加, 而能量约在-6~-2.5eV范围的态密度随d 的增加而减小(0eV对应费密能级)，即金属铁在脆性断裂过程中，一部分电子从低能级转移到高能级，这部分电子主要来源于断裂面附近的原子。
本文系统研究了Nb、Ti和V等重要合金化元素在bcc 和fcc Fe 晶界中的电子效应及其与物性的关联，给出了Nb, Ti和V的热力学判据；研究了bcc和fcc Fe晶界沿晶界面或非晶界面脆性断裂过程中的能量变化和键合的变化, 发现了晶界在脆性断裂过程中的能量及键合的变化规律，给出了分离能与分离距离的关系曲线。
Investigation of
electronic structure and energetics on interface complex of metals
ABSTRACT
Gain boundary is one of the most important defects
in materials, especially in fine-grain materials. It is closely related to the
mechanical, chemical and optical properties of materials. The segregation of
impurities on grain boundary can alter the atomic structure and electronic
structure of grain boundary, so affect the mechanical, chemical and optical
properties of materials. It is significant to study the effect of segregation
as well as the nature of brittle fracture for preventing brittle fracture of
grain boundary.
In this dissertation, we
studied the effects of alloying elements Nb, Ti and V on bcc Fe 
and fcc Fe 
grain boundaries cohesion, as well as the nature of brittle
cleavage fracture of Fe grain boundary from electronic structures and
energetics, by using discrete variational (DV) and DMol methods within the
framework of the local density functional theory combined with the molecular
dynamics (MD). We conduct a direct first-principles calculation from electronic
and atomic structure level and explore a connection between microstructure and
macro-properties as well as provide a theoretical basis for the materials
design. This work was supported by the National Natural Science Foundation of
China (59971041) “Interface and dislocation design and materials strength and
materials character” and the 973 National project (G2000067102) “The
multi-scales modeling in material design”.
Rice-Wang thermodynamic model:
Interface cohesion strength is described by the ideal fracture work of interface 2gint. It can be defined that the work is done when the interface material be pull apart according to the Griffith elastic theory. That is
2gint=fsA+fsB-fbA/B
Where f is the free energy of unit area.
Rice and Wang proposed a model to
describe the mechanism of fracture through the competition between plastic
crack blunting by dislocation emission and brittle boundary separation. By
comparing the segregation energy in grain boundary and free surface, we can
predict that the solute atom strengthens or weakens the grain boundary cohesion
by this model. That is
. Here 2gint and 2gint0 are ideal cleavage work with or
without solute atom, respectively. Γis the solute coverage of GB. DEgb and DEs are the segregation energy at grain boundary and free surface,
respectively. If DEgb- DEs<0, solute atom enhances
the grain boundary cohesion.
This work consists of three parts:
(1) The segregation
effects of Nb, Ti and V on the bcc Fe 
grain boundary cohesion.
The segregation effects of Nb, Ti and
V on bcc Fe 
grain
boundary cohesion are studied by an electronic structure calculation using DMol
method within the framework of density functional theory. The segregation
energy differences between the grain boundary and the corresponding free
surface are –0.51eV, -0.37eV and –0.58eV for solute Nb, Ti and V, respectively.
That indicates that Nb, Ti and V can increase the grain boundary cohesion in
bcc Fe. Further analyses show that the chemical effect of Nb, Ti and V play a
major role, the contributions of the chemical effect to DEgb-DEs are –0.95eV, -0.72eV and –0.75eV for Nb, Ti and V
respectively. Contrary to chemical effects, the mechanical effect of Nb, Ti and
V, which is related to atomic size effect, displays decreasing the grain
boundary cohesion. The contributions
of the mechanical effect to DEgb-DEs are 0.44eV, 0.34eV and 0.17eV for Nb, Ti and V
respectively, it also plays an important role and should be considered in computation. When Nb, Ti and V occupy grain boundary, they lose some electrons, the neighboring host atoms get some electrons, which makes the bonds across grain boundary stronger than those of clean grain boundary. It can be predicted that Nb, Ti and V can enhance the bcc Fe grain boundary cohesion.
(2) The segragation effects of Nb, Ti and V on
fcc Fe 
grain boundary cohesion.
The discrete variational (DV) and DMol methods within the framework
of density functional theory are used to study the effects of Nb, Ti and V on
the electronic structure of 
grain boundary
in FCC Fe. The results show that comparing with the bulk site, Nb, Ti and V
prefer to segregate at grain boundary. The differences of segregation energies
between the grain boundary and the corresponding free surface are –0.39eV,
–0.12 eV and –0.46eV for solute Nb, Ti and V, respectively. According to
Rice-Wang model, our results imply that Nb, Ti and V can enhance the grain
boundary cohesion in FCC Fe. The calculating results of interatomic energy and
charge distribution show that when Nb, Ti and V segregate at grain boundary,
the electron will redistribute, and the Nb, Ti and V lose some electrons, the
neighboring host atoms get some electrons. This work also shows that the
effects of Ti and V on the bonding behavior are different. When Nb (Ti)
segregates at grain boundary, the bonds across grain boundary are strengthened,
while the interactions between Nb (Ti) and its neighboring atoms are weakened.
But for V-doped grain boundary, V interacts with its neighboring atoms stronger
than that of clean grain boundary and V also makes the bonds across the grain
boundary stronger.
(3) The first-principles study of brittle
cleavage fracture of Fe grain boundaries.
Based
on the density functional theory, discrete variational (DV) method is used
to study the
process of brittle cleavage fracture of bcc and fcc Fe grain boundaries. The
energies and bonding characters in the process of brittle fracture are given.
Followings are the main results: The separation energy Esep increases monotonously with the increase of d when d < 6.0 a.u.; Esep
changes little with d increasing in the region of 6.0<d<10.0a.u., then it
gets to a stable value at d>10.0a.u.. Esep(d) can be expressed as
a function of separation d
where c0, c1, c2 and c3
are fit constants, they are different for different system. The c0 is the fracture energy.
The results of interatomic energy and electron distribution show that the
strength of fracture bonds decreases rapidly when d<6.0a.u., and decreases to zero at d=10.0a.u.; the strength of surfaces bonds that the angle between
surface bonds and fracture plane <45° is increased; but the strength of surface bonds the angle between
bond and fracture plane >45° changes
a little with increase of d, which means the strength of surface bonds whose
angle between bond and fracture plane <45° is greater after fracture than that of corresponding bonds in gain
boundary. In contrast, the strength of bonds far from fracture plane keeps
unchanged in the fracture process. The electron transfers from the region to be
fractured to the surface region in the process of fracture. The Fermi level is
shifted to the higher level in the process of brittle fracture, and 0.2eV
higher after fracture than that of before fracture. The DOS at higher energy
level is increases and decreased at lower energy level with the increase of
separation d. Some electrons are
transferred from the lower energy level (about –6 ～ –2.5eV) to the higher energy level
(about -2.5～0.0eV) (0
corresponding to Fermi energy level). The electrons transferred to higher
energy level come mainly from the atoms near to fracture plane.
In the work
the segregation effects of Nb, Ti and V on BCC Fe
and FCC Fe
grain boundaries
cohesion are studied by the first-principles DV and DMol methods within the
framework of density functional theory. We explore a connection between
microstructure and macro-properties as well as provide a theoretical basis for
the materials design. We also study the
fracture process of BCC and FCC Fe grain boundaries, and give a rule about
energy and bonds in the process.
The separation energy can be described as a function of separation
distant.
