原子分子在δ-Pu上的吸附、离解与扩散过程研究
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摘要
随着计算机技术和计算方法的飞速发展,计算材料学已成为材料研究中的重要手段。计算材料学是连接材料学理论与实验的桥梁,能够提供原子分子水平的微观信息,将实验结果上升为一般的、定量的理论,从而使材料的研究与开发更具方向性和前瞻性,大大提高了研究效率。本论文中,开展了钚腐蚀老化行为相关的计算模拟研究,重点在于一些气体原子、分子在δ-Pu金属低指数表面吸附行为的第一性原理研究,同时对部分原子在完备δ-Pu金属中的结构和扩散行为进行了讨论,另外对δ-Pu金属中氦行为开展了初步的分子动力学模拟。论文研究结果能够对认识钚的表面吸附行为和体相行为提供一定理论参考,也为进一步开展钚腐蚀老化行为的材料模拟研究打下了基础。
论文第一章简要介绍了钚的腐蚀老化机理,介绍了研究该问题的实验、理论方法及基本情况。在当前认识水平下,对几种老化机制的深入解释还有许多争议,尤其从微观变化去推演宏观的物理性质变化更加缺乏理论和实验的支持。钚的腐蚀老化研究是对当今材料学、固体物理和大规模计算机模拟的挑战。计算材料学研究对认识老化机理,明确腐蚀过程,解释实验现象,进而指导实验工作有着重要的意义。在充分调研钚材料计算模拟研究现状的基础上,明确了论文的研究思路,提出了开展的研究内容。
论文第二章简要介绍了论文研究所涉及的理论和计算方法,包括绝热近似、密度泛函理论、布洛赫定理、交换关联能的LDA、GGA近似等,简述了赝势方法和处理表面的超原胞方法。对分子动力学的理论基础、势函数的建立和分子动力学方法在材料模拟中的应用也做了必要的叙述。最后介绍了计算使用的主要程序。
论文第三章,使用密度泛函方法结合平板周期性模型对了气体原子/分子在钚表面吸附行为开展了研究。计算获得了原子、分子δ-Pu表面的吸附结构和吸附能,分析了吸附作用的主要因素,揭示了吸附相互作用的电子态。对于吸附分子在钚表面吸附后的活化和离解情况也进行了讨论。在较宽范围的吸附覆盖度下对部分原子、分子的吸附行为进行了讨论。其中C、N2和H2O等的吸附行为是首次报道,不同覆盖度下对吸附行为影响的讨论也属首次。研究结果对钚的表面腐蚀行为提供了初步理论参考,为进一步表面计算模拟工作打下了基础。主要结果如下：
覆盖度(θ)0.25ML时,H、O的吸附均为化学吸附,最稳定吸附位都为心位,桥位次之,顶位最不稳定,(111)面的Hcp心位和Fcc心位吸附行为几乎一致。自旋限制(NSP)和自旋极化(SP)水平,(111)面H吸附能和吸附距离分别为3.10eV,1.39A和2.20eV,1.39A；(100)面分别为3.16eV、0.63(?)(NSP)和2.26eV、0.60(?)(SP)。(111)面O吸附能6.153eV(NSP)和7.454eV(SP),吸附距离1.31A。(100)面为6.326 eV(NSP)和7.614 eV(SP),吸附距离0.51 A。与H、O作用的Pu原子数目是决定吸附的主要因素。电子从表面转移到H原子,吸附作用主要发生在第一层。Pu 5f,6s,6d电子和H的2s电子有杂化成键作用。O吸附作用主要发生在第一层,但(100)面心位吸附时第二层Pu原子也发生电子相关作用。相对裸露表面,O的吸附使Pu的5f轨道向费米能级更低处移动,成键主要为O 2p轨道和Pu 5f 6s,6d轨道杂化成键,O从金属获得电子形成σ键。吸附后的表面功函都有增加,电子转移量,表面功函增加量和吸附稳定性都是O吸附大于H吸附的情况。
H和O在(100)面心位吸附的计算结果与文献有很大差别,主要是由于模型和吸附覆盖度的不同造成,因此应用不同的表面模型考察了吸附覆盖度的影响。在0.11ML到1.0ML覆盖度范围内,C在Pu表面不同吸附位的稳定规律类似与H和O,其中Hcp位仅略高于Fcc位。C的吸附能对覆盖度变化敏感,随着θ的增大而减小,变化几乎是线性的。(111)面吸附能最高点出现在0.25ML-0.33ML附近,最稳定吸附位的吸附能在5.3-5.6 eV范围。(100)面吸附能最高点在0.125ML-0.25ML附近,最稳定吸附位的吸附能为6.13 eV-6.60 eV。吸附C原子到表面的距离随着覆盖度的增加而减小。C吸附造成Pu表面电子向C偏移,形成表面偶极子,表面功函增加量和覆盖度成近线性关系。存在退极化效应,偶极矩随覆盖度的减小而增加。投影态密度和局域态密度表明C-Pu的相互作用主要为C2p轨道和Pu5f、Pu6p及Pu6d轨道成键,C-Pu键较强,是稳定的化学吸附。
N最稳定吸附位也为高对称心位。(111)面最稳定态的吸附能在2.4-2.7 eV范围,(100)面在3.2-3.9eV范围,强于(111)面,都属于化学吸附,但远弱于C、O原子而稍强于H原子。随着N原子覆盖度增加,吸附能变小。在高覆盖度下,Hcp或Fcc吸附位的N原子轻微偏离高对称的吸附位,N原子之间的核间距变小,N、N原子间有轻微的横向吸引作用。N吸附诱导表面功函数增加量与覆盖度成近线性关系,随着覆盖度的增加而增加。N原子的净的负电荷约多于C吸附情况,但吸附作用却小于C原子,这是因为部份电子进入了反键态。态密度分析表明N-Pu的相互作用形成成键态和反键态,成键态为N2p轨道和Pu5f、Pu6p及Pu6d轨道成键,反键态为N3s轨道和Pu7s轨道成键。反键态有占据电子,造成N-Pu键较弱,N吸附能较小。
覆盖度将影响H、O的吸附能和吸附结构,特别是在覆盖度较高的情况下。在较高覆盖度下,由于吸附原子之间会发生吸引或排斥作用,将使吸附结构较低覆盖度下的发生明显变化,吸附能也有所变化。(111)面吸附能最大值出现在0.25ML附近,(100)面最大值在0.4ML到0.5ML之间。覆盖度的影响要比C和N原子的影响小,特别是(100)面心位吸附情况。但电子态和吸附作用本质不发生改变。
H2分子的吸附是物理吸附。垂直吸附构型优于两种平行构型,其中心位垂直吸附为最稳定吸附结构。(100)面吸附能和吸附距离分别为0.1147eV,3.78(?)(NSP)和0.0961V,3.51(?)(SP)。(111)面为0.0940eV,3.85(?)(NSP)和0.0879eV,3.68(?)(SP)。相互作用只发生在第一层,吸附前后只有很少的电荷转移,表面功函轻微增加。H2在表面吸附后,键长增长,伸缩振动频率红移,分子得到活化。(100)面可能的离解方式有,从顶位Horl出发,离解为两个处于桥位吸附的H原子,或从顶位Hor2出发,离解为两个处于心位吸附的H原子,解离的能垒分别为0.527eV和0.562eV。(111)面,从顶位Horl吸附出发,离解为位于相邻两个中心位置的原子态吸附,离解能垒0.226eV。从顶位Hor2吸附出发,离解成两个处于相邻Fcc心位吸附位置的H原子,此时体系能量要比前一方式离解后体系能量稍低,但需要越过能垒稍大,为0.543eV。上述可能离解过程在热力学和动力学上均容易发生。以分子态吸附时,Pu的5f轨道和H的2s轨道能量差别相当大,Pu的5f电子和H的2s电子没有杂化成键作用,氢分子和钚表面的作用为Van der Waals相互作用。当离解为原子态吸附时,Pu的5f电子和H的2s电子有杂化相互作用,此时有更多的电子相互作用。
CO分子在δ-Pu表面分子态吸附为C端吸附,吸附主要发生在第一层。电子从Pu表面转移到CO分子上,表面功函明显的增加。相互作用主要源于CO分子的5σ和2π*轨道与Pu5f、Pu7s、Pu6d、Pu6p杂化轨道相互作用。(111)面最稳定吸附态是Hcp心位垂直吸附,吸附能为1.764eV(SP)和1.791eV(NSP), C原子距离Pu表面为1.922A和1.950A。离解为C原子和O原子吸附的体系能量稍高于分子态最稳定吸附体系能量,在较低温度下倾向于以分子态吸附。(100)面心位垂直吸附是最稳定的吸附态,其次是象桥位>桥位垂直>顶位垂直。心位垂直和象桥位吸附的吸附能分别为1.754eV(SP, center)和1.780eV(NSP, center)、1.717eV(SP, like-bridge)和1.778eV(NSP, like-bridge),相应的CO分子键长为1.23(?) (center)和1.20(?)(like-bridge)。键长增加、伸缩振动红移,表明CO分子活化。离解能垒为0.2eV,离解的C、O原子将占据能量最低的心位,与(111)面相反,离解吸附在能量上优于分子态吸附。
0：在Pu表面吸附后发生活化,O2分子键长增加,直到键断裂,离解成两个原子态发生吸附,氧原子优先处于心位和桥位。优化过程能量变化曲线和过渡态搜索结果都表明O2分子的离解吸附没有较大的能垒需要克服,这一过程在室温下自发发生。吸附能大小为两个氧原子的吸附能减去氧分子离解能。(100)面吸附能为8.14eV(NSP)和7.29eV(SP)。(111)面为7.56eV(NSP)和6.82eV(SP)。离解吸附后的电荷布局数,诱导表面功函、电子态等和前面O原子吸附的研究结果一致。
N2在δ-Pu表面各个吸附构型的吸附能相差较小,都在0.25-0.45eV范围内,属于较弱物理吸附,各个构型在一定温度内都可能存在。在低覆盖度(0.25ML)下,顶位垂直吸附相对最稳定,垂直吸附优于平行吸附。而到了较高的覆盖度,所有垂直吸附的吸附能大小几乎相同,而所有平行吸附构型优化后都翻转为垂直吸附,这是由于高覆盖度下,N2分子之间的排斥力使得发生构型翻转,最终的平衡结构都近于垂直或倾斜吸附。电子从第一层Pu原子流向吸附的N2,但电子转移作用很小,N2分子的负电荷一般在-0.3 eV以内,态密度分析表明成键态的占据电子很少。
H2O分子为较弱的物理吸附,(100)面各吸附能在0.05eV-0.20eV,(111)面在0.02eV-0.15eV,在有限温度下可以多种吸附态并存,吸附使水分子本身结构的改变极其微小,电子转移是极其微弱的,表面功函增加也很小。HO基面的吸附以氧端垂直吸附为优,稳定性为心位>桥位>顶位。Pu原子和OH基团之间有明显的电子转移。
论文第四章使用密度泛函理论计算了H、O、He等原子在δ-Pu金属体相中可能存在的结构和嵌入能。所有原子稳定存在于间隙位正中心,八面体间隙位较四面体间隙位更稳定。八面体间隙嵌入能,H为-3.12 eV(NSP)和-2.22eV(SP), O为-7.21eV(NSP)和-6.14eV(SP)。四面体间隙嵌入能,H为-2.43 eV(NSP)和-1.53eV(SP), O为-4.76eV(NSP)和-3.49 eV(SP)。H原子在八面体间隙位有更多的电子转移到H原子,H与Pu的作用更强,体系也更稳定,空间几何效应也使八面体间隙位更稳定。而两种间隙位氧原子负电荷差别很小,电子相互作用近似,能量的差别主要和空间几何效应有关。H原子最可能扩散路径为相邻不同间隙位的交替扩散,八面体间隙到四面体间隙的扩散能垒为1.06eV,反向扩散能垒0.38eV。平行晶轴方向四面体间隙到四面体间隙交替直线扩散的能垒为1.83eV,八面体间隙到八面体间隙交替扩散路径的势垒最高,大小为2.52eV。O最可几扩散路径为相邻不同间隙位之间的交替扩散,八面体间隙到四面体间隙的扩散能垒为1.12eV,反向2.72eV。四面体间隙到四面体间隙扩散能垒为6.40eV,八面体间隙到八面体间隙扩散能垒8.85eV。O扩散势垒都较高,氧原子在δ-Pu金属完美晶体中不易移动,稳定存在各个间隙位。钚金属在含氧气氛中易被氧化,形成很薄的氧化膜后不易进一步氧化,这可能也与氧原子不易向体相迁移有关。
与O和H的情况不同,氦原子嵌入能为正值,即使体系能量升高,向不稳定发展。氦原子使周围最近的一圈Pu原子向外扩张,使体系能量降低,不同间隙位的能差变小。对比H、O原子,氦对结构的影响要稍大。扩散能垒计算结果为：八面体到八面体间隙为3.51 eV；四面体到四面体间隙为2.16 eV；八面体到四面体间隙1.42 eV,四面体到八面体间隙0.34 eV。不同间歇位交替扩散为最可几的扩散路径。He在晶体中的迁移要比O原子的迁移容易的多。同样计算了C和N的间隙位结构和能量。对比可知,只有氦的嵌入使体系热力学稳定降低,且氦原子对结构的影响最大,由于Pu-He的相互作用较小,间隙扩散能垒较低,因此氦容易在金属体相中扩散迁移。C、N、O、H能稳定存在钚金属中的间隙位,和Pu原子发生强相互作用。其中C、O的嵌入能近似,成键作用非常强,可以推断能够形成稳定的钚氧和钚碳化合物。由于扩散能垒较高,表面的化合物一旦形成,就不容易向体相进一步演化。H和N的相互作用要相对较弱,扩散也相对容易。
δ-Pu金属体相单个空穴形成能时为0.786 eV(NSP)、0.784 eV (SP)。不同文献报道值介于0.7eV-1.7 eV之间,由于模型和方法不同,存在一定区别是合理的。以空穴为中心,空穴周围最近一圈的Pu原子向内收缩,第二圈的Pu原子略向外移。当两个空穴距离较远位置时,平均空穴形成能为0.767eV (NSP)和0.764eV(SP),和单个空穴形成能相差不大,结构变化也类似于单个空穴的情况。当两个空穴聚集在一起时,平均空穴形成能为0.636eV (NSP)和0.628eV(SP),小于单个空穴形成所需的能量。这表明聚集的空穴二聚体要比两个单独存在的空穴更稳定,预示着自辐射损伤产生的空穴有逐渐聚集的趋势。
第五章中,参考Baskes方法建立了针对δ-Pu金属的MEAM势。使用不同从头算方法和基组对Pu-He和He-He势能曲线进行了扫描,然后利用非线性最小二乘法拟合势能函数。将势函数引入相应的分子动力学程序,建立了Pu中氦行为的MD模拟方法。初步模拟表明,He原子位于八面体间隙位,最近的一圈Pu原子以He为中心向外驰豫,He原子结合能为2.90 eV,与前期的密度泛函计算结果一致。He原子在钚金属中形成了氦团簇,随着氦原子的增加,氦团簇也逐渐长大,一直到26个氦原子时,氦团簇仍然在生长。氦团簇周围的位错缺陷随着氦团簇的生长形成加剧,在氦团簇尺寸较小时(n<26),缺陷没有发生集体漂移。较小尺寸的两个氦团簇在一定临界距离内会发生融合的现象。初步模拟验证工作表明建立的方法能够准确的描述氦在钚金属中的体相行为。
在最后的第六章中,我们对整个计算模拟工作的结果进行了回顾,并提出了后续研究方向。
In the past decade, with the rapid development of computer hardware and quantum mechanics algorithm, computational modeling has become a powerful tool which can provide great insight in predicting properties of materials. This dissertation is devoted to the study of plutonium aging mechanism by computational modeling. Atomic and molecular adsorption onδ-plutonium surface have been studied in detail using the generalized gradient approximation to density functional theory, while some atoms diffusion behavior in perfect 8-Pu metal was studied by using density functional theory. Also the simulations of helium behaviors inδ-Pu metal are carried by molecular dynamics method.
In the first chapter, we focus on the research status of plutonium aging mechanism, and three mechanisms induced the aging of plutonium are presented. Methods and means, especially the results of the research are also presented to give some references to the related study. Based on the review of the status of plutonium computer simulation study, we presented our research ideas and direction.
Chapter 2 gives a brief description of the calculation methods which include the Born-Oppenheimer approximation, density-functional theory, Bloch theorem, local density approximation and generalized gradient approximation of the exchange-correlation energy, pseudo-potential methods, and supercell method. Also, the principle of molecular dynamics, the progress in related finite difference technique and interatomic potentials are summarized. At last some software using in this work are pointed out.
In chapter3, Adsorption of some atom and molecule onδ-Pu surfaces using the generalized gradient approximation of the density functional theory with RPBE functional have been studied at both the spin-polarized level and the nonspin-polarized level.
For hydrogen atom, we find that the center position of the (100) surface is the most favorable site with a adsorption energy of 3.16eV and an optimum distance of the hydrogen adatom to the Pu surface of 0.063nm at the non-spin-polarized level (NSP). For the spin-polarized (SP) (100) surface, the center site is again the preferred site with an adsorption energy of 2.26eV and an optimum hydrogen distance of 0.060nm. For theδ-Pu(111) surface, there is the same adsorption behavior of H atom. At NSP level, the center position ofδ-Pu(111) surface is the preferred adsorption site with adsorption energy 3.10eV and distance 0.139nm. At SP level, the center site is also the preferred site with adsorption energy of 2.20eV and a hydrogen distance of 0.139nm. The coordination numbers have a significant role in the chemical bonding process. Mulliken charge distribution analysis indicates that the interaction of Pu with H mainly takes place in the first layer and that the other two layers are only slightly affected. The adsorption of hydrogen atom onδ-Pu surfaces make the surface work functions of Pu metal distinctly increased.
For oxygen atom, the center position of the (100) surface is the most favorable site both at NSP and SP level calculation. The chemisorption energy and optimum distance of the oxygen adatom to the Pu surface are 7.614 eV,0.051nm (NSP) and 6.326eV,0.051 nm (SP) respectively. For theδ-Pu(111) surface, Hcp and Fcc sites are both favorable adsorption site with the same chemisorption energy and geometric structure. At the NSP level, chemisorption energy is 7.454 eV and optimum distance of the oxygen adatom to the Pu surface is 0.131 nm. For the SP surface, these values are 6.153eV and 0.131 nm respectively. The coordination numbers have a significant role in the chemical bonding process. Mulliken charge distribution analysis indicates that the interaction of Pu with O mainly takes place in the first layer and that the other two layers are only slightly affected. The surface work functions increases due to oxygen atom adsorption. The adsorption is strong ionic bonding action. The bonding between the oxygen and the Pu atom is due to the hydridization of O2p and Pu5f, Pu7s, Pu6d orbitals.
Adsorption of atomic carbon onδ-Pu surfaces have been investigated systematically using DFT with RPBE functional. The adsorption energies, adsorption structures, Mulliken population, work functions, layer and projected density of states have been calculated in wide ranges of coverage, which have never been studied before as far as we know. It is found that forδ-Pu(111) surface the Hcp-center sites are the energetically favorable sites for all the coverage range considered. Forδ-Pu(100) surface the center sites are the energetically favorable sites. The repulsive interaction has been identified, and the adsorption energy decreases with the coverage, while work function increases linearly with the coverage. It has been found that the C-Pu interaction is very strong due to the hybridization between the C2p states and the Pu5f, Pu6p, Pu6d states of topmost layer plutonium atoms.
Adsorption of atomic nitrogen has been investigated systematically in wide ranges of coverage. It is found that the center sites are the energetically favorable sites for all the coverage range considered adsorption energy 2.4-2.7 eV. Forδ-Pu(111) surface Hcp site are slightly more stable than Fcc site, which differed from most transition metal surfaces with hexagonal close-packed structure. The repulsive interaction has been identified, and the adsorption energy decreases with the coverage, while work function increases linearly with the coverage. It has been found that the N-Pu interaction is due to the hybridization between the N2p states and the Pu5f, Pu 6p, Pu 6d states of topmost layer Plutonium atoms. The N-Pu interaction is weak due to the partially occupied anti-bonding states from N 3s and Pu 7s hybridization.
Molecule hydrogen adsorption and the reaction barrier for dissociation onδ-Pu surfaces have been studied. On the 100 surface, vertical approaches on the center site both without and with spin polarization were found to be the most favorable molecular adsorption sites. The adsorption energy and the optimum distance were 0.1147eV,0.378nm and 0.0554eV,0.386nm respectively. Molecule hydrogen is active, for dissociate adsorption it was found that the most favorable dissociation channel needs activation energies of 0.527eV or 0.562eV On 111 surface, vertical approaches on the center site are also the most favorable molecular adsorption sites, with adsorption energy 0.0940eV at the non-spin-polarized and 0.0554eV at spin-polarized levels. The most favorable dissociation activation energy is 0.226eV, which molecule hydrogen dissociated to two center adsorption atomic hydrogen.
For CO molecule, the C-side center vertical position ofδ-Pu(100) surface is the preferred adsorption site with adsorption energy of 1.754eV (SP) and 1.780eV(NSP). And, the stability of adsorption configuration at other sites is like-bridge> bridge vertical> top vertical. Meanwhile, all parallel approaches turn to the corresponding C-side vertical or bridge vertical approaches, indicating C-side adsorption are more stable than O-side adsorption, and parallel approaches will not existent. The difference of adsorption energies for different sites such as like-bridge, bridge vertical, top vertical and center vertical is less than 0.2eV, that shows that CO adsorption on Pu(100) surface is the coexistence of several adsorbed at a limited temperature range. The hcp center Vertical position ofδ-Pu(111) surface is the preferred adsorption site with adsorption energy of 1.764eV (SP) and 1.791eV(NSP). The coordination numbers have a significant role in the chemical bonding process. The interaction between Pu atom and CO molecule results mainly from the contribution of 4σ、5σand 2π* orbital of CO molecule and 5f、7s、6d and 6p orbital of surface Pu atom. CO adsorption on Pu(111) surface tend to molecule adsorption state.
For oxygen molecule, dissociative adsorption is found to be energetically more favorable compared to molecular adsorption. The dissociative oxygen atom preferred adsorption on center site. For (100) surface the most stable chemisorbed site has an energy 8.14 eV(NSP) and 7.29 eV(SP). For (111) surface the most stable chemisorbed site has an energy 7.56 eV(NSP) and 6.82 eV(SP). The work functions increase, charge population, DOS and PDOS are similar with atomic oxygen adsorption behaviors.
Adsorption of molecule nitrogen has been investigated systematically in wide ranges of coverage. The adsorption energies are in the range of 0.25-0.45eV for all the case. It indicates that adsorption of molecule nitrogen is weak physical adsorption. The difference of adsorption energies for different adsorption configurations is less than 0.2 eV, it shows there are several adsorption configurations coexistence at a limited temperature range. At lower adsorption coverage (0= 0.25 ML), Top vertical adsorption configuration is most stable adsorption situation and all vertical configurations are more stable than corresponding parallel configurations. But at higher adsorption coverage all parallel configurations are turn to vertical configurations. This is due to repulsive interaction between molecule nitrogen. DOS and PDOS show occupation of bonding states is weak.
The adsorption energy of molecule water is very small. For (100) surface, the value are in the range of 0.05eV-0.20eV. For (111) surface, the value are in the range of 0.02eV-0.15eV. This indicates adsorption belong very weak physical adsorption.
In chapter4, The diffusion behavior of atom such as hydrogen, oxygen in perfect 8-Pu metal was studied by use of the density functional theory Doml3 and periodical model. The embedding energy and diffusion barriers of the single hydrogen were calculated at GGA level. A single hydrogen atom has the minimum embedding energy about -3.12eV and-2.22eV in the octahedral interstitial site of fccδ-Pu at Non-spin polarization and Spin-polarization level respectively. Hydrogen atom inδ-Pu crystal most preferably diffuses along the path linked with different interstitials. The diffusion barrier of along the path from octahedral interstitial site to tetrahedral interstitial site is 1.06eV. The diffusion barrier of reverse path is 0.38eV.
A single oxygen atom has the minimum embedding energy about -7.205eV and-6.140eV in the octahedral interstitial site of fccδ-Pu at Non-spin polarization and Spin-polarization level respectively. The embedding energy in tetrahedral interstitial site is little larger than that in tetrahedral interstitial site. Oxygen atom in 8-Pu crystal most preferably diffuses along the path linked with different interstitials. The diffusion barrier of along the path from octahedral interstitial site to tetrahedral interstitial site is 1.12eV. The diffusion barrier of reverse path is 2.72eV.
A single helium is stable in octahedral interstitial site with less embedding energy of 3.371 eV(NSP) and 3.137eV(SP). The embedding energy in tetrahedral interstitial site is 4.452 eV(NSP) and 4.433 eV(SP). Differed from hydrogen and oxygen atom, the embedding energy of helium is positive, which indicate that helium atoms embedding increase the total energy of system and make system instable. Helium atom inδ-Pu crystal most preferably diffuses along the path linked with different interstitials. The diffusion barrier of along the path from octahedral interstitial site to tetrahedral interstitial site is 0.34 eV. The diffusion barrier of reverse path is 1.42 eV. The diffusion of helium is easy.
The mono-cavity formation energy inδ-Pu metal is 0.786 eV(NSP) or 0.784 eV(SP). The di-cavity formation energy inδ-Pu metal is 0.636 eV(NSP) or 0.628 eV(SP). This shows there is a trend of cavity accumulation.
In chapter 5, the helium behavior in plutonium crystals has been simulated by molecular dynamics method. The modified embedded atom method (MEAM) potential is use for describing the interactions of plutonium-plutonium. The analytical potential energy curve for the Pu-He and He-He are scanned using B3P86 method, and then fitted to the exp-6 function using least squares. The growing and coalescence of helium clusters have been investigated at 300 K.
In the final Chapter, we summarize the computer simulation results, and some directions of further researches are pointed out.
论文第一章简要介绍了钚的腐蚀老化机理,介绍了研究该问题的实验、理论方法及基本情况。在当前认识水平下,对几种老化机制的深入解释还有许多争议,尤其从微观变化去推演宏观的物理性质变化更加缺乏理论和实验的支持。钚的腐蚀老化研究是对当今材料学、固体物理和大规模计算机模拟的挑战。计算材料学研究对认识老化机理,明确腐蚀过程,解释实验现象,进而指导实验工作有着重要的意义。在充分调研钚材料计算模拟研究现状的基础上,明确了论文的研究思路,提出了开展的研究内容。
论文第二章简要介绍了论文研究所涉及的理论和计算方法,包括绝热近似、密度泛函理论、布洛赫定理、交换关联能的LDA、GGA近似等,简述了赝势方法和处理表面的超原胞方法。对分子动力学的理论基础、势函数的建立和分子动力学方法在材料模拟中的应用也做了必要的叙述。最后介绍了计算使用的主要程序。
论文第三章,使用密度泛函方法结合平板周期性模型对了气体原子/分子在钚表面吸附行为开展了研究。计算获得了原子、分子δ-Pu表面的吸附结构和吸附能,分析了吸附作用的主要因素,揭示了吸附相互作用的电子态。对于吸附分子在钚表面吸附后的活化和离解情况也进行了讨论。在较宽范围的吸附覆盖度下对部分原子、分子的吸附行为进行了讨论。其中C、N2和H2O等的吸附行为是首次报道,不同覆盖度下对吸附行为影响的讨论也属首次。研究结果对钚的表面腐蚀行为提供了初步理论参考,为进一步表面计算模拟工作打下了基础。主要结果如下：
覆盖度(θ)0.25ML时,H、O的吸附均为化学吸附,最稳定吸附位都为心位,桥位次之,顶位最不稳定,(111)面的Hcp心位和Fcc心位吸附行为几乎一致。自旋限制(NSP)和自旋极化(SP)水平,(111)面H吸附能和吸附距离分别为3.10eV,1.39A和2.20eV,1.39A；(100)面分别为3.16eV、0.63(?)(NSP)和2.26eV、0.60(?)(SP)。(111)面O吸附能6.153eV(NSP)和7.454eV(SP),吸附距离1.31A。(100)面为6.326 eV(NSP)和7.614 eV(SP),吸附距离0.51 A。与H、O作用的Pu原子数目是决定吸附的主要因素。电子从表面转移到H原子,吸附作用主要发生在第一层。Pu 5f,6s,6d电子和H的2s电子有杂化成键作用。O吸附作用主要发生在第一层,但(100)面心位吸附时第二层Pu原子也发生电子相关作用。相对裸露表面,O的吸附使Pu的5f轨道向费米能级更低处移动,成键主要为O 2p轨道和Pu 5f 6s,6d轨道杂化成键,O从金属获得电子形成σ键。吸附后的表面功函都有增加,电子转移量,表面功函增加量和吸附稳定性都是O吸附大于H吸附的情况。
H和O在(100)面心位吸附的计算结果与文献有很大差别,主要是由于模型和吸附覆盖度的不同造成,因此应用不同的表面模型考察了吸附覆盖度的影响。在0.11ML到1.0ML覆盖度范围内,C在Pu表面不同吸附位的稳定规律类似与H和O,其中Hcp位仅略高于Fcc位。C的吸附能对覆盖度变化敏感,随着θ的增大而减小,变化几乎是线性的。(111)面吸附能最高点出现在0.25ML-0.33ML附近,最稳定吸附位的吸附能在5.3-5.6 eV范围。(100)面吸附能最高点在0.125ML-0.25ML附近,最稳定吸附位的吸附能为6.13 eV-6.60 eV。吸附C原子到表面的距离随着覆盖度的增加而减小。C吸附造成Pu表面电子向C偏移,形成表面偶极子,表面功函增加量和覆盖度成近线性关系。存在退极化效应,偶极矩随覆盖度的减小而增加。投影态密度和局域态密度表明C-Pu的相互作用主要为C2p轨道和Pu5f、Pu6p及Pu6d轨道成键,C-Pu键较强,是稳定的化学吸附。
N最稳定吸附位也为高对称心位。(111)面最稳定态的吸附能在2.4-2.7 eV范围,(100)面在3.2-3.9eV范围,强于(111)面,都属于化学吸附,但远弱于C、O原子而稍强于H原子。随着N原子覆盖度增加,吸附能变小。在高覆盖度下,Hcp或Fcc吸附位的N原子轻微偏离高对称的吸附位,N原子之间的核间距变小,N、N原子间有轻微的横向吸引作用。N吸附诱导表面功函数增加量与覆盖度成近线性关系,随着覆盖度的增加而增加。N原子的净的负电荷约多于C吸附情况,但吸附作用却小于C原子,这是因为部份电子进入了反键态。态密度分析表明N-Pu的相互作用形成成键态和反键态,成键态为N2p轨道和Pu5f、Pu6p及Pu6d轨道成键,反键态为N3s轨道和Pu7s轨道成键。反键态有占据电子,造成N-Pu键较弱,N吸附能较小。
覆盖度将影响H、O的吸附能和吸附结构,特别是在覆盖度较高的情况下。在较高覆盖度下,由于吸附原子之间会发生吸引或排斥作用,将使吸附结构较低覆盖度下的发生明显变化,吸附能也有所变化。(111)面吸附能最大值出现在0.25ML附近,(100)面最大值在0.4ML到0.5ML之间。覆盖度的影响要比C和N原子的影响小,特别是(100)面心位吸附情况。但电子态和吸附作用本质不发生改变。
H2分子的吸附是物理吸附。垂直吸附构型优于两种平行构型,其中心位垂直吸附为最稳定吸附结构。(100)面吸附能和吸附距离分别为0.1147eV,3.78(?)(NSP)和0.0961V,3.51(?)(SP)。(111)面为0.0940eV,3.85(?)(NSP)和0.0879eV,3.68(?)(SP)。相互作用只发生在第一层,吸附前后只有很少的电荷转移,表面功函轻微增加。H2在表面吸附后,键长增长,伸缩振动频率红移,分子得到活化。(100)面可能的离解方式有,从顶位Horl出发,离解为两个处于桥位吸附的H原子,或从顶位Hor2出发,离解为两个处于心位吸附的H原子,解离的能垒分别为0.527eV和0.562eV。(111)面,从顶位Horl吸附出发,离解为位于相邻两个中心位置的原子态吸附,离解能垒0.226eV。从顶位Hor2吸附出发,离解成两个处于相邻Fcc心位吸附位置的H原子,此时体系能量要比前一方式离解后体系能量稍低,但需要越过能垒稍大,为0.543eV。上述可能离解过程在热力学和动力学上均容易发生。以分子态吸附时,Pu的5f轨道和H的2s轨道能量差别相当大,Pu的5f电子和H的2s电子没有杂化成键作用,氢分子和钚表面的作用为Van der Waals相互作用。当离解为原子态吸附时,Pu的5f电子和H的2s电子有杂化相互作用,此时有更多的电子相互作用。
CO分子在δ-Pu表面分子态吸附为C端吸附,吸附主要发生在第一层。电子从Pu表面转移到CO分子上,表面功函明显的增加。相互作用主要源于CO分子的5σ和2π*轨道与Pu5f、Pu7s、Pu6d、Pu6p杂化轨道相互作用。(111)面最稳定吸附态是Hcp心位垂直吸附,吸附能为1.764eV(SP)和1.791eV(NSP), C原子距离Pu表面为1.922A和1.950A。离解为C原子和O原子吸附的体系能量稍高于分子态最稳定吸附体系能量,在较低温度下倾向于以分子态吸附。(100)面心位垂直吸附是最稳定的吸附态,其次是象桥位>桥位垂直>顶位垂直。心位垂直和象桥位吸附的吸附能分别为1.754eV(SP, center)和1.780eV(NSP, center)、1.717eV(SP, like-bridge)和1.778eV(NSP, like-bridge),相应的CO分子键长为1.23(?) (center)和1.20(?)(like-bridge)。键长增加、伸缩振动红移,表明CO分子活化。离解能垒为0.2eV,离解的C、O原子将占据能量最低的心位,与(111)面相反,离解吸附在能量上优于分子态吸附。
0：在Pu表面吸附后发生活化,O2分子键长增加,直到键断裂,离解成两个原子态发生吸附,氧原子优先处于心位和桥位。优化过程能量变化曲线和过渡态搜索结果都表明O2分子的离解吸附没有较大的能垒需要克服,这一过程在室温下自发发生。吸附能大小为两个氧原子的吸附能减去氧分子离解能。(100)面吸附能为8.14eV(NSP)和7.29eV(SP)。(111)面为7.56eV(NSP)和6.82eV(SP)。离解吸附后的电荷布局数,诱导表面功函、电子态等和前面O原子吸附的研究结果一致。
N2在δ-Pu表面各个吸附构型的吸附能相差较小,都在0.25-0.45eV范围内,属于较弱物理吸附,各个构型在一定温度内都可能存在。在低覆盖度(0.25ML)下,顶位垂直吸附相对最稳定,垂直吸附优于平行吸附。而到了较高的覆盖度,所有垂直吸附的吸附能大小几乎相同,而所有平行吸附构型优化后都翻转为垂直吸附,这是由于高覆盖度下,N2分子之间的排斥力使得发生构型翻转,最终的平衡结构都近于垂直或倾斜吸附。电子从第一层Pu原子流向吸附的N2,但电子转移作用很小,N2分子的负电荷一般在-0.3 eV以内,态密度分析表明成键态的占据电子很少。
H2O分子为较弱的物理吸附,(100)面各吸附能在0.05eV-0.20eV,(111)面在0.02eV-0.15eV,在有限温度下可以多种吸附态并存,吸附使水分子本身结构的改变极其微小,电子转移是极其微弱的,表面功函增加也很小。HO基面的吸附以氧端垂直吸附为优,稳定性为心位>桥位>顶位。Pu原子和OH基团之间有明显的电子转移。
论文第四章使用密度泛函理论计算了H、O、He等原子在δ-Pu金属体相中可能存在的结构和嵌入能。所有原子稳定存在于间隙位正中心,八面体间隙位较四面体间隙位更稳定。八面体间隙嵌入能,H为-3.12 eV(NSP)和-2.22eV(SP), O为-7.21eV(NSP)和-6.14eV(SP)。四面体间隙嵌入能,H为-2.43 eV(NSP)和-1.53eV(SP), O为-4.76eV(NSP)和-3.49 eV(SP)。H原子在八面体间隙位有更多的电子转移到H原子,H与Pu的作用更强,体系也更稳定,空间几何效应也使八面体间隙位更稳定。而两种间隙位氧原子负电荷差别很小,电子相互作用近似,能量的差别主要和空间几何效应有关。H原子最可能扩散路径为相邻不同间隙位的交替扩散,八面体间隙到四面体间隙的扩散能垒为1.06eV,反向扩散能垒0.38eV。平行晶轴方向四面体间隙到四面体间隙交替直线扩散的能垒为1.83eV,八面体间隙到八面体间隙交替扩散路径的势垒最高,大小为2.52eV。O最可几扩散路径为相邻不同间隙位之间的交替扩散,八面体间隙到四面体间隙的扩散能垒为1.12eV,反向2.72eV。四面体间隙到四面体间隙扩散能垒为6.40eV,八面体间隙到八面体间隙扩散能垒8.85eV。O扩散势垒都较高,氧原子在δ-Pu金属完美晶体中不易移动,稳定存在各个间隙位。钚金属在含氧气氛中易被氧化,形成很薄的氧化膜后不易进一步氧化,这可能也与氧原子不易向体相迁移有关。
与O和H的情况不同,氦原子嵌入能为正值,即使体系能量升高,向不稳定发展。氦原子使周围最近的一圈Pu原子向外扩张,使体系能量降低,不同间隙位的能差变小。对比H、O原子,氦对结构的影响要稍大。扩散能垒计算结果为：八面体到八面体间隙为3.51 eV；四面体到四面体间隙为2.16 eV；八面体到四面体间隙1.42 eV,四面体到八面体间隙0.34 eV。不同间歇位交替扩散为最可几的扩散路径。He在晶体中的迁移要比O原子的迁移容易的多。同样计算了C和N的间隙位结构和能量。对比可知,只有氦的嵌入使体系热力学稳定降低,且氦原子对结构的影响最大,由于Pu-He的相互作用较小,间隙扩散能垒较低,因此氦容易在金属体相中扩散迁移。C、N、O、H能稳定存在钚金属中的间隙位,和Pu原子发生强相互作用。其中C、O的嵌入能近似,成键作用非常强,可以推断能够形成稳定的钚氧和钚碳化合物。由于扩散能垒较高,表面的化合物一旦形成,就不容易向体相进一步演化。H和N的相互作用要相对较弱,扩散也相对容易。
δ-Pu金属体相单个空穴形成能时为0.786 eV(NSP)、0.784 eV (SP)。不同文献报道值介于0.7eV-1.7 eV之间,由于模型和方法不同,存在一定区别是合理的。以空穴为中心,空穴周围最近一圈的Pu原子向内收缩,第二圈的Pu原子略向外移。当两个空穴距离较远位置时,平均空穴形成能为0.767eV (NSP)和0.764eV(SP),和单个空穴形成能相差不大,结构变化也类似于单个空穴的情况。当两个空穴聚集在一起时,平均空穴形成能为0.636eV (NSP)和0.628eV(SP),小于单个空穴形成所需的能量。这表明聚集的空穴二聚体要比两个单独存在的空穴更稳定,预示着自辐射损伤产生的空穴有逐渐聚集的趋势。
第五章中,参考Baskes方法建立了针对δ-Pu金属的MEAM势。使用不同从头算方法和基组对Pu-He和He-He势能曲线进行了扫描,然后利用非线性最小二乘法拟合势能函数。将势函数引入相应的分子动力学程序,建立了Pu中氦行为的MD模拟方法。初步模拟表明,He原子位于八面体间隙位,最近的一圈Pu原子以He为中心向外驰豫,He原子结合能为2.90 eV,与前期的密度泛函计算结果一致。He原子在钚金属中形成了氦团簇,随着氦原子的增加,氦团簇也逐渐长大,一直到26个氦原子时,氦团簇仍然在生长。氦团簇周围的位错缺陷随着氦团簇的生长形成加剧,在氦团簇尺寸较小时(n<26),缺陷没有发生集体漂移。较小尺寸的两个氦团簇在一定临界距离内会发生融合的现象。初步模拟验证工作表明建立的方法能够准确的描述氦在钚金属中的体相行为。
在最后的第六章中,我们对整个计算模拟工作的结果进行了回顾,并提出了后续研究方向。
In the past decade, with the rapid development of computer hardware and quantum mechanics algorithm, computational modeling has become a powerful tool which can provide great insight in predicting properties of materials. This dissertation is devoted to the study of plutonium aging mechanism by computational modeling. Atomic and molecular adsorption onδ-plutonium surface have been studied in detail using the generalized gradient approximation to density functional theory, while some atoms diffusion behavior in perfect 8-Pu metal was studied by using density functional theory. Also the simulations of helium behaviors inδ-Pu metal are carried by molecular dynamics method.
In the first chapter, we focus on the research status of plutonium aging mechanism, and three mechanisms induced the aging of plutonium are presented. Methods and means, especially the results of the research are also presented to give some references to the related study. Based on the review of the status of plutonium computer simulation study, we presented our research ideas and direction.
Chapter 2 gives a brief description of the calculation methods which include the Born-Oppenheimer approximation, density-functional theory, Bloch theorem, local density approximation and generalized gradient approximation of the exchange-correlation energy, pseudo-potential methods, and supercell method. Also, the principle of molecular dynamics, the progress in related finite difference technique and interatomic potentials are summarized. At last some software using in this work are pointed out.
In chapter3, Adsorption of some atom and molecule onδ-Pu surfaces using the generalized gradient approximation of the density functional theory with RPBE functional have been studied at both the spin-polarized level and the nonspin-polarized level.
For hydrogen atom, we find that the center position of the (100) surface is the most favorable site with a adsorption energy of 3.16eV and an optimum distance of the hydrogen adatom to the Pu surface of 0.063nm at the non-spin-polarized level (NSP). For the spin-polarized (SP) (100) surface, the center site is again the preferred site with an adsorption energy of 2.26eV and an optimum hydrogen distance of 0.060nm. For theδ-Pu(111) surface, there is the same adsorption behavior of H atom. At NSP level, the center position ofδ-Pu(111) surface is the preferred adsorption site with adsorption energy 3.10eV and distance 0.139nm. At SP level, the center site is also the preferred site with adsorption energy of 2.20eV and a hydrogen distance of 0.139nm. The coordination numbers have a significant role in the chemical bonding process. Mulliken charge distribution analysis indicates that the interaction of Pu with H mainly takes place in the first layer and that the other two layers are only slightly affected. The adsorption of hydrogen atom onδ-Pu surfaces make the surface work functions of Pu metal distinctly increased.
For oxygen atom, the center position of the (100) surface is the most favorable site both at NSP and SP level calculation. The chemisorption energy and optimum distance of the oxygen adatom to the Pu surface are 7.614 eV,0.051nm (NSP) and 6.326eV,0.051 nm (SP) respectively. For theδ-Pu(111) surface, Hcp and Fcc sites are both favorable adsorption site with the same chemisorption energy and geometric structure. At the NSP level, chemisorption energy is 7.454 eV and optimum distance of the oxygen adatom to the Pu surface is 0.131 nm. For the SP surface, these values are 6.153eV and 0.131 nm respectively. The coordination numbers have a significant role in the chemical bonding process. Mulliken charge distribution analysis indicates that the interaction of Pu with O mainly takes place in the first layer and that the other two layers are only slightly affected. The surface work functions increases due to oxygen atom adsorption. The adsorption is strong ionic bonding action. The bonding between the oxygen and the Pu atom is due to the hydridization of O2p and Pu5f, Pu7s, Pu6d orbitals.
Adsorption of atomic carbon onδ-Pu surfaces have been investigated systematically using DFT with RPBE functional. The adsorption energies, adsorption structures, Mulliken population, work functions, layer and projected density of states have been calculated in wide ranges of coverage, which have never been studied before as far as we know. It is found that forδ-Pu(111) surface the Hcp-center sites are the energetically favorable sites for all the coverage range considered. Forδ-Pu(100) surface the center sites are the energetically favorable sites. The repulsive interaction has been identified, and the adsorption energy decreases with the coverage, while work function increases linearly with the coverage. It has been found that the C-Pu interaction is very strong due to the hybridization between the C2p states and the Pu5f, Pu6p, Pu6d states of topmost layer plutonium atoms.
Adsorption of atomic nitrogen has been investigated systematically in wide ranges of coverage. It is found that the center sites are the energetically favorable sites for all the coverage range considered adsorption energy 2.4-2.7 eV. Forδ-Pu(111) surface Hcp site are slightly more stable than Fcc site, which differed from most transition metal surfaces with hexagonal close-packed structure. The repulsive interaction has been identified, and the adsorption energy decreases with the coverage, while work function increases linearly with the coverage. It has been found that the N-Pu interaction is due to the hybridization between the N2p states and the Pu5f, Pu 6p, Pu 6d states of topmost layer Plutonium atoms. The N-Pu interaction is weak due to the partially occupied anti-bonding states from N 3s and Pu 7s hybridization.
Molecule hydrogen adsorption and the reaction barrier for dissociation onδ-Pu surfaces have been studied. On the 100 surface, vertical approaches on the center site both without and with spin polarization were found to be the most favorable molecular adsorption sites. The adsorption energy and the optimum distance were 0.1147eV,0.378nm and 0.0554eV,0.386nm respectively. Molecule hydrogen is active, for dissociate adsorption it was found that the most favorable dissociation channel needs activation energies of 0.527eV or 0.562eV On 111 surface, vertical approaches on the center site are also the most favorable molecular adsorption sites, with adsorption energy 0.0940eV at the non-spin-polarized and 0.0554eV at spin-polarized levels. The most favorable dissociation activation energy is 0.226eV, which molecule hydrogen dissociated to two center adsorption atomic hydrogen.
For CO molecule, the C-side center vertical position ofδ-Pu(100) surface is the preferred adsorption site with adsorption energy of 1.754eV (SP) and 1.780eV(NSP). And, the stability of adsorption configuration at other sites is like-bridge> bridge vertical> top vertical. Meanwhile, all parallel approaches turn to the corresponding C-side vertical or bridge vertical approaches, indicating C-side adsorption are more stable than O-side adsorption, and parallel approaches will not existent. The difference of adsorption energies for different sites such as like-bridge, bridge vertical, top vertical and center vertical is less than 0.2eV, that shows that CO adsorption on Pu(100) surface is the coexistence of several adsorbed at a limited temperature range. The hcp center Vertical position ofδ-Pu(111) surface is the preferred adsorption site with adsorption energy of 1.764eV (SP) and 1.791eV(NSP). The coordination numbers have a significant role in the chemical bonding process. The interaction between Pu atom and CO molecule results mainly from the contribution of 4σ、5σand 2π* orbital of CO molecule and 5f、7s、6d and 6p orbital of surface Pu atom. CO adsorption on Pu(111) surface tend to molecule adsorption state.
For oxygen molecule, dissociative adsorption is found to be energetically more favorable compared to molecular adsorption. The dissociative oxygen atom preferred adsorption on center site. For (100) surface the most stable chemisorbed site has an energy 8.14 eV(NSP) and 7.29 eV(SP). For (111) surface the most stable chemisorbed site has an energy 7.56 eV(NSP) and 6.82 eV(SP). The work functions increase, charge population, DOS and PDOS are similar with atomic oxygen adsorption behaviors.
Adsorption of molecule nitrogen has been investigated systematically in wide ranges of coverage. The adsorption energies are in the range of 0.25-0.45eV for all the case. It indicates that adsorption of molecule nitrogen is weak physical adsorption. The difference of adsorption energies for different adsorption configurations is less than 0.2 eV, it shows there are several adsorption configurations coexistence at a limited temperature range. At lower adsorption coverage (0= 0.25 ML), Top vertical adsorption configuration is most stable adsorption situation and all vertical configurations are more stable than corresponding parallel configurations. But at higher adsorption coverage all parallel configurations are turn to vertical configurations. This is due to repulsive interaction between molecule nitrogen. DOS and PDOS show occupation of bonding states is weak.
The adsorption energy of molecule water is very small. For (100) surface, the value are in the range of 0.05eV-0.20eV. For (111) surface, the value are in the range of 0.02eV-0.15eV. This indicates adsorption belong very weak physical adsorption.
In chapter4, The diffusion behavior of atom such as hydrogen, oxygen in perfect 8-Pu metal was studied by use of the density functional theory Doml3 and periodical model. The embedding energy and diffusion barriers of the single hydrogen were calculated at GGA level. A single hydrogen atom has the minimum embedding energy about -3.12eV and-2.22eV in the octahedral interstitial site of fccδ-Pu at Non-spin polarization and Spin-polarization level respectively. Hydrogen atom inδ-Pu crystal most preferably diffuses along the path linked with different interstitials. The diffusion barrier of along the path from octahedral interstitial site to tetrahedral interstitial site is 1.06eV. The diffusion barrier of reverse path is 0.38eV.
A single oxygen atom has the minimum embedding energy about -7.205eV and-6.140eV in the octahedral interstitial site of fccδ-Pu at Non-spin polarization and Spin-polarization level respectively. The embedding energy in tetrahedral interstitial site is little larger than that in tetrahedral interstitial site. Oxygen atom in 8-Pu crystal most preferably diffuses along the path linked with different interstitials. The diffusion barrier of along the path from octahedral interstitial site to tetrahedral interstitial site is 1.12eV. The diffusion barrier of reverse path is 2.72eV.
A single helium is stable in octahedral interstitial site with less embedding energy of 3.371 eV(NSP) and 3.137eV(SP). The embedding energy in tetrahedral interstitial site is 4.452 eV(NSP) and 4.433 eV(SP). Differed from hydrogen and oxygen atom, the embedding energy of helium is positive, which indicate that helium atoms embedding increase the total energy of system and make system instable. Helium atom inδ-Pu crystal most preferably diffuses along the path linked with different interstitials. The diffusion barrier of along the path from octahedral interstitial site to tetrahedral interstitial site is 0.34 eV. The diffusion barrier of reverse path is 1.42 eV. The diffusion of helium is easy.
The mono-cavity formation energy inδ-Pu metal is 0.786 eV(NSP) or 0.784 eV(SP). The di-cavity formation energy inδ-Pu metal is 0.636 eV(NSP) or 0.628 eV(SP). This shows there is a trend of cavity accumulation.
In chapter 5, the helium behavior in plutonium crystals has been simulated by molecular dynamics method. The modified embedded atom method (MEAM) potential is use for describing the interactions of plutonium-plutonium. The analytical potential energy curve for the Pu-He and He-He are scanned using B3P86 method, and then fitted to the exp-6 function using least squares. The growing and coalescence of helium clusters have been investigated at 300 K.
In the final Chapter, we summarize the computer simulation results, and some directions of further researches are pointed out.
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