1.College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China 2.College of Aeronautics and Astronautics, Taiyuan University of Technology, Jinzhong 030600, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 51871159, U1860204) and the Natural Science Foundation of Shanxi Province, China (Grant No. 201801D221125)
Received Date:24 February 2021
Accepted Date:12 April 2021
Available Online:07 June 2021
Published Online:20 August 2021
Abstract:Boron, a commonly used microalloying element in steel, is distributed mainly at the grain boundary of stainless steel and plays an important role in regulating the mechanical, corrosion resistance and grain boundary structure of stainless steel. Owing to the small amount of boron added into the steel, it is difficult experimentally to detect the traces of boron segregation at the grain boundary, not to mention analyzing the structural characteristics of the boron segregation grain boundary. First-principles density functional theory (DFT) provides convenience in analyzing the existence mode and mechanism of boron in austenitic steel from the atomic level. Combining with the actual grain boundary structure types in austenitic stainless steel, Fcc-Fe Σ3(112), Σ5(210), Σ5(310), Σ9(114), Σ9(221) and Σ11(113) symmetric tilt grain boundaries are constructed based on DFT, and the segregation behaviors of boron atoms at the six grain boundaries are studied to reveal the segregation mechanism from the atomic and electronic level. The results show that boron segregation occurs mostly at Σ5(210), Σ5(310) and Σ9(114) grain boundaries, while a relatively weak segregation tendency is observed at Σ9(221), Σ3(112) and Σ11(113) grain boundaries; boron atom preferentially occupies the pentahedral or hexahedral segregation position with the largest coordination number; the interface adhesive strength at grain boundaries is improved by the segregation of boron according to the tensile test, which complies with the calculation results of Rice-Wang thermodynamic model; the chemical effect caused by the increase of local charge density after boron segregation at Σ9(114) grain boundary outstrips the adverse effect of structural changes, and the strong interaction between B-p electrons and Fe-s electrons improves the interface adhesive strength. The results provide a reference for using boron to optimize the interface structure of austenitic stainless-steel. Keywords:austenite steel/ boron/ first-principles/ segregation/ interface adhesive strength
图2为B原子在六种晶界不同间隙位的溶解能$ {E}_{\mathrm{B}}^{\mathrm{s}\mathrm{o}\mathrm{l}} $, 可以看出B原子在Σ3(112)晶界3种间隙位的溶解能差异较大, 在2, 3号间隙位溶解能为负值, 分别是–1.14和–6.63 eV, 即B原子在3号间隙位要比2号更为稳定. B原子在Σ5(210)晶界最佳的稳定间隙位是3号位, 次稳定偏析位置是2号位; B原子在Σ5(310)晶界最佳的稳定析出间隙位是1号位. 结合表1, Σ9(114)与Σ5(210)晶界有相近的晶界能和过剩体积, 它们对应的B原子的稳定存在间隙位的数量和溶解能数值很相近, 溶解能均为较小的负值. B原子在Σ9(114)晶界最佳的稳定析出间隙位是3号位, 溶解能为–8.02 eV. 对于Σ9(221)晶界, B原子只有1个间隙位的溶解能为负值, 即3号位, 溶解能为–7.32 eV. B原子在Σ11(113)晶界2—4号间隙位的溶解能均为负值, 其中3, 4号位的溶解能最小, 均为–6.27 eV, 所以B原子在Σ11(113)晶界有2个稳定析出间隙位. 后边所做的讨论, 均是针对B原子在这6个晶界的稳定析出间隙位(图1(a)—(f)晶界模型中以红色标注)进行的. 结合表1对比, B原子在各晶界溶解能的大小与晶界处可能的间隙位多面体的体积没有明显的相关性, 这与已有杂质偏析的研究结果类似[16,17,48,49]. 图 2 B在6个晶界中不同间隙位置的溶解能 Figure2. The solution energies for B at different interstitial sites in the six studied grain boundaries.
由上述B在6个晶界的稳定间隙位, 分析其偏析能$ {E}_{\mathrm{s}\mathrm{e}\mathrm{g}}^{\mathrm{B}} $. 图3为B原子在6个晶界对应的偏析能, B原子在Σ5(210)、Σ5(310)和Σ9(114)晶界最佳的稳定偏析位的偏析能显著低于其在Σ3(112)、Σ9(221)和Σ11(113)晶界的偏析能, 表明这3个晶界捕获B原子的能力更强, 明显优于Σ3(112)等3个晶界. B原子在其他3个晶界偏析能分别为: Σ9(221)(–3.86 eV) < Σ3(112)(–3.17 eV) < Σ11(113)(–2.81 eV). 结合表1来看, 由于Σ3(112)和Σ11(113)晶界的晶界能和过剩体积都较小, 结构更紧凑, 所以奥氏体钢中晶界占比最大的Σ3(112)晶界相比于Σ5(210)、Σ5(310)和Σ9(114), 捕获B原子的能力较弱. 图 3 B原子在6个晶界中最稳定的偏析位点上的偏析能 Figure3. The segregation energies for B at the most stable segregation sites of the six studied grain boundaries.
图4给出了B原子在6个晶界相对稳定的偏析位的强化能$ {E}_{\mathrm{s}\mathrm{t}\mathrm{r}} $. 由于B原子在Σ5(210), Σ9(114)和Σ11(113)晶界有2个相对稳定的析出位, 所以本部分对B原子在Σ5(210)等3个晶界的2个稳定析出位均计算了强化能, 见图4. 可以看出, B原子在Σ5(210)、Σ9(114)和Σ11(113)晶界2个相对稳定析出位的强化能的数值接近. B原子在6个晶界稳定偏析位的强化能均为负值, 说明B原子处于这些析出位时都能增强晶界的内聚能力、强化晶界, 这与目前已知的实验结果一致[50]. 对比发现, B原子在Σ9(114)晶界的强化能最低, 说明B原子对Σ9(114)晶界的强化程度最强, 对Σ9(221)晶界的强化效果次之, 强化程度依次为: Σ9(114) > Σ9(221) > Σ3(112) > Σ5(210) > Σ5(310) > Σ11(113). 结合图3, 对于奥氏体钢, B原子增强了易偏析Σ5(210), Σ5(310)和Σ9(114)晶界的结合能力, 同时也可改善晶界占比最大的Σ3(112)晶界的结合能力, 该结果为B原子偏析于奥氏体不锈钢晶界对界面结合能力的研究提供了理论依据. 图 4 B原子在6个晶界稳定偏析位的强化能 Figure4. The strengthening energies for B at the stable segregation sites of the six studied grain boundaries.
表2B原子在各晶界最佳偏析位的多面体结构模型、添加B原子前后的多面体的体积和体积增量、B原子与近邻Fe原子的键长, 以及引起晶界能的变化量 Table2.The local atomic configurations of the stable segregation sites, the volume and volume increment of the polyhedron without and with B, the bond length between B and neighboring Fe atoms, and the change of grain boundary energy caused by B segregation when B at the stable segregation sites.
图5给出了晶界加B原子前后对各晶界拉伸获得的抗拉强度曲线, 曲线的峰值对应其理论抗拉强度σmax. 可以看出, Σ5(310)晶界的理论抗拉强度最大, Σ11(113)和Σ9(114)晶界次之, 然后是Σ5(210)和Σ9(114)晶界, Σ3(112)晶界的理论抗拉强度最小. 添加B原子之后, 可以看出, 除Σ5(310)晶界外, 界面含B后均可提高晶界的理论抗拉强度值, B对Σ9(221)晶界强度的影响最明显, 理论抗拉强度增加了16%. 这应该与Σ9(221)晶界有最大的过剩体积相关, 而Σ3(112)和Σ11(113)晶界结构紧凑, 对比来看该晶界理论抗拉强度增量相对较少. 与其他5个晶界不同, B原子偏析对Σ5(310)晶界的拉伸强度有一定的减弱, 结合表1, Σ5(310)晶界具有最大的晶界能, 晶界失配度最大, 相对稳定性较弱, 以上因素造成B原子偏析使Σ5(310)晶界拉伸强度降低. 6个晶界的断裂能的变化规律与理论抗拉强度一致, 除Σ9(114)晶界的分离特征长度基本不变, B原子处于晶界后, 其他5个晶界的分离特征长度都减小, Σ3(112)晶界减少的最多. 图 5 添加B原子前后6个晶界的抗拉强度曲线 Figure5. Tensile strength curves of the six studied grain boundaries without and with B.
Σ9晶界属于Σ3n (1 ≤ n ≤ 3)类型晶界, Σ3和Σ9晶界在奥氏体不锈钢中占比很高, 因为B原子在Σ9(114)晶界易偏析且强化晶界, 故本部分以Σ9(114)晶界为研究对象, 计算其电荷密度及态密度. 图6给出了添加B原子前、后Σ9(114)晶界的电荷密度图, 对比发现, 尽管B原子偏析使Σ9(114)晶界处上下层的Fe原子之间的距离由偏析前的2.57 ?增加到偏析后的3.04 ?, 但晶界处原子电荷得到补充, 晶界处原来的电荷低密度区域消失, 而晶胞内的电荷密度几乎没有变化. 图 6 添加B原子前后, Σ9(114)晶界体系(a)未形变及(b)均匀拉伸12%变形量后的电荷密度图 Figure6. The charge density of (a) undeformed and (b) 12% tensile deformed Σ9(114) grain boundary without and with B
图6给出了添加B原子前后, Σ9(114)晶界体系均匀拉伸12%变形量后晶界的电荷密度图. 可以发现, 经过12%的拉伸形变后, 无B晶界处原来的电荷低密度区域明显扩大, 说明晶界处是材料结构的最薄弱处, 随变形量的增加材料将在晶界界面处发生断裂. 而晶界含B后, B原子在晶界间隙位的偏析使得晶界处的电荷分布区域发生了变化, 尤其形变后的晶界结构仍保持完整, 且B原子使得周围的电荷密度增多、晶界的抗拉能力明显增强. 晶内的电荷密度变化不大, 晶界处较大空隙处开始出现电荷低密度区, 这说明B原子偏析前后的断裂面均通过晶界中心面. 基于Rice-Wang热力学模型, 计算出B原子偏析前后Σ9(114)晶界的断裂能, 由5.696 J/m2增大到6.032 J/m2, 与拉伸曲线得到的断裂能数值(5.732 J/m2和6.047 J/m2)基本一致. 综上, 该结果为B偏析于晶界后对界面结合能力的影响给出了直观的认识. 图7给出了添加B原子前后Σ9(114)晶界的总态密度图, 以及B原子附近的Fe1, Fe2原子(标号与表2相同)和B原子的分波态密度图. 从添加B原子前后Σ9(114)晶界的总态密度图可以看出, 总态密度主要来源于Fe-d电子贡献, B偏析到晶界对总态密度无明显的影响, 但是使费米能级附近的峰值高度下降, 总态密度略向低能方向偏移, 使体系更加稳定. 从分波态密度来看, B-s电子的贡献主要来源于费米能级以下–9 eV至–8 eV区域, B-p电子主要来源于–7—1 eV区域, 使得紧邻的Fe-s、Fe-p电子态在–10 eV至–7 eV能量范围的态密度有所升高且区域明显变宽, Fe-d尤其是Fe2-d电子态在费米能级附近的态密度明显升高. 这说明Fe电子的自由度更强, 离域性变大, 与B原子成键的程度增强. 另B-p电子与Fe-s特别是Fe2-s电子的态密度峰形一致, 说明B-p和Fe-s电子之间存在轨道杂化. 综上, 偏析的B原子和Fe1、Fe2原子之间的电荷富集, 提高了B、Fe原子间的化学键合强度, 有利于B与邻近区域原子的结合. 图 7 (a)未添加B原子和(b)添加B原子Σ9(114)晶界的总态密度图, 以及B原子附近Fe1, Fe2和B原子的分波态密度图 Figure7. The total density of states (TDOS) of Σ9(114) grain boundary without and with B atom, correspond to (a) and (b) respectively, and the projected density of states (PDOS) of Fe atoms in the vicinity of B atom (Fe1 and Fe2)and B atom.