P在α-Al2O3中电场梯度的第一性原理计算 学 生：张乔丽 指导老师：张焕乔院士 朱升云研究员

张乔丽，袁大庆，张焕乔，范平，左翼，郑永男，朱升云 China Institute of Atomic Energy, Beijing, China K.Masuta，M.Fukuda，M.Mihara Department of Physics, Osaka University, Osaka Japan T.Minamisono Fukui University of Technology, Fukui Japan A.Kitagawa National Institute of Radiological Sciences, Chiba, Japan

引言 理论基础与计算方法 晶格结构与计算模型 结果与讨论

β-NQR spectrum for 28P in α-Al3O2 引言 核四极矩测量 β-NQR 28P：Iπ=3+,T1/2=270.3ms 2011.6 该实验是在日本放射线医学综合研究所的HIMAC重离子加速器上进行 νQ=190 kHz β-NQR spectrum for 28P in α-Al3O2

q:EFG traceless tensor β-NQR νQ=3eVzzQ/2I(2I-1)h q:EFG traceless tensor With traceless principal component asymmetric parameter Vzz η

理论基础 第一性原理密度泛函理论 Hohenberg-Kohn定理 （多体理论） 1、不计自旋全同费米子系统的基态能量是粒子数密度函数的唯一泛函。 2、能量泛函在粒子数不变条件下对正确的粒子数密度函数取极小值，并等于基态能量。

Kohn-Sham方程 （ 有效单体理论） 粒子数密度 Local Densities Approximation (LDA) 核心思想：用无相互作用电子系统的动能代替有相互作用的动能，而将有相互作用的电子系统的全部复杂性归入交换关联相互作用泛函。 Local Densities Approximation (LDA) General Gradient Approximation (GGA)

计算方法 Augmented Plane Wave method 将原胞分成两部分 计算量很大 ——Slater’s APW (1937) Ⅰ Ⅱ Rt Ⅱ: Ⅰ: 组合系数 径向波函数 球谐函数 计算量很大

Linearized APW method LAPW Full Potential LAPW —by O.K.Andersen 1975 LAPW Full Potential LAPW The potential (and charge density) can be of general form (no shape approximation) inside sphere outside sphere Inside each atomic sphere a local coordinate system is used (defining LM)

Wien2k程序包 EFG V(0) :Coulomb potential Coulomb potential can be determined from the total charge density in the crystal by solving Poisson’s equation. P.Blaha Austria Vienna University of Technology

晶格结构与计算模型 Al2O3 hexagonal structure space group: R-3c 167 Lattice parameter a =b=4.757Å, c = 12.9877 Å muffin-tin radii: for Al, P, O 1.7 a.u,1.7 a.u and 1.5 a.u. RKMAX= 8 controls the size of the basis set Brillouin zone: 6×6×6 k-mesh, corresponding to 44 k-point tolerance value: 0.025eV/Å Parameters for calculation O1 O2 Al2O3的空间构型

影响EFG的因素 P-doped Al2O3 P的化合价： (1) P +3价 中性胞 (2) P +5价 电荷胞 晶格弛豫：最近邻两个氧原子（O1和O2）晶格位置的弛豫主要影响P的EFG 交换关联势

and EFGs at the substituted Al site for the relaxed structure 结果与讨论 Calculated distances between the P impurity and its nearest oxygen neighbors and EFGs at the substituted Al site for the un-relaxed structure d (P-O1) Å d (P-O2) Vzz 1021Vm-2 Vzz direction η LDA (Neutral cell) 1.854 1.971 0.208 Z WC-GGA(Neutral cell) 0.193 LDA (Charged cell) 0.478 WC-GGA(Charged cell) 0.476 Calculated distances between the P impurity to its nearest oxygen neighbors and EFGs at the substituted Al site for the relaxed structure d (P-O1) Å d (P-O2) Vzz 1021Vm-2 Vzz direction η LDA (Neutral cell) 1.948 2.121 0.436 Z WC-GGA(Neutral cell) 1.940 2.125 0.338 LDA (Charged cell) 1.719 1.782 0.497 WC-GGA(Charged cell) 1.723 1.789 0.516

P-doped Al2O3 Densities of States The DOS of pure Al2O3 and the two relaxed cells The partial DOS of P and O atoms

2×2×1Al2O3超胞空间结构 WC-GGA d (P-O1) Å d (P-O2) V33 1021V/m2 V33 direction η Charged cell 1.723 1.789 0.516 Z 2×2×1 charged supercell 1.730 1.798 0.573

Thank you！ 结论 Q EFG νQ=3eVzzQ/2I(2I-1)h νQ=190 kHz EFG /1021V/m2 LDA WC-GGA Supercell 0.497 0.516 0.573 Deduced Q 158mb 152mb 137mb Shell model 120mb Thank you！