固体内及び固体表面上における水素同位体の量子状態

Abstract

これまで，固体中および固体表面上における軽元素原子の量子状態を第一原理的に計算する手法を開発してきた．特に対象となる原子は，軽水素(H)，重水素(D)，三重水素(T)，ミュオニウム(Mu)等の水素同位体である．本稿では現状の計算手法とそれを用いたいくつかの計算結果を紹介する．この手法による計算結果は，定量的に実験結果と良い一致を示しており，材料中水素の特性解析に有用である．水素同位体原子の量子状態は，学術的興味だけでなく，今後の水素関連技術の材料開発に，必須の知見になると考えられる．

Figures

Figure 1.

 Potential energy, U₀, for hydrogen motion near Pd(111), as a function of the hydrogen position vectors, (X,Y,Z) [1]. Z-axis is perpendicular to the surface and the origin of Z is at the position of the Pd atom in the first surface layer. The areas of Z > 0 and Z < 0 correspond to vacuum and subsurface areas. The blue balls indicate the Pd atom positions. (a)Z-dependence of U₀ at Top, Bridge, FCC hollow and HCP hollow sites. (b) Top view of unite cell. (c) Bird's eye view of U₀(X,Y,Z). Its energy scale color bar is shown in the upper part of (a).

Figure 2.

 Eigenenergies E_n,0of the ground state (n = 0) and the nth excited states (n > 0) of hydrogen isotope atom (Mu, H, D, T) motion on Pd(111) [1]. The energy origin is the sum of the total energies of hydrogen isotope atom and Pd surface isolated from each other.

Figure 3.

 Isosurface of the wave function for H motion on Pd(111) in its ground (a), 1^st excited (b), 2^nd excited (c), 3^rd excited (d) and 4^th excited (e) states [1]. The yellow and cyan areas show the positive (+0.23 Å^-3/2) and negative (−0.23 Å^-3/2) value parts of wave functions.

Figure 4.

 Same as Figure 3 but for Mu motion on Pd(111) [1].

Figure 5.

 The hydrogen adsorbed graphene structure optimized by VASP [1]. Yellow (blue) balls indicate the carbon (hydrogen) atoms.

Figure 6.

 Eigenenergy spectrum for hydrogen motion adsorbed on graphene [1,9]. The numbers in parentheses are degeneracies of the energy levels of a hydrogen atom motion.

Figure 7.

 Hyperfine interaction of the positive muon as a function of its position along the line of Si atom position, BC-site, Si atom position, T-site and Si atom position in the diamond structure silicon crystal [11].

Figure 8.

 The ground state wave function (yellow) and eigenenergy spectrum (green) for Mu motion in α-SiO₂ crystal. Red (cyan) balls indicate the oxygen (silicon) atoms. Lattice structure figures were plotted using the VESTA package [23].

Tables

Table 1.  The vibrational excitation energies of H atom adsorbed on Pd(111) [1].

	Vibrational excitation energy (meV)
	Parallel to the surface (||)	Perpendicular to the surface (⊥)
Calculation results	101	121
Experimental results [19]	96	124
Relative differences	+5.2%	−2.4%

Table 2.  The isotope effects on the vibrational excitation energies between H and D atoms adsorbed on Cu(111) [1].

	Vibrational excitation energy (meV)		Isotope effects
	H on Cu(111)	D on Cu(111)	Ratio
Calculation results	135	104	1.29
Experimental results [20]	129	96	1.34
Relative differences	+4.7%	+8.3%	−3.4%

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