Annihilation of Positrons in Hydrogen-Saturated Titanium K
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Physics of the Solid State, Vol. 45, No. 1, 2003, pp. 1–5. Translated from Fizika Tverdogo Tela, Vol. 45, No. 1, 2003, pp. 3–7. Original Russian Text Copyright © 2003 by Aref’ev, Boev, Imas, Lider, Surkov, Chernov. METALS AND SUPERCONDUCTORS Annihilation of Positrons in Hydrogen-Saturated Titanium K. P. Aref’ev*, O. V. Boev*, O. N. Imas*, A. M. Lider*, A. S. Surkov**, and I. P. Chernov* * Tomsk Polytechnical University, Tomsk, 634034 Russia ** Fraunhofer Institute of Nondestructive Control Methods, Saarbrücken, D-66123 Germany e-mail: [email protected] Received May 4, 2002 Abstract—The effect of atomic hydrogen on the electronic structure of α-titanium samples is studied using the electron–positron annihilation methods. It is shown that different states of hydrogen atoms are manifested in different ways in the positron lifetime distribution spectrum. The results of theoretical calculations of the first component of the positron lifetime are in accord with the obtained experimental data. © 2003 MAIK “Nauka/Interperiodica”. 1. INTRODUCTION genated titanium and the experimental data. A unique instrument for solving this problem is the electron– Metals are the most important structural materials. positron annihilation (EPA) method, which directly However, hydrogen corrosion of metals can become a provides information on the electronic structure of hazard. In this respect, commercial operation of equip- defects in the material under investigation. In this work, ment used in the oil-and-gas, chemical, and nuclear- the EPA method was used in the diagnostics of the state power industries, where hydrogen and hydrogenous of titanium articles and structures in contact with media constitute a considerable part of the working hydrogenous media at the stage preceding brittle frac- atmosphere, can be highly dangerous. The change in ture. We measured the positron lifetime and Doppler the physical and mechanical properties of metals and broadening of the annihilation γ line (DBAL). The alloys under the action of hydrogen is a serious prob- DBAL parameters, the mean positron lifetime, and its lem. The materials used usually have to combine resis- different components associated with annihilation of tance to high stresses with an admissible high-temper- positrons in the region of positron-sensitive defects ature strain. However, the effect of hydrogen on their provide quantitative and qualitative information on the strength parameters is determined to a considerable type and concentration of such defects. extent by the chemical composition of the material. For Positron annihilation in metal hydrides was studied example, the limiting admissible concentration of earlier in [3–5] by analyzing the angular distribution of hydrogen is 0.5 at. % for commercially pure titanium annihilation photons (ADAP) and the positron lifetime. (BT1-0) and 1.0 at. % for the alloy TiV13Cr11Al13 [1]. The lifetime of quasi-free positrons was calculated the- This study is devoted to the effect of atomic hydro- oretically only for “complete” hydrides (TiH2) [6]. The gen on the mechanical properties of titanium. Upon the effect of hydrogen on the dynamics of formation of absorption of hydrogen under normal pressure, the defects (craters and cracks) in titanium BT1-0 was crystal lattice of α titanium expands and the ratio c/a of investigated visually in [2] with the help of scanning the hcp-lattice parameters decreases. Hydrogen disso- microscopy and by measuring the mean positron life- lution in a metal is characterized by a nonuniform dis- time. In this work, we investigated samples of commer- tribution of this gas from the surface to the bulk. It is cially pure titanium hydrogenated to the composition this nonuniform distribution that explains the occur- TiH0.01 and calculated the electronic structure, the rence of different extents of material degradation at the positron spectrum, and positron characteristics of α-Ti α surface and in the bulk. For example, after electrolytic and -TiH0.125, which were then compared with the saturation of titanium samples with hydrogen for experimental data obtained by the EPA method. 360 min, “traces of damage” can be fixed on the surface in the form of an elevated concentration of dislocations [2]. However, we did not observe destruction of the 2. MATERIALS AND EXPERIMENTAL entire titanium sample in the atomic-hydrogen concen- TECHNIQUE tration range up to 11 × 10–5 at. %. We endeavored to The electronic band structures of pure α-Ti and α establish the mechanisms of variation of the properties -TiH0.125 were calculated using the self-consistent of titanium under the action of hydrogen by comparing method of linearized muffin-tin orbitals in the atomic- the calculated electronic structures of ideal and hydro- sphere approximation (LMTO-ASA) with the Ceper- 1063-7834/03/4501-0001 $24.00 © 2003 MAIK “Nauka/Interperiodica” 2 AREF’EV et al. Table 1. Parameters of the electronic structure of ideal α-Ti: abilities of positron location in various atomic spheres Γ Fermi energy EF relative to zero crystal energy, width EF – 1 (including the sphere occupied by a defect such as of the occupied part of the conduction band, total energy Etot, hydrogen), as well as the annihilation rates and the density of states N(EF) at the Fermi level, and hcp lattice positron lifetime. The method of calculating positron parameters a and c states is described in detail in [10, 11]. Simple Large Simple unit Annihilation parameters of positrons were mea- Parameter unit cell unit cell cell, APW sured on paired BT1-0 titanium samples (with contents (2 atoms/cell) (8 atoms/cell) method [8]* of Fe less than 0.18 at. %, Si less than 0.10 at. %, C less a, nm 0.2951 0.5902 0.2951 than 0.07 at. %, O less than 0.12 at. %, and N less than 0.04 at. %). A sample of BT1-0 was subjected to pre- c, nm 0.4684 0.4684 0.4684 liminary annealing at 750°C in vacuum, followed by ° EF, Ry 0.630 0.631 0.5953 slow cooling to 20 C. Paired samples were saturated Γ electrochemically with hydrogen in monomolar elec- EF – 1, Ry 0.475 0.474 0.466 trolyte LiOH (the electrolyte was thermostatically con- Etot, Ry –15.107 –15.101 trolled at 20°C) for 20, 60, 120, and 360 min. Immedi- N(E ), states/Ry 30.37 24.25 16.12 ately after the saturation of a sample with hydrogen, the F lifetime and Doppler spectra were measured simulta- * The augmented plane wave method. neously at T = 25°C. An Na22 isotope having an activity of the order of 106 Bq was placed between two identical τ parts of the sample under investigation and used as a Table 2. Theoretically calculated positron lifetime and the 22 positron probability distribution w over atomic spheres s, as source of positrons. The radioactive source was Na Cl well as the corresponding electron charge Q in atomic salt vapor-deposited on a 20-µm-thick aluminum foil. spheres and the probability ω of positron annihilation with The instant of position creation was detected by nuclear conduction electrons γ radiation with an energy of 1.28 MeV emitted almost simultaneously with the positron, while the instant of α-Ti α-TiH γ τ τ 0.125 annihilation was determined from the annihilation = 158.1 ps = 154.5 ps radiation with energy 0.511 MeV; the time resolution of s s s s the setup used was 240 ps. The positron lifetime distri- Ti Ti H E bution was processed using the standard Resolution w, % 100 32.25 4.90 62.85 program [12]. The DBAL was measured synchronously ω with the positron lifetime by using a Ge detector with a , % 100 42.19 5.35 52.46 resolution of 1.2 keV operating on the 0.5-MeV line. Q, el./atom 22 20.47 2.48 1.48 The DBAL spectrum was processed with the help of the LIFESPECFIT program [13, 14]. ley–Alder exchange-correlation potential [7]. The crys- tal lattice was simulated by repetitive hexagonal large 3. DISCUSSION unit cells with eight titanium atoms (the lattice param- eters for titanium are a = 0.2951 nm and c = 0.4684 nm In the low-hydrogen-concentration simulation of [8]). A hydrogen atom was placed in an octahedral pore the unit cell of the titanium crystal, an hcp unit cell with a doubled parameter a was used for calculating the with coordinates (1/4; 3 /12; c/4) in the units of the electronic structure. In order to unify the approach, the lattice parameter a. The remaining seven octahedral electronic structure of perfect α-Ti was calculated pores were filled with additional empty spheres (E) using the same algorithm. The correctness of this with zero charge density to include the crystal-potential approach is confirmed by the closeness of the results anisotropy in the model. The self-consistence proce- obtained with different schemes [calculations with a dure was carried out over 90 k points in the irreducible simple and a large unit cell (two and eight atoms per part of the Brillouin zone for an hcp unit cell and termi- unit cell, respectively)] in our work and in the literature nated when the change in the energy eigenvalues did [8] (Table 1). The electron energy spectrum and the not exceed 0.003 Ry and when the change in pressure lower positron band for TiH0.125 are shown in Fig. 1. calculated from the Pettifor formula [9] on each itera- The positron band has a parabolic form corresponding tion did not exceed 1 kbar. The quasi-free states of a to the quasi-free positron state [10]. Table 2 lists the positron in the crystal were described under the charge distribution, the positron probability distribution assumption that the effect of the positron on the elec- over atomic spheres, and the positron annihilation tron system is negligibly small; positron states were probability in the atomic spheres, as well as the calculated on the basis of the electron density, which positron lifetime, which will be henceforth associated was self-consistent in the absence of a positron.