Monovacancy Formation Enthalpy Research Articles

Assessing the high concentration of vacancies in refractory high entropy alloys

Accurate determination of monovacancy formation enthalpy is vital for work on diffusion, melting point determination of high temperature materials, radiation damage, and thermophysical stability of alloys. These enthalpies take on a single value in pure metals but is made more complex in concentrated solid solutions due to the local chemical environments possible around each vacancy. Herein, using first-principles density functional theory, we report the distributions of vacancy formation enthalpies in 21 equiatomic 5-component solid-solution alloys from the Hf-Mo-Nb-Ta-Ti-W-Zr system. Chemical disorder is treated using the special quasi-random structure method, and the chemical potential of vacant element is treated by approximating it to its total energy in its standard state. We find that the highest vacancy formation enthalpies belong to the MoNbTaTiW alloy (which incidentally is the most reported in literature) and the lowest belongs to HfNbTaTiZr, with other alloys in-between. We use the whole distribution of formation enthalpies to estimate the equilibrium concentration of vacancies as a function of temperature.

Theoretical calculation on electronic excitation and compression effect in tungsten

The vacancy formation enthalpy of tungsten under the condition of intense laser irradiation and compression has been investigated from first-principles, respectively. The results show that the monovacancy formation enthalpy of tungsten tends to increase as the electronic temperature is increased, which can explain the fact that the melting process becomes more difficult under high electronic temperature. In addition, the monovacancy formation enthalpy of tungsten is found to increase from 3.198eV at 0GPa to 4.184eV at 100GPa, which results in the retardation of diffusion under the condition of compression.

First-principles investigation on metal tantalum under conditions of electronic excitation

Intense laser irradiated on metals can excite the electrons to high energy levels, and lead to a high electronic temperature established in a period of 10–100fs. The properties of metals would be affected by the high electronic temperature. In this paper, finite-temperature density functional theory with hot electron is used to investigate the free energy F and DFT energy E of metal tantalum varying with the supercell volume at different electronic temperatures. In addition, the formation enthalpies of a monovacancy are calculated at different electronic temperatures. The convergence tests for the k-points grid, the bands and the supercell size we selected are carefully carried out to improve accuracy of calculation. The calculated value of monovacancy formation enthalpy at ambient pressure and temperature is good agreement with previous experimental and theoretical values. What is more, the tendency of the monovacancy formation enthalpy increasing as the increment of the electronic temperature can explain the fact that the increase of the melting temperature under high electronic temperature.

Formation enthalpies of monovacancies in aluminum and gold under the condition of intense laser irradiation

The formation enthalpy of a monovacancy in gold and aluminum under the condition of intense laser irradiation is evaluated by means of ab initio calculations. These simulations are performed using norm-conserving pseudopotentials and by taking advantage of an efficient parallelization scheme. Using constant-pressure simulations and for a set of electronic temperatures ranging from $0.01\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}6.0\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, fully relaxed geometries are thus obtained. Particular attention has been paid to the size of the supercell. We found that calculations up to 108 atoms are needed in order to obtain well-converged thermodynamic quantities. In this respect, the monovacancy formation enthalpy of gold increases more rapidly than for aluminum at high electronic temperatures, leading to a reduction of the monovacancy concentration. This result confirms the increase of the melting temperature and is in good agreement with ab initio linear response calculations previously reported.

Monovacancies and divacancies in copper: Reanalysis of experimental data

The vacancy concentrations c v in copper measured by means of the absolute technique (Hehenkamp et al., Phys. Rev. B 45 (1992) 1998) and those derived from positron lifetime studies (Kluin, Philos. Mag A 65 (1992) 1263) are reanalysed. Taking into account the results of quenching and annealing investigations the best fit to the temperature function of c v is described by H F 1v=1.03 eV and S F 1v/ k=1.1 for the monovacancy formation enthalpy and entropy and a divacancy binding enthalpy and entropy of H B 2v=−0.23 eV (attractive interaction) and S B 2v/ k=2.8, respectively. Accordingly, the divacancy concentration amounts to 1.5×10 −4 at the melting temperature.

Lattice Vacancies in High-Purity α-Iron

The paper is both a review of the properties of vacancies in high-purity α-iron and an original contribution. In the review part it is shown that self-diffusion in α-iron occurs by the vacancy mechanism, that the sum of the monovacancy formation and migration enthalphies in the magnetically fully ordered state is HF1V + HM1V = (2.91 ± 0.04) eV, and that for the monovacancy formation enthalpy 1.61 eV ≤ HF1V ≤ 1.75 eV holds. The result for the monovacancy migration energy, HM1V = (1.23 ± 0.11) eV, excludes with certainty the attribution of Stage-III recovery to vacancy migration and supports the view that the Stage-III defect is a self-interstitial. It is shown that at elevated temperatures positrons trapped in vacancies in body-centred cubic iron may escape from them. The binding energy of positrons to the vacancies is estimated to be about 1.1 eV. This estimate is in agreement with the analysis of the high-temperature trapping of positive muon by vacancies, which in the present case proved to be the most sensitive technique for detecting vacancies present in thermal equilibrium.

Monovacancy Formation Enthalpy in Silicon

Positron-lifetime experiments have been conducted on silicon at temperatures between 300 and 1523 K. A lifetime attributable to positrons annihilating in monovacancies is directly observed above 1450 K. This lifetime has the same value as that associated with monovacancies at low temperature indicating that the character of the monovacancy is essentially independent of temperature. The results yield an activation enthalpy for neutral monovacancy formation of 3.6 \ifmmode\pm\else\textpm\fi{} 0.2 eV. No evidence for divacancy formation could be found.

A monovacancy-divacancy model interpretation of positron annihilation measurements in aluminium

A monovacancy-model analysis of new temperature-dependent (in the range 293-903K) data of the peak-count rate, long-slit angular correlation of annihilation radiation (1D ACAR) for Al single crystals yields an apparent value for the monovacancy formation enthalpy (H1vF) of (0.76+or-0.04) eV. However, lifetime experiments of lower temperatures (293-645K) have yielded H1vF=(0.66+or-0.02) eV. A constrained monovacancy-divacancy analysis of the 1D ACAR data, incorporating theoretical predictions of the relative peak-count rates arising from monovacancy- and divacancy-trapped positrons, can resolve this apparent discrepancy between the lifetime results and momentum measurements (Doppler broadening or angular correlation) of the vacancy formation enthalpy in Al. This analysis yields a divacancy binding enthalpy of H2vb=(0.30+or-0.13) eV, and indicates that at the melting point about 60% of the positrons annihilate from divacancy-trapped states in Al, consistent with the interpretation of recent 2D ACAR results. Introduction of the ratio of the positron trapping rate into divacancies to that into monovacancies, mu 2v/ mu 1v, as deduced from the jellium-model calculations of McMullen et al. (1981) allows one to estimate the divacancy binding entropy S2vb as well. The results are compared with those of previous investigations of vacancy formation and self-diffusion in Al.

Temperature dependence of positron annihilation in tin

The Doppler broadening of the positron annihilation line in tin has been studied as a function of temperature in the range 295-640 K. The line shape was measured with an intrinsic germanium spectrometer and was analyzed in terms of a parameter $S$ which measures the peak-to-area ratio. A slow linear rise of $S$ with temperature $T$, $S=0.511(1+32\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}T)$ was observed up to $T=420\ifmmode\pm\else\textpm\fi{}10$ K followed by a steeper rise at higher temperatures. If this steeper rise is attributed to the onset of thermal vacancy effects, the monovacancy formation enthalpy ${H}_{1v}^{F}$ can be calculated using the semiempirical relationship ${H}_{1v}^{F}=14{k}_{B}{T}_{t}$ where ${k}_{B}$ is the Boltzmann constant and ${T}_{t}$ the threshold temperature for the appearance of thermal vacancies. A value ${H}_{1v}^{F}=0.51\ifmmode\pm\else\textpm\fi{}0.01$ eV is obtained. At the melting point, $S$ is found to increase abruptly and remain essentially constant thereafter. Cyclings of the sample temperature around the melting point revealed a large hysteresis effect, which is attributed to supercooling.

On the temperature dependence of the positron annihilation spectrum from a single crystal of zinc

The Doppler-broadened positron annihilation spectrum from a single crystal of zinc has been studied as a function of temperature and of the direction of photon emission. An anisotropy in the behaviour of the spectrum line height parameter was observed in the prevacancy temperature region with linear slopes 0.60*10-4K-1 in the (0001) direction and 1.02*10-4K-1 for (1010). Optimum fittings with the two-state trapping model gave differing values for the monovacancy formation enthalpy, implying an inadequacy in the present understanding of the prevacancy rise.

Precise Positron Lifetime Measurements in Indium

AbstractThe positron lifetime is measured in polycrystalline indium in the temperature range between 80 and 420 K. The data show a pronounced prevacancy effect which is fairly well approximated by a straigth line. The results suggest transient dilatation trapping rather than metastable self‐trapping. The occurrence of this effect has some influence on the values deduced for the monovacancy formation enthalpy. In the temperature range below 180 K detrapping of positrons cannot be ruled out.

A quantitative study of vacancy defects in quenched tungsten by combined field-ion microscopy and electrical resistometry

Abstract A study of quenched, high-purity tungsten has been carried out with a combination of field-ion microscopy (FIM) and electrical resistivity measurements. It is concluded that the quenched-in vacancy defects observed by FIM are monovacan-cies and nearest-neighbour divacancies. From the partitioning during quenching between these two species, a divacancy binding enthalpy H2V b≃0·7eV is deduced. A monovacancy resistivity of 7 × 10−4 Ω cm is obtained from the combined measurements. The quenched-in vacancy concentrations measured directly by FIM are consistent with previous results, if the total vacancy concentration at the melting temperature of tungsten (3695 K) is about 3 × 10−4 and the monovacancy formation enthalpy and entropy are 3·6 eV and 3·2k, respectively. The results are discussed in terms of the atomic-defect mechanisms for self-diffusion in tungsten.

The vacancy formation enthalpy in Ni determined by positron annihilation

The monovacancy formation enthalpy, H1vF, was determined for Ni using the Doppler broadening technique. The 58Co positron source was ion implanted in Ni of 99.995 wt.% purity. A 103Ru gamma -ray line (497 keV) was recorded simultaneously with the positron annihilation 511 keV line, and was used in stabilising the data. Measurements were performed on three similar Ni samples, which were annealed in an ultra-high vacuum chamber (10-8-10-9 Torr) at approximately 30 degrees C below their melting point for at least two hours prior to the in situ measurements. For one of the samples, a comparison was made of H1vF values deduced prior to and after in situ melting. A value of H1vF=1.8+or-0.1 eV was determined from the present data. In addition, a value for the monovacancy migration enthalpy, H1vM=1.1+or-0.1 eV, has been deduced from a comparison of the present H1vF measurement with previous self-diffusion results.

Lattice defects of V3Si single crystals studied by positron annihilation

The sensitivity of positrons to point defects created by the irradiation of V3Si with neutrons is demonstrated. We found no indication of thermal vacancies by thermal equilibrium measurement up to 1273 K which indicates that the monovacancy formation enthalpy for V3Si isH 1V F ≧(1.84±0.14) eV. Investigations within the range of homogeneity for excess vanadium suppot the idea that substitutional defects are the dominating defect type, whereas for excess silicon a direct confirmation of existing structural vacancies as the dominating defect type is given.

Positron lifetime studies of pure Ni from 4.2 to 1700K

Positron annihilation lifetime measurements are made for Ni over a temperature range from 4.2 to 1700K. It is found that there is almost no change in the lifetime from 4.2 to 900K indicating a very small thermal-expansion effect. A small precursor effect is observed before the onset of significant vacancy trapping. A monovacancy formation enthalpy of 1.54+0.2-0.1 eV is extracted from an analysis in which divacancies are not taken into consideration. No detrapping from monovacancies is observed even at the higher temperatures. An analysis wherein EF is deduced from a 'threshold temperature' for the lifetime data produces a value lower than that obtained in similar analyses involving Doppler broadening or angular-correlation measurements. The lower value of the threshold temperature found in this work is largely attributable to the value for the precursor slope obtained from lifetime measurements, being smaller than the values obtained by use of the other two methods.

Observation of Surface Traps and Vacancy Trapping with Slow Positrons

A beam of monoenergetic positrons incident on clean metallic surfaces has been employed to measure positronium yield as a function of sample temperature and positron energy. These results show an increase in the positronium fraction as a function of temperature which is identified as thermally activated detrapping of positrons from a surface trap. Estimates are made of the depths of these traps. Positrons are observed to trap at vacancies and a monovacancy formation enthalpy is extracted from the data utilizing a simple model.

Measurement of the monovacancy formation enthalpy in copper

The monovacancy formation enthalpy in copper, H1vF=(1.30+or-0.05) eV, has been measured using precision electrical resistometry on samples quenched from temperatures in the range 525-650 degrees C. Comparison of this value for H1vF with the activation enthalpy for self-diffusion via a monovacancy mechanism in copper, previously measured over the same temperature range, yields H1vM=0.77 eV for the enthalpy for monovacancy migration. This value compares well with the activation enthalpy for post-quench vacancy annealing, (0.76+or-0.04) eV, measured in the present work. The results are compared with those of previous investigations.

Positron annihilation in lead

Abstract The Doppler-broadening of the radiation from positrons annihilating in lead has been measured over the temperature range 4·2–600 K. The creation of mono-vacancies at the higher temperatures has been studied. On the basis of several hypotheses, including positron self-trapping and divacancy production, values of the monovacancy formation enthalpy have been estimated. The trapping of positrons by defects introduced by compression of the lead at 77 K has been investigated : complete annealing occurs before 300 K.

Measurements of the vacancy formation enthalpy in aluminum using positron annihilation spectroscopy

The temperature dependence of positron annihilation in aluminum has been investigated over the range 20-435\ifmmode^\circ\else\textdegree\fi{}C by simultaneous measurements of positron lifetime and Doppler broadening of the annihilation spectrum. The analyses of lifetime data are critically examined, especially with respect to the effects of instrumental resolution-function uncertainties. The lifetime and Doppler-broadening data have been analyzed in terms of the two-state trapping model. Application of this model to the measurement of the vacancy-formation enthalpy ${E}_{\mathrm{v}}^{F}$ in aluminum is discussed in light of the observation of a strong temperature dependence of the apparent positron lifetime in the bulk or lattice state above 370\ifmmode^\circ\else\textdegree\fi{}C. The monovacancy formation enthalpy in aluminum, ${E}_{1\mathrm{v}}^{F}=0.66\ifmmode\pm\else\textpm\fi{}0.02$ eV, was determined for temperatures below 372\ifmmode^\circ\else\textdegree\fi{}C. This is compared with values previously reported.

Positron trapping in indium

Simultaneous positron mean lifetime and annihilation photon lineshape studies of indium provide a value for the monovacancy formation enthalpy of (0.39±0.04) eV.