3.7 Изучение структурных дефектов в квазикристаллических и нано-материалах.
Schematic illustration of considered collinear magnetic spin configurations for (a) FM, (b) AFM[0001]1, (c) AFM[0001]A2 , (d) AFM[0001]X2 , (e) in-AFM1, (f) in-AFM2, (g) AFM[0001]A4 , (h) AFM[0001]A6 , (i) AFM[0001]A8 , (j) AFM[0001]X4 , (k) AFM[0001]X6 , and (l) AFM[0001]X8 seen along the [112 ̄0] direction. Spin directions of Mn atoms are indicated by up and down arrows. |
The in-plane magnetization measured with VSM for selected temperatures in the range (a) 3 to 50 K and (b) 50 to 300 K. Below 230 K a sharp FM transition is seen, see inset in (a) at low fields, followed by an increasing magnetization with field. Above 250 K there is no FM response and a new field-driven transition is observed. The inset in panel (b) shows the magnetic moment at 5 T, m5T, as a function of temperature. Note that symbols used for the different temperatures in (a) and (b) are only shown for every 50 to 100 data points whereas the lines represent every data point. |
Stability and structure from first-principles calculations. (a)Energyasafunctionofvolumefordifferentcollinearspinconfigurations of Mn GaC. Energies are given relative to the minimum energy of the nonmagnetic state ENM. The measured volume at room temperature is 20 shown by a vertical line [37]. (b) Magnetic unit cell schematics of selected low-energy spin configurations showing three different interlayer distances within the lattice. In (c) the Mn-Ga-Mn interlayer distance is displayed as a function of volume for the three configurations displayed in (b) showing two distinct distances, d+/+ and d+/−, for the AFM[0001]A. Panel (d) shows the c and a lattice parameters as a function of AA4 energy difference for relaxed FM, AFM[0001]Aα , and AFM[0001]Xα spin configurations. All data presented here are based on first-principles calculations employing the generalized gradient approximation (GGA), see Sec. II for more details. |
(a) 2θ − ω scans of Mn2GaC at room temperature (RT) and 150 K. A shift in the 0006 peak position is accompanied by a new peak appearing at ∼35° for the 150 K scan, compared to RT. The theoretical peak positions and their relative intensities for three different spin configurations are also presented. The inset shows a close-up of the 0006 peak shift. (b) Remanent moment mr measured with MOKE (in arbitrary units) as a function of temperature T, and the relative change in c-lattice parameter with respect to measurement at RT. |
Heisenberg Monte Carlo simulations with (a)netmoment of lowest-energy configurations as a function of volume. Results from different chain lengths for GGA ( ) and LDA ( ) based MEI, with corresponding average in solid red and dashed green lines, respectively. (b) Selected lowest-energy spin spirals at different volumes, as indicated in (a), where each arrow represents the spin direction of a Mn-C-Mn supermoment. |
Schematic of a possible transition between magnetic states and explanation for the observed FM response. (a) Schematic of a canting transition from AFM[0001]A4 to FM using the coarse-grained model with Mn moments in a Mn-C-Mn trilayer represented by a supermoment. The crystal configuration of AFM[0001]A4 and FM is also seen as a reference. (b) Change in energy of the canted AFM[0001]A4 with canting angle (filled circles) along with the corresponding net moment (open circles). Note that θc = 90 corresponds to an FM state. The gray box indicates the region where the angle is degenerate to within 0.2 meV/atom. Also shown are the energies for selected low-energy spin spirals IV ( ), V ( ), and VI ( ) as well as for AFM[0001]A4 ( ), relative to that of AFM[0001]A4 . |
Ratio of the NE-AIMD to AIMD jump rate kNE/kE obtained as a function of F at 2000 K. The inset illustrates the linear-fitting range, previously used to extrapolate equilibrium rates [14]. |
Model used to clarify the colored-atom jump rate de- pendence on the intensity F of an applied force seen in Fig. 1. The unperturbed (F = 0) potential-energy profile ELS0 along the diffusion path x is approximated by a sinusoidal curve. With increasing force intensities F, the colored-atom equilibrium position xeq and the transition-state coordinate xTS move toward each other, whereas the effective jump activation energy Ea decreases monotonically. xeq 0 , xTS0 , and Ea0 are zero-field quantities. xvac indicates the vacancy position. |
Numerical evaluation of accelerated-rates k(F) as a function of the intensity F of the force applied to the colored-atom based on the model illustrated in Fig. 2, and fit of k(F) up to F ′ ∼= 0.75 Fmax [Eqs. (1) and (2)]. |
Non equilibrium jump rates ln[kNE(F,T )] obtained as a function of F for T = 1600, 1800, and 2000 K. The inset illustrates the agreement between equilibrium rates kNE→E extrapolated by non equilibrium kNE results and equilibrium rates kE obtained by nonaccelerated AIMD. ln(kE) is shown with corresponding error bars. The force limit used for kNE-result-fitting, as determined in our model calculations (Fig. 3), is F ′ ∼= 0.75 Fmax . |
Convergence of extrapolated equilibrium rates kNE→E, normalized by AIMD rate kE values with the number of non equilibrium kNE interpolation points. kNE→E/kE ratios are obtained for f = 0.7 and 0.8 eV/A ̊ (two interpolated rates) and f ranging between 0.3 and 0.8 eV/A ̊ (six interpolated rates). The vertical scale is logarithmic (base 10). Shaded red, green, and blue regions with limits marked by arrows (on the right) correspond to kE error bars at 2000, 1800, and 1600 K, respectively. |
Comparison between theoretical and experimental dif- fusion coefficients D [36]. The error bars on DE(T )[∝kE(T )cV (T )] and DNE→E (T )[∝kNE→E (T )cV (T )] values account only for the experi- mental uncertainty on equilibrium vacancy concentrations cV (T ). The table in the inset lists the gain in computational efficiency tE/tNE→E achieved by our approach, where tE and tNE→E are approximate simulation times required to obtain well-converged equilibrium vacancy jump rates as a function of T in nonaccelerated AIMD and accelerated NE-AIMD simulations, respectively. |
A flow chart for the OML/CEC model. Circles denote parameters and diamonds denote processes. Solid red lines mark parameters and processes that are included in the model. Dashed yellow lines mark parameters and processes that are only treated as needed to assess its limits of applicability. The small (~5%) contribution to the growth by collection of neutral metal atoms is not drawn in the figure in order to improve its clarity. |
(a) Sketch of the collection processes for orbit motion limited (OML) collection and collision enhanced collection (CEC) of argon (Ar+) and copper (Cu+) ions to a negatively charged nanoparticle (NP) with potential ΦNP. The dashed lines of the CEC processes symbolize what happens between a first ion-neutral collision within the capture radius rcap and the final capture on a nanoparticle. This process can include a sequence of closed (trapped) orbits and several ion-neutral collisions before the ion finally reaches the nanoparticle. (b) Length scales calculated for our reference case with typical parameters from the experiment [1, 33]: pAr = 107 Pa, Ti=TAr=300K(26meV), n _{Ar+ }=3 ⋅1018 m−3, n _{CU+ }= 3 ⋅1018 m−3, ne =6⋅1018m−3, Te=1eV and r NP = 5nm–20nm.The values of rOML and rCAP are calculated for r NP = 10 nm. |
The evaporation rate as a function of temperature, calculated by molecular dynamics simulations, for nanoparticles with cluster sizes from 108–2048 atoms. For comparison, the maximum bulk evaporation rates were calculated using equation (11) with data from [26]. |
Thermionic electron emission current according to the Richardson – Dushman equation calculated for a nanoparticle radius of 10 nm (black solid line). The red dashed lines represent lower and upper values estimated for a nanoparticle embedded in a dc plasma (ne = 1015 m−3, Te = 1 eV) and a pulsed plasma (ne = 1020 m−3, Te = 3 eV). The black dotted lines indicate temperatures below which the emission current density is a factor 10 smaller than the OML currents to a nanoparticle of the respective case. |
The electron emission current IEFE from nanoparticles at 300 K temperature (where TIE is negligible) as a function of the normalized radius r NP / | Ф_{NP}|. The data points are simulated values for given nanoparticle potentials: −4V (black circles), −5V (red circles), −7V (green circles), −10V (magenta circles), −12V (cyan circles), and −15V (yellow circles). The solid line is a tted curve (equation (14)) to estimate the eld emission current. The dashed black lines show that a variation in electron emission currents by several orders of magnitude correspond to only small variations in the normalized radius r NP / | Ф_{NP}|. |
(a) and (b) Potential of a nanoparticle calculated as function of radius assuming OML theory (black dashed line) including the collisional currents and EFE (black solid line). The curves were calculated for (a) the reference case (pAr = 107 Pa, Ti = TAr = 26 meV, n _{Ar+ }=3 ⋅1018 m−3, n _{CU+ }= 3 ⋅1018 m−3, ne = 6 ⋅ 1018 m−3, Te = 1 eV) and (b) a higher electron temperature of Te = 6 eV. The plot is shaded in the range where the calculated potential is uncertain, both because the analytical expression of Murphy and Good [5] becomes uncertain and because a statistical model should be used with discrete charges in units e. (c) and (d) Individual currents calculated with the OML/CEC model for (a) the reference case and (b) a higher electron temperature of Te = 6 eV. The positive charging currents for EFE IEFE (blue dashed–dotted line), orbital motion limited ion current Ii, OML (OML, black lines) and collision-enhanced collection ion current Ii,CEC (CEC, red lines) are all normalized to the electron current Ie. The dashed lines represent the contribution of argon ions to the total current contribution (solid lines), and the fraction of copper ions contributing to the total is given by the difference of the solid and the dashed curves. The plot is shaded in the range where the result is uncertain, as discussed in the text. |