3.3. Моделирование многокомпонентных наноструктурных покрытий.
The mixing enthalpy of bulk Ti1−x Alx N (ab initio), the mixing enthalpy with the coherency strain effect, and the mixing enthalpy (ab initio) of Ti1−x Alx N/TiN multilayer (ML). (a) 6/6 ML and (b) 12/6 ML. The dashed lines show the maximum of the mixing enthalpy values for the bulk and the different ML case. |
In-plane lattice parameters of multilayers 6/6 and 12/6: aTi1−x Alx N/TiN and bulk: aTi1−x Alx N . |
The calculated averaged interlayer distances d using the fully relaxed structures of both MLs. (a) 6/6 ML and (b) 12/6 ML. The solid lines show the average of the interlayer distance for Ti1−xAlxN and TiN in the MLs, while the dashed lines show the bulk cases. |
Comparison of the two chemical effects (normalized binding energy), the one from Ti1−xAlxN/TiN and the other form AlN/TiN in the mixing enthalpy of the Ti1−x Alx N/TiN multilayer. (a) shows the 6/6 ML while (b) displays the 12/6 ML. |
The atomic relaxations with respect to the ideal positions in each layer for x = 0.55 of bulk Ti1−x Alx N and 6/6 ML (a) in the x direction and (b) in the z direction. (c) The relaxations of the N atoms with different types of neighbors (Al-N-Al, Ti-N-Al, and Ti-N-Ti) along the z direction. (d) The relaxations of the Ti and Al atoms along the z direction. See the text for more details. |
Thefittedslopesvalues(%)ofthestraightlinesandthe corresponding shifts of the layers in the ML slabs (A ̊ ) (in parentheses). |
Bulk and the 6/6 multilayer d-orbital partial density of states (PDOS) at the Fermi energy (εF) of the Ti atoms from only the Ti1−x Alx N slab. |
Schematic representation of the DLM-MD process. Starting with a random arrangement of magnetic moments, an MD calculation is run for NSF MD = t SF /t MD steps during which the magnetic configuration is allowed to evolve according to the solution of the electronic structure problem. At the tSF, the moments are flipped and rearranged in another random magnetic configuration, while positions and velocities of all the atoms are preserved. Then the MD simulation continues. The figure shows only one layer of Cr atoms from the CrN supercell and the N atoms are not shown here. The spin-flip time is chosen to be tSF = 5 fs. The Born-Oppenheimer MD time step is chosen as tMD = 1 fs. The phonon time scale is also shown as tph >100fs.Thelengthsofthetimearrowsdemonstratethatthetime scale of the collective atomic vibrational modes are much slower than the time scales of both the electronic and transverse local magnetic moments (tMD tSF < tph). |
Calculated temperature-dependent single-crystal elastic constants of PM CrN obtained by using different theoretical methods. The error bars correspond to the standard deviation of the molecular dynamics simulations with a 95% confidence interval. |
Temperature-dependent elastic constants of PM B1 CrN obtained by different methods including experimental, static (T = 0 K) nonmagnetic (NM) and antiferromagnetic (AFM) values for comparison. |
Calculated Voigt-Reuss-Hill averages [Eqs. (13)–(15)]of polycrystalline elastic constants of PM CrN from top to bottom (a) bulk modulus, (b) Young’s modulus, (c) shear modulus, and (d) Poisson ratio, as a function of temperature. The error bars correspond to the standard deviation of the molecular dynamics simulations with a 95% confidence interval. |
Calculated Voigt-Reuss-Hill anisotropy AVR, and Zenner elastic shear AZ of PM CrN as a function of temperature. The error bars correspond to the standard deviation of the molecular dynamics simulations with a 95% confidence interval. |