PDF Publication Title:
Text from PDF Page: 005
Condens. Matter 2019, 4, 80 5 of 12 Condens. Matter 2019, 4 5 expand along the last cell vector (the adaptation of the structure at the grain interfaces takes normally larger volume compared to bulk). Whereas dimensions parallel to the interface are not changed, as the the interface are not changed, as the same type of periodicity is kept as in the bulk. The curves same type of periodicity is kept as in the bulk. The curves showing how the cells’ energy is changed showing how the cells’ energy is changed with the dimension zc are presented in Figure 2. In fact, the with the dimension zc are presented in Figure 2. In fact, the grain boundary energy, γ, is plotted here grain boundary energy, γ, is plotted here against zc for both GB configurations, and the minimum against zc for both GB configurations, and the minimum corresponds to equilibrium, i.e., the optimal corresponds to equilibrium, i.e., the optimal dimension. The GB energy (or interface energy) is given dimension. The GB energy (or interface energy) is given by relation: by relation: where A is the area of the GB in the supercell/box, considering that there are two GBs in each γ = [E (GB) − E (bulk)]/2A (1) tot tot γ = [ Etot(GB) − Etot(bulk) ]/2A (1) where A is the area of the GB in the supercell/box, considering that there are two GBs in each supercell. supercell. Using the dimensions ar, br, and cr of the relaxed bulk supercell, A can be calculated as a2rbr Usingthedimensionsar,br,andcroftherelaxedbulksupercell,Acanbecalculatedasarbr≈b(a + ≈2 b1/(2a2+c2)1/2 when we relate it to the original primitive lattice dimensions. The minimum along this c ) when we relate it to the original primitive lattice dimensions. The minimum along this relaxation relaxation path corresponds to the equilibrium volume. Our results on the GB interface energy are path corresponds to the equilibrium volume. Our results on the GB interface energy are given in given in Table 1. One can see that the GB energies are quite low compared to a typical GB energ2y Table 1. One can see that the GB energies are quite low compared to a typical GB energy around 1 J/m , around 1 J/m2, which indicates that the studied interfaces should be relatively easy to form. It also which indicates that the studied interfaces should be relatively easy to form. It also holds that γ (C1) > holds that γ (C1) > γ (C2), showing that the configuration C2 is more energetically favorable than C1 γ (C2), showing that the configuration C2 is more energetically favorable than C1 even if the difference even if the difference is smaller than 10%. This is an expected result, since C2 exhibits better is smaller than 10%. This is an expected result, since C2 exhibits better coherence than C1, as discussed coherence than C1, as discussed above. Tab2le 1 contains2 γ values both in J/m2 and meV/Å2 units, above.Table1containsγvaluesbothinJ/m andmeV/Å units,sincethelatterismoresuitablefor since the latter is more suitable for co2nsiderations at the atomic 2level (1 J/m2 corresponds to 62.4 considerationsattheatomiclevel(1J/m correspondsto62.4meV/Å).Inprinciple,theGBenergycan meV/Å2). In principle, the GB energy can be recalculated to the excess energy per one atom/ion at the be recalculated to the excess energy per one atom/ion at the interface (here ~0.5 eV/Li), which could be interface (here ~0.5 eV/Li), which could be related, for example, to the point defect formation related, for example, to the point defect formation energies that are of the same order. energies that are of the same order. Figure 2. Relaxation of the LFP GB boxes along the last cell vector for configurations C1 and C2: grain Figure 2. Relaxation of the LFP GB boxes along the last cell vector for configurations C1 and C2: grain boundary energy (γ) versus box last dimension (z ). boundary energy (γ) versus box last dimension (zc). Table 1. GB interface energy for LFP and iron phosphate (FP) configurations. Table 1. GB interface energy for LFP and iron phosphate (FP) configurations. GB Configuration γ (meV/Å2) γ (meV/Å2) 31 29 69 58 γ (J/m2) γ (J/m2) GB Configuration LFP C1 31 29 69 58 0.50 LFP C2 0.46 FP C1 1.11 FP C2 0.92 LFP C1 0.50 LFP C2 0.46 FP C1 FP C2 1.11 0.92 Another observation is that C2 expands more than C1, as it is reflected by the GB excess free Another observation is that C2 expands more than C1, as it is reflected by the GB excess free 32 32 volumes δV(C1) = 0.26 Å /3Å 2and δV (C2) = 0.36 Å /Å3. Th2 is quantity can be determined as an extra volumes δV(C1) = 0.26 Å /Å and δV (C2) = 0.36 Å /Å . This quantity can be determined as an volume due to the introduction of the GB into the bulk related to the GB area (units are usually extra volume due to the introduction of the GB into the bulk related to the GB area (units are usually expressed in the form volume per area), and can be easily calculated using Equation (1) where expressed in the form volume per area), and can be easily calculated using Equation (1) where energies energies are replaced by cell volumes. The property δV should be viewed as an increase in the are replaced by cell volumes. The property δV should be viewed as an increase in the interstitial interstitial space at the GB regions. The GB excess free volumes can be also connected to positron space at the GB regions. The GB excess free volumes can be also connected to positron characteristics, characteristics, especially regarding the lifetime. The bulk positron lifetime for the LFP structure was especially regarding the lifetime. The bulk positron lifetime for the LFP structure was calculated in calculated in Refs. [28,29] and amounts to 157.5 ps (LDA) and 169.7 ps (GGA) considering the room temperature lattice parameters. Here, we are getting [30] slightly longer values—159 ps and 171 ps—for respective treatments of electron–positron correlations, considering the relaxed lattice parameters for which the volume per formula unit is larger (and consequently is the positronPDF Image | First-Principles Grain Boundary Formation in the Cathode Material LiFePO4
PDF Search Title:
First-Principles Grain Boundary Formation in the Cathode Material LiFePO4Original File Name Searched:
condensedmatter-04-00080.pdfDIY PDF Search: Google It | Yahoo | Bing
Sulfur Deposition on Carbon Nanofibers using Supercritical CO2 Sulfur Deposition on Carbon Nanofibers using Supercritical CO2. Gamma sulfur also known as mother of pearl sulfur and nacreous sulfur... More Info
CO2 Organic Rankine Cycle Experimenter Platform The supercritical CO2 phase change system is both a heat pump and organic rankine cycle which can be used for those purposes and as a supercritical extractor for advanced subcritical and supercritical extraction technology. Uses include producing nanoparticles, precious metal CO2 extraction, lithium battery recycling, and other applications... More Info
| CONTACT TEL: 608-238-6001 Email: greg@infinityturbine.com | RSS | AMP |