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Important Variation in Vibrational Properties of LiFePO 4 and FePO 4 Induced by Magnetism

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ABSTRACT

A new thermodynamically self-consistent (TSC) method, based on the quasi-harmonic approximation (QHA), is used to obtain the Debye temperatures of LiFePO4 (LFP) and FePO4 (FP) from available experimental specific heat capacities for a wide temperature range. The calculated Debye temperatures show an interesting critical and peculiar behavior so that a steep increase in the Debye temperatures is observed by increasing the temperature. This critical behavior is fitted by the critical function and the adjusted critical temperatures are very close to the magnetic phase transition temperatures in LFP and FP. Hence, the critical behavior of the Debye temperatures is correlated with the magnetic phase transitions in these compounds. Our first-principle calculations support our conjecture that the change in electronic structures, i.e. electron density of state and electron localization function, and consequently the change in thermophysical properties due to the magnetic transition may be the reason for the observation of this peculiar behavior of the Debye temperatures.

No MeSH data available.


Projected d-band density of state (DOS) for AFM (black line) and NS (red line) LFP.The dot lines show the relevant calculated d-band centers (εd).
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f4: Projected d-band density of state (DOS) for AFM (black line) and NS (red line) LFP.The dot lines show the relevant calculated d-band centers (εd).

Mentions: Our first-principle calculations prove that the magnetic phase transition alters the electronic structure and consequently the physical properties of both FP and LFP. The calculated Debye temperatures from the DFT computations, for magnetic (375 K for LFP and 294 K for FP) and non-magnetic (668 K for LFP and 649 K for FP) phases, show reasonable accordance with the extracted Debye temperatures from the experimental data at low and high temperatures, respectively. Electronic structure analysis showed that, despite a very similar charge density distribution for both magnetic and non-magnetic systems, there is a considerable difference in the d-band states between AFM and NS phases. Figure 4 shows that the d-band center increases from −0.15 eV below the Fermi level in AFM LFP to 0.76 eV above the Fermi level in NS LFP. Consequently, d-band width decreases from 4.46 to 3.20 eV from AFM to NS systems, respectively. This might affect the interaction between the iron 3d orbital and phosphorus and oxygen 2p orbitals. The visualized ELF in Fig. 5 shows the different electron localizations in AFM and NS LFP. The ELF is a very powerful tool to categorize and evaluate the chemical bonding between elements in a molecule. In general, this function has a value between 0 and 1. Regions close to unity (red area) contain many localized electrons, which are either localized around a nucleus or in a very strong covalent bond. Values close to zero (blue area) show the region with low electron density and the value close to 0.5 (green area) represents a homogeneous electron gas where the bonding might have metallic character. In both magnetic and non-magnetic LFPs we see that lithium electrons are much localized around the Li nucleus, with a minor contribution making chemical bonding with other elements. However, the interactions between Fe and P and also between Fe and O are much stronger in NS LFP than those in AFM LFP. These stronger interactions are evident in interstitial regions between Fe, P and O with a greater electron density. In fact, in NS LFP, Fe tends more to form a hybridized p-d orbital through sharing its d-band electrons with p-band electrons of P and O. Due to the stronger interactions in NS LFP, we see that the Fe-O average bond length decreases from ca. 2.26 Å in AFM to 2.09 Å in NS LFP. In addition, the Fe-P average bond length decreases from 2.87 Å in AFM to 2.69 Å in NS LFP. These results, which are in complete agreement with our TSC calculations, are consistent with the greater bulk modulus and Debye temperature in NS LFP compared to AFM LFP. We have obtained similar results for FP; however, to avoid repetition we omit them here.


Important Variation in Vibrational Properties of LiFePO 4 and FePO 4 Induced by Magnetism
Projected d-band density of state (DOS) for AFM (black line) and NS (red line) LFP.The dot lines show the relevant calculated d-band centers (εd).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5015091&req=5

f4: Projected d-band density of state (DOS) for AFM (black line) and NS (red line) LFP.The dot lines show the relevant calculated d-band centers (εd).
Mentions: Our first-principle calculations prove that the magnetic phase transition alters the electronic structure and consequently the physical properties of both FP and LFP. The calculated Debye temperatures from the DFT computations, for magnetic (375 K for LFP and 294 K for FP) and non-magnetic (668 K for LFP and 649 K for FP) phases, show reasonable accordance with the extracted Debye temperatures from the experimental data at low and high temperatures, respectively. Electronic structure analysis showed that, despite a very similar charge density distribution for both magnetic and non-magnetic systems, there is a considerable difference in the d-band states between AFM and NS phases. Figure 4 shows that the d-band center increases from −0.15 eV below the Fermi level in AFM LFP to 0.76 eV above the Fermi level in NS LFP. Consequently, d-band width decreases from 4.46 to 3.20 eV from AFM to NS systems, respectively. This might affect the interaction between the iron 3d orbital and phosphorus and oxygen 2p orbitals. The visualized ELF in Fig. 5 shows the different electron localizations in AFM and NS LFP. The ELF is a very powerful tool to categorize and evaluate the chemical bonding between elements in a molecule. In general, this function has a value between 0 and 1. Regions close to unity (red area) contain many localized electrons, which are either localized around a nucleus or in a very strong covalent bond. Values close to zero (blue area) show the region with low electron density and the value close to 0.5 (green area) represents a homogeneous electron gas where the bonding might have metallic character. In both magnetic and non-magnetic LFPs we see that lithium electrons are much localized around the Li nucleus, with a minor contribution making chemical bonding with other elements. However, the interactions between Fe and P and also between Fe and O are much stronger in NS LFP than those in AFM LFP. These stronger interactions are evident in interstitial regions between Fe, P and O with a greater electron density. In fact, in NS LFP, Fe tends more to form a hybridized p-d orbital through sharing its d-band electrons with p-band electrons of P and O. Due to the stronger interactions in NS LFP, we see that the Fe-O average bond length decreases from ca. 2.26 Å in AFM to 2.09 Å in NS LFP. In addition, the Fe-P average bond length decreases from 2.87 Å in AFM to 2.69 Å in NS LFP. These results, which are in complete agreement with our TSC calculations, are consistent with the greater bulk modulus and Debye temperature in NS LFP compared to AFM LFP. We have obtained similar results for FP; however, to avoid repetition we omit them here.

View Article: PubMed Central - PubMed

ABSTRACT

A new thermodynamically self-consistent (TSC) method, based on the quasi-harmonic approximation (QHA), is used to obtain the Debye temperatures of LiFePO4 (LFP) and FePO4 (FP) from available experimental specific heat capacities for a wide temperature range. The calculated Debye temperatures show an interesting critical and peculiar behavior so that a steep increase in the Debye temperatures is observed by increasing the temperature. This critical behavior is fitted by the critical function and the adjusted critical temperatures are very close to the magnetic phase transition temperatures in LFP and FP. Hence, the critical behavior of the Debye temperatures is correlated with the magnetic phase transitions in these compounds. Our first-principle calculations support our conjecture that the change in electronic structures, i.e. electron density of state and electron localization function, and consequently the change in thermophysical properties due to the magnetic transition may be the reason for the observation of this peculiar behavior of the Debye temperatures.

No MeSH data available.