**5. Conclusion**

102 Polycrystalline Materials – Theoretical and Practical Aspects

extracted. The maximum value of Mp″ is found at p=1/p and p shifts to higher

The charge carriers are mobile over long distances in the region left to peak; while right to the peak ions are spatially confined to the potential wells. The frequency of relaxation, p, where Mp″() is an indicative of transition from short-range to long-range mobility at the decreasing frequency. The p exponentially increases with temperature and the activation energy for relaxation is calculated from the Arrhenius behaviour. The scaling of modulus spectra is shown in Fig. 23(a), for Na3Cr2(PO4)3-G1:3 and inset shows the Arrhenius plot of p. Grain contribution is dominant in Na3Cr2(PO4)3-G1:3, over the frequency and

Fig. 23. (a) The modulus scaling in Na3Cr2(PO4)3-G1:3 at different temperatures and (b)

Further, in Fig. 23(b), Z) and Mpeaks are almost coincident and there is no additional peak in these representations. The single relaxation peak in the modulus representation of Na3Cr2(PO4)3-G1:3 is contributed from the grain part since the electrode contribution is suppressed. The Z) and Mpeaks are almost coincident, which implies that the grain contributes for impedance relaxation. The small separation in the modulus

Material Activation energy for

Na3Cr2(PO4)3-G1:3 (0.66±0.01) Na3Cr2(PO4)3-U1:1 (0.93±0.04) Na3Cr2(PO4)3-U1:2 (0.89±0.04) Li3Fe2(PO4)3-CA:EG (0.71±0.02)

Conductivity spectra at different temperatures collapsed to a single curve at higher frequencies on appropriate scaling, which implies that the relaxation mechanism at the higher frequency is independent of temperature. But in some cases, as shown in Figs. 24(a)- (b), low frequency part of the plot is not scaled due to contribution from electrode

Table 10. The activation energy for electrical relaxation obtained from Modulus

relaxation, Eh[eV]

2

Z"(

)x103 [

]

4

413K

 Z"() M"()

6

8

Na3 Cr2 (PO4 ) 3 -G1:3

102 103 104 105 106 10 0 <sup>7</sup> 0.0 0.5 1.0 1.5 M"(

)x10-3

2.0 (b)

 [rads-1 ]

frequencies with increase in temperature.

temperature range of the experiment.

105 106 107 p [Hz]

> Na3 Cr2 (PO4 ) 3 -G1:3

0

M"/M"

1

p

Frequency dependence of Z"() and M"() at 413K.

1.8 2.1 2.4 2.7

1000/T[ K-1 ]

10-4 10-2 100 102 104

/p

(a)

representation

and impedance peak positions points to the good grain connectivity.

In the present study, NASICON materials of two different symmetry, *i.e. rhombohedral (NASICON type) and modifications of monoclinic (Fe2(SO4)3-type),* are investigated. Different characterization techniques are used for the confirmation of structural, magnetic and electrical properties. The main initiative of the present study is to correlate the ion mobility with the symmetry.

Out of these, LiTi2(PO4)3 family based on rhombohedral symmetry is synthesized by high energy ball-milling. Due to strain effect, defects like grain-boundaries are introduced in these materials. These grain-boundaries are less activation energy path for mobile ions and thus enhancing the electrical conductivity. The A3M2(PO4)3 (where A=Li, Na and M=Fe, Cr) family is prepared by solution combustion technique. By solution combustion synthesis technique, thermal stability is achieved for room temperature phase of Na3Cr2(PO4)3 and Li3Fe2(PO4)3 materials. The fuels/complexing agents played a major role in controlling the physical and electrical properties in these materials. This study concluded that, the fuel molar ratio play a major role in deciding the physical and electrical properties and 1:1 glycine molar ratio is found to be the optimized value to obtain the highest electrical conductivity in Na3Cr2(PO4)3 materials. While, the charge carrier density in Na3Cr2(PO4)3 and Li3Fe2(PO4)3 was independent of the fuels/complexing agents.

Structural distortions, involving a symmetry lowering to orthorhombic, monoclinic or triclinic, are possible and that may affect the disorder state and mobility of lithium/sodium substantially. Mobile cation occupies a six coordination site in the NASICON-type structure and a four coordination site in the Fe2(SO4)3-type compounds. The activation energies for ionic conduction of Fe2(SO4)3-type structure is a little lower than that of the NASICON. This

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indicates that the four coordination site of the Fe2(SO4)3-type structure is preferable to the six coordination of the NASICON-type structure for ionic conduction. This is the reason behind the enhanced conduction in combustion synthesized Li3Fe2(PO4)3 and Na3Fe2(PO4)3 materials.

The scaling of ac conductivity and modulus spectra provided time-temperature superposition principle of ion dynamics in these materials. The ability to scale different data sets to one common curve indicated that the common physical mechanism in a process can be separated by thermodynamic scales. These materials find application in sensors, rechargeable batteries *etc.*
