**3.1 Composition dependence of precursor and high temperature stable phases**

Fig. 4 shows the composition dependence of both the precursor phases and the high temperature stable phases of glass-ceramic NaYPSi on the maps of phosphorus-yttrium (P-Y, Fig. 4(a)), yttrium-sodium (Y-Na, Fig. 4(b)) and phosphorus-sodium (P-Na, Fig. 4(c)), where the variables on the abscissas and ordinals are expressed with the composition parameters 1-*x*, *y* and 3+3*x*-*y* for yttrium, phosphorus and sodium, respectively. As reported before, N3- and N9-type NaYPSi glass-ceramics can be crystallized as the high-temperature stable phases at the regions of higher [Y] (1-*x*>ca. 0.8) and rather lower [Y] (1-*x*<ca. 0.55), respectively, in the [Y]-[P] relation.

Fig. 2. Equivalent circuit employed for the admittance analysis.

E-B INT, GB, and G represent the electrode-bulk interface, grain-boundaries and grains, respectively, and (*R*1, *C*1), (*R*2, *C*2), and *R*3 are their resistances and capacitances.

Concerning the precursor phases, only either N3- or N9-type NaYPSi was found in any composition, while N5-type NaYPSi was difficult to crystallize from glasses at low temperatures. It is also seen in the [P]-[Y] map (Fig. 4(a)) that, under a given phosphorus content ([P]<0.6) a composition with higher content of yttrium gives N3-type NaYPSi (○) as the precursor phase, while lower [Y] content results in N9-type phase (open square). The values of [Y] dividing the regions allowed for N3- and N9-type NaYPSi glass-ceramics decreased with increasing [P], and the boundary seems to locate slightly apart from the deduced line of [Y]=0.75-0.5[P] shown with the solid line. Around the boundary region N5 type NaYPSi can be obtained as the stable phase at high temperatures (solid marks of circle or square). In the [Y]-[Na] or [P]-[Na] relations (Figs. 4(b) and 4(c)), the region where

Crystalline phases of glass-ceramic specimens were identified by X-ray diffraction (XRD) method. The lattice parameters of the N5-type hexagonal unit cell were calculated by a leastsquares method using the XRD peaks of (054), (044), (134), (440) and (024). Glass-ceramics of Y3+-contained NaRPSi were subjected to scanning (SEM) and transmission electron microscope (TEM) for microstructural analysis. Electron diffraction and compositional

For the description of a specific NaRPSi, R of the term will be replaced, respectively, with Y, Sc, In, Er, Gd, Sm, Eu, Nd and La as NaYPSi, NaScPSi, NaInPSi, NaErPSi, NaGdPSi, NaSmPSi, NaEuPSi, NaNdPSi and NaLaPSi for Y2O3, Sc2O3, In2O3, Er2O3, Gd2O3, Sm2O3.,

analyses were also performed to characterize the structure of the grain boundary.

**3. Thermodynamic and kinetic study on the phase transformation** 

**3.1 Composition dependence of precursor and high temperature stable phases** 

Fig. 4 shows the composition dependence of both the precursor phases and the high temperature stable phases of glass-ceramic NaYPSi on the maps of phosphorus-yttrium (P-Y, Fig. 4(a)), yttrium-sodium (Y-Na, Fig. 4(b)) and phosphorus-sodium (P-Na, Fig. 4(c)), where the variables on the abscissas and ordinals are expressed with the composition parameters 1-*x*, *y* and 3+3*x*-*y* for yttrium, phosphorus and sodium, respectively. As reported before, N3- and N9-type NaYPSi glass-ceramics can be crystallized as the high-temperature stable phases at the regions of higher [Y] (1-*x*>ca. 0.8) and rather lower [Y] (1-*x*<ca. 0.55),

*R***2**

**GB**

*R***3**

**G**

*C***2**

E-B INT, GB, and G represent the electrode-bulk interface, grain-boundaries and grains,

Concerning the precursor phases, only either N3- or N9-type NaYPSi was found in any composition, while N5-type NaYPSi was difficult to crystallize from glasses at low temperatures. It is also seen in the [P]-[Y] map (Fig. 4(a)) that, under a given phosphorus content ([P]<0.6) a composition with higher content of yttrium gives N3-type NaYPSi (○) as the precursor phase, while lower [Y] content results in N9-type phase (open square). The values of [Y] dividing the regions allowed for N3- and N9-type NaYPSi glass-ceramics decreased with increasing [P], and the boundary seems to locate slightly apart from the deduced line of [Y]=0.75-0.5[P] shown with the solid line. Around the boundary region N5 type NaYPSi can be obtained as the stable phase at high temperatures (solid marks of circle or square). In the [Y]-[Na] or [P]-[Na] relations (Figs. 4(b) and 4(c)), the region where

respectively, and (*R*1, *C*1), (*R*2, *C*2), and *R*3 are their resistances and capacitances.

*R***1**

Eu2O3, Nd2O3 and La2O3.

respectively, in the [Y]-[P] relation.

**E-B INT**

*C***1**

Fig. 2. Equivalent circuit employed for the admittance analysis.

Fig. 3. An idealized diagram of complex admittance for glass-ceramics, in which arc 1 (ARC 1) and arc 2 (ARC 2) are related to the crystallized grains (G(c)) and remaining glasses (GB(g)). L1, L2, *R*G(c), and *R*GB(g) are, respectively, the radii of arcs 1 and 2, the resistances of G(c) and GB(g).

Fig. 4. Composition dependence of precursor (*pp*) and high temperature-stable phases (*sp*) of glass-ceramic NaRPSi on P-Y (a), Y-Na (b) and P-Na (c) maps, where precursor phases N3 and N9 are shown with *circles* and *squares*, respectively. High temperature-stable phases are shown in such a way that solid marks means that N5-NaRSi is the stable, while *open marks* indicate that the precursor phases are also stable even at high temperatures. Mixed phases are also shown: *open circle* pp = sp = N3; *filled circle* pp = N3, sp = N5; *open square* pp = sp = N9; *filled circle* pp = N9, sp = N5; *open split square* pp = N9, sp = N9 + N5

Preparation of Na<sup>+</sup>

Free energy

annealing: (■)).

Superionic Conductors by Crystallization of Glass 89

**a b**

**N3** 

**(N9)**

Fig. 6. Schematic figures of temperature dependence of free energy change of N5- and N3 or N9- type NaYPSi in the cases assuming N5- (a) and N3- (b) or N9-type (b) NaYPSi as the

( ) ) (

T T

**N N**

Fig. 7. Comparison of phase transformation rate (αv) between specimens Na3.9Y0.6P0.3Si2.7O9 (1h-annealing: (○); 3h-annealing: (●)) and Na3.75Y0.65P0.3Si2.7o9 (1h-annealing: (□), 3h-

The kinetic effects of composition on the phase transformation are shown in Fig. 7, which compares the phase transformation rates of specimens Na3.9Y0.6P0.3Si2.7O9 and Na3.75Y0.65P0.3Si2.7O9. The transformation rate (αv) of a precursor phase to the stable N5 phase was determined as the weight ratio of N5-type NaYPSi in a glass-ceramic specimen. The value of αv was experimentally obtained from the relationship of weight ratio to XRD intensity ratio, which relationship had been made previously by XRD intensity measurement on specimens with given weight ratio of N5-type NaYPSi to metastable phases. It is seen that the composition Na3.9Y0.6P0.3Si2.7O9 is superior to the other, for the N5 single phase NaYPSi was difficult to obtain in the latter specimen. In specimen

**3.2 Kinetic effects of composition on the phase transformation** 

high temperature-stable phase, where *T*c is the crystallization temperature.

**N3** 

*<sup>T</sup> TT*<sup>c</sup> *<sup>T</sup>*c**N5 N5 (N9)**

Tc Tc

.

N5-type NaYPSi can be found as the high-temperature stable phase is found under ca. 3.6<[Na]<4.3. The effect of sodium content seems insignificant, because the value of [Na] is subordinately determined as [Na]=6-3[Y]-[P] (=3+3*x*-*y*) depending on the contents of both yttrium and phosphorus.

The above results may suggest that the [P]-[Y] relation dominates the region which is allowed for each NaYPSi at high temperatures. Considering this inference, we calculated the products of [P]×[Y] for all of the specimens. The values of [P]×[Y] were as follows (shown in Fig. 5); 0.16-0.25 for single phase N3-type NaYPSi, 0.14 for mixed phases of N3 and N5-type NaYPSi, 0.12-0.20 for single phase N5-type NaYPSi, 0-0.14 for the mixed phases of N5- and N9-type NaYPSi, and 0-0.17 for single phase N9-type NaYPSi, respectively. It was therefore deduced (Fig. 5) that the free energy of formation (Δ*G*f) of N9-type NaYPSi would be the lowest in a lower region of [P]×[Y], N5-type NaYPSi may have the lowest Δ*G*f in a medium [P]×[Y] region, and higher [P]×[Y] would lower Δ*G*f of N3-type NaYPSi.

For a specimen in which N5-type NaYPSi is the stable phase at high temperatures, the aspect such as Fig. 6a would be illustrated in that Δ*G* of N3- or N9-type NaYPSi would be much smaller than that of N5-type NaYPSi near the crystallization temperature (*T*c), and the value of N5-type NaYPSi would be lowered much less than of the two. Fig. 6b indicates the aspect that Δ*G* or N3- or N9-type NaYPSi stable.

Fig. 5. Schematic figure of composition ([Y]×[P]) dependence of free energy of N5-, N3- and N9-type NaYPSi.

N5-type NaYPSi can be found as the high-temperature stable phase is found under ca. 3.6<[Na]<4.3. The effect of sodium content seems insignificant, because the value of [Na] is subordinately determined as [Na]=6-3[Y]-[P] (=3+3*x*-*y*) depending on the contents of both

The above results may suggest that the [P]-[Y] relation dominates the region which is allowed for each NaYPSi at high temperatures. Considering this inference, we calculated the products of [P]×[Y] for all of the specimens. The values of [P]×[Y] were as follows (shown in Fig. 5); 0.16-0.25 for single phase N3-type NaYPSi, 0.14 for mixed phases of N3 and N5-type NaYPSi, 0.12-0.20 for single phase N5-type NaYPSi, 0-0.14 for the mixed phases of N5- and N9-type NaYPSi, and 0-0.17 for single phase N9-type NaYPSi, respectively. It was therefore deduced (Fig. 5) that the free energy of formation (Δ*G*f) of N9-type NaYPSi would be the lowest in a lower region of [P]×[Y], N5-type NaYPSi may have the lowest Δ*G*f in a medium [P]×[Y] region, and higher [P]×[Y] would lower Δ*G*f of

For a specimen in which N5-type NaYPSi is the stable phase at high temperatures, the aspect such as Fig. 6a would be illustrated in that Δ*G* of N3- or N9-type NaYPSi would be much smaller than that of N5-type NaYPSi near the crystallization temperature (*T*c), and the value of N5-type NaYPSi would be lowered much less than of the two. Fig. 6b indicates the

**N3**

**N9**

**N5**

**N9 N9+N5**

**N3**

Y×P 0 0 0.05 .1 0.15 0.2 0.25

Fig. 5. Schematic figure of composition ([Y]×[P]) dependence of free energy of N5-, N3- and

yttrium and phosphorus.

N3-type NaYPSi.

N9-type NaYPSi.

aspect that Δ*G* or N3- or N9-type NaYPSi stable.

Free energy

**N5**

Fig. 6. Schematic figures of temperature dependence of free energy change of N5- and N3 or N9- type NaYPSi in the cases assuming N5- (a) and N3- (b) or N9-type (b) NaYPSi as the high temperature-stable phase, where *T*c is the crystallization temperature.

Fig. 7. Comparison of phase transformation rate (αv) between specimens Na3.9Y0.6P0.3Si2.7O9 (1h-annealing: (○); 3h-annealing: (●)) and Na3.75Y0.65P0.3Si2.7o9 (1h-annealing: (□), 3hannealing: (■)).

#### **3.2 Kinetic effects of composition on the phase transformation**

The kinetic effects of composition on the phase transformation are shown in Fig. 7, which compares the phase transformation rates of specimens Na3.9Y0.6P0.3Si2.7O9 and Na3.75Y0.65P0.3Si2.7O9. The transformation rate (αv) of a precursor phase to the stable N5 phase was determined as the weight ratio of N5-type NaYPSi in a glass-ceramic specimen. The value of αv was experimentally obtained from the relationship of weight ratio to XRD intensity ratio, which relationship had been made previously by XRD intensity measurement on specimens with given weight ratio of N5-type NaYPSi to metastable phases. It is seen that the composition Na3.9Y0.6P0.3Si2.7O9 is superior to the other, for the N5 single phase NaYPSi was difficult to obtain in the latter specimen. In specimen

.

Preparation of Na<sup>+</sup>

N5-type phase.

Na3.9R0.6Si2.7O9.

N5-type crystal structure.

Superionic Conductors by Crystallization of Glass 91

**0.75 -4.41 1.39 -9.54 1.94 -14.6 2.61 -20.7**

**ln** *k*

 Na3.9R0.6P0.3Si2.7O9 (7) was experimentally shown as the most appropriate composition for the crystallization of

> **Avrami modulus** *n*

Table 1. Kinetic parameters of phase-transformation of N3- to N5-type NaYPSi of

Fig. 9. Arrhenius-type plot of ln *k* with 1000/T of specimen Na3.9Y0.6Si2.7O9.

The relationship between the ionic radius of R3+ (*r*R) and the hexagonal lattice parameters of N5-type single phase is consistent with the previous report on Na5RSi4O12 (R=Sc-Sm) in the tendency that both lattice parameters increased with increasing *r*R. The elongation of these lattice axes is attributed to the octahedral coordination of R3+ with the O2- of SiO4- or PO4 tetrahedra of the 12-membered rings. The local structure around R3+ ions is to be further discussed below in relation to conduction properties. On the formation of N5-type single phase, the incorporation of excess sodium ions [4(3+3*x*-*y*)/3-5=(12*x*-4*y*-3)/3 in composition 3] and substitution of rare earth ions [1-4(1-x)/3=(4*x*-1)/3] must be accounted for in view of

Banks *et al*. have reported the values of σ300 as 5×10-3 to 1×10-2 S/cm for glass-ceramic Na5RSi4O12 (R=Er, Y, Gd, Sm), which are as low as those of the mixed phase NaRPSi specimens. The single phase N5-type glass-ceramic was not obtained in the present work. Based on the above crystallization analysis, their glass-ceramic specimens are reasonably

**Anneling temp. (K)**

Na3.9Y0.6P0.3Si2.7O9 a glass-ceramic of N5 single phase NaYPSi was easily obtained at a temperature higher than 900°C for only three hours. The composition Na3.75Y0.75Si3O9 (or Na5YSi4O12) was inferior in the same meaning.

Fig. 8. Phase transformation rate (αv) of N3- to N5-type NaYPSi on the specimen Na3.9Y0.6P0.3Si2.7O9.

Fig. 8 shows the kinetic characteristics of phase transformation of the metastable phase of N3- to N5-type NaYPSi of specimen Na3.9Y0.6P0.3Si2.7O9 at various temperatures. The transition rates, αv, of the silicophosphate NaYPSi were much higher than those of the Na3.75Y0.75Si3O9 silicate material.

The results shown were analyzed with the Avrami empirical equation, αv=1-exp(-*ktn*), where *k* is the rate constant, and *n* is a constant. The data on αv obtained at the initial and intermediate stages gave a linear relationship between ln(ln(1-αv)-1) and ln(*t*) with a correlation coefficient of more than 0.99. The Avrami parameter and rate constants obtained are summarized in Table 1. Based on the Arrhenius relationship (Fig. 9), *k*=*A*exp(-*E*v/*RT*) with *E*v as the activation energy and constants *A* and *R*, on those *k* values which increased with increasing temperature, we obtained an activation energy of 1.2×103 kJ/mol, suggesting that the phase transformation can be rather difficult to take place. An addition of phosphorus and the excess sodium seem effective to the promotion of the phase transformation.
