92
6 Combinatorial Studies of Compositions Containing Layered Phases . . .
samples since the slow-cooled samples never reached equilibrium. For the regular
cooled samples, the boundary was made using a polynomial function through five
points: the R, M, and N corners, Li 2 MnO 3 (which was on the boundary as determined
in Sect. 6.3), and the single-phase point found on the edge of the layered–layered
coexistence region (Sect. 6.4). Since only five points were used, the precision of
this line is limited, particularly in the region below the RN line, where no samples
were synthesized in the small two-phase region that must exist below the three-phase
NSR region. It should also be noted that in the three-phase regions equilibrium is
not reached during regular cooling so this could be the case in the layered–spinel
two-phase region as well, making the layered boundary obtained by slow cooling
particularly difficult to identify. Nonetheless, the boundary shown in Figs. 5.2b and
6.1a is in good agreement with the data at hand.
Figure 6.1b shows that for quenched samples the region near Li 2 MnO 3 shows a
sharper “bump” than that seen for slow cooled materials. The points generated in
Sect. 6.3 using the lever rule were used in addition to the five points mentioned here.
The narrow “bump” seems strange in contrast to the rest of the boundaries which
are smooth broad curves. Again this feature is based on a relatively small number
of data points and the quenching required about a minute suggesting that the high
temperature structure may not have been frozen in. As such, more data was required
to conclude that this feature was in fact the equilibrium boundary at 800
◦ C. This
region will, therefore, be examined in more detail in Chap. 8. The phase diagram
shown in Fig. 5.2a is in agreement with all quenched samples synthesized with the
combinatorial robot. It is also worth noting that the boundaries of the single-phase
regions were obtained by fitting polynomials to a relatively small number of points.
The curvature at some points may therefore not be perfect, but the boundaries are
consistent with all experimental data.
6.9 Conclusions Regarding Combinatorial Studies
of Li–Mn–Ni–O Materials
The phase diagrams obtained for quenched samples show that in both three-phase
regions all samples contain some of the N and S phases, while during slow cooling
they convert to structures containing at least some R and M phases. Though the
thermodynamics of this are complex, a qualitative understanding can be achieved
by considering the results of the Rietveld refinement. The R and M phases were
collectively more ordered than the N and S phases (the N phase in particular showed
considerable disorder in the hexagonal layers). This would suggest that the R and
M phases have lower combined internal energies and lower combined entropies
than the combination of the N and S phases. Since the structure of the three-phase
regions at high temperature is driven by entropy, the N and S phases are present in
all points in the regions. Upon slow cooling, a temperature is reached where internal
energy becomes more important and there is still sufficient thermal energy for atomic
transport such that the R and M phases begin to appear in all samples. Further study
6 Combinatorial Studies of Compositions Containing Layered Phases . . .
samples since the slow-cooled samples never reached equilibrium. For the regular
cooled samples, the boundary was made using a polynomial function through five
points: the R, M, and N corners, Li 2 MnO 3 (which was on the boundary as determined
in Sect. 6.3), and the single-phase point found on the edge of the layered–layered
coexistence region (Sect. 6.4). Since only five points were used, the precision of
this line is limited, particularly in the region below the RN line, where no samples
were synthesized in the small two-phase region that must exist below the three-phase
NSR region. It should also be noted that in the three-phase regions equilibrium is
not reached during regular cooling so this could be the case in the layered–spinel
two-phase region as well, making the layered boundary obtained by slow cooling
particularly difficult to identify. Nonetheless, the boundary shown in Figs. 5.2b and
6.1a is in good agreement with the data at hand.
Figure 6.1b shows that for quenched samples the region near Li 2 MnO 3 shows a
sharper “bump” than that seen for slow cooled materials. The points generated in
Sect. 6.3 using the lever rule were used in addition to the five points mentioned here.
The narrow “bump” seems strange in contrast to the rest of the boundaries which
are smooth broad curves. Again this feature is based on a relatively small number
of data points and the quenching required about a minute suggesting that the high
temperature structure may not have been frozen in. As such, more data was required
to conclude that this feature was in fact the equilibrium boundary at 800
◦ C. This
region will, therefore, be examined in more detail in Chap. 8. The phase diagram
shown in Fig. 5.2a is in agreement with all quenched samples synthesized with the
combinatorial robot. It is also worth noting that the boundaries of the single-phase
regions were obtained by fitting polynomials to a relatively small number of points.
The curvature at some points may therefore not be perfect, but the boundaries are
consistent with all experimental data.
6.9 Conclusions Regarding Combinatorial Studies
of Li–Mn–Ni–O Materials
The phase diagrams obtained for quenched samples show that in both three-phase
regions all samples contain some of the N and S phases, while during slow cooling
they convert to structures containing at least some R and M phases. Though the
thermodynamics of this are complex, a qualitative understanding can be achieved
by considering the results of the Rietveld refinement. The R and M phases were
collectively more ordered than the N and S phases (the N phase in particular showed
considerable disorder in the hexagonal layers). This would suggest that the R and
M phases have lower combined internal energies and lower combined entropies
than the combination of the N and S phases. Since the structure of the three-phase
regions at high temperature is driven by entropy, the N and S phases are present in
all points in the regions. Upon slow cooling, a temperature is reached where internal
energy becomes more important and there is still sufficient thermal energy for atomic
transport such that the R and M phases begin to appear in all samples. Further study