Lithium doped sodium niobate is an ecofriendly piezoelectric material that exhibits a variety of structural phase transitions with composition and temperature. We have investigated the phase stabilities of an important composition Li0.12Na0.88NbO3 (L
NN12) using a combination of powder x-ray and neutron diffraction techniques in the temperature range 300 - 1100 K. Detailed Rietveld analyses of thermo-diffractograms show a variety of structural phase transitions ranging from non-polar antiferrodistortive to ferroelectric in nature. In the temperature range of 525 K to 675 K, unambiguous experimental evidence is shown for phase coexistence of orthorhombic paraelectric O1 phase (space group Cmcm) and orthorhombic ferroelectric O2 phase (space group Pmc21). The bp primitive lattice parameter of the ferroelectric orthorhombic phase (O2 phase) decreases, while the ap and cp primitive lattice parameters show normal increase with increase in temperature. Above 675 K, in the O1 phase, all lattice parameters come close to each other and increase continuously with increase of temperature, and around 925 K, ap parameter approaches bp parameter and thus the sample undergoes an orthorhombic to tetragonal phase transition. Further as temperature increases, the cp lattice parameter decreases, and finally approaches to ap parameter, and the sample transform into the cubic phase. The continuous change in the lattice parameters reveals that the successive phase transformations from orthorhombic O1 to high temperature tetragonal phase and finally to the cubic phase are not of a strong first order type in nature. We argue that application of chemical pressure as a result of Li substitution in NaNbO3 matrix, favours the freezing of zone centre phonons over the zone boundary phonons that are known to freeze in pure NaNbO3 as function of temperature.
The structural properties of the CaFe2As2 have been investigated by x-ray and neutron powder diffraction techniques as a function of temperature. Unambiguous experimental evidence is shown for coexistence of tetragonal and orthorhombic phases below 1
70 K in contrast to existing literature. Detailed Rietveld analyses of thermo-diffractograms show that the sample does not transform completely in to the orthorhombic phase at the lowest temperature even though it is the majority phase. We have found that the unit cell volume of the orthorhombic phase is higher compared to that of the tetragonal phase for all the temperatures. X-ray data on CaFe2As2 shows anomalous (at) lattice parameter contraction with increasing temperature and phase co-existence behavior below 170 K unlike other members of the 122 family of compounds like SrFe2As2 and EuFe2As2. Temperature dependent magnetization of polycrystalline CaFe2As2 sample show weak anomalies below 170 K. This behavior of the polycrystalline sample is in contrast to that of a single crystal reported earlier.
We have explained in detail why the canonical partition function of Interacting Self Avoiding Walk (ISAW), is exactly equivalent to the configurational average of the weights associated with growth walks, such as the Interacting Growth Walk (IGW), if
the average is taken over the entire genealogical tree of the walk. In this context, we have shown that it is not always possible to factor the the density of states out of the canonical partition function if the local growth rule is temperature-dependent. We have presented Monte Carlo results for IGWs on a diamond lattice in order to demonstrate that the actual set of IGW configurations available for study is temperature-dependent even though the weighted averages lead to the expected thermodynamic behavior of Interacting Self Avoiding Walk (ISAW).
