Spin-state equilibria in the LCoO3 system from 59Co NMR

Spin-state equilibria in the whole set of LCoO3 (where L stands for a rare-earth metal or Y) have been investigated with the use of 59Co NMR as a probe for the polycrystalline samples (except Ce) in the temperature interval 110-550 K and frequency range 3- 11.6 MHz. Besides confirming the coexistence of the high-spin—low-spin state in this temperature range, a quadrupolar interaction of ∼0.1 -0.5 MHz has been detected for the first time from 59Co NMR. The NMR line shape is found to depend strongly on the relative magnitude of the magnetic and quadrupolar interactions present. Analysis of the powder pattern reveals two basically different types of transferred hyperfine interaction between the lighter and heavier members of the rare-earth series. The first three members of the lighter rare-earth metals La, Pr (rhombohedral), and Nd (tetragonal), exhibit second-order quadrupolar interaction with a zero-asymmetry parameter at lower temperatures. Above a critical temperature TS (dependent on the size of the rare-earth ion), the quadrupolar interaction becomes temperature dependent and eventually gives rise to a first-order interaction thus indicating a possible second-order phase change. Sm and Eu (orthorhombic) exhibit also a second-order quadrupolar interaction with a nonzero asymmetry parameter ((η∼0.47)) at 300 K, while the orthorhombic second-half members (Dy,..., Lu and Y) exhibit first-order quadrupolar interaction at all temperatures. Normal paramagnetic behavior, i.e., a linear variation of Kiso with T-1, has been observed in the heavier rare-earth cobaltites (Er,..., Lu and Y), whereas an anomalous variation has been observed in (La,..., Nd)CoO3. Thus, Kiso increases with increasing temperature in PrCoO3 and NdCoO3. These observations corroborate the model of the spin-state equilibria in LCoO3 originally proposed by Raccah and Goodenough. A high-spin—low-spin ratio, r=1, can be stabilized in the perovskite structure by a cooperative displacement of the oxygen atoms from the high-spin towards the low-spin cation. Where this ordering into high- and low-spin sublattices occurs at r=1, one can anticipate equivalent displacement of all near-neighbor oxygen atoms towards a low-spin cobalt ion. Thus the heavier LCoO3 exhibits a small temperature-independent first-order quadrupolar interaction. Where r<1, the high- and low-spin states are disordered, giving rise to a temperature-dependent second-order quadrupolar interaction with an anomalous Kiso for the lighter LCoO3.

The paribhasas arthavadgrahane nanarthakasya, laksanapratipadoktayoh pratipadoktasyaiva grahanam and ekadesavikrtam ananyavat : Studies on some Metarules in Paninian system

In his grammatical treatise, the Astadhyayi, Panini includes sutras that state guiding rules for the right interpretation and application of his other directly grammatical sutras. These sutras are called paribhasas. In addition to these paribhasas, the various commentaries on Panini frequently invoke supplementary paribhasas which are not stated explicitly in his Astadhyayi. These paribhasas have been a subject of study since early times after Panini and have also occupied modern scholars on Panini s grammar. In regard to most of them, it remains unsettled even today whether they are used in the Astadhyayi, where they apply, what is their role, and whether they are necessary in arriving at the desired grammatical form. Some scholars go even further and argue that none of such paribhasas were intended by Panini. This study aims to settle this question by dealing with three such of these paribhasas individually considering all the information available in the commentaries in their regard and examining the cases in which, according to commentaries, the paribhasas apply. I select the paribhasas arthavadgrahane nanarthakasya, laksanapratipadoktayoh pratipadoktasyaiva grahanam and ekadesavikrtam ananyavat, which are all considered nyayasiddha or lokanyayasiddha; they express logical and obvious principles which are found in daily life. On this basis, Paniniyas explain why Panini did not mention them in the Astadhyayi. I discuss each paribhasa separately and all the issues it involves. I present and explain the cases where the specified paribhasas are invoked in the major commentaries, the Mahabhasya, the Kasika and the Siddhantakaumudi and the arguments found in the commentaries concerning these cases. If available, I supply other solutions to the difficulties for which these paribhasas are invoked. The study aims to make the issue of these paribhasas clearer, which will help us to reach a solution to the key question, that is, whether Panini has presupposed them in his Astadhyayi. My study shows that Panini has presupposed the paribhasa ekadesavikrtam ananyavat (or a similar principle). He also may have used the paribhasa arthavadgrahane nanarthakasya (or a similar principle) as this paribhasa does not lead to undesired results. As for the paribhasa laksanapratipadoktayoh pratipadoktasyaiva grahanam (or a similar principle), the original scope of this paribhasa was clearly extended by later Paniniyas. Moreover, their interpretation of this paribhasa conflicts with Panini s procedure. If Panini has used this paribhasa, he has used it in a very limited way.