Successive Ostwald rule

Ostwald proposed that when two or more new phases may form from existing phase or phases, that is, when new phases are more stable than the existing phase(s), the least stable new phase would form first and then transform into more stable phases. This is called the Ostwald rule, the Ostwald step rule, or the law of successive reactions. An alternative statement of the Ostwald rule is as follows ... 

Zeolites are thermodynamically metastable phases that can be transformed at longer synthesis times into more stable (and more dense) structures [93]. This phenomenon is known as the Ostwald rule of successive phase transformations. 

Based on the reversibility of their phase transformation behavior, polymorphs can easily be classified as being either enantiotropic (interchange reversibly with temperature) or monotropic (irreversible phase transformation). Enantiotropic polymorphs are each characterized by phase stability over well-defined temperature ranges. In the monotropic system, one polymorph will be stable at all temperatures, and the other is only metastable. Ostwald formulated the rule of successive reactions, which states that the phase that will crystallize out of a melt will be the state that can be reached with the minimum loss of free... 

Formation of trimetaphosphate anions from those of Graham s salt also occurs in solution. In water this process is not associated with hydrolytic cleavage of the P—0—P bonds, as was at first assumed (10, 322), but is independent of it (361). Thus polyphosphates of long-chain amines which are soluble in benzene form trimetaphosphate quantitatively on warming the anhydrous solution (359). This transformation follows Ostwald s rule for successive transformations, since trimetaphosphates are more stable than polyphosphates (322). 

Also,if the solutions had an initial Si02/Al20 ratio of 73,S formed but no Y, while if this initial ratio was 102,P formed but no S. This behaviour suggests caution in interpreting all crystallisation sequences as examples of Ostwald s rule of successive transformations. The rule states that in a crystallisation sequence the new phases replace each other in the order of a step by step descent of a ladder of increasing thermodynamic stability. An example in a hydrothermal system is ( ) ... 

The optimum check of Ostwald s rule would, as in the above sequence, involve parent gel and successive phases all of the same composition. This condition is not met in many crystallisation sequences. 

The Ostwald step rule is, evidently, a particular case of the general requirement (see Section 1.3.3) for a sequential decrease in chemical potentials of the transformation intermediates in the course of a stepwise transformation. In the transformation of the constant composition soHd phases, the said requirement refers to chemical potentials of the soHd phases. If the state diagram of a particular matter comprises several allowed phases (the ones differing, for example, by their crystal structures, etc.), the initial phase transformation into the thermodynamically stable state at a constant temperature will be successively mediated by aU of the phases along the reaction pathway from the initial point to the stable phase. 

Ostwald (1897) was aware of the fact that his rule was tenuous, since it was not based on a very large set of observations. In addition, if the metastable region were to shrink to a vanishingly small value, then sufficient time would not be allowed for crystallization of Form I to appear, and the rule would be invalidated. In fact, this does happen in many cases. Nevertheless, Ostwald s Rule has remained in the lexicon of crystal chemists, probably because it is generally observed that if a succession of polymorphic forms is obtained, those which appear later are generally more stable than those whieh appear earlier. 

Fig. 1.4 Example of Ostwald s Rule of Successive Reactions. 2,4-dibromoacetanilide initially crystallizes from alcoholic solutions as small needle-shaped crystals, forming the voluminous mass in (1). Successive photos (2,3,4) of the same crystallization vessel, taken at two-day intervals show the transformation to the more stable chunky rhombic crystals (from Findlay 1951, with permission).

There are significant flaws in Ostwald s conclusion that led to his rule. For instance, when a crystallization experiment yields only a single form there is the question of whether it contradicts the Rule or whether the material is simply not polymorphic. Moreover, there is no way of answering this question. However, a sufficient number of cases of successively crystallizing polymorphic forms have been observed to warrant considering the principles behind Ostwald s Rule as guidelines for understanding the phenomenon of the successive crystallization of different polymorphic phases. 

A primary concern is polymorphic crystallization in which the Ostwald step rule is very useful (9). This rule predicts that phase changes occur step by step by way of successively more stable phases. For the relative rate of nucleation of polymorphic crystals shown in Figure 2, it follows that nucleation of the metastable forms such as a and p occurs first before the most stable p form, when nucleation occurs under a large supercooling or high supersaturation. When the amount of supercooling or supersaturation is decreased, the law is broken and the most stable form tends to nucleate at a relatively slow rate. 

Closely allied with the concepts of metastable equilibrium and suspended transformations is Ostwald s rule (Ostwald s step rule or law of successive reactions). Essentially Ostwald s rule states that in all processes it is not the most stable state with the least amount of free energy that is initially obtained but the least stable state lying nearest to the original state in free energy (Ostwald 1897). It is easy to see how this rule and the concept of suspended transformations can explain the production of a metastable polymorph through crystallization from a melt or solution. 

In crystallization processes involving a material that displays polymorphism, it is quite common for an unstable polymorph to appear first and then transform into a stable form. This observation is summarized by Ostwald s step rule, sometimes referred to as the Law of Successive Reactions, which says that in any process, the state which is initially obtained is not the stablest state but the least stable state that is closest in terms of free energy change, to the original state. What this means, therefore, is that a crystallization process, the initial solid phase, can be the least stable polymorph that will then transform into successively more stable forms until the stable form, at the conditions of the system, is reached. With some systems this can mean the formation of an... 

During the 19th century. Gay Lussac observed that, during crystallization, an unstable form is frequently obtained first that subsequently transforms into a stable form [13]. This observation was later explained thermodynamically by Ostwald [13,16-19], who formulated the law of successive reactions, also known as Ostwald s step rule. This... 

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