Nucleation of a Stable Solid from Melt in the Presence of Multiple Metastable Intermediate Phases: Wetting, Ostwald’s Step Rule, and Vanishing Polymorphs

Abstract

In many systems, nucleation of a stable solid may occur in the presence of other (often more than one) metastable phases. These may be polymorphic solids or even liquid phases. Sometimes, the metastable phase might have a lower free energy minimum than the liquid but higher than the stable-solid-phase minimum and have characteristics in between the parent liquid and the globally stable solid phase. In such cases, nucleation of the solid phase from the melt may be facilitated by the metastable phase because the latter can "wet" the interface between the parent and the daughter phases, even though there may be no signature of the existence of metastable phase in the thermodynamic properties of the parent liquid and the stable solid phase. Straightforward application of classical nucleation theory (CNT) is flawed here as it overestimates the nucleation barrier because surface tension is overestimated (by neglecting the metastable phases of intermediate order) while the thermodynamic free energy gap between daughter and parent phases remains unchanged. In this work, we discuss a density functional theory (DFT)-based statistical mechanical approach to explore and quantify such facilitation. We construct a simple order-parameter-dependent free energy surface that we then use in DFT to calculate (i) the order parameter profile, (ii) the overall nucleation free energy barrier, and (iii) the surface tension between the parent liquid and the metastable solid and also parent liquid and stable solid phases. The theory indeed finds that the nucleation free energy barrier can decrease significantly in the presence of wetting. This approach can provide a microscopic explanation of the Ostwald step rule and the well-known phenomenon of "disappearing polymorphs" that depends on temperature and other thermodynamic conditions. Theory reveals a diverse scenario for phase transformation kinetics, some of which may be explored via modern nanoscopic synthetic methods.

Crystallization Kinetics of Concurrent Liquid–Metastable and Metastable–Stable Transitions, and Ostwald’s Step Rule

“…31 Their study shows "nucleation of the solid phase from the melt may be facilitated by the metastable phase because the latter can "wet" the interface between the parent and the daughter phases, even though there may be no signature of the existence of metastable phase in the thermodynamic properties of the parent liquid and the stable solid phase." 31 They find that "the nucleation free energy barrier can decrease significantly in the presence of wetting." 31 Apparently, the existence of metastable phase lowers the interface tension between the parent and the daughter phases and therefore reduces the nucleation barrier or the critical nucleus size.…”

“…31 They find that "the nucleation free energy barrier can decrease significantly in the presence of wetting." 31 Apparently, the existence of metastable phase lowers the interface tension between the parent and the daughter phases and therefore reduces the nucleation barrier or the critical nucleus size.…”

Shear moduli in bcc-fcc structure transition of colloidal crystals

“…[22][23][24][25] This step rule states that in general it is not the most stable but the least stable polymorph that crystallizes first. This stepwise crystallization phenomenon usually causes crystals with different structures before they reach the final stable state.…”

Experimental and Theoretical Substantiations of Stepwise Mechanism of Crystal Formation From Liquid Phase

“…Однако некоторые метастабильные кристаллические фазы могут далее последовательно претерпевать серию фазовых превращений «твердое -твердое», например, многие полимеры [2,3]. В последние годы это эмпирическое правило нашло дальнейшее теоретическое и экспериментальное обоснование для последовательности фазовых переходов «метастабильное твердое -метастабильная жидкость -стабильная твердая фаза» [4][5][6][7][8][9]. Образование метастабильной жидкой фазы экспериментально доказано во многих работах при контактном плавление двух металлов [10].…”

“…Ранее в ряде работ нами было показано, что вид функции распределения времени ожидания первого зародыша при постоянном переохлаждении расплава (кривые выживания), или при постоянном пересыщении раствора позволяет выявить 5 …”