Kinetics Of Materials Balluffi Pdf

[Jenn Smotherman]

Thankyou for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Phase diagrams offer substantial predictive power for materials synthesis by identifying the stability regions of target phases. However, thermodynamic phase diagrams do not offer explicit information regarding the kinetic competitiveness of undesired by-product phases. Here we propose a quantitative and computable thermodynamic metric to identify synthesis conditions under which the propensity to form kinetically competing by-products is minimized. We hypothesize that thermodynamic competition is minimized when the difference in free energy between a target phase and the minimal energy of all other competing phases is maximized. We validate this hypothesis for aqueous materials synthesis through two empirical approaches: first, by analysing 331 aqueous synthesis recipes text-mined from the literature; and second, by systematic experimental synthesis of LiIn(IO3)4 and LiFePO4 across a wide range of aqueous electrochemical conditions. Our results show that even for synthesis conditions that are within the stability region of a thermodynamic Pourbaix diagram, phase-pure synthesis occurs only when thermodynamic competition with undesired phases is minimized.

Over the past decade, the Materials Genome Initiative has made it possible to discover and design new materials from first principles1,2,3,4. However, synthesizing a computationally predicted material remains a challenging but necessary step before any further investigation into its functional properties5,6,7. Thermodynamic phase diagrams are routinely used to guide scientists to synthesize a target phase by indicating its region of thermodynamic stability8,9,10,11. However, from a practical experimental perspective, one must carefully optimize reaction conditions to eliminate any undesired competing phases, which often appear as kinetic by-products12,13,14. Traditional phase diagrams do not visualize the free-energy axis, which contains essential information regarding the thermodynamic competition from these competing phases. Even within the same stability region of a thermodynamic phase diagram, the details of nucleation kinetics can drive a reaction through different intermediate phases15,16, which can persist in the final product as undesired by-products.

a, Generation of the hypothesis: conditions where the target phase experiences minimum thermodynamic competition from other phases are favoured for synthesis. Upper: the 2D plot depicts this general concept. The different coloured lines represent the energy of various phases. The green line represents the desired target phase; the other lines depict the energies of competing phases. Double-headed arrows between the lines illustrate the difference in free energy between the desired target phase and the minimum free energy among all competing phases, which is the thermodynamic competition denoted as ΔΦ. The solid arrow indicates the MTC, and stars denote the conditions at which MTC is achieved. The projection of the phases with the lowest energy under different conditions forms the thermodynamic phase diagram, with the stability regions of phases indicated by blocks of corresponding colours. Lower: the 3D plot represents the energy landscape of thermodynamic competition in a multidimensional Pourbaix system. The dotted line axes represent the high-dimensional aspect for the other conditions. b, Predictive synthesis: minimizing thermodynamic competition to predict synthesis conditions. E, redox potential. c, Hypothesis testing: large-scale analysis based on the text-mined dataset and detailed investigation of LiIn(IO3)4 and LiFePO4.

Here we present an optimization strategy that relies on the inherent concave geometry of the free-energy landscape of an aqueous electrochemical system (see Methods section), which leads to an efficient computational algorithm that can be readily scaled to high-dimensional (multicomponent) optimization spaces21. We provide empirical confirmation of our MTC hypothesis using two complementary approaches, as shown in Fig. 1c. First, we perform a large-scale analysis on a text-mined dataset of solution synthesis recipes22, and find that within the available parameter space of synthesis conditions, the experimentally reported (and probably optimized) synthesis conditions lie near the conditions predicted by our MTC criteria. Second, we perform a detailed thermodynamic competition analysis of two systems, LiIn(IO3)4 and LiFePO4, and confirm by systematic experimental investigations that the desired target materials can only be synthesized in phase-pure form when the thermodynamic competition is minimized. Our work illustrates how a comprehensive understanding of the free-energy axis of a phase diagram, considering not only the stable phase but also its competing phases, enables the computational design and guidance of optimal materials synthesis conditions.

From this geometric description of the energy landscape, the thermodynamic competition that a target phase experiences from the other phases is defined as the difference in free energy between the desired target phase and the minimum free energy of all competing phases, and is schematically shown in Fig. 1a. We denote phase k as the desired target phase, Y as intensive variables and Ic as the index set of other competing phases. The thermodynamic competition that the phase k experiences from other phases, ΔΦ(Y), can be written as:

According to our proposed definition, the ΔΦ for a thermodynamically stable phase is always negative, indicating that the target compound possesses a lower free-energy state than all its competing phases. Minimizing the thermodynamic competition with undesired phases is equivalent to maximizing the energy difference from the most competitive competing phase to the target phase.

In the Methods, we describe the procedure for converting a reported synthesis recipe into metal ion concentrations, pH values and effective redox potential, and the calculation of thermodynamic competition under given text-mined conditions. Our text-mined dataset contains 331 synthesis recipes, including recipes for 200 ternary metal oxides, 64 phosphates, 29 carbonates, 15 iodates, 12 sulfates and 11 silicates.

a, Gaussian kernel density estimates of thermodynamic competition distributions of different multicomponent functional oxides. b, Gaussian kernel density estimates of the thermodynamic competition differences of different compounds between the text-mined conditions and their corresponding thermodynamically optimal conditions. The highlighted number is the median for all entries.

Overall, our text-mined dataset provides explicit post hoc empirical validation of the MTC hypothesis, and furthermore highlights the value of such text-mined datasets in not only providing data to train machine-learning models35, but also in empirically validating new mechanistic theories36.

Results reported by Liu et al.44 indicate that LiFePO4 was not successfully synthesized even within this thermodynamically stable region. Here we experimentally validate that the MTC identifies the optimal conditions within the LiFePO4 stability window to successfully produce phase-pure LiFePO4.

Our ability to rationalize the kinetic unsuitability of certain conditions that are within the thermodynamic stability region of the Pourbaix diagram demonstrates the advantage of our MTC theory over traditional phase diagram methods.

We have presented here a computable thermodynamic strategy to navigate a multidimensional thermodynamic space and identify optimal experimental conditions to synthesize a phase-pure target material. Our approach adds to traditional phase diagrams a quantitative measure to approximate the kinetic competitiveness of potential competing phases. Both our large-scale analysis on text-mined synthesis recipes, and our experimental synthesis of LiIn(IO3)4 and LiFePO4 under varying aqueous electrochemical conditions, demonstrate that thermodynamic stability alone may not be sufficient to predict conditions that result in phase-pure synthesis. Instead, target phases are more likely to be synthesized when the energy difference with undesired phases is maximized, such that ΔΦ is as negative as possible, and therefore thermodynamic competition with undesired by-products is minimized. The relevance of the quantitative competition measurement for successful synthesis is consistent with our mechanistic understanding of the kinetic processes that can bias reaction kinetics away from thermodynamic end-products. The more negative the ΔΦ for a target phase is, the stronger the required kinetic bias needs to be to form other phases (lower surface energy15, faster monomer diffusion or attachment rates12). As such, while the MTC does not explicitly include kinetics calculations, by minimizing the energetic competition from other phases, the MTC safeguards the synthesis of the target phases as much as possible from undesired by-products.

Beyond synthesis from aqueous solutions, we note that our schema is generalizable to other synthesis scenarios. For other synthesis methods, appropriate thermodynamic potentials based on different natural intensive variables are also viable. Fortunately, Materials Genome Initiative efforts have not only led to large-scale ab initio computed databases1,3 that provide reliable sources of thermodynamic data, but also deliver materials analysis platforms2 that can automate competing phase-generation and grand-potential calculations. Therefore, different thermodynamic potentials can be easily constructed from this thermodynamic data using Legendre transformations based on the relevant boundary conditions of the thermodynamic system27,50. For example, the surface-energy term should be considered in nanoparticle synthesis analysis15,51,52; mechanical work should be included in ball-milling synthesis53,54,55; and an electromagnetic-susceptibility term is important to take into account when electric and magnetic fields are applied56,57. Thus, the MTC hypothesis can be extended to different synthesis scenarios, although the applicability of MTC in different syntheses requires further comprehensive and systematic evaluation.

3a8082e126