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The crystallization proceeds by the advance of the crystal faces into the disordered phase at the expense of the material excess, the supersaturation. Using a conservation constraint for the transformation ratio α∈[0,1] as complementing the rescaled supersaturation to 1 and a kinetic law for the normal growth velocity as function of the supersaturation raised to power g, the growth order, we derive an equation for the rate of transformation dα/dt. We integrate it for the six combinations of the three spatial dimensions D = 1, 2, 3 and the two canonical values of g = 1, 2 towards obtaining expressions for αDg. The same equation, with g = 1 and D = n (n is the so called Avrami exponent) is obtained when taking only the linear in α term from the Taylor’s expansion around α = 0 of the model equation of Johnson-Mehl-Avrami-Kolmogorov (JMAK). We verify our model by fitting datasets of α21 and α31 (from α = 0 to αupper = 0.999) with JMAK to obtain from the fit n = 1.725, 2.43, resp. We show
further how the values of n depend on the value of αupper to which the fit is performed starting always from 0. Towards building a validation protocol, we start with validating α21 with published results.
The fundamental processes of nucleation and crystallization are widely observed in systems relevant to material synthesis and biomineralization; yet most often, their mechanism remains unclear. In this study, we unravel the discrete stages of nucleation and crystallization of Fe3(PO4)2·8H2O (vivianite). We experimentally monitored the formation and transformation from ions to solid products by employing correlated, time-resolved in situ and ex situ approaches. We show that vivianite crystallization occurs in distinct stages via a transient amorphous precursor phase. The metastable amorphous ferrous phosphate (AFEP) intermediate could be isolated and stabilized. We resolved the differences in bonding environments, structure, and symmetric changes of the Fe site during the transformation of AFEP to crystalline vivianite through synchrotron X-ray absorption spectroscopy at the Fe K-edge. This intermediate AFEP phase has a lower water content and less distorted local symmetry, compared to the crystalline end product vivianite. Our combined results indicate that a nonclassical, hydration-induced nucleation and transformation driven by the incorporation and rearrangement of water molecules and ions (Fe2+ and PO4 3−) within the AFEP is the dominating mechanism of vivianite formation at moderately high to low vivianite supersaturations (saturation index ≤ 10.19). We offer fundamental insights into the aqueous, amorphous-to-crystalline transformations in the Fe2+−PO4 system and highlight the different attributes of the AFEP, compared to its crystalline counterpart.
Inconel 718 is a precipitation strengthened, nickel-based super alloy of interest for the Additive Manufacturing (AM) of low volume, complex parts to reduce production time and cost compared to conventional subtractive processes. The AM process involves repeated rapid melting, solidification and reheating, which exposes the material to non-equilibrium conditions that affect elemental segregation and the subsequent formation of solidification phases, either beneficial or detrimental. These variations are difficult to characterize due to the small length scale within the micron sized melt pool. To understand how the non-equilibrium conditions affect the initial solidification phases and their critical temperatures, a multi-length scale, multi modal approach has been taken to evaluate various methods for identifying the initial phases formed in the as-built Inconel 718 produced by laser-powder bed fusion (L-PBF) additive manufacturing (AM). Using a range of characterization tools from the bulk differential thermal analysis (DTA) and x-ray diffraction (XRD) to spatially resolved images using a variety of electron microscopy tools, a better understanding is obtained of how these minor phases can be properly identified regarding the amount and size, morphology and distribution. Using the most promising characterization techniques for investigation of the as-built specimens, those techniques were used to evaluate the specimens after various heat treatments. During the sequence of heat treatments, the initial as-built dendritic structures recrystallized into well-defined grains whose size was dependent on the temperature. Although the resulting strength was similar in all heat treated specimens, the elongation increased as the grain size was refined due to differences in the precipitated phase distribution and morphology.
Barium silicate glass powders 4 h milled in CO2 and Ar and sintered in air are studied with microscopy, total carbon analysis, differential thermal Analysis (DTA), vacuum hot extraction mass spectroscopy (VHE-MS), Fourier-transformed infrared (FTIR) spectroscopy, X-ray photoelectron spectroscopy (XPS), and time-of-flight secondary-ion mass spectrometry (TOF-SIMS). Intensive foaming of powder compacts is evident, and VHE studies prove that foaming is predominantly caused by carbonaceous species for both milling gases. DTA Shows that the decomposition of BaCO3 particles mix-milled with glass powders occurs at similar temperatures as foaming of compacts. However, no carbonate at the glass surface could be detected by FTIR spectroscopy, XPS, and TOF-SIMS after heating to the temperature of sintering. Instead, CO2 molecules unable to rotate identified by FTIR spectroscopy after milling, probably trapped by mechanical dissolution into the glass bulk. Such a mechanism or microencapsulation in cracks and particle aggregates can explain the contribution of Ar to foaming after intense milling in Ar atmosphere. The amount of CO2 molecules and Ar, however, cannot fully explain the extent of foaming. Carbonates mechanically dissolved beneath the surface or encapsulated in cracks and micropores of particle aggregates are therefore probably the major foaming source.
To explore the impact of ambient and structural water on static fatigue, the initiation and growth of 3279 Vickers induced median radial cracks were automatically recorded and analyzed. We find that humidity is more efficient in initiating cracks and promoting their growth than water, which is dissolved in the glass structure. In particular for slow crack growth (< 3x10-6 m s-1), tests in dry nitrogen showed a considerable decrease in the crack growth exponent with increasing water content of the glasses. On the other hand, if tests were performed in humid air, the crack growth exponent was independent of the water content of the hydrous glasses, while stress intensity decreased slightly. These observations indicate that water promotes the processes at the crack-tip regardless of its origin. However, ambient water is more efficient.
To understand the influence of water and alkalis on aluminosilicate glasses, three polymerized glasses with varying ratios of Na/K were synthesized [(22. 5-x)Na2O-xK2O-22.5 Al2O3-55 SiO2 with x = 0, 7.5, and 11.25]. Subsequently, these glasses were hydrated (up to 8 wt% H2O) in an internally heated gas pressure vessel. The density of hydrous glasses linearly decreased with water content above 1 wt%, consistent with the partial molar volume of H2O of 12 cm3/mol. Near-infrared spectroscopy revealed that hydroxyl groups are the dominant species at water content of <4 wt%, and molecular water becomes dominating at water content of >5 wt%. The fraction of OH is particularly high in the pure Na-bearing glass compared to the mixed alkali glasses. 27Al magic angle spinning-NMR spectroscopy shows that aluminum is exclusively fourfold coordinated with some variations in the local geometry. It appears that the local structure around Al becomes more ordered with increasing K/Na ratio. The incorporation of H2O reinforces this effect. The differential thermal analysis of hydrous glasses shows a significant mass loss in the range of glass transition already during the first upscan, implying the high mobility of water in the glasses. This observation can be explained by the open structure of the aluminosilicate network and by the low dissociation enthalpy of H2O in the glasses (≈ 8 kJ/mol). The effect of the dissolved H2O on the glass transition temperature is less pronounced than for other aluminosilicate glasses, probably because of the large fraction of Al in the glasses.
Stable crack growth was measured for nominal dry and water-bearing (6 wt%) soda-lime silicate glasses in double cantilever beam geometry and combined with DMA studies on the effects of dissolved water on internal friction and glass transition, respectively. In vacuum, a decreased slope of logarithmic crack growth velocity versus stress intensity factor is evident for the hydrous glass in line with an increase of b-relaxation intensity indicating more energy Dissipation during fracture. Further, inert crack growth in hydrous glass is found to be divided into sections of different slope, which indicates different water related crack propagation mechanism. In ambient air, a largely extended region II is observed for the hydrous glass, which indicates that crack growth is more sensitive to ambient water.