Use of Phase Diagrams in the Study of Silicon Nitride Ceramics

TSENG-YING TIEN , in Phase Diagrams in Advanced Ceramics, 1995

3. Si3N4–Al2O3 SYSTEM

Oyama [ 13 ] and Jack [ 14 ] reported the solid solution formation of aluminum oxide in silicon nitride. In these solid solutions, aluminum ions replace silicon ions and nitrogen ions replace oxygen ions in the lattice. Oyama [ 13 ] and Jack [ 14 ] both presented their phase diagrams as triangular ternary systems. These solid solutions were named by Jack [ 14 ] as β′-SiAlON and he has suggested that these solid solutions contain lattice vacancies and hence an increase in the ionic nature of the chemical bond. If this is true, a high-density silicon nitride ceramic should be able to be made by solid-state sintering through lattice diffusion without the aid of a liquid phase, and thus without the need of sintering additives. A polycrystalline material without a grain-boundary liquid phase should therefore have better creep resistance. The inferior high-temperature properties of sintered and hot-pressed silicon nitride ceramics have been attributed to the glassy grain-boundary, which becomes soft at high temperatures [ 15 ]. Thus, it was believed that these single-phase silicon nitride solid solutions (β–SiAlONs) will not contain grain-boundary glass if properly made. This possibility has led to many investigations in an attempt to obtain silicon nitride ceramics with no grain-boundary glass and hence better high-temperature properties.

In a later study, Gauckler [ 2 ] demonstrated that these solid solutions are substitutional and contain no lattice vacancies. These solid solutions were described by Gauckler by the formula β–Si6-x AlxN8-x O x . The limiting composition has an x value of 4. The phase diagram of the Si3N4–SiO2–AlN–Al2O3 system is shown in Fig. 2 as a reciprocal salt system. Gauckler [ 2 ] was the first to present the phase diagram in this manner.

Boskovic et al. [ 16 ] sintered compacts of presynthesized β′–SiAlON powder and found that no densification occurred at temperatures as high as 1900°C. In these studies, Boskovic showed the sintering behavior of some selected compositions in the Si3N4–SiO2–AlN–Al2O3 system, using different combinations of the individual compounds as the starting materials, to produce a single-phase, β–Si6-xAl x N8-x O x solid solution. Since the system is a reciprocal salt system, the compositions as marked in Fig. 7 can be produced using different combinations of different groups of starting materials [ 17 ], i.e., combinations of Si3N4, SiO2, and AlN, or Si3N4, AlN, and Al2O3. Boskovic's results showed that all compositions can be sintered to high density as shown in Fig. 8. The sintering of these mixtures can be described as transient liquid phase sintering. When mixtures are heated at high temperatures, liquid forms at the contact points of the particles, which aids densification. During the later stages of sintering, the liquid reacts with the starting material to form crystalline β′–SiAlON. When the reaction is completed, the liquid is exhausted. Compositions using mixtures of Si3N4, SiO2, and AlN had a higher weight loss and could only be sintered at high temperatures where large amounts of liquid were formed, sealing the open pores in the beginning of the sintering process, and thus preventing vaporization. This can be explained using the phase diagram shown in Fig. 9, which was published by Naik et al. [ 18 ]. In the initial stages of the reaction, AlN reacts with SiO2 to form a liquid with a composition near the SiO2 corner of the diagram. This liquid decomposes easily and vaporizes, resulting in a high weight loss and low density. For mixtures using Si3N4, AlN and Al2O3 as starting materials, Si3N4 and Al2O3 react to form a liquid with low SiO2 content, which is more stable. This produces a lower weight loss and results in a higher density material at lower temperatures.

FIG. 7. The Si3N4–SiO2–Al2O3–AlN system, showing the compositions that can be prepared from any combination of the starting materials in the triangles defined by either Si3N4–AlN–SiO2 or Si3N4–AlN–Al2O3 [ 17 ].

FIG. 8. Sintering rate curves by Boskovic [ 16 ] for the composition, β–Si6–x Al x N8–x O x (x = 4, or 60 equivalent percent of aluminum) in the Si3N4–SiO2–Al2O3–AlN system using different starting materials. Δ, Si2Al4O4N4;

, Si3N4; □, SiO2 + AlN; ○, SiO2 + AlN.

FIG. 9. The 1750°C isotherm (18) for the Si3N4–SiO2–Al2O3–AlN system.

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Rapid Solidification Processing

C. Suryanarayana , in Encyclopedia of Materials: Science and Technology, 2002

3.3 Models

Equilibrium solid solubility limits have been explained on the basis of the Hume–Rothery rules for solid solution formation. The atomic size factor is considered as the primary responsible factor for this and reasonable success has been achieved using this criterion. The ability to explain the solubility levels is further enhanced by the Darken–Gurry plots, wherein the atomic size (corrected to a coordination number of 12) is plotted against electronegativity. In this case, the more soluble elements cluster around the solvent in the form of an ellipse within the range of ±15% of the atomic size and ±0.3 of the electronegativity. Even though this appears to be true in some cases, the Darken–Gurry plot is not able to satisfactorily explain the achieved solid solubility extensions in aluminum alloys ( Fig. 2). Note, for example, that copper and magnesium with extended solubilities of 18 at.% and 36.8 at.%, respectively, are outside the ellipse. Better success has been achieved in separating the more soluble and less soluble elements by plotting the semi-empirical parameters to heat of formation and of mixing, or the Wigner–Seitz radius against heat of solution. Only some of these empirical relationships are suited to explain the solubility levels achieved in rapidly solidified alloys, and as such their utility is limited.

Figure 2. Darken–Gurry (electronegativity vs. atomic size) plot for aluminum alloys. The ellipse represents a deviation of ±0.3 units in electronegativity and ±15% of the atomic size of aluminum. Note that elements that show large amounts of solid solubility in aluminum (Table 1) are expected to be inside the ellipse, but they are not.

Some thermodynamic attempts have been made to predict the maximum solubility values under RSP conditions. These investigations use the concept of T o, the temperature at which the molar free energies of the liquid and solid phases are equal for the composition of interest. The locus of T o over a range of composition constitutes a T o curve and represents useful thermodynamic information.

A use of these curves is to determine whether a limit exists for the extension of solid solubility by RSP methods. The T o curve lies between the liquidus and solidus temperatures and three different possibilities can be visualized as shown for a eutectic phase diagram in Fig. 3. In Fig. 3(a), the T o curve is continuous from the pure A to the pure B component and the minimum in the T o curve exists above room temperature. In this situation it is possible to obtain complete solid solubility of A in B (and B in A) by rapidly solidifying the liquid alloy to a temperature below T o, i.e., massive or partitionless solidification takes place. The Cu–Ag system falls under this category. The T o curve plunges to very low temperatures in Fig. 3(b). In this situation, the maximum solid solubility extension is limited by the T o curve, i.e., at compositions to the right of the T o curve on the A-rich side and to the left of the T o curve on the B-rich side it will not be possible to obtain massive solidification.The majority of the systems which do not exhibit complete solid solubility under non-equilibrium conditions come under this category. Alloy compositions in the center of these two extremes are good candidate materials for glass formation, provided the alloy is solidified without crystallization to below the glass transition temperature T g. In alloy systems with retrograde solubility under equilibrium conditions, the T o curve plunges to absolute zero at a composition corresponding to the liquidus composition at the retrograde temperature. Thus, it is impossible to achieve any extension of solid solubility limit. The Cd–Zn system comes under this category. The third possibility arises when the T o curves for the A-rich and B-rich alloys intersect in the middle of the phase diagram (Fig. 3(c)), i.e., when the T o are only slightly depressed below the stable liquidus temperature. In this situation, significant solid solubility extension can occur, but not complete solid solubility of one element in the other.

Figure 3. (a)–(c) Schematic representation of the T o curves (dashed lines) for the liquid-to-solid transformation during RSP of three different types of alloys exhibiting a eutectic reaction. In these diagrams α and β represent the equilibrium solid solutions of B in A and A in B, respectively, α ss and β ss represent the supersaturated solid solutions, and T g the glass-transition temperature. In (b) and (c), the dashed lines represent the T o lines for the α/L on the A-rich side and β/L on the B-rich side, respectively.

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Rare-Earth Doped Upconversion Nanophosphors☆

F. Wang , X. Liu , in Comprehensive Nanoscience and Nanotechnology (Second Edition), 2011

1.18.3.1.1 Coprecipitation

Coprecipitation is one of the most convenient techniques for the incorporation of trace RE elements into nanophosphors with a narrow size distribution, during solid solution formation and recrystallization. In contrast to other techniques, the coprecipitation technique does not require costly equipment, stringent reaction conditions, or complex procedures. In some rare instances, crystalline nanophosphors can be obtained directly by coprecipitation without a calcination step or postannealing process.

Stouwdam and van Veggel [5] first demonstrated the synthesis of downconversion LaF3 nanophosphors doped with RE3+ (RE   =   Eu, Er, Nd, and Ho) by coprecipitation. The approach was then expanded and refined by Yi and Chow [14] who prepared UC LaF3 nanophosphors with smaller particle size (~5   nm) and a narrower size distribution from simple water-soluble inorganic precursors. In their studies, synthetic ammonium di-n-octadecyldithiophosphate was used as a capping ligand to control particle growth and stabilize the nanophosphors against aggregation. These sub-10   nm UC crystals can be redispersed in solutions, offering promising applications as luminescent probes for biomolecules with dimensions from two to several tens of nanometers.

In addition to LaF3 nanophosphors, LuPO4:Yb/Tm, YbPO4:Er, NaYF4:Yb/Er(Tm), NaGdF4:Yb/Er, and Y3A15O12 (YAG):Yb/Tm nanophosphors were also synthesized through the coprecipitation approach coupled with heat treatment (or postannealing process) by the groups of Haase, Güdel, Chen, Li, and Wang [15–20]. Recently, polymeric ligands such as polyvinylpyrrolidone (PVP) and polyethylenimine (PEI) were also used to control particle growth and provide the nanophosphors with improved solubility and desired surface functionality [21–24]. For example, the PEI-coated nanophosphors can be readily attached to biomolecules with carboxylic acid functional groups by coupling the acid groups to the pendant amine moieties at the particle surface [25].

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Polymer Characterization

Douglas L. Dorset , in Comprehensive Polymer Science and Supplements, 1989

29.6.2.3 Binary mixtures

Polydispersity in polymer crystals implies the capability to form solid solution beyond the limits found for monodisperse oligomers, 100 even though fractionation can be visualized for the chain folded systems. 101, 102 Although solid solution formation has been often studied by powder X-ray diffraction techniques, 103 recent quantitative electron diffraction structure analyses have been made on epitaxially oriented binary single crystal alkane systems. 104, 109 The symmetry criterion for chain mixing 105 was also found to be less important than relative chain length, in agreement with recent theoretical analyses. 106 This study has been recently extended to fractionated mixtures. 107

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Safety assessment of nuclear waste repositories: a radionuclide migration perspective

J. Bruno , A. Delos , in Radionuclide Behaviour in the Natural Environment, 2012

17.5.1 The SKB safety assessment

As already pointed out in the previous discussions, it is clear that while solubility calculations are fully consistent from a thermodynamic point of view, the description of the various radionuclide sorption processes (surface complexation, co-precipitation and solid solution formation) is not thermodynamically consistent. This probably has no major practical consequences when assessing the radiological risk of the KBS3 repository in the Forsmark site but it brings inherent inconsistencies that should and probably could be avoided. One of the main reasons for not integrating a fully thermodynamic model for the description of radionuclide sorption in the migration pathways is the perceived complexity of coupling chemical and hydraulic models. This perception is totally unjustified in the light of the current development of computer models and only reflects an inherent conservatism of SA modellers.

Hence, the challenge from the scientific community is to practically demonstrate that the concepts and parameters for the thermodynamic description of the sorption processes are available (see, for instance, Bruno et al. 2007) and the response from the SA applicants should be to make a real effort in integrating the chemical uncertainties as they are obliged to do for the hydrogeological ones, with much less conceptual and experimental back-up.

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A(B′1/3B″2/3)O3 COMPLEX PEROVSKITES

MAILADIL T. SEBASTIAN , in Dielectric Materials for Wireless Communication, 2008

8.7 Ba(Co1/3Nb2/3)O3

Several authors investigated [18, 19, 31, 223, 259] the microwave dielectric properties of Ba(Co1/2Nb1/2)O3 (BCN). Melodetsky and Davies studied [31 ] the effect of different solid solution formation and heat-treatment on the cation ordering and dielectric properties of Ba(Co1/3Nb2/3)O3. Pure BCN undergoes an order–disorder transition at 1400°C. The substitution of BaZrO3 destabilizes the 1:2 order and a 1:1 ordered phase is formed for 10−20 mol% BaZrO3. The order–disorder transition temperatures for the 1:1 BCN–BaZrO3 phases are quite low (<1300°C) and lead to lower degrees of order and lower Qf values. The substitution of Ba(Y1/2Nb1/2)O3 also induces a transition to 1:1 ordering, but in this case the stability of the order is significantly higher and the samples remain ordered to at least 1550°C. The high degree of order in the BYN-based system is accompanied by a higher Qf value compared to their BaZrO3 counterparts. However, none of the samples reach the Qf values of the ordered BCN end member. Ahn et al. [18, 223] reported that BCN has a 1:2 ordered hexagonal structure when sintered below 1400°C and showed the highest Qf of 78 000 GHz with ɛr = 32 and τf = −12 ppm/°C. Sintering above 1400°C led to evaporation of CoO and the formation of Ba- and Nb-rich liquid phases which led to grain growth and the degradation of microwave dielectric properties. It was found [19] that Co deficiency in BCN degraded the quality factor. In Co-deficient compositions, cobalt-deficient secondary phases such as Ba8CoNb6O24 and Ba5Nb4O15 were developed.

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LOW TEMPERATURE COFIRED CERAMICS

MAILADIL T. SEBASTIAN , in Dielectric Materials for Wireless Communication, 2008

12.7.15 Mg4(Nb/Ta)2O9

The Mg4Nb2O9 can be sintered at 850°C by the addition of 3 wt% LiF with excellent quality factor of 103 600 GHz and ɛr of 12.6 [327]. Substitution of a small amount of V for Nb in Mg4Nb2O9 can considerably improve the quality factor with a decrease in the sintering temperature [328 ]. The limit of solid solution formation is close to x = 0.125. Secondary phases of Mg3(VO4)2 formed for x > 0.25. The highest Qf of 160 000 GHz was obtained for Mg4(Nb2− x V x )O9 for x = 0.0625 sintered at 1025°C with ɛr = 11.6. Small amount of V substitution is effective in lowering the sintering temperature without deterioration in the microwave dielectric properties. However, the τf is relatively high (−70 ppm/°C) for practical applications. To lower the τf, Yokoi et al. [329] added 6 wt% CaTiO3 and sintered at 950°C for 10 hours to obtain ɛr = 15.7, Qf = 22 100 GHz and τf = −3.3 ppm/°C. Although the microwave dielectric properties are useful, the compatibility with electrode materials needs to be investigated for practical use.

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Cement Components and Their Phase Relations

Donald E. Macphee , Eric E. Lachowski , in Lea's Chemistry of Cement and Concrete (Fourth Edition), 1998

Fluorides and fluorosilicates

Fluoride may be present due to the raw materials or as a deliberate addition as a fluxing agent. It can have a strong accelerating influence on the formation of C3S and C2S and has a deleterious effect on the strength development of their hydrates. It also stabilises α-and α′-C2S, but only in the presence of C3S; this is attributed to the liberation of free lime due to the substitution of F− for O2− 71 C3 S itself undergoes solid solution formation with CaF 2, with about 0.74 per cent (as F−) being dissolved. However, XRD shows that the resulting solid solution has the structure of alite. The relevant portion of the CaO SiO2-CaF2 system, modified from the version of Gutt and Osborne, 72 is shown in Figure 3.25 and features C3S, C2S and the ternary phases 2C2S·CaF2 and Ca5.5Si2O9F (equivalent to C10S4·CaF2). The latter was formerly described as 3C3S·CaF2 but Perez-Mendez et al. 73 , 74 revised this composition on the basis of structural determination and proposed the general formula Ca6-0.5xSi2O,10-xFx. However, levels of fluoride in single crystals were found to be much lower than previously supposed. They also suspected that the phase may indeed be metastable.

Fig. 3.25. The portion of the CaO-SiO2-CaF2 system relevant to Portland cement

 (adapted from Ref. 72).

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Components in Portland Cement Clinker and Their Phase Relationships

Duncan Herfort , Donald E. Macphee , in Lea's Chemistry of Cement and Concrete (Fifth Edition), 2019

3.4.3.1.7 Fluorides and Fluorosilicates

Fluoride may be present due to the raw materials or as a deliberate addition as a mineraliser. It can have a strong mineralising influence on the formation of C3S and enhance strength development in concentrations below about 0.3%, and progressively retard strength development at higher concentrations. C3 S itself undergoes solid solution formation with CaF 2, with concentrations up to about 0.74% (as F−) being dissolved. XRD shows that the resulting solid solution has the structure of alite. The relevant portion of the CaO–SiO2–CaF2 system, modified from the version of Gutt and Osborne, 74 is shown in Fig. 3.27 and features C3S, C2S and the ternary phases 2C2S.CaF2 and Ca5.5Si2O9F (equivalent to C10S4 CaF2). The latter was formerly described as 3C3S.CaF2 but Perez-Mendez et al. 75,76 revised this composition on the basis of structural determination and proposed the general formula Ca6–0.5x Si2O10   − x F x . However, levels of fluoride in single crystals were found to be much lower than previously supposed. They also suspected that the phase may indeed be metastable. However, in Portland cement systems, the mechanism of substitution has been shown to involve a coupled substitution with aluminium, with 1F− replacing O2   −, and one Al3   + replacing Si4   +. 77 The thermodynamic role played by F in stabilising alite is discussed further in the next section.

Fig. 3.27

Fig. 3.27. The portion of the CaO–SiO2–CaF2 system relevant to Portland cement.

 (Source: Adapted from Gutt W, Osborne GJ. The system CaO–2CaO SiO2–CaF2. Trans Br Ceram Soc 1970;69:125–9.)

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Cluster Beam Deposition of Functional Nanomaterials and Devices

Jeffrey E. Shield , in Frontiers of Nanoscience, 2020

6.6 Solid solution extension

The far-from-equilibrium processing afforded by inert gas condensation can produce novel structures, notably extended solid solutions (Fig. 6.8C). Further, creating solid solutions in otherwise immiscible systems can be a pathway to new atomic structures—especially ordered structures (Fig. 6.8D). These structures in turn could lead to new magnetic materials. For instance, first-principles calculations suggest that the addition of heavy 5d transition metals such as W or Mo into Fe or Co could significantly enhance the magnetocrystalline anisotropy [47,48]. However, in equilibrium these systems have low or negligible solid solubility; for example, Fig. 6.14 shows the Co-rich section of the Co-W phase diagram, where there is negligible solubility of W in Co.

Figure 6.14. Co-rich section of the Co-W phase diagram (after [51]).

From our explorations of immiscible systems, we were able to create extended or complete solid solutions in a number of systems, although there is a strong size dependence on complete solid solution formation. In larger clusters, core/shell structures formed ( Fig. 6.15) [39,49], while smaller clusters formed complete solid solutions. Interestingly, the transition is abrupt, and several systems displayed a transition at about 8   nm (Fig. 6.16) [39]. The formation of a solid solution may be driven by surface energy considerations, where the energy required to form an interface is not offset by the decrease in free energy realized by forming two phases [50]. Additionally, the thermodynamics of nanosystems may lead to changes in the enthalpy (heat of mixing) in small systems, leading to conditions more favorable for mixing (solid solution formation).

Figure 6.15. Core/shell clusters formed in the Fe(Co)-Au system. The lower surface energy Au forms on the surface.

Figure 6.16. Size-dependence of core/shell formation in Fe-W clusters. The HAADF STEM images show core/shell behavior at sizes above 8   nm, and single-phase structures in smaller clusters.

The uptick in rare earth commodity prices and increasing demand for high-end Nd-Fe-B-based materials for wind turbine and electrical vehicle uses provided the impetus to search for rare earth-free permanent magnet materials. Co in the hcp form has a relatively high magnetocrystalline anisotropy constant, but generally not high enough for permanent magnetic applications. Thus, the means to inject higher 5d transition metal content into Co via inert gas condensation was explored, with the goal to increase the magnetocrystalline anisotropy [47,48]. The W content was controlled by the number of W plugs in the composite target. At high W content (above at least 12 atomic percent), two-phase hcp Co   +   Co3W clusters were produced [52]. However, at 5 and 12 atomic percent W, single-phase clusters consisting of hcp Co with W dissolved into solid solution were produced (Fig. 6.17). The magnetic properties were measured at 10   K and 300   K (Fig. 6.18). The effective anisotropy constant, Ku, was determined from fitting the high-field data [53, 54]. The coercivity and Ku both increased between 5 and 12 atomic percent W, suggesting that the addition of 5d transition metal does indeed improve anisotropy (Fig. 6.19). The dramatic decrease at 23 atomic percent W is due to the presence of Co3W, which has a low magnetocrystalline anisotropy. However, the high fraction of surface atoms in clusters tends to decrease intrinsic properties of a material due to broken symmetry. For example, clusters of hcp Co were observed to have lower magnetocrystalline anisotropy and saturation magnetization [55]. With these Co-W solid solution alloys, the gain realized by substituting additional W into the structure just offset the decrease arising due to the size of the system. Further, W, in a magnetic sublattice, carries a small magnetic moment that couples antiparallel with the Co, negatively influencing saturation magnetization. Nevertheless, increasing solid solubility of 5d transition metals in bulk systems may be a viable route for the development of future rare earth-free permanent magnets, given a suitable system is identified.

Figure 6.17. High-resolution TEM image of a Co-5 atomic percent cluster showing single-crystallinity. The fast Fourier transform indexed to the hcp structure.

Figure 6.18. Hysteresis loops of the Co-W alloys at 10 and 300   K, with (A) 5, (B) 12, and (C) 23 atomic percent W.

Figure 6.19. Coercivity (red diamonds) and effective anisotropy constant Ku (blue squares) of Co-W alloys.

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