The Development of “Macroscopic Composition Gradient Method” and its Application to the Precipitate-Nucleation Near the Edge of Miscibility Gap

2008 ◽  
Vol 138 ◽  
pp. 43-56
Author(s):  
Toru Miyazaki
Keyword(s):  
Phase Boundary ◽  
Critical Phenomena ◽  
Composition Range ◽  
Solubility Limit ◽  
Nucleation Theory ◽  
Minimum Size ◽  
Miscibility Gap ◽  
Composition Gradient ◽  
Phase Decomposition ◽  
Nucleus Size

A new characterization method, "Macroscopic Composition Gradient (MCG) Method" is proposed to investigate the phase transformations near the phase boundaries, such as the solubility limit, order/disorder line and so on. Since the macroscopic composition gradient in the alloy is prepared so as to step over the phase boundary, the morphological transition of critical phenomena at the phase boundary can be observed by means of analytical transmission electron microscopy. By utilizing this method, the critical minimum size of stable precipitate in the vicinity of edge of miscibility gap is experimentally determined for the Ni3Si in Ni-Si, Ni3Al in Ni-Al, Cu4Ti in Cu-Ti and Co in Cu-Co binary alloy systems. The results are as follows: The critical nucleus size shows a steep increase up to several tens of nm in a very narrow composition range less than 0.3at% from the phase boundary. The Gibbs-Thomson relation and the conventional nucleation theory statistically rationalize such the composition dependence of nucleus size change. However, the nucleus formation is kinetically never rationalized by the conventional nucleation theories. The phase decomposition of supersaturated solid solution progresses by a mechanism of spinodal phase decomposition, even in the composition range near the solubility limit, i.e. a so-called Nucleation- Growth region. Such the phase decomposition behavior is never rationalized by the Boltzmann- Gibbs free energy, which is based on the extensive entropy. The experimental facts obtained here are explained by Tsallis's non-extensive entropy. It should be noted that the present experiments can systematically be conducted in the composition range very near the solubility limit where they has hardly been examined in the past. The MCG method proposed here is considered to open a new way to investigate the microstructure evaluation, particularly for the critical phenomena near the phase boundary.

The Precipitate-Nucleation in the Vicinity of Solubility Limit

2005 ◽  
Vol 502 ◽  
pp. 139-144 ◽  
Author(s):  
Toru Miyazaki ◽  
Takao Kozakai ◽  
Claudio G. Schoen
Keyword(s):  
Critical Nucleus ◽  
Critical Size ◽  
Solubility Limit ◽  
Minimum Size ◽  
Miscibility Gap ◽  
Composition Gradient ◽  
Nucleus Size ◽  
Precipitate Particle ◽  
Composition Region ◽  
Precipitate Nucleation

The critical minimum size of stable precipitate in the vicinity of edge of miscibility gap is experimentally determined for the Ni3Si precipitate particle in Ni-Si, Ni3Al in Ni-Al, Cu4Ti in Cu-Ti and Co in Cu-Co binary alloy systems by utilizing the macroscopic composition gradient method recently proposed. The results obtained are as follows: The critical nucleus size shows a rapid increase to several tens of nm in a very narrow composition region less than 0.3at% from the phase boundary. Such a big critical size of nucleus is statistically rationalized by the conventional nucleation theories.

Using phase boundary mapping to resolve discrepancies in the Mg2Si–Mg2Sn miscibility gap

2021 ◽  
Author(s):  
Rachel Orenstein ◽  
James P. Male ◽  
Michael Toriyama ◽  
Shashwat Anand ◽  
G. Jeffrey Snyder
Keyword(s):  
Phase Diagram ◽  
Phase Boundary ◽  
Ternary Phase ◽  
Ternary Phase Diagram ◽  
Miscibility Gap ◽  
Boundary Mapping

A new understanding of the MgSi–MgSn miscibility gap is reached through phase boundary mapping the Mg–Si–Sn ternary phase diagram.

Experimental Studies of Critical Phenomena in the Miscibility Gap of the Tl–Te System

1992 ◽  
Vol 134 (1) ◽  
pp. 133-137 ◽  
Author(s):  
B. Sokolovskii ◽  
V. Didoukh ◽  
M. Wobst ◽  
W. Hoyer
Keyword(s):  
Critical Phenomena ◽  
Experimental Studies ◽  
Miscibility Gap

Growth of GaN:Sb MBE-Layers

2001 ◽  
Vol 693 ◽  
Author(s):  
P. Cristea ◽  
D.G. Ebling ◽  
K.W. Benz
Keyword(s):  
Composition Range ◽  
Miscibility Gap ◽  
Side Reactions ◽  
Equilibrium Conditions ◽  
Mbe Growth ◽  
Single Crystalline ◽  
N Source ◽  
Atomic Radii ◽  
Crystalline Growth

AbstractThe single crystalline growth of the GaNxSb1-x system is difficult due to the miscibility gap expected for nearly the whole composition range under thermodynamic equilibrium conditions. The gap is determined by the differences of the atomic radii and of the electro negativities for N and Sb. To overcome this problem crystal growth has to be performed under non-equilibrium conditions with kinetically controlled growth, as it is observed for molecular beam epitaxy (MBE) growth. A single crystalline MBE-growth within the miscibility gap has been demonstrated already in the GaAsxN1-x system exhibiting a similar large miscibility gap. GaN:Sb-layers were grown on Si(111)-substrates by MBE using NH3 as a N-source and solid element sources for Ga and Sb. The parameter window for growth was limited due to side reactions like the decomposition of NH3, the desorption of (at high temperature volatile) compounds like Sb and GaSb or the reaction of Sb with NH3. The composition of the layers was analyzed by XRD and RBS. Antimony bulk concentrations of up to 1.6 % could be obtained in GaN. Optical characterization of the samples was performed by CL-measurements and indicate Sb-induced transitions in the 2.2 eV and 1.42 eV range.

Incomplete Solubility in Nitride Alloys

1996 ◽  
Vol 449 ◽  
Author(s):  
I. H. Ho ◽  
G.B. Stringfellow
Keyword(s):  
Experimental Data ◽  
Nearest Neighbor ◽  
Solubility Limit ◽  
Lattice Parameter ◽  
Miscibility Gap ◽  
Recent Experimental Data ◽  
Virtual Crystal Approximation ◽  
Group V ◽  
Group Iii ◽  
Nitride Alloys

ABSTRACTA model based on the valence-force-field (VFF) model has been developed specifically for the calculation of the irascibility gaps in III-V nitride alloys. In the dilute limit, this model allows the relaxation of the atoms on both sublattices. It was found that the energy due to bond stretching and bond bending was lowered and the solubility limit was increased substantially when both sublattices were allowed to relax to distances as large as the sixth nearest neighbor positions. Using this model, the equilibrium mole fraction of N in GaP was calculated to be 6×l0−7 at 700°C. This is slightly higher than the calculated results from the semi-empirical delta lattice parameter (DLP) model. Both the temperature dependence and the absolute values of the calculated solubility agree closely with the experimental data. The solubility is more than three orders of magnitude larger than the result obtained using the VFF model with the group V atom positions given by the virtual crystal approximation, i.e., with relaxation of only the first neighbor bonds. Other nitride systems, such as GaAsN, AlPN, AlAsN, InPN, and InAsN were investigated as well. The equilibrium mole fractions of nitrogen in InP and InAs are the highest, which agrees well with recent experimental data where high N concentrations have been produced in InAsN alloys. Calculations were also performed for the alloy systems with mixing on the group III sublattice that are so important for device applications. Allowing relaxation to the 3rd nearest neighbor gives an In solubility in GaN at 800°C of less than 6%. Again, this is in agreement with the results of the DLP model calculation. This result may partially explain the difficulties experienced with the growth of these alloys. Indeed, evidence of solid immiscibility has recently been reported. A significant miscibility gap was also calculated for the AlInN system, but the AlGaN system is completely miscible.

Microstructure and Piezoelectric Properties of (0.996-x) K0.5Na0.5NbO3 - 0.004 BiFeO3 - x LiSbO3 Ceramics

2012 ◽  
Vol 531-532 ◽  
pp. 632-635
Author(s):  
Min Hong Jiang ◽  
Xin Yu Liu ◽  
Guo Hua Chen ◽  
Jia Feng Ma ◽  
Gui Sheng Zhu ◽  
...  
Keyword(s):  
Electrical Properties ◽  
Phase Boundary ◽  
Pore Size ◽  
Mixed Oxide ◽  
Phase Structure ◽  
Composition Range ◽  
Piezoelectric Properties ◽  
Lead Free ◽  
Compositional Dependence ◽  
Tan Δ

(0.996-x) K0.5Na0.5NbO3- 0.004 BiFeO3- x LiSbO3 (x =0.00, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07) lead-free piezoelectric ceramics were prepared by the conventional mixed oxide method. The compositional dependence of the phase structure and the electrical properties of the ceramics were studied. A morphotropic phase boundary between the orthorhombic and tetragonal phases was identified in the composition range of 0.03 < x < 0.06. With the content of LS increases, the size of the pores significantly decreases. However, adding larger amount of LS makes the pore size increase slightly. The (0.996-x)KNN-0.004 BF-xLS(x=0.05) ceramics possess good electrical properties: d33 = 280 pC/N, kp = 53.3%, Tc = 345 °C, εr = 1613, Tan δ =2.07%. These results show that the ceramic is a promising lead-free piezoelectric material.

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