Mechanical alloying—a novel synthesis route for amorphous phases

Mechanical alloying (MA) pioneered by Benjamin is a technique for the extension of solid solubility in systems where the equilibrium solid solubility is limited. This technique has, in recent years, emerged as a novel alternate route for rapid solidification processing (RSP) for the production of metastable crystalline, quasicrystalline, amorphous phases and nanocrystalline materials. The glass-forming composition range (GFR), in general, is found to be much wider in case of MA in comparison with RSP. The amorphous powders produced by MA can be compacted to bulk shapes and sizes and can be used as precursors to obtain high strength materials. This paper reports the work done on solid state amorphization by MA in Ti-Ni-Cu and Al-Ti systems where a wide GFR has been obtained. Al-Ti is a classic case where no glass formation has been observed by RSP, while a GFR of 25–90 at.% Ti has been obtained in this system, thus demonstrating the superiority of MA over RSP. The free energy calculations made to explain GFR are also presented.

Nonlinear hydrodynamics of a hard-sphere fluid near the glass transition

We conduct a numerical study of the dynamic behavior of a dense hard-sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free-energy functional of the Ramakrishnan-Yussouff form. We find that the system exhibits glassy behavior as evidenced through a stretched exponential decay and a two-stage relaxation of the density correlation function. The characteristic times grow with increasing density according to the Vogel-Fulcher law. The wave-number dependence of the kinetics is extensively explored. The connection of our results with experiment, mode-coupling theory, and molecular-dynamics results is discussed.

Phenomenological Ginzburg-Landau-like theory for superconductivity in the cuprates

We propose and develop here a phenomenological Ginzburg-Landau-like theory of cuprate high-temperature superconductivity. The free energy of a cuprate superconductor is expressed as a functional F of the complex spin-singlet pair amplitude psi(ij) equivalent to psi(m) = Delta(m) exp(i phi(m)), where i and j are nearest-neighbor sites of the square planar Cu lattice in which the superconductivity is believed to primarily reside, and m labels the site located at the center of the bond between i and j. The system is modeled as a weakly coupled stack of such planes. We hypothesize a simple form FDelta, phi] = Sigma(m)A Delta(2)(m) + (B/2)Delta(4)(m)] + C Sigma(< mn >) Delta(m) Delta(n) cos(phi(m) - phi(n)) for the functional, where m and n are nearest-neighbor sites on the bond-center lattice. This form is analogous to the original continuum Ginzburg-Landau free-energy functional; the coefficients A, B, and C are determined from comparison with experiments. A combination of analytic approximations, numerical minimization, and Monte Carlo simulations is used to work out a number of consequences of the proposed functional for specific choices of A, B, and C as functions of hole density x and temperature T. There can be a rapid crossover of from small to large values as A changes sign from positive to negative on lowering T; this crossover temperature T-ms(x) is identified with the observed pseudogap temperature T*(x). The thermodynamic superconducting phase-coherence transition occurs at a lower temperature T-c(x), and describes superconductivity with d-wave symmetry for positive C. The calculated T-c(x) curve has the observed parabolic shape. The results for the superfluid density rho(s)(x, T), the local gap magnitude , the specific heat C-v(x, T) (with and without a magnetic field), as well as vortex properties, all obtained using the proposed functional, are compared successfully with experiments. We also obtain the electron spectral density as influenced by the coupling between the electrons and the correlation function of the pair amplitude calculated from the functional, and compare the results successfully with the electronic spectrum measured through angle resolved photoemission spectroscopy (ARPES). For the specific heat, vortex structure, and electron spectral density, only some of the final results are reported here; the details are presented in subsequent papers.

Thermodynamics and phase equilibria in the Ga---Sb system

The optimum values of the solution parameters of a multiparameter integral free-energy function have been determined using experimental data from the Ga-Sb system. The equation is represented as DELTAG(xs) = x(1 - x)[(1 - x)(a1 + a2T + a3T ln T) + x(a4 + a5T + a6T ln T) + x(1 - x)(a7 + a8T + a9xT)].The integral and the corresponding partial form of the free energy function have been found to be of use when interpreting the high temperature thermodynamic data, atomic interactions and phase equilibria in the Ga-Sb system.

Glass Transition in the Density Functional Theory of Freezing

A mean-field description of the glass transition in the hard-sphere system is obtained by numerically locating "glassy" minima of a model free-energy functional. These minima, characterized by inhomogeneous but aperiodic density distributions, appear as the average density is increased above the value at which equilibrium crystallization takes place. Investigations of the density distribution and local bond-orientational order at these minima yield results similar to those obtained from simulations.

Barrier crossing in one and three dimensions by a long chain

We consider the Kramers problem for a long chain polymer trapped in a biased double-well potential. Initially the polymer is in the less stable well and it can escape from this well to the other well by the motion of its N beads across the barrier to attain the configuration having lower free energy. In one dimension we simulate the crossing and show that the results are in agreement with the kink mechanism suggested earlier. In three dimensions, it has not been possible to get an analytical `kink solution' for an arbitrary potential; however, one can assume the form of the solution of the nonlinear equation as a kink solution and then find a double-well potential in three dimensions. To verify the kink mechanism, simulations of the dynamics of a discrete Rouse polymer model in a double well in three dimensions are carried out. We find that the time of crossing is proportional to the chain length, which is in agreement with the results for the kink mechanism. The shape of the kink solution is also in agreement with the analytical solution in both one and three dimensions.

Structure evolution and phase change in Ag-5.1 at.% Bi alloy during mechanical alloying

In this paper we explore the enhancement of solubility in a mechanically driven immiscible system experimentally using a mixture of Ag and Bi powders corresponding to a composition of Ag-5.1 at.% Bi. Increase in solubility can be correlated with the combination of sizes of both Ag and Bi at the nanometric scale. It is shown that complete solid solution of Ag-5.1 at.% Bi forms when the respective sizes of :Bi and Ag exceed 13 and 8 nm respectively. We have carried out a thermodynamic analysis of the size- and strain-dependent free energy landscape and compared the results to the initial mixture of microsized particles to rationalize the evolution of Ag solid solution. The agreement indicates that the emerging driving force for the formation of solid solution is primarily due to size reduction rather than the enhanced kinetics of mass transport due to mechanical driving. (c) 2011 Published by Elsevier Ltd. on behalf of Acta Materialia Inc.

Shear alignment of a disordered lamellar mesophase

The shear alignment of an initially disordered lamellar phase is examined using lattice Boltzmann simulations of a mesoscopic model based on a free-energy functional for the concentration modulation. For a small shear cell of width 8 lambda, the qualitative features of the alignment process are strongly dependent on the Schmidt number Sc = nu/D (ratio of kinematic viscosity and mass diffusion coefficient). Here, lambda is the wavelength of the concentration modulation. At low Schmidt number, it is found that there is a significant initial increase in the viscosity, coinciding with the alignment of layers along the extensional axis, followed by a decrease at long times due to the alignment along the flow direction. At high Schmidt number, alignment takes place due to the breakage and reformation of layers because diffusion is slow compared to shear deformation; this results in faster alignment. The system size has a strong effect on the alignment process; perfect alignment takes place for a small systems of width 8 lambda and 16 lambda, while a larger system of width 32 lambda does not align completely even at long times. In the larger system, there appears to be a dynamical steady state in which the layers are not perfectly aligned-where there is a balance between the annealing of defects due to shear and the creation due to an instability of the aligned lamellar phase under shear. We observe two types of defect creation mechanisms: the buckling instability under dilation, which was reported earlier, as well as a second mechanism due to layer compression.

Metastable extension of the fluorite phase field in Y2O3---ZrO2 and its effect on grain growth

Pure Y2O3 and Y2O3---ZrO2 solid solutions have been prepared by melt atomization and by pyrolysis of nitrate solutions. Extended solubility is readily achieved in both techniques for the entire composition range investigated: melts with 0–30% ZrO2 and precursors with 0–50% ZrO2. However, solidification of under cooled droplets yields almost exclusively single phase powders with the structure of cubic yttria (D53). In contrast, the pyrolysis route leads to a sequence of metastable microstructures beginning with a nanocrystalline disordered fluorite-based (C1) solid solution. Further heating leads to the evolution of much larger (micron size) flake crystals with a {001} texture, concurrent with partial ordering of the oxygen ions to the sites occupied in the D53 structure. The driving force for ordering and the rate of grain growth decrease with increasing ZrO2 addition. Abrupt heating to high temperatures or electron irradiation can induce ordering without substantial grain growth. There is no significant reduction in porosity during the recrystallization, which with the other observations suggests that grain growth is driven by the free energy available for the ordering transformation from fluorite to the yttria structure. This route offers opportunities for single crystal thin film development at relatively low processing temperatures.

High-temperature stability of Ca2ZrSi4O12

The standard Gibbs free energy of formation of orthorhombic Ca2ZrSi4O12 from component oxides ZrO2 (monoclinic), CaO (rock salt), and SiO2 (quartz) has been determined in the temperature range 973 to 1273 K using a solid-state cell incorporating single-crystal CaF2 as the electrolyte: Delta G(f) degrees = -219930 + 11.77T (+/- 1500) J.mol(-1) This is the only quantitative information now available on the stability of Ca2ZrSi4O12.

Metastable extension of the fluorite phase field in Y2O3---ZrO2 and its effect on grain growth

Pure Y2O3 and Y2O3-ZrO2 solid solutions have been prepared by melt atomization and by pyrolysis of nitrate solutions. Extended solubility is readily achieved in both techniques for the entire composition range investigated: melts with 0-30% ZrO2 and precursors with 0-50% ZrO2. However, solidification of under cooled droplets yields almost exclusively single phase powders with the structure of cubic yttria (D5(3)). In contrast, the pyrolysis route leads to a sequence of metastable microstructures beginning with a nanocrystalline disordered fluorite-based (C1) solid solution. Further heating leads to the evolution of much larger (micron size) flake crystals with a {001} texture, concurrent with partial ordering of the oxygen ions to the sites occupied in the D5(3) structure. The driving force for ordering and the rate of grain growth decrease with increasing ZrO2 addition. Abrupt heating to high temperatures or electron irradiation can induce ordering without substantial grain growth. There is no significant reduction in porosity during the recrystallization, which with the other observations suggests that grain growth is driven by the free energy available for the ordering transformation from fluorite to the yttria structure. This route offers opportunities for single crystal thin film development at relatively low processing temperatures.

Phase relations in the system Cu─Ho─O and stability of Cu2Ho2O5

The phase relations in the system Cu-Ho-O have been determined at 1300 K using X-ray diffraction, optical microscopy, and electron microprobe analysis of samples equilibrated in evacuated quartz ampules and in pure oxygen. Only one ternary compound, Cu2Ho2O5, was found to be stable. The Gibbs free energy of formation of this compound has been measured using the solid-state cell Pt,Cu2O + Cu2Ho2O5 + Ho2O3/(Y2O3)ZrO2/CuO + Cu2O,Pt in the temperature range of 973 to 1350 K. For the formation of Cu2Ho2O5 from its binary component oxides, 2CuO(s) + Ho2O3(S) --> Cu2Ho2O5(s) DELTAG-degrees = 11190 - 13.8T(+/- 120) J-mol-1 Since the formation is endothermic, CU2Ho2O5 becomes thermodynamically unstable with respect to CuO and Ho2O3 below 810 K. When the oxygen partial pressure over Cu2Ho2O5 is lowered, it decomposes according to the reaction 2Cu2Ho2O5(s) --> 2Ho2O3(s) + 2Cu2O(S) + O2(g) for which the equilibrium oxygen potential is given by DELTAmu(O2) = - 238510 + 160.2T(+/- 450) J.mol-1 The decomposition temperature at an oxygen partial pressure of 1.52 x 10(4) Pa was measured using a combined DTA-TGA apparatus. Based on these results, an oxygen potential diagram for the system Cu-Ho-O at 1300 K is presented.

Crossover dynamics at large metastability in gas-liquid nucleation

We have developed an alternate description of dynamics of nucleation in terms of an extended set of order parameters. The order parameters consist of an ordered set of kth largest clusters, ordered such that k = 1 is the largest cluster in the system, k = 2 is the second largest cluster, and so on. We have derived an analytic expression for the free energy for the kth largest cluster, which is in excellent agreement with the simulated results. At large supersaturation, the free energy barrier for the growth of the kth largest cluster disappears and the nucleation becomes barrierless. The major success of this extended theoretical formalism is that it can clearly explain the observed change in mechanism at large metastability P. Bhimalapuram et al., Phys. Rev. Lett. 98, 206104 (2007)] and the associated dynamical crossover. The classical nucleation theory cannot explain this crossover. The crossover from activated to barrierless nucleation is found to occur at a supersaturation where multiple clusters cross the critical size. We attribute the crossover as the onset of the kinetic spinodal. We have derived an expression for the rate of nucleation in the barrierless regime by modeling growth as diffusion on the free energy surface of the largest cluster. The model reproduces the slower increase in the rate of growth as a function of supersaturation, as observed in experiments.

Thickness-dependent fcc-hcp phase transformation in polycrystalline titanium thin films

Polycrystalline Ti thin films are shown to gradually transform from face-centered cubic (fcc) to hexagonal close-packed structure (hcp) with increasing film thickness. Diffraction stress analysis revealed that the fcc phase is formed in a highly compressive hcp matrix (>= 2 GPa), the magnitude of which decreases with increasing film thickness. A correlation between stress and crystallographic texture vis-a-vis the fcc-hcp phase transformation has been established. The total free energy change of the system upon phase transformation calculated using the experimental results shows that the fcc-hcp transformation is theoretically possible in the investigated film thickness regime (144-720 nm) and the hcp structure is stable for films thicker than 720 nm, whereas the fcc structure can be stabilized in Ti films much thinner than 144 nm. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A thermodynamic criterion for selection of gas compositions for diamond deposition

Isoactivity lines for carbon with respect to diamond as the standard state have been calculated in the ternary system C-H-O at 1223 K to identify the diamond deposition domain. The gas composition is calculated by suppressing the formation of all condensed forms of carbon using the SOLGASMIX free-energy minimization program. Thirty six gas species were included in the calculation. From the gas composition, isoactivity lines are computed using recent data on the Gibbs energy of diamond. Except for activities less than 0.1, the isoactivity lines are almost linear on the C-H-O ternary diagram. Gas compositions which generate activity of diamond ranging from 1 to 100 at 1223 K fall inside a narrow wedge originating from the point representing CO. This wedge is very similar to the revised lens-shaped diamond growth domain identified by Bachman et al., using inputs from experiment. The small difference between the calculated and observed domains may be attributed to variation in the supersaturation required for diamond deposition with gas composition. The diamond solubility in the gas phase along the isoactivity line for a(di)=100 and P=6.7 kPa exhibits a minimum at 1280 K, which is close to the optimum temperature found experimentally. At higher supersaturations, non-diamond forms of carbon, including amorphous varieties, are expected. The results suggest that thermodynamic calculations can be useful for locating diamond growth domains in more complex CVD systems containing halogens, for which very little experimental data is available.