Vibrational properties of phonons in random binary alloys: An augmented space recursive technique in the k-representation

We present here an augmented space recursive technique in the k-representation which include diagonal, off-diagonal and the environmental disorder explicitly : an analytic, translationally invariant, multiple scattering theory for phonons in random binary alloys.We propose the augmented space recursion (ASR) as a computationally fast and accurate technique which will incorporate configuration fluctuations over a large local environment. We apply the formalism to $Ni_{55}Pd_{45}$, Ni_{88}Cr_12} and $Ni_{50}Pt_{50}$ alloys which is not a random choice. Numerical results on spectral functions, coherent structure factors, dispersion curves and disordered induced FWHM's are presented. Finally the results are compared with the recent itinerant coherent potential approximation (ICPA) and also with experiments.Comment: 20 pages, LaTeX, 23 figure

Isotope effect on the transition temperature TcT_c in Fe-based superconductors: the current status

The results of the Fe isotope effect (Fe-IE) on the transition temperature $T_c$ obtained up to date in various Fe-based high temperature superconductors are summarized and reanalyzed by following the approach developed in [Phys. Rev. B 82, 212505 (2010)]. It is demonstrated that the very controversial results for Fe-IE on $T_c$ are caused by small structural changes occurring simultaneously with the Fe isotope exchange. The Fe-IE exponent on $T_c$ [$\alpha_{\rm Fe}=-(\Delta T_c/T_c)/(\Delta M/M)$, $M$ is the isotope mass] needs to be decomposed into two components with the one related to the structural changes ($\alpha_{\rm Fe}^{\rm str}$) and the genuine (intrinsic) one ($\alpha_{\rm Fe}^{\rm int}$). The validity of such decomposition is further confirmed by the fact that $\alpha_{\rm Fe}^{\rm int}$ coincides with the Fe-IE exponent on the characteristic phonon frequencies $\alpha_{\rm Fe}^{\rm ph}$ as is reported in recent EXAFS and Raman experiments.Comment: 7 pages, 4 figures. The paper is partially based on the results published in [New J. Phys. 12, 073024 (2010) = arXiv:1002.2510] and [Phys. Rev. B 82, 212505 (2010) = arXiv:1008.4540

Phonons in random alloys: the itinerant coherent-potential approximation

We present the itinerant coherent-potential approximation(ICPA), an analytic, translationally invariant and tractable form of augmented-space-based, multiple-scattering theory in a single-site approximation for harmonic phonons in realistic random binary alloys with mass and force-constant disorder. We provide expressions for quantities needed for comparison with experimental structure factors such as partial and average spectral functions and derive the sum rules associated with them. Numerical results are presented for Ni_{55} Pd_{45} and Ni_{50} Pt_{50} alloys which serve as test cases, the former for weak force-constant disorder and the latter for strong. We present results on dispersion curves and disorder-induced widths. Direct comparisons with the single-site coherent potential approximation(CPA) and experiment are made which provide insight into the physics of force-constant changes in random alloys. The CPA accounts well for the weak force-constant disorder case but fails for strong force-constant disorder where the ICPA succeeds.Comment: 19 pages, 12 eps figures, uses RevTex

First-principles order-parameter theory of freezing

A first-principles order-parameter theory of the fluid-solid transition is presented in this paper. The thermodynamic potential Ω of the system is computed as a function of order parameters λi(=λk→i) proportional to the lattice periodic components of the one-particle density ρ(r→), K→i's being the reciprocal-lattice vectors (RLV) of the crystal. Computation of Ω({λi}) is shown to require knowing Ω for a fluid placed in lattice periodic potentials with amplitudes depending on λi. Using systematic nonperturbative functional methods for calculating the response of the fluid to such potentials, we find Ω({λi}). The fluid properties (response functions) determining it are the Fourier coefficients ci(=cK→i) and c0(=cq→=0) of the direct correlation function c(r→). The system freezes when at constant chemical potential µ and pressure P, locally stable fluid and solid phases [i.e., minima of Ω({λi}) with {λi}=0 and {λi}≠0, respectively] have the same Ω. The order-parameter mode most effective in reducing Ω({λi}) corresponds to K→j being of the smallest-length RLV set (cq→ is largest for |q→|~=|K→j|). In some cases one has to consider a second order parameter λn with a RLV K→n lying near the second peak in cq→. The effect of further order-parameter modes on Ω is shown to be small. The theory can be viewed as one of a strongly first-order density-wave phase transition in a dense classical system. The transition is a purely structural one, occurring when the fluid-phase structural correlations (measured by cj, etc.) are strong enough. This fact has been brought out clearly by computer experiments but had not been theoretically understood so far. Calculations are presented for freezing into some simple crystal structures, i.e., fcc, bcc, and two-dimensional hcp. The input information is only the crystal structure and the fluid compressibility (related to c0). We obtain as output the freezing criterion stated as a condition on cj or as a relation between cj and cn, the volume change V, the entropy change Δs, and the Debye-Waller factor at freezing for various RLV values. The numbers are all in very good agreement with those available experimentally

Theory of the liquid-solid transition

The liquid-solid transition is found by calculating the thermodynamic potential of a dense classical system as a function of order parameters which are proportional to the lattice Fourier components of the density. Properties of the fluid enter only through the direct two-particle correlation function near freezing. Calculated parameters for freezing into bcc, fcc and hexagonal structures are in good agreement with experimental results

Cluster kinetics on surfaces involving addition and decomposition via monomers

SIGLEITItal