The role of rigid unit modes in negative thermal expansion

The rigid unit mode (RUM) model provides a valuable computational method to investigate correlations of transverse thermal motions of atoms important in negative thermal expansion (NTE) materials. We report here detailed RUM calculations of ten framework oxide structures that have been studied for their negative (or ultra low) thermal expansion properties. The results negate any simple and direct correlation between presence or absence of RUMs in a structure and its NTE property. All the structures considered can be viewed as networks of polyhedral connected by corners only. All evidence supports the importance the transverse motion of the atoms at the corners, but NTE does not correlate well with the presence RUMs for the polyhedra.     

Corrosion-stable nickel- and cobalt-based alloys for dental applications

In a comparative study the in vitro corrosion behavior of a selection of nickel- and cobalt-based alloys for application in dentistry containing no noble metals was studied with slow scan cyclic voltammetry. The obtained breakthrough potentials, the repassivation behavior and further typical features of the cyclic voltamograms are correlated with the chemical composition as measured with electron beam microanalysis. Surface inhomogenities detected with the latter method are discussed with respect to the electrochemical behavior. For all alloys stabilities in terms of breakthrough potential superior to previously reported data for nickel-base alloys are found.     

Closer asymptotic approximations for the distributions of the power divergence goodness-of-fit statistics

Summary The members of the power divergence family of statistics all have an asymptotically equivalent χ² distribution (Cressie and Read [1]). An asymptotic expansion for the distribution function is derived which shows that the speed of convergence to this asymptotic limit is dependent on λ. Known results for Pearson'sX ² statistic and the log-likelihood ratio statistic then appear as special cases in a continuum rather than as separate (unrelated) expansions.     

Sol-gel ZrO2 coatings for chemical protection of stainless steel

ZrO₂ coatings deposited on 316 L stainless steel sheets were synthesized by sol-gel method using Zr(OC₃H₇)₄ as precursor and isopropanol, glacial acetic acid, and water as solvents for application with ultrasounds. Different solutions for dip-coating were prepared with compositions varying between 0.025 and 0.9 mol/dm³ of ZrO₂. X-ray diffraction shows that the films densified at 800°C are crystalline with a tetragonal structure. The thickness of the coatings varied from 0.35–0.75 m. The influence of the ZrO₂ coatings on the corrosion behavior of stainless steel substrates in aqueous NaCl was studied through potentiodynamic polarization curves at 1 mV/s. The values of the electrochemical parameters allow for an explanation of the role of the films in the increased resistance of steel against corrosion in moderately aggressive environments.     

Oxidative cleavage of a tricyclic pyridone to a bicyclic lactam-dione

Two equivalents cf anhydrous m-chloroperbenzoic acid (m-CPBA) cleaved the pyridone ring of 10-(3-chlorophenyl)-6,8,9,10-tetrahydrobenzo[b][1,8]naph forming; the ten-membered lactam α-diketone 12-(3-chlorophenyl)-7,8,9,10-tetrahydropyrido[2,3-b]azecine-5,6,11(12H)-trione. Under aqueous conditions, one equivalent of m-CPBA and the same pyridone formed the lactam α-ketol 12-(3-chlorophenyl)-7,8,9,10-tetrahydro-6-hydroxypyrido[2,3-b]azecine-5,11(6H, 12H)-dio     

Asymptotic Behavior of the t Expansion

The asymptotic behavior of a system's ground-state energy from the t expansion of Horn and Weinstein has been suggested to have the form E ₁(t)=E ₁+exp(–a _n t+b _n ). In the limit of very large t, this becomes E ₁(t)=E ₁+exp(–a ₁ t+b ₁). A simple analysis shows that the parameters are a ₁=E ₂–E ₁ and b ₁=ln[(E ₂–E ₁)|c ₂|²/|c ₁|²]. Functions are introduced which allow determination of a ₁, b ₁ and lower bounds to E ₁.     

Phase transitions in ternary caesium lead bromide

Phase transitions in ternary caesium lead bromide (CsPbBr₃) were studied by means of DSC, TMA and high temperature X-ray diffraction. The samples were prepared from the solution by water evaporation and from the melt. on the DSC curves as well as on the temperature dependence of the lattice constants of CsPbBr₃ only two effects were found belonging to the earlier published phase transitions at 88 and 130°C and no further effects. Linear thermal expansion coefficient α of individual CsPbBr₃ modifications were calculated from both TMA and high temperature X-ray diffraction. The structural parameters of the room temperature orthorhombic phase were refined and the results are presented. CsPbBr₃ prepared from the solution contained about 10% of CsPb₂Br₅ and so the DSC curve of pure CsPb₂Br₅ was also measured and an effect at a temperature of 68.5°C was found. This revised version was published online in July 2006 with corrections to the Cover Date.     

Strong coupling expansion for classical statistical dynamics

We discuss the simple, randomly driven systemdx/dt = –x –x³ +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)ⁿ, whereR is the internal Reynolds number ()^1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp ²/2 +m ² x ²/2 +vx ⁴ +x ⁶/2, we evaluate the path integral on a lattice by assuming that thex ⁶ term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)^1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.     

Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling

Exact renormalization group equations are derived for a position-space renormalization of spin systems with weak long-range forces. It is shown how an apparent dependence of the critical exponents on the choice of the renormalization group can be resolved via the mechanism of dangerous irrelevant variables and that this same mechanism is responsible for the breakdown of hyperscaling. The dimensiond=4 can be seen to be a borderline dimension above which classical critical exponents are expected.