Non Local Electron-Phonon Correlations in a Dispersive Holstein Model

Due to the dispersion of optical phonons, long range electron-phonon correlations renormalize downwards the coupling strength in the Holstein model. We evaluate the size of this effect both in a linear chain and in a square lattice for a time averaged {\it e-ph} potential, where the time variable is introduced according to the Matsubara formalism. Mapping the Holstein Hamiltonian onto the time scale we derive the perturbing source current which appears to be non time retarded. This property permits to disentangle phonon and electron coordinates in the general path integral for an electron coupled to dispersive phonons. While the phonon paths can be integrated out analytically, the electron path integrations have to be done numerically. The equilibrium thermodynamic properties of the model are thus obtained as a function of the electron hopping value and of the phonon spectrum parameters. We derive the {\it e-ph} corrections to the phonon free energy and show that its temperature derivatives do not depend on the {\it e-ph} effective coupling hence, the Holstein phonon heat capacity is strictly harmonic. A significant upturn in the low temperature total heat capacity over $T$ ratio is attributed to the electron hopping which largely contributes to the action.Comment: Phys.Rev.B (2005

Path Integral Method for DNA Denaturation

The statistical physics of homogeneous DNA is investigated by the imaginary time path integral formalism. The base pair stretchings are described by an ensemble of paths selected through a macroscopic constraint, the fulfillement of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature $T^*_c$ whereas the fraction of unbound base pairs grows continuosly around and above $T^*_c$. The latter is identified with the denaturation temperature. Thus, the separation of the two complementary strands appears as a highly cooperative phenomenon displaying a smooth crossover versus $T$. The thermodynamical properties have been computed in a large temperature range by varying the size of the path ensemble at the lower bound of the range. No significant physical dependence on the system size has been envisaged. The entropy grows continuosly versus $T$ while the specific heat displays a remarkable peak at $T^*_c$. The location of the peak versus $T$ varies with the stiffness of the anharmonic stacking interaction along the strand. The presented results suggest that denaturation in homogeneous DNA has the features of a second order phase transition. The method accounts for the cooperative behavior of a very large number of degrees of freedom while the computation time is kept within a reasonable limit.Comment: Physical Review E 2009 in pres

Advances and challenges in the development of UHTCMCs - A review of the C3harme project

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J-factors of short DNA molecules

The propensity of short DNA sequences to convert to the circular form is studied by a mesoscopic Hamiltonian method which incorporates both the bending of the molecule axis and the intrinsic twist of the DNA strands. The base pair fluctuations with respect to the helix diameter are treated as path trajectories in the imaginary time path integral formalism. The partition function for the sub-ensemble of closed molecules is computed by imposing chain ends boundary conditions both on the radial fluctuations and on the angular degrees of freedom. The cyclization probability, the J-factor, proves to be highly sensitive to the stacking potential, mostly to its nonlinear parameters. We find that the J-factor generally decreases by reducing the sequence length ( N ) and, more significantly, below N = 100 base pairs. However, even for very small molecules, the J-factors remain sizeable in line with recent experimental indications. Large bending angles between adjacent base pairs and anharmonic stacking appear as the causes of the helix flexibility at short length scales.Comment: The Journal of Chemical Physics - May 2016 ; 9 page

Exact solutions of classical scalar field equations

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term renormalized in the dispersion relation through a term depending on the coupling and an integration constant. When spontaneous breaking of symmetry is considered, such wave-like solutions show how a mass term with the wrong sign and the nonlinearity give rise to a proper dispersion relation. These latter solutions do not change the sign maintaining the property of the selected value of the equilibrium state. Then, we use these solutions to obtain a quantum field theory for the case of a quartic massless field. We get the propagator from a first order correction showing that is consistent in the limit of a very large coupling. The spectrum of a massless quartic scalar field theory is then provided. From this we can conclude that, for an infinite countable number of exact classical solutions, there exist an infinite number of equivalent quantum field theories that are trivial in the limit of the coupling going to infinity.Comment: 7 pages, no figures. Added proof of existence of a zero mode and two more references. Accepted for publication in Journal of Nonlinear Mathematical Physic

Influence of SiC on the oxidation resistance of carbon fibre reinforced UHTCMCsAntonio Vinci

Ultra-High-Temperature-Ceramics (UHTCs) are a novel class of refractory materials characterized by melting points exceeding 3000°C and very good thermo-mechanical properties [1]. In particular, ZrB2 composites have been extensively investigated as potential candidates for the fabrication of reusable Thermal Protection Systems (TPS) for aerospace applications due to their relatively low density and high thermal conductivity. The main drawbacks are the low oxidation resistance of ZrB2 above 1000°C, due to the formation of a porous ZrO2 scale and evaporation of B2O3, and low fracture toughness. Silicon carbide has been found to increase its oxidation resistance up to 1650 owing to the formation of a protective, viscous borosilicate scale [2][3]. However, their low fracture toughness and thermal shock resistance remain major obstacles for their application [4][5]. For this purpose, continuous carbon fibres (~45 vol.%) were used as reinforcement in order to increase their fracture toughness and thermal shock resistance. The resulting materials were labeled “UHTCMCs” (Ultra High Temperature Ceramic Matrix Composites). In the present work, the oxidation resistance of carbon fibre reinforced ZrB2/SiC composites was studied. Composites with SiC amounts ranging from 5-20 vol.% were fabricated by slurry infiltration and hot pressing at 1900°C and 40 MPa. Oxidation tests were carried out on cut specimen (2 x 2.5 x 12 mm3) in a bottom-up loading furnace at 1500°C and 1650°C. The resulting microstructures were analysed by SEM-EDS and X-ray diffraction analysis. Weight loss per surface area was recorded after each test. Results show that the formation of a viscous borosilicate glass phase is essential for the protection of carbon fibres from oxidation; low amounts of SiC do not provide enough protection against fibre degradation, but with increasing the SiC amount there is an increase in the thickness of the protective layer and a decrease in weight loss. References [1] W.G. Fahrenholtz, G.E. Hilmas, I.G. Talmy, J.A. Zaykoski, Refractory diborides of zirconium and hafnium, J. Am. Ceram. Soc. 90 (2007) 1347–1364. doi:10.1111/j.1551-2916.2007.01583.x. [2] L. Zhang, K. Kurokawa, Effect of SiC Addition on Oxidation Behavior of ZrB2 at 1273??K and 1473??K, Oxid. Met. 85 (2016) 311–320. doi:10.1007/s11085-015-9585-9. [3] J. He, Y. Wang, L. Luo, L. An, Oxidation behaviour of ZrB2–SiC (Al/Y) ceramics at 1700°C, J. Eur. Ceram. Soc. (2016). doi:10.1016/j.jeurceramsoc.2016.02.037. [4] R. Zhang, X. Cheng, D. Fang, L. Ke, Y. Wang, Ultra-high-temperature tensile properties and fracture behavior of ZrB2-based ceramics in air above 1500??C, Mater. Des. 52 (2013) 17–22. doi:10.1016/j.matdes.2013.05.045. [5] E. Zapata-Solvas, D.D. Jayaseelan, H.T. Lin, P. Brown, W.E. Lee, Mechanical properties of ZrB2- and HfB2-based ultra-high temperature ceramics fabricated by spark plasma sintering, J. Eur. Ceram. Soc. 33 (2013) 1373–1386. doi:10.1016/j.jeurceramsoc.2012.12.009

Thermodynamics of Twisted DNA with Solvent Interaction

The imaginary time path integral formalism is applied to a nonlinear Hamiltonian for a short fragment of heterogeneous DNA with a stabilizing solvent interaction term. Torsional effects are modeled by a twist angle between neighboring base pairs stacked along the molecule backbone. The base pair displacements are described by an ensemble of temperature dependent paths thus incorporating those fluctuational effects which shape the multisteps thermal denaturation. By summing over $\sim 10^7 - 10^8$ base pair paths, a large number of double helix configurations is taken into account consistently with the physical requirements of the model potential. The partition function is computed as a function of the twist. It is found that the equilibrium twist angle, peculiar of B-DNA at room temperature, yields the stablest helicoidal geometry against thermal disruption of the base pair hydrogen bonds. This result is corroborated by the computation of thermodynamical properties such as fractions of open base pairs and specific heat.Comment: The Journal of Chemical Physics (2011) in pres

Ti3SiC2-Cf composites by spark plasma sintering: Processing, microstructure and thermo-mechanical properties

MAX phases, and particularly Ti3SiC2, are interesting for high temperature applications. The addition of carbon fibers can be used to reduce the density and to modify the properties of the matrix. This work presents the densification and characterization of Ti3SiC2 based composites with short carbon fibers using a fast and simple fabrication approach: dry mixing and densification by Spark Plasma Sintering. Good densification level was obtained below 1400 °C even with a high amount of fibers. The reaction of the fibers with the matrix is limited thanks to the fast processing time and depends on the amount of fibers in the composite. Bending strength at room temperature, between 437 and 120 MPa, is in the range of conventional CMCs with short fibers and according to the resistance of the matrix and the presence of residual porosity. Thermo-mechanical properties of the composites up to 1500 °C are also presented.This work has received funding from the European Union’s Horizon2020 “Research and innovation programme” under grant agreement No 685594 (C3HARME

Thermodynamic properties of Holstein polarons and the effects of disorder

The ground state and finite temperature properties of polarons are studied considering a two-site and a four-site Holstein model by exact diagonalization of the Hamiltonian. The kinetic energy, Drude weight, correlation functions involving charge and lattice deformations, and the specific heat have been evaluated as a function of electron-phonon (e-ph) coupling strength and temperature. The effects of site diagonal disorder on the above properties have been investigated. The disorder is found to suppress the kinetic energy and the Drude weight, reduces the spatial extension of the polaron, and makes the large-to-small polaron crossover smoother. Increasing temperature also plays similar role. For strong coupling the kinetic energy arises mainly from the incoherent hopping processes owing to the motion of electrons within the polaron and is almost independent of the disorder strength. From the coherent and incoherent contributions to the kinetic energy, the temperature above which the incoherent part dominates is determined as a function of e-ph coupling strength.Comment: 17 pages. 17 figure

Influence of Y2O3 addition on the mechanical and oxidation behaviour of carbon fibre reinforced ZrB2/SiC composites

The influence of Y2O3 addition on the microstructure, thermo-mechanical properties and oxidation resistance of carbon fibre reinforced ZrB2/SiC composites was investigated. Y2O3 reacted with oxide impurities present on the surface of ZrB2 and SiC grains and formed a liquid phase, effectively lowering the sintering temperature and allowing to reach full density at 1900 °C. The presence of a carbon source (fibres) led to additional reactions which resulted in the formation of new secondary phases such as yttrium boro-carbides. Mechanical properties were significantly enhanced compared to the un-doped composite. Further tests at high temperatures resulted in strength increase up to 700 MPa at 1500 °C which was attributed to stress relaxation. Oxidation tests carried out at 1500 °C and 1650 °C in air showed that the presence of the Y-based secondary phases enhanced the growth of ZrO2 grains, but offered limited protection to oxygen due to the lower availability of surficial SiO2 formed from SiC