First-order Irreversible Phase Transition Research Articles

Phase Behavior of TmVO4 under Hydrostatic Compression: An Experimental and Theoretical Study.

We present a structural and optical characterization of magnetoelastic zircon-type TmVO4 at ambient pressure and under high pressure. The properties under high pressure have been determined experimentally under hydrostatic conditions and theoretically using density functional theory. By powder X-ray diffraction we show that TmVO4 undergoes a first-order irreversible phase transition to a scheelite structure above 6 GPa. We have also determined (from powder and single-crystal X-ray diffraction) the bulk moduli of both phases and found that their compressibilities are anisotropic. The band gap of TmVO4 is found to be Eg = 3.7(2) eV. Under compression the band gap opens linearly, until it undergoes a huge collapse following the structural phase transition (ΔEg = 1.15 eV). Ab initio structural and free energy calculations support our findings. Moreover, calculations of the band structure and density of states reveal that for both zircon and scheelite TmVO4 the band gap is entirely determined by the V 3d and O 2p states of the VO43- ion. The behavior of the band gap can thus be understood entirely in terms of the structural modifications of the VO4 units under compression. Additionally, we have calculated the evolution of the infrared and Raman phonons of both phases upon compression. The presence of soft modes is related to the dynamic instability of the low-pressure phase and to the phase transition.

Noise-and delay-induced phase transitions of the dimer–monomer surface reaction model

The effects of noise and time-delayed feedback in the dimer–monomer (DM) surface reaction model are investigated. Applying small delay approximation, we construct a stochastic delayed differential equation and its Fokker–Planck equation to describe the state evolution of the DM reaction model. We show that the noise can only induce first-order irreversible phase transition (IPT) characteristic of the DM model, however the combination of the noise and time-delayed feedback can simultaneously induce first- and second-order IPT characteristics of the DM model. Therefore, it is shown that the well-known first- and second-order IPT characteristics of the DM model may be viewed as noise-and delay-induced phase transitions.

Hysteretic effects in the first-order irreversible phase transition of the ZGB model

The first-order irreversible phase transition (FOIPT) of the ZGB model [Ziff, Gulari, Barshad, Phys. Rev. Lett. 56 (1986) 2553] for the catalytic oxidation of carbon monoxide is studied numerically by using the constant-coverage (CC) ensemble. The CC method allows us to study hysteretic effects close to coexistence, as well as the location of the coexistence point. Also, evidence that the FOIPT exhibits a condensation/evaporation pseudo-transition (in finite samples), as observed in its reversible counterparts, is presented and discussed.

Numerical study of a first-order irreversible phase transition in a CO+NO catalyzed reaction model.

The first-order irreversible phase transition (IPT) of the Yaldran-Khan model [Yaldran-Khan, J. Catal. 131, 369 (1991)] for the CO+NO reaction is studied using the constant-coverage (CC) ensemble and performing epidemic simulations. The CC method allows the study of hysteretic effects close to coexistence as well as the location of both the upper spinodal point and the coexistence point. Epidemic studies show that at coexistence the number of active sites decreases according to a (short-time) power law followed by a (long-time) exponential decay. It is concluded that first-order IPT's share many characteristics of their reversible counterparts, such as the development of short-ranged correlations, hysteretic effects, metastabilities, etc.

First-order irreversible phase transitions in a nonequilibrium system: mean-field analysis and simulation results.

First-order irreversible phase transitions (IPT's) between an active regime and an absorbing state are studied in a single-component, two-dimensional interacting particle system by means of both simulations and a mean-field analysis. Several features obtained using the mean-field approximation such as the presence of a first-order IPT and hysteresis effects, are in excellent agreement with simulation results. In addition, extensive epidemic simulations show that the dynamical critical behavior of the system is by no means scale invariant.

Monte Carlo simulations of the short time dynamics of a first-order irreversible phase transition

The ZGB model (Ziff–Gulari–Barshad, Phys. Rev. Lett. 56 (1986) 2553) for the catalytic oxidation of carbon monoxide has a single parameter given by the normalized partial pressure of CO molecules ( P CO). For P CO⩾ P CO Coex≃0.52583 the surface of the catalyst becomes irreversibly covered by CO molecules and the system cannot escape from this state. However, for P CO slightly below P CO Coex the system reaches an active stationary state. So, just at P CO Coex a sharp first-order irreversible phase transition is observed. It is shown that a study of the short time dynamics of the ZGB model allows to obtain a fairly accurate evaluation of the upper spinodal point given by P CO Usp≃0.52675(5). This figure is in excellent agreement with extensive simulations performed using the constant coverage ensemble.

Numerical study of persistence in models with absorbing states.

Extensive Monte Carlo simulations are performed in order to evaluate both the local (straight theta(l)) and global (straight theta(g)) persistence exponents in the Ziff-Gulari-Barshad (ZGB) [Phys. Rev. Lett. 56, 2553 (1986)] irreversible reaction model. At the second-order irreversible phase transition (IPT) we find that both the local and the global persistence exhibit power-law behavior with a crossover between two different time regimes. On the other hand, at the ZGB first-order IPT, active sites are short lived and the persistence decays more abruptly; it is not clear whether it shows power-law behavior or not. In order to analyze universality issues, we have also studied another model with absorbing states, the contact process, and evaluated the local persistence exponent in dimensions from 1 to 4. A striking apparent superuniversality is reported: the local persistence exponent seems to coincide in both one- and two-dimensional systems. Some other aspects of persistence in systems with absorbing states are also analyzed.

Revisiting the first-order irreversible phase transition of the Ziff-Gulari-Barshad model

The first-order irreversible phase transition (IPT) characteristic of the Ziff-Gulari-Barshad (ZGB) model is studied by means of extensive numerical simulations. Using the constant-coverage method it is found that hysteresis effects hinder the location of the coexistence point. However, the hysteresis loop is unstable against a negligible small external perturbation, allowing the determination of the coexistence point quite accurately. Also, by means of epidemic studies, an existing controversy on the occurrence of scale invariance in the dynamical behaviour of the system at coexistence is resolved. Our findings reconcile the behaviour of the first-order IPTs of the ZGB model with their reversible counterparts.

Dynamics of reactant interfaces in irreversible reaction systems

Recent progress in the study and understanding of the properties of interfaces between reactants in irreversible reaction systems, gained from Monte Carlo simulations, is reviewed and discussed. The displacement of unstable phases by stable ones causes the formation of interfaces. This mechanism is particularly relevant close to first-order irreversible phase transitions, where phase coexistence is observed. Different variants of the monomer-momomer and the monomer-dimer models exhibit such transitions, and they are therefore suitable for the study of interfacial properties. More specifically, due to stimulating experimental findings, the monomer-dimer model, which mimics the catalytic oxidation of carbon monoxide, has been the subject of extensive studies, which are discussed in detail.

Critical behavior of a one-dimensional monomer-dimer reaction model with lateral interactions

A monomer-dimer reaction lattice model with lateral repulsion among the same species is studied using a mean-field analysis and Monte Carlo simulations. For weak repulsions, the model exhibits a first-order irreversible phase transition between two absorbing states saturated by each different species. Increasing the repulsion, a reactive stationary state appears in addition to the saturated states. The irreversible phase transitions from the reactive phase to any of the saturated states are continuous and belong to the directed percolation universality class. However, a different critical behavior is found at the point where the directed percolation phase boundaries meet. The values of the critical exponents calculated at the bicritical point are in good agreement with the exponents corresponding to the parity-conserving universality class. Since the adsorption-reaction processes does not lead to a non-trivial local parity-conserving dynamics, this result confirms that the twofold symmetry between absorbing states plays a relevant role in determining the universality class. The value of the exponent $\delta_2$, which characterizes the fluctuations of an interface at the bicritical point, supports the Bassler-Brown's conjecture which states that this is a new exponent in the parity-conserving universality class.

Noise-induced phase transition of the dimer-monomer (DM) reaction model

Considering the gas-phase fluctuations in the Monte Carlo simulation, we construct a stochastic differential equation and the corresponding Fokker-Planck equation to describe the state evolution of the dimer-monomer (DM) surface reaction model. We find that the well-known first-order irreversible phase transition characteristic of the DM model may be viewed as a noise-induced transition.

A Dimer−Monomer Catalyzed Reaction Process with Surface Reconstruction Coupled to Reactant Coverages

A lattice gas model for the catalyzed reaction A + 1/2B 2 → AB is studied. Motivated from experiments on the catalytic oxidation of CO on Pt surfaces, it is assumed that the catalyst surface undergoes reactant-induced reversible phase transitions between two different structures, i.e., a stable (reconstructed) phase in the low (high) A coverage limit. Also the sticking coefficient of B 2 species depends on the surface structure, being negligible in the stable phase. For low pressures ofA species the systems have a reactive regime, while increasing such pressure a first-order irreversible phase transition onto an A poisoned state is observed. The structural transitions of the surface coupled with reactant coverages causes an oscillatory behavior in the reactive regime of the reaction. Away from the critical point, oscillations are periodic; however, close to criticality the onset of no-periodic oscillations is observed. Also, on approaching criticality the average period of the A rich phase diverges algebraically with exponent η = 1, in agreement with the fact that just at the critical edge and in the t → ∞ limit the surface will be fully covered with A species.

Irreversible phase transitions in a dimer - monomer - monomer reaction model

A multiple-reaction irreversible surface reaction model involving one dimer and two different monomers (A and C) is proposed and studied by means of Monte Carlo simulations. This dimer - monomer - monomer (DMM) model is suitable to investigate, on the one hand, the influence caused by dimer traces on the behaviour of the monomer - monomer (MM) model, i.e. , and on the other hand, the effects of monomer traces on the dimer - monomer (DM) model, i.e. , which mimics the catalytic oxidation of carbon monoxide (B is O, A is CO and AB is CO). The DMM model exhibits irreversible phase transitions (IPTs) between poisoned states with the surface saturated by adsorbed species and reactive regimes with production of AB, AC and BC. The critical points at which second- and first-order IPTs take place are determined. Second-order IPTs belong to the universality class of directed percolation. However, universality is not found to hold at first-order IPTs due to short-range correlations. So, each critical point has its own set of critical exponents. These exponents smoothly cross over from values characteristic of the DM model to those of the MM model.

On the influence of the hot dimer adsorption mechanism in the critical behaviour of the ZGB model

Hot dimers are molecules that dissociate after adsorption and the resulting monomers undergo a ballistic flight up to a distance R from the adsorption site. The influence of this adsorption mechanism on the critical behaviour of the ZGB model for the catalysed reaction CO+ 1/2 O2(Hot) to CO2 is studied by means of Monte Carlo simulations. It is found that the critical thresholds at which second and first-order irreversible phase transitions (IPTS) take place depend on R. The universality class of the second-order IPT is independent of R, e.g. The evaluated critical exponents are the same than those of the standard ZGB model with R=0. However, critical exponents characteristic of the first-order IPT can be tuned varying R, indicating nonuniversal behaviour. The evolution of empty surface patches in a sea of CO-species, close to the first-order IPT, can be understood in terms of an epidemic oxidation growth.

On the universality classes of the discontinuous irreversible phase transitions of a multicomponent reaction system

Discontinuous irreversible phase transitions (IPTs) from active states to absorbing (poisoned) states in a trimolecular irreversible reaction model, which involves one monomer and two different dimers, are studied by means of Monte Carlo simulations. Evaluated dynamic critical exponents strongly suggest that each first-order IPT has its own universality class.