Computer simulation of order-disorder phase transition in the intercalation compounds M_(1/2)TiS_2 (M=Fe, Co, Ni)

Based on cluster variation method (CVM) and natural iteration method (MM),order-disorder phase transition in the intercalation compounds M_(1/2)TiS_2 is simulated bycomputer. The favorable conditions, under which 3^(1/2)a_0 x a_0 superstructure is formed, aregiven, and the results are in good agreement with the experiments and theoretical calculations. Therelationship between critical temperature and M-ion-vacancy interaction parameter is linear.

First Order Phase Transitions as Radiation Processes

This paper presents new experimental evidence of the PeTa effect—infrared characteristic radiation under first order phase transitions, especially the crystallization of melts and the deposition and condensation of vapours/gases. The PeTa effect describes the transient radiation that a particle (i.e., atom, molecule or/and cluster) emits transient radiation during a transition from a meta-stable higher energetic level (in a super-cooled melt or a super-saturated vapour) to the stable condensed lower level (in a crystal or a liquid). The radiation removes latent heat with photons of characteristic frequencies that are generated under this transition. The abbreviation “PeTa effect” means Perel’man-Tatartchenko’s effect.

First Order Phase Transitions as Radiation Processes, Part Two

This paper presents new experimental results concerning the PeTa effect—infrared characteristic radiation under first order phase transitions, especially during deposition and condensation of vapours/gases and the crystallisation of melts. The abbreviation “PeTa effect” means Perel’man-Tatartchenko’s effect. The nature of the PeTa effect is transient radiation that a particle (i.e., atom, molecule or/and cluster) emits during a transition from a meta-stable higher energetic level (in a super-cooled melt or super-saturated vapour) to the stable condensed lower level (in a crystal or liquid). The radiation removes latent heat with photons of characteristic frequencies that are generated under this transition. This paper is the second in a set describing the appearance of PeTa radiation under air cooling with deposition and condensation of air components. The radiation was recorded using an IR Fourier Spectrometer with a highly sensitive MCT detector. Certain peculiarities of the recorded radiation as well as its applications in the physics of the atmospheres of Earth and Jupiter are analysed.

Theoretical study on order–disorder phase transition of CH3NH3PbCl3

Order–disorder phase transitions for CH3NH3PbCl3 are studied with density functional theory. Our calculations show that the disorder is manifested in two aspects in the cubic phase, namely, the disorder of orientation and rotation of organic groups. Organic groups of [CH3] and [NH3] in cubic crystals can easily rotate around its C3 axis. At the same time,[CH3NH3]^+ organic groups can also orient to different spatial directions due to the weak interactions between organic group and inorganic frame. Our results show that its possible phase transition path starts from the deviation of organic groups from the crystal c-axis. Its structural transition changes from disordered cubic phase to hydrogen-only disordered tetragonal structure in the process of decreasing symmetry. The disordered high temperature cubic phase can be expressed as a statistical average of substructures we rebuilt. The electrostatic repulsive force between adjacent organic groups triggers out the formation of low temperature phase on cooling.

A Note on an Order Level Inventory Model with Varying Two-Phased Demand and Time-Proportional Deterioration

The main purpose of this paper is to generalize the effect of two-phased demand and variable deterioration within the EOQ (Economic Order Quantity) framework. The rate of deterioration is a linear function of time. The two-phased demand function states the constant function for a certain period and the quadratic function of time for the rest part of the cycle time. No shortages as well as partial backlogging are allowed to occur. The mathematical expressions are derived for determining the optimal cycle time, order quantity and total cost function. An easy-to-use working procedure is provided to calculate the above quantities. A couple of numerical examples are cited to explain the theoretical results and sensitivity analysis of some selected examples is carried out.

NANOGrav results and dark first order phase transitions

The recent NANOGrav evidence of a common-source stochastic background provides a hint to gravitational waves(GW)radiation from the Early Universe.We show that this result can be interpreted as a GW spectrum produced from first order phase transitions(FOPTs)around a temperature in the keV-MeV window.Such a class of FOPTs at temperatures much below the electroweak scale can be naturally envisaged in several warm dark matter models such as Majoron dark matter.

Renormalization-group theory of first-order phase transition dynamics in field-driven scalar model

Through a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a φ^3 theory, we show that the instability fixed points of the theory, together with their associated instability exponents, are quite probably relevant to the scaling and universality behavior exhibited by the first-order phase transitions in a field-driven scalar Ca model, below its critical temperature and near the instability points. Finite- time scaling and leading corrections to the scaling are considered. We also show that the instability exponents of the first-order phase transitions are equivalent to those of the Yang-Lee edge singularity, and employ the latter to improve our estimates of the former. The outcomes agree well with existing numerical results.

Tuning Order-Disorder Phase Transition through Regulating the Substituent Group of Anion

The structural phase transition compound {[（CH3）2CHCH2]2NH2}·[CF3COO] （1） has been synthesized based on the diisobutylamine and trifluoroacetic acid. The DSC data reveal that 1 undergoes a phase transition at 277 K （Tc）. When one chlorine atom replaces one fluorine atom on trifluoroacetate anion, three order-disorder phase transitions at 251 K （Ti）, 282 K （T2） and 290 K could be achieved owing to a stepwise release of rotation motions of the anion and cation in {[（CH3）2CHCH2]2NH2}·[CF2C[COO] （2）. Based on the variable temperature crystal structures, the phase transition in compound 1 is triggered by the rotation of three fluorine atoms on the trifluoroacetate anion synchronized with the motions of the methyl groups on the diisobutylammonium cation. However, in compound 2, the phase transitions can be realized by a sequence of motions of both the anion and cation. Besides, the dielectric- temperature dependences were investigated in order to prove this regulation process. All of this investigation will be beneficial to design and synthesis of the novel phase transition materials and molecular dielectric materials on pur- pose.

Renormalization group theory for temperature-driven first-order phase transitions in scalar models

We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of imaginary fixed points of φ3 theory. Scaling theories and renormalization group theories are developed to account for the phenomena, and three universality classes with their own hysteresis exponents are found： a field-like thermal class, a partly thermal class, and a purely thermal class, designated, respectively, as Thermal Classes I, II, and III. The first two classes arise from the opposite limits of the scaling forms proposed and may cross over to each other depending on the temperature sweep rate. They are both described by a massless model and a purely massive model, both of which are equivalent and are derived from φ3 theory via symmetry. Thermal Class III characterizes the cooling transitions in the absence of applied external fields and is described by purely thermal models, which include cases in which the order parameters possess different symmetries and thus exhibit different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only at the mean-field level and is identical to Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and two- loop results for the static and dynamic exponents for the Yang-Lee edge singularity, respectively, which falls into the same universality class as φ3 theory, we estimate the thermal hysteresis exponents of the various classes to the same precision. Comparisons with numerical results and experiments are briefly discussed.

Effect of the interaction between the chemical and the magnetic ordering on the phase equilibria of iron base alloys

It is well known that the magnetic properties such as the Curie temperature Tmag <sub>C and the mean magnetic moment β of ordered compounds have different values from those of the disordered solutions. For instance, both Tmag c and β of the Ni3Pt （L12） and NiPt （L10） and Tmag <sub>c of the CoPt （L10） and CoPt3 （L12） ordered compounds are strongly depressed due to the ordering compared with those of the metastable disordered Ni-Pt and Co-Pt alloys. On the other hand, the γ’-FeNi3 （L12） and the α’-FeCo （B2） ordered compounds have higher Tmag <sub>c and β values comparing with the disordered solution phases, γ （A1） and α （A2）, respectively. In consequence, the stability of the ordered phase is depressed or enhanced due to the interaction between the chemical and magnetic ordering caused by the decrease or increase of Tmag <sub>c and β values. The purpose of this study is to investigate the effect of the interaction between the chemical and the magnetic ordering on the phase equilibria in the Fe-X（X=Al, Co, Ni, Rh, Si） binary systems.The Gibbs energy of the α（A2）, γ（A1） and liquid phases is described by a sub-regular solution approximation. The ordering contribution to the Gibbs energy ,ΔGorder <sub>m, and deviations of magnetic properties, ΔTmag <sub>c and Δβ, of the ordered compounds, FeAl （B2）, Fe3Al （D03）, FeCo （B2）, FeRh （B2）, FeSi （B2）, Fe3Si （D03） and FeNi3 （L12） is introduced by the split compound energy formalism. Effect of the interaction between the chemical ordering, B2, D03 and L12 and the magnetic ordering on the phase equilibria will be discussed according to the calculated phase diagrams of the Fe-X binary systems.

Effect of Li on formation of long period stacking ordered phases and mechanical properties of Mg-Gd-Zn alloy

Alloys with composition of Mg_(96-x)Gd_3Zn_1Li_x(at.%)(x=0, 2, 4, and 6) were prepared by conventional casting. The microstructures of these alloys under as-cast and solid-solution conditions have been observed, and the mechanical properties were investigated. The results showed that Li is an effective element to refine the grains and break the eutectic networks in as-cast MgGd_3Zn_1 alloy. During solid solution treatment, these broken eutectic networks are spheroidized and highly dispersed. In addition, plentiful lamellar long period stacking ordered(LPSO) phases are precipitated in an α-Mg matrix when the Li addition is not more than 4%. Solid-solution treated Mg_(92)Gd_3Zn_1Li_4 alloy exhibits an optimal ultimate tensile strength(UTS) of 226 MPa and elongation of 5.8%. The strength of MgGd_3Zn_1 alloy is improved significantly, meanwhile, the toughness is apparently increased.

Multi-threshold second-order phase transition in laser

We present a theory of the multi-threshold second-order phase transition,and experimentally demonstrate the multi-threshold secondorder phase transition phenomenon.With carefully selected parameters,in an external cavity diode laser system,we observe secondorder phase transition with multiple(three or four) thresholds in the measured power-current-temperature three dimensional phase diagram.Such controlled death and revival of second-order phase transition sheds new insight into the nature of ubiquitous secondorder phase transition.Our theory and experiment show that the single threshold second-order phase transition is only a special case of the more general multi-threshold second-order phase transition,which is an even richer phenomenon.

GLOBAL PERIODIC ATTRACTOR OF ATHIRD-ORDER PHASE-LOCKED LOOP

In this paper, the existence of a global periodic attractor for a third-order phase-lockedloop with tangential phase detector characteristic and frequency modulation input is provedunder some condition on the parameters.

Precipitation of ordered α_2 phase in a near-α titanium alloy with duplex microstructure

The precipitation of ordered alpha_2 phase in a near - alphaTi-6.3Al-4.8Sn-2.0Zr-1.0Mo-0.34Si-0.9Nd (mass fraction) alloy with duplex microstructure, duringaging at various temperatures, was investigated. It is concluded that the precipitation and growthof the alpha_2 phase can be controlled by suitable selection of the aging temperature. Aging athigher temperatures can result in the uniform precipitation and growth of alpha_2 ordered phase inalpha_p whereas the alpha_2 ordered phase precipitated only at the lamella boundaries anddislocations in beta_t. Aging at a moderate temperature can promote the tendency of uniformprecipitation of alpha_2 phase in both alpha_p and beta_t. Aging at a relatively low temperature issuitable for the uniform precipitation and growth of fine alpha_2 particles throughout both thealpha_p and beta_t matrix.

Effect of long period stacking ordered phase on damping capacities of as-cast Mg-Zn-Y alloys

The microstructure and damping capacities of MgZnxYi.33x(x=l-4at.%)alloys were discussed and researched.The main phase composition of the alloys consists of a_Mg and long-period stacking ordered(LPSO)phase.Due to increasedLPSO phase,grain size was refined.LPSO phase was advantageous to the damping properties of the Mg-Zn-Y alloys.Mg-7%Zn-12.8%Y has the highest damping capacity up to0.04.Due to stacking fault probability,the LPSO phase in the Mg-Zn-Yalloys could be new damping source to dissipate energy so as to contribute to the improvement of damping capacities.

Dilute long period stacking/order(LPSO)-variant phases along the composition gradient in a Mg-Ho-Cu alloy

We have systematically investigated the microstructures of as-cast Mg_(97.49)Ho_(1.99)Cu_(0.43)Zr_(0.09)alloy by atomic resolution high-angle annular dark field scanning transmission electron microscopy(HAADF-STEM), revealing the coexistence of 18R, 14H and 24R long period stacking/order(LPSO) phases with fully coherent interfaces along step-like composition gradient in a blocky intermetallic compound distributed at grain boundary. The short-range order(SRO) L1_(2)-type Cu_(6)Ho_(8)clusters embedded across AB’C’A-stacking fault layers are directly revealed at atomic scale. Importantly, the order degree of SRO clusters in the present dilute alloy is significant lower than previous 6M and 7M in-plane order reported in ternary Mg-TM(transition metal)-RE(rare earth) alloys, which can be well matched by 9M in-plane order. This directly demonstrates that SRO in-plane L1_(2)-type clusters can be expanded into more dilute composition regions bounded along the definite TM/RE ratio of 3/4. In addition, the estimated chemical compositions of solute enriched stacking fault(SESF) in all LPSO variants are almost identical with the ideal SESF composition of 9M in-plane order, regardless of the type of LPSO phases. The results further support the viewpoint that robust L1_(2)-type TM_(6)RE_(8)clusters play an important role in governing LPSO phase formation.

CRYSTAL STRUCTURE OF A LONG－PERIOD ORDERED PHASE IN Fe－C MARTENSITE AND COMPUTER SIMULATION OF ITS ELECTRON DIFFRACTION PATTERNS

Different structure models of a long-period ordered phase in Fe-C martenstie formed during aging have been checked by computer simulation of electron diffraction(ED) patterns based on these models.The results showed that the simulated ED pattern of γ'-FexC(Ⅱ) model proposed by the present authors is in good agreement with experimentally observed ED pattern.It was also confirmed that the incommensurate superperiod stems from the coexistence of several γ'-Fe_xC(H) phases with different superperiods.The Fe(144)C(24)(Fe6C) model proposed by Uwakweh et al.generated ED patterns remarkably different from the experimental ones.

Effect of Al Content on Precipitation of α_2 Ordered Phase in Ti-Al-Sn-Zr-Mo-Si-Nd Alloys

The precipitation characteristics of the α2 ordered phase in Ti-AI-Sn-Zr-Mo-Si-Nd alloys with various content of Al, under different aging conditions, were investigated. The distribution and size of the α2 ordered phase changed with temperature and Al content. The dislocations were the only places where the α2 ordered phase could precipitate at higher temperature near the critical transformation temperature for each alloy experimented. With the addition of Al content, the critical transformation temperature of α2 ordered phase increased. When the aging temperature was relatively low (650℃), the precedent precipitation of α2 ordered phase took place in primary a phase at the early stage of aging, in the duplex microstructure (the primary a with the transformed (3) of the alloys with lower Al content. But after certain aging time (50 h), the size of α2 particles was almost equal in both the primary a and the transformed β. And no obvious growth of α2 particles could be observed after 50 h.

New ordered MAX phase Mo_2 TiAlC_2: Elastic and electronic properties from first-principles

First-principles computation on the basis of density functional theory(DFT) is executed with the CASTEP code to explore the structural, elastic, and electronic properties along with Debye temperature and theoretical Vickers’ hardness of newly discovered ordered MAX phase carbide Mo2TiAlC2. The computed structural parameters are very reasonable compared with the experimental results. The mechanical stability is verified by using the computed elastic constants. The brittleness of the compound is indicated by both the Poisson’s and Pugh’s ratios. The new MAX phase is capable of resisting the pressure and tension and also has the clear directional bonding between atoms. The compound shows significant elastic anisotropy. The Debye temperature estimated from elastic moduli(B, G) is found to be 413.6 K. The electronic structure indicates that the bonding nature of Mo2TiAlC2is a mixture of covalent and metallic with few ionic characters. The electron charge density map shows a strong directional Mo–C–Mo covalent bonding associated with a relatively weak Ti–C bond.The calculated Fermi surface is due to the low-dispersive Mo 4d-like bands, which makes the compound a conductive one.The hardness of the compound is also evaluated and a high value of 9.01 GPa is an indication of its strong covalent bonding.

Effects of Alloying Elements on the Volume Fraction of Ordered α_2 Phase Precipitated in Ti-Al-Sn-Zr Alloys

An ideal method has been established for calculating the precipitation of α2 ordered phase in near-α titanium alloys based on the theory on the critical electron concentration for the precipitation of α2 ordered phase in near-α titanium alloys. With complete precipitation of α2 phase in near-α titanium alloys, the alloys can be considered to be composed of two parts： （1） the α2 ordered phase with the stoichiometric atomic ratio of Ti3X; （2） the disorder solid solution with the critical composition in which the α2 ordered phase is just unable to precipitate. By using this method, the volume fractions of α2 ordered phase precipitated in Ti-Al, Ti-Sn, Ti-Al-Sn-Zr alloys with various AI, Sn and/or Zr contents have been calculated. The influences of AI and Sn on the precipitation of α2 ordered phase are discussed. The calculating results show substantial agreement with the experimental ones.