Vol. 50, No. 7 (2001)
2001, 50 (7): 1201-1206. doi: 10.7498/aps.50.1201
By virtue of the method of multiple scales, we have investigated the behavior of waves in a one-dimensional nonlinear monoatomic chain under damping and found that the amplitude of the lattice waves decreases and the group velocity becomes slow under the action of damping of an order of O(ε). At the same time, we have derived PDNLS equation and obtained its analytical solution. Our results show that: there exists propagating envelope soliton in the one-dimensional nonlinear monoatomic chain under the damping, provided the damping is of an order of O(ε). However, the chain supports the propagation of the soliton of bell shape or kink as the damping is of an order of O(ε2).
2001, 50 (7): 1207-1212. doi: 10.7498/aps.50.1207
A new lattice Boltzmann equation(LBE) model is developed based on the previous LBE model and the conservative criteria of mass, momentum and energy. The result shows that the LBE model is further improved in an external force field. The relation between the buoyancy strength parameter and the Grashof number is obtained through the recovery of dynamic equations. The viscosity transport term is obviously improved by comparing the derived momentum equation with Navier-Stokes equation. It is shown that the viscosity stress not only depends on the velocity gradient and the compressibility of the fluid, but also depends on the gradient of unsteady internal energy and unsteady momentum flux. The flow field with nonuniform temperature has been simulated by using the model. It is shown that the model is valid both in theory and in numerical experiment.
2001, 50 (7): 1213-1216. doi: 10.7498/aps.50.1213
By virtue of the singular perturbation expansion,we have developed a theory for the study of dynamical behaviours of the kink of sine-Gordon equation,and acquired that the kink of sine-Gordon equation behaves very much like a classical particle under the action of a constant external force,its motion satisfies the Newton's law.Still,we have derived a simple analytical expression for the dispersive wave radiated by the kink in the process of propagation.
2001, 50 (7): 1217-1220. doi: 10.7498/aps.50.1217
Based on the operator-sum representation of quantum channel, the quantum channel of a single-mode Fermi system is parameterized. By the parameterization another kind of Fermi thermal noise quantum channel is found. The maximum values of coherent information of two kinds of channels are obtained to estimate the quantum capacities of the channels.
2001, 50 (7): 1221-1225. doi: 10.7498/aps.50.1221
Some researchers used the conception of phase transition to explain ubiquitous power laws in the complex Internet. However, this explanation obviously ignores the correlation between nodes' behaviors. In this paper, we compare the phase transition with the collective correlation behaviors of nodes by use of a computer network model. It is shown that when the load of network is increased, the spatial and time correlation between nodes'behaviors is also strengthened and the collective correlation phenomenon emerges gradually. At the critical state, the system load fluctuates with a 1/f2 power spectrum, and the power spectra of buffer contents fluctuations vary as 1/fα noise where α≤2. The existence of spatial-temporal correlation among nodes'behaviors is further demonstrated.
CHARACTERISTICS OF THE LAMINAR REGIONS DISPLAYED BY TYPE-V INTERMITTENCIES IN SOME TWO-DIMENSIONAL MAPS
2001, 50 (7): 1226-1231. doi: 10.7498/aps.50.1226
Through an analysis on several examples we show that the phase space regions occupied by the laminar phases displayed by type-V intermittencies in two-dimensional maps often possess one-dimensional characteristics. These one-dimensional regions correspond to parts of the stable manifolds belonging to the “ghosts” of the periodic orbits that have already vanished via border-collision bifurcations. They form channels with an apparent exit similar to that the laminar iterations go through when intermittencies happen in one-dimensional maps. At the same time the phase space regions occupied by turbulent phases possess two-dimensional features.The mechanisms of all these characteristics are also discussed.
NEW LAX INTEGRABLE HIERARCHY OF EVOLUTION EQUATIONS AND ITS INFINITE-DIMENSIONAL BI-HAMILTONIAN STRUCTURE
2001, 50 (7): 1232-1236. doi: 10.7498/aps.50.1232
Based on a new isospectral problem with three potential functions (q,r,s),a new Lax integrable hierarchy of evolution equations with an arbitrary function is obtained in this paper.When the potential,s,is put into differential functions,the hierarchy of equations can reduce to several kinds of systems of equations.By using the trace identity,their bi-Hamiltonian structures are given,and it is shown that they are integrable in the Liouville's sense.Moreover,the conserved densities and symmetries are also found.
2001, 50 (7): 1237-1240. doi: 10.7498/aps.50.1237
In this paper,a method based on intermittent parametric adaptive control algorithm is presented for chaos synchronization.A satisfactory result of chaos synchronization is obtained in the case of appropriate intermittent feedback period N and feedback coefficient r.A simulation on two logistic maps with different parameters is conducted.The results show that chaos synchronization will be achieved at very low cost of control when feedback coefficient r is adopted appropriately.
2001, 50 (7): 1241-1247. doi: 10.7498/aps.50.1241
Surrogate data testing is a popular method to detect nonlinearity and chaos in time series and has been widely used in many applications with erratic time series.With the explicit null hypothesis that the time series is generated from a linear,stochastic,Gaussian stationary process,the surrogate data test based on phase randomization may give false alarm for nonlinearity at a linear non-minimum phase non-Gaussian sequence.So,we propose a new method to test the hypothesis of linear non-Gaussian process in light of typical realization of surrogates.With the ARMA parameters estimated from high-order cumulants and the series itself,a method to estimate the input noise of a non-minimum phase sequence is developed based on power spectrum equivalence,which is the bottle-neck to generate surrogates for non-minimum phase time series.The results of numerical experiments confirm our approach to test non-minimum phase non-Gaussian process.
A REDUCED PARAMETER SECOND-ORDER VOLTERRA FILTER WITH APPLICATION TO NONLINEAR ADAPTIVE PREDICTION OF CHAOTIC TIME SERIES
2001, 50 (7): 1248-1254. doi: 10.7498/aps.50.1248
A reduced parameter second-order Volterra filter (RPSOVF) which is constructed by the multiplication-coupled two linear FIR filters, and its nonlinear normalized least mean square (NLMS) algorithm is proposed; and this RPSOVF with nonlinear NLMS algorithm are used to make adaptive predictions of chaotic time series. The rule of selecting convergent assistant parameters of the nonlinear NLMS algorithm is obtained. Experimental results show that this reduced parameter second-order Volterra filter with the nonlinear NLMS algorithm can be successfully used to make adaptive predictions of chaotic time series, and the modified nonlinear NLMS algorithm enables RPSOVF to converge and stabilize.
2001, 50 (7): 1255-1259. doi: 10.7498/aps.50.1255
By introducing a break noise,create and disappear probability,we obtain a wholly stochastic cellular automaton traffic model.Through studying its microscopic evolution rule,we build its macroscopic dynamical equation under the Boltzmann approximation.We analyzed the solution of the equation under special conditions and did some computer simulation experiments.
2001, 50 (7): 1260-1263. doi: 10.7498/aps.50.1260
The simulated annealing algorithm was modified and realized on a home-made parallel super computer system THNPSC-1. The program was applied to the data analyses of two different physical domains: Convergent Beam Electron Diffraction and Auger Electron Spectroscopy. The good results obtained from these two domains indicated that the program is of high-performance and is applicable to various research regions. The source code is available free of charge from the authors.
2001, 50 (7): 1264-1267. doi: 10.7498/aps.50.1264
The preparation of carbon buckonions is reported.Large quantities and high percentage of carbon buckonions can be synthesised by radio frequency plasma-enhanced chemical vapor deposition on the Co catalysts and Co-SiO2 catalysts.The product contains no carbon tubes,only carbon onions,which are solid,smooth and clean and can be separated easily from the catalystic particles.The growth of carbon buckonions is based on the formation of many cages in successive stages from the core to the surface.High-resolution transmission electron microscopy indicates that the outer layers of the carbon buckonions produced on Co-SiO2 comprise unclosed small waving graphitic flakes.The formation process of these graphitic flakes is discussed.
ATOMIC AND MOLECULAR PHYSICS
2001, 50 (7): 1268-1273. doi: 10.7498/aps.50.1268
Density functional (B3LYP) method with relativistic effective core potential (RECP) has been used to optimize the structures of Pu2 and Pu3 molecules. The results show that the ground states of Pu2 and Pu3 molecules are of D∞h and D3h symmetry, and of 13 and 19 fold, respectively. The spectral constants of Pu2, ωe=52.3845 cm-1 and ωe χe=0.0201 cm-1, and the harmonic frequencies of Pu3,ν1=56.9007 cm-1,ν2=57.1816 cm-1 and ν3=64.0785 cm-1, have also been obtained on the B3LYP/RECP level. The potential energy functions of Pu2 and Pu3 have been derived, for the first time so far as we know,from normal equation fitting and the many-body expansion theory.
2001, 50 (7): 1274-1278. doi: 10.7498/aps.50.1274
We report a set-up for cavity ringdown absorption spectroscopy, and we have measured the line profile of the resonance 6s6p1P1←6s6s1S0 of barium atoms using cavity ringdown spectroscopy method. The absorption spectroscopy line profile of Ba at different temperatures near 553.548nm is gained. The experimental results indicate that the precision for the absorption measurement has reached up to 6×10-7.
CLASSICAL AREA OF PHENOMENOLOGY
INFLUENCE OF NONLINEARITIES OF BOTH THE FIELD AND THE INTENSITY-DEPENDENT ATOM-FIELD COUPLING ON THE EMISSION SPECTRUM OF AN ATOM IN A CAVITY
2001, 50 (7): 1279-1283. doi: 10.7498/aps.50.1279
The emission spectrum of a single atom in the nonlinear coupling J-C (Jaynes-Cummings) model including any forms of nonlinearities of both the field and the intensity-dependent atom-field coupling is studied.The effects of nonlinearities on the spectrum are demonstrated.It is shown that features of the emission spectrum are influenced significantly by the kinds of the field nonlinearity term R(a+a) and the intensity-dependent atom-field nonlinear coupling factor f(a+a).The structure of the spectrum is quite different from that of the standard J-C model.It is found that when f(a+a)=1/(a+a)1/2,the emission spectra always show the definite three-peak structure for any initial state of the field,which implies that the effects on the emission spectrum of both the specific intensity-dependent nonlinear medium with f(a+a)=1/(a+a)1/2 and the initial field photon statistics can be counterbalanced.This feature is analyzed with an analytic method.
EFFECT OF FIELD POLARIZATION DIRECTION ON ACCELERATING ELECTRON WITH EXTRA-INTENSE STATIONARY LASER BEAM
2001, 50 (7): 1284-1289. doi: 10.7498/aps.50.1284
This article studies the effect of laser-field polarization direction on accelerating electrons with extra-intense stationary linear-polarization laser beam with 3D simulation of the relativistic Newton-Lorentz equation of motion.It is shown that there will exhibit remarkable inelastic effect of the electron scattering on the laser beam when the laser intensity a0=eE0/mecω～102.But this effect is dependent on the angle between the incident direction of the electron and the field polarization direction plane of the laser.When the electron is injected along the electric field polarization plane, the inelastic effect of scattering becomes maximum.However,with increasing angle,this effect will come down gradually,even disappears.This means the electron cannot be captured or accelerated violently.Thus,as for the scattering of electrons the strong laser beam field displays anisotropic feature,and we cannot describe it by the conventional ponderomotive potential model.This study is of significance in experimentally testing the laser acceleration effect, as well as designing laser accelerators in the future.
2001, 50 (7): 1290-1293. doi: 10.7498/aps.50.1290
Simultaneous oscillation of resonance-metastable transition laser in calcium atoms and ions was obtained in a discharge tube with 1.3cm inner diameter and 46cm electrode separation through longitudinal high frequency pulse discharge.The maximum laser output power and laser efficiency reach 1.1W and 0.1 percent respectively.Laser output characteristics depend on various working parameters and the ratio of Pi/Pa were measured and analyzed.
2001, 50 (7): 1294-1297. doi: 10.7498/aps.50.1294
Simultaneous oscillation of self-terminating lasing in strontium atoms(6.45μm)and ions(1.03μm/1.09μm)was obtained by high-repetition-rate pulsed discharge.The maximum average output power reaches 273mW.The effects on laser output characteristics versus main working parameters were analyzed and discussed on the basis of comparison of experiments.
EXPERIMENTAL STUDY ON THE MECHANISM OF A SELF-STARTING KERR-LENS-MODE-LOCKING USING A SEMICONDUCTOR SATURABLE ABSORBER MIRROR
2001, 50 (7): 1298-1301. doi: 10.7498/aps.50.1298
The self-starting dynamics of the Kerr-lens-mode-locking (KLM) in a Ti:sapphire laser using an intracavity broadband semiconductor saturable absorber mirror (SESAM) was investigated experimentally.The mechanism of the self-starting KLM using a SESAM was investigated and discussed.
2001, 50 (7): 1302-1307. doi: 10.7498/aps.50.1302
According to the experimental facts that the structure and the dielectric property of electro-rheology (ER) fluid change under the external electric field, a model of microwave transmittance in ER fluid was established, and the formula of transmittance was given also. Theoretical simulation shows that the transmittance of microwave increases with increasing electric field, if the dielectric constant of ER fluid is greater than that of its container. On the contrary, it decreases with the electric field. Our experiment results revealed that the microwave attenuation in ER fluid could be adjusted by changing the external electric field. We think the change of the structure and dielectric property of ER fluid are the main cause of the fact that the transmittance could be adjusted under the external electric field.
PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES
2001, 50 (7): 1308-1312. doi: 10.7498/aps.50.1308
Dense plasmas with uniform and constant density and temperature are generated by passage of a planar shock wave through argon gas. Our experiments in argon have produced plasmas with a temperature of 1.4—2.2eV and a density of 0.0083—0.015gcm3. The opacity of the plasma is measured versus wavelength by recording the rise time of emitted light. Measurements in visible light are compared with the calculations using the average atom model, and the agreement is well. In data treatments, the opacity and the reflectance R(λ) at the baseplate / argon interface are simultaneously worked out. The resultant R(λ) in this work are all around 0.4, which is in agreement with that given by Erskine.
2001, 50 (7): 1313-1317. doi: 10.7498/aps.50.1313
Langmuir probe is an important diagnostic tool for measuring plasma parameters. A tuned single probe has been used to diagnostic the electron energy distribution function in Ar radio frequency (13.56MHz) glow plasma. The second derivative of probe I-V characteristic was obtained after using numerical filter procedure to eliminate the statistical noise in measured I-V characteristic. A differential circuit has been designed and applied to measure the second derivative of I-V characteristic on line under the same discharge conditions. The results of the two methods are in agreement with each other.
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES
2001, 50 (7): 1318-1323. doi: 10.7498/aps.50.1318
Chemical coprecipitated amorphous and nanocrystalline ZrO2·Y2O3(15%) was studied by Powder X-ray diffraction(XRD) and extended X-ray absorption fine structure(EXAFS). XRD result shows that the sample is an amorphous phase annealed below 300℃; and it crystallizes into cubic nanocrystalline zirconia at 500℃. EXAFS analysis indicates that the coordination number and bond length of Zr-O shell has not changed when transforming from amorphous into nanocrystalline. This suggests that at 300℃,it has formed the same nearest-neighbor local structure as at 900℃. For Zr-Zr(Y) shell, with the reducing of grain size, the coordination number decreases obviously: the bond length is shorter and the disorder becomes larger. This result suggests that the grain size effect is much stronger for more distant coordination shell (Zr-Zr ) than for the first nearest-neighbor shell(Zr-O).
INFLUENCE OF ION ENERGY AND DEPOSITION TEMPERATURE ON THE SURFACE MORPHOLOGY OF CARBON FILMS DEPOSITED BY ION BEAMS
2001, 50 (7): 1324-1328. doi: 10.7498/aps.50.1324
Carbon films were deposited by mass-selected ion beam technique with ion energies 50—200eV at a substrate temperature from room temperature to 800℃. For the energies used, smooth diamond-like carbon films were deposited at room temperature. When the substrate temperature was 600℃,rough graphitic films were produced. But highly oriented carbon tubes were observed when the energies were larger than 140eV at 800℃. They were perpendicular to the surface and parallel to each other. Preferred orientation of graphite basic plane was observed by high-resolution electron microscopy. Shallow ion implantation and stress are responsible for this orientation.
2001, 50 (7): 1329-1333. doi: 10.7498/aps.50.1329
Carbon ions were implanted into crystal Si to a concentration of(06—15)at% at room temperature. Some samples were pre-irradiated with 29Si+ ions, while others were not pre-irradiated. Then the two kinds of samples were implanted with 29C+ ions simultaneously, and Si1-xCx alloys were grown by solid phase epitaxy with high-temperature annealing. The effects of pre-irradiation on the formation of Si1-xCx alloys were studied. If the dose of implanted C ion was less than that for amorphizing Si crystals, the implanted C atoms would like to combine with defects produced during implantation, and then it was difficult for Si1-xCx alloys to form after annealing at 950℃. Pre-irradiation was advantageous for Si1-xCx alloy formation. With the increase of C ion dose, the damage produced by C ions increased. Pre-irradiation was unfavorable for Si1-xCx alloy formation. If the implanted C concentration was higher than that for solid phase epitaxy solution, only part of the implanted C atoms form Si1-xCx alloys and the effects of pre-irradiation could be neglected. As the annealing temperature was increased to 1050℃, Si1-xCx alloys in both pre-irradiated and unpreirradiated samples of low C concentration remained, whereas most part of Si1-xCx alloys in samples with high C concentration vanished.
2001, 50 (7): 1334-1339. doi: 10.7498/aps.50.1334
Based on the crystal lattices oscillator model, a thermodynamic equation of state is derived using a statistical dynamics method. The new parameter R of this equation of state is independent of the Grüneisen parameter, as compared with its predecessor, which was given by Q. Wu and F. Q. Jing. The calculated shock Hugoniot loci based on this new parameter are in good agreement with those calculated by the original parameter over a wide pressure range. This validates the new form of the R parameter.
2001, 50 (7): 1340-1345. doi: 10.7498/aps.50.1340
Based on the single-spin transition critical dynamics, we investigate the critical slowing down of the Gaussian spin model on dilational symmetric Sierpinski gaskets. We calculate the dynamical critical exponent z using the dynamical decimation renormalization-group technique in the assumption of the magnetic-lile perturbation, and found that the dynamical critical exponent z of the system is only related to the static length-correlation exponent ν, but is foreign to the fractal dimenionality Df. The result of the universal conclusion z=1/ν has been verified again in this paper.
2001, 50 (7): 1346-1349. doi: 10.7498/aps.50.1346
The fluctuation patterns observed in the Cu-Zn-Al alloy are reported and calculated by using a nonlinear approach in this paper.The results show that the fluid-like oscillations of the atom-cells of μm order have exhibited the feature of solitary waves. The oscillation can be maintained by the external driving,and as the internal friction becomes strong,the decay of the amplitude of solitary wave with respect to the time obeys the exponential rule exp (-kt).The calculation is in good agreement with the experimental observations.
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES
2001, 50 (7): 1350-1354. doi: 10.7498/aps.50.1350
A new interface roughness scattering model is developed using exponential autocovariance functions.The electron mobility in 6H-SiC inversion layers is studied by single-electron Monte Carlo approach that takes into account the size quantization and the main scattering mechanisms in SiC inversion layers.The simulation results show that the electron mobility calculated using the exponential model presented in this paper are in good agreement with the experimental data. Interface roughness scattering is shown to play a strong role in the high effective transverse field.The electron mobility falls as the temperature increases.The roughness scattering under higher effective fields is reduced significantly by screening effects.
2001, 50 (7): 1355-1358. doi: 10.7498/aps.50.1355
The electronic resistivity and thermopower of liquid InSb as a function of temperature have been measured using the d.c. four-probe method and also from the electromotive force produced by the temperature gradient. Abnormal behavior is observed and more accurate data are obtained. For liquid InSb, the temperature dependence of resistivity increases with temperature near the melting point, and almost is constant when the temperature is above 716℃. The abnormal behavior has also been found in the temperature dependence of thermopower almost at the same temperature. Based on other physical properties changing with temperature and the structure of liquid InSb near melting point, the result obtained in this work suggests that the liquid structure of InSb may be changed at 716℃.
2001, 50 (7): 1359-1365. doi: 10.7498/aps.50.1359
Three kinds of critical state models, such as Bean's model, Kim's model and Power model, are selected to analyze numerically the initial magnetic curve and hysteresis loop of Bi2223 high-Tc superconductor, as an example, with a simple method. Programs are made to calculate the magnetization as a function of applied magnetic field and temperature. The results are discussed compare the three kinds of critical state models. The hysteresis losses of superconductors at different temperatures and under different amplitudes of applied magnetic field are studied according to functions derived using these models.
2001, 50 (7): 1366-1370. doi: 10.7498/aps.50.1366
According to the Blonder-Tinkham-Klapwijk approach,we calculate the electron transport coefficients through a junction of a mixed d(x2-y2)+idxy wave superconductor and a normal metal with a rough interface. We investigate the effects of rough strength of the interface and the mixing of the two symmetries on electron tunneling.It is found that the tunneling spectrum depends strongly on the relative strength of the two components. The zero-bias conductance peak splits into two peaks due to the mixing.
YVO4 crystal has high laser output slope efficiency and damage threshold,good mechanical property and chemical stability.We have measured the absorption of Tm:YVO4 crystal.The anisotropy effect is taken account.The optical intensity parameters are fitted out.And the oscillator strength f,the radiative transition rate,the integral emission section Σ are calculated.In the wavelength range of 350—2500nm,the absorption of YVO4 crystal itself is rather small.However,Tm3+ ions in the YVO4 crystal have very strong luminescent ability. Especially,the 1D2→3F4 (about 454nm) blue transition has excellent oscillator strength (f=38×10-6) and integral emission section (Σ=33×10-18cm).It is quite benefit to achieve laser lasing in short-wavelength.In brief,the rare earth ion doped YVO4 crystal is a kind of wonderful laser material,which has great applications in future.
2001, 50 (7): 1378-1384. doi: 10.7498/aps.50.1378
The tetraphosphate glasses with various Yb3+ dopant were prepared. The absorption and fluorescence emission spectra were measured. The spectroscopic properties and laser performance parameters of Yb3+ in tetraphosphate glasses were calculated. The disagreement between the reciprocity method and Fuchtbauer-Ladenburg formula was discussed using the radiation trapping effect. The effects of Yb3+ and OH- contents on emission properties were investigated. The result shows that Yb3+-doped tetraphosphate glass exhibits excellent spectroscopic properties.
2001, 50 (7): 1385-1389. doi: 10.7498/aps.50.1385
We adopted an analytical approach based on fitting of the full band structure of ZnS by polynomials.We studied the electron transport process in phosphor layer of thin-film electroluminescent divices by Monte Carlo Simulation.Two kinds of spatial distributions of electron energy are obtained in phosphor layers of the sandwich structure and the layered optimization structure,and the explanation about it is also given.
INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY
2001, 50 (7): 1390-1395. doi: 10.7498/aps.50.1390
TiO2 thin films were prepared by reactive magnetron sputtering.The influences of O2 partial pressure,substrate temperature and annealing temperature on the structural properties of the films have been studied.In these films anatase and rutile phases were observed and their respective preferred crystallizing conditions were analyzed.In this paper,the morphological characteristic of TiO2 film was also discussed.
STRUCTURAL CHARACTERIZATION OF C3N4 THIN FILMS SYNTHESIZED BY MICROWAVE PLASMA CHEMICAL VAPOR DEPOSITION
2001, 50 (7): 1396-1400. doi: 10.7498/aps.50.1396
Crystalline carbon nitride films have been synthesized on Si substrates by microwave plasma chemical vapor deposition technique, using a gas mixture of nitrogen and methane. Scanning electron microscopy shows that the film consisted of hexagonal crystalline rods. X-ray diffraction and transmission electron microscopy indicate the films are mainly composed of α-and β-C3N4, and these results match more closely with α-C3N4 than with β-C3N4 phase. Fourier transform infrared (FTIR) and Raman spectra of carbon nitride were calculated through Hooke's law. The observed FTIR and Raman spectra support the existence of α- and β-C3N4 in the films.
2001, 50 (7): 1401-1404. doi: 10.7498/aps.50.1401
Small-angle X-ray scattering has been used to study the precipitation behavior of the δ′ phase in an Al-2.70mass%Li alloy treated by aging-retrogression-reaging. The results show that a transitional interfacial layer exists between the δ′ phase and the matrix in 8h reaging, but the transitional interfacial layer disappears in 16h reaging. This suggests that the δ′ phase particles are coarsened by “licking up” the transition interfacial layer before 16h reaging and swallow up each other after 16h reaging.