Modification of streamer-to-leader transition model based on radial thermal expansion in the sphere-plane gap discharge at high altitude

Historically,streamer-to-leader transition studies mainly focused on the rod-plane gap and low altitude analysis,with limited attention paid to the sphere-plane gap at high altitude analysis.In this work,sphere-plane gap discharge tests were carried out under the gap distance of 5 m at the Qinghai Ultra High Voltage(UHV)test base at an altitude of 2200 m.The experiments measured the physical parameters such as the discharge current,electric field intensity and instantaneous optical power.The duration of the dark period and the critical charge of streamer-toleader transition were obtained at high altitude.Based on radial thermal expansion of the streamer stem,we established a modified streamer-to-leader transition model of the sphere-plane gap discharge at high altitude,and calculated the stem temperature,stem radii and the duration of streamer-to-leader transition.Compared with the measured duration of sphere-plane electrode discharge at an altitude of 2200 m,the error rate of the modified model was 0.94%,while the classical model was 6.97%,demonstrating the effectiveness of the modified model.From the comparisons and analysis,several suggestions are proposed to improve the numerical model for further quantitative investigations of the leader inception.

The Negative Thermal Expansion Property of NdMnO_(3) Based on Pores Effect and Phase Transition

A novel negative thermal expansion(NTE) material NdMnO_(3) was synthesized by solid-state method at 1 523 K. The crystal structure, phase transition, pores effect and negative expansion properties of NdMnO_(3) were investigated by variable temperature X-ray diffraction(XRD), scanning electron microscope(SEM) and variable temperature Raman spectra. The compound exhibits NTE properties in the orderly O' phase crystal structure. When the temperature is from 293 to 759 K, the ceramic NdMnO_(3) shows negative thermal expansion of-4.7×10^(-6)/K. As temperature increases, the ceramic NdMnO_(3) presents NTE property range from 759 to 1 007 K. The average linear expansion coefficient is-18.88×10^(-6)/K. The physical mechanism of NTE is discussed and clarified through experiments.

Properties of Ultra-low Thermal Expansion LAS Transparent Glass-ceramics Prepared by Spodumene

The glass-ceramics were prepared with the spodumene mineral as the main raw material,and the effects of ZrO_(2)replacing TiO_(2)on the samples were systematically investigated.The results show that the substitution of ZrO_(2)for TiO_(2)is not conductive to precipitate𝛽β-quartz solid solution phase,but can improve the transparency and flexural strength of glass-ceramics.And the glass-ceramic with the highest visible light transmittance(87%)and flexural strength(231.80 MPa)exhibits an ultra-low thermal expansion of-0.028×10^(-7)K^(-1)in the region of 30-700℃.

Microstructure evolution and thermal expansion of Cu-Zn alloy after high pressure heat treatment

The thermal expansion coefficients of Cu-Zn alloy before and after high pressure treatment were measured by thermal expansion instrument in the temperature range of 25？700 ℃,and the microstructure and phase transformation of the alloy were examined by optical microscope,X-ray diffractometer（XRD） and differential scanning calorimeter（DSC）.Based on the experimental results,the effects of high pressure treatment on the microstructure and thermal expansion of Cu-Zn alloy were investigated.The results show that the high pressure treatment can refine the grain and increase the thermal expansion coefficient of the Cu-Zn alloy,resulting in that the thermal expansion coefficient exhibits a high peak value on the α-T curve,and the peak value decreases with increasing the pressure.

Effects of cooling rate on thermal expansion of Cu_(49)Hf_(42)Al_9 metallic glass

Effects of cooling rate on thermal expansion of Cu49Hf42Al9 metallic glass were studied. Five types of amorphous samples with different sizes were prepared in order to get a broad range of cooling rates （from 102 to 107 K/s）. The average thermal expansion coefficients （αaver） of as-quenched samples range from 6.14×10-6 to 9.20×10-6 K-1. When the temperature is below the glass transformation temperature （Tg）, αaver of as-quenched samples has a negative correlation with cooling rate; the values of αaver of annealed and crystallized samples are closed to each other. The results indicate that the amount and motion of free volume play important roles in thermal expansion of metallic glasses.

Interface and thermal expansion of carbon fiber reinforced aluminum matrix composites

Two kinds of unidirectional PAN M40 carbon fiber （55%, volume fraction） reinforced 6061Al and 5A06Al composites were fabricated by the squeeze-casting technology and their interface structure and thermal expansion properties were investigated. Results showed that the combination between aluminum alloy and fibers was well in two composites and interface reaction in M40/5A06Al composite was weaker than that in M40/6061Al composite. Coefficients of thermal expansion （CTE） of M40/Al composites varied approximately from （1.45-2.68）×10^-6 K^-1 to （0.35-1.44）×10^-6 K^-1 between 20℃ and 450℃, and decreased slowly with the increase of temperature. In addition, the CTE of M40/6061Al composite was lower than that of M40/SA06Al composite. It was observed that fibers were protruded significantly from the matrix after thermal expansion, which demonstrated the existence of interface sliding between fiber and matrix during the thermal expansion. It was believed that weak interracial reaction resulted in a higher CTE. It was found that the experimental CTEs were closer to the predicted values by Schapery model.

Synthesis and thermal expansion of 4J36/ZrW_2O_8 composites

Gas atomized 4J36 alloy powder was milled for 72 h then mixed with ZrW2O8 powder and sintered at 600℃ for 4 h under argon atmosphere. 4J36/ZrW2O8 composites containing 10 vol.%, 20 vol.%, 30 vol.%, and 40 vol.% ZrW2Os were fabricated, the relative density of which ranged from 70% to 80%. Thermal expansion coefficients of the composites decreased as the amount of ZrW2O8 increased, in agreement with the rule of the mixture. The coefficient of thermal expansion of the 4J36/40 vol.%ZrW2O8 composite in 25-100℃ is 0.55 × 10^＋6/℃.

Zero and controllable thermal expansion in HfMgMo(3-x)WxO(12)

HfMgMo（3-x）WxO（12） with x = 0.5, 1.0, 1.5, 2.0, and 2.5 are developed with a simple solid state method. With increasing the content of W, solid solutions of Hf Mg Mo3-xWx O12 crystallize in an orthorhombic structure for x≤2.0 and a monoclinic structure for x2.0. A near-zero thermal expansion（ZTE） is realized for HfMgMo（2.5）W（0.5）O（12） and negative coefficients of thermal expansion（NCTE） are achieved for other compositions with different values. The ZTE and variation of NCTE are attributed to the difference in electronegativity between W and Mo and incorporation of a different amount of W, which cause variable distortion of the octahedra and softening of the MoO4 tetrahedra, and hence an enhanced NCTE in the a- and c-axis and reduced CTE in the b-axis as revealed by Raman spectroscopy and x-ray diffraction.

Tailoring of thermal expansion and phase transition temperature of ZrW_(2)O_8 with phosphorus and enhancement of negative thermal expansion of ZrW_(1.5)P_(0.5)O_(7.75)

ZrW_(2)O_(8)is a typical isotropic negative thermal expansion material with cubic structure.However,quenching preparation,pressure phase transition and metastable structure influence its practical applications.Adopting P to part-substitute W for ZrW_(2-x)P_(x)O_(8-0.5x)has decreased the sintering temperature and avoided the quenching process.When x=0.1,ZrW_(1.9)P_(0.1)O_(7.95)with a stable cubic structure can be obtained at 1150℃.The thermal expansion coefficient is tailored with the P content,and phase transition temperature is lowered.When x=0.5,thermal expansion coefficient attains-13.6×10^(-6)℃^(-1),ZrW_(1.5)P_(0.5)O_(7.75)exhibits enhance negative thermal expansion property.The difference of electronegativity leads to the decrease of phase transition temperature with the increase of P content.The different radii of ions lead to new structure of materials when P substitutes more.The results suggest that the P atom plays the stabilization role in the crystal structure of ZrW_(2-x)P_(x)O_(8-0.5x).

Zero thermal expansion in metal-organic framework with imidazole dicarboxylate ligands

Exploring new abnormal thermal expansion materials is important to understand the nature of thermal expansion.Metal-organic framework(MOF)with unique structure flexibility is an ideal material to study the thermal expansion.This work adopts the high-resolution variable-temperature powder x-ray diffraction to investigate the structure and intrinsic thermal expansion in Sr-MOF([Sr(DMPhH_(2)IDC)_(2)]_n).It has the unique honeycomb structure with one-dimensional(1 D)channels along the c-axis direction,the a-b plane displays layer structure.The thermal expansion behavior has strong relationship with the structure,ZTE appears in the a-b plane and large PTE along the c-axis direction.The possible mechanism is that the a/b layers have enough space for the transverse thermal vibration of polydentate ligands,while along the c-axis direction is not.This work not only reports one interesting zero thermal expansion material,but also provides new understanding for thermal expansion mechanism from the perspective of the structural model.

Thermal expansion behavior, microhardness and electrochemical corrosion resistance properties of Au_(52)Cu_(27)Ag_(17-x)(NiZn_(0.5))_x alloys

The thermal expansion behavior, microhardness and electrochemical corrosion resistance of Au52Cu27Ag17-x（NiZn0.5）x （x=0,6 and 12） alloys were investigated by dilatometer （DIL）, microhardness tester, electrochemical workstation, X-ray diffractometer（XRD）, scanning electron microscopy （SEM）, transmission electron microscopy （TEM） and X-ray photoelectron spectroscopy （XPS）.With increasing x, the relative length expansion and DIL maximum temperature Tl m （i.e., thermal stability） of the alloys increase inthermal expansion measurements, which can be explained by the change of the atomic binding energy, mismatch entropy togetherwith phase transformation. With the increase of x, the microhardness can be improved, but the corrosion resistance decreases; inaddition, the anodic peak current densities of polarization curves decrease, which are related closely with the solid solution degreeand dissolution of Ag, Ni and Zn alloying elements in Cl^- -containing solution.

Thermal Expansion of Solids

The work covers a novel approach to the description of the phenomenon of thermal expansion of solids. The reason for undertaking the scientific quest is presented to follow with the analysis of existing knowledge on the characteristics of phenomenon of thermal expansion of bodies being in the state of aggregation. A critical approach to the existing law of the linear thermal expansion is given. The paper presents an adequate approach to this considered phenomenon. The description provides parametric and functional characteristics of this phenomenon. The relationships of the coefficients of linear expansion on temperature for particular interstate zones, as well as the initial coefficients related to these zones, are presented. In the summary a synthesis of all actions and considerations with the directions to the adequate knowledge with advantage on the subjected phenomenon has been performed. It regards also to the latest thermal characteristics of solids, referred to the phase transformations. All they are realized by dilatometric studies together with determination of curves of thermal expansions of solids.

Thermal expansion of kyanite at ambient pressure:An X-ray powder diffraction study up to 1000℃

The thermal expansion coefficients of kyanite at ambient pressure have been investigated by an X-ray powder diffraction technique with temperatures up to 1000 ℃. No phase transition was observed in the experimental temperature range. Data for the unit-cell parameters and temperatures were fitted empirically resulting in the following thermal expansion coefficients： αa = 5.8（3） × 10^-5, αb = 5.8 （1）× 10^-5, αc = 5.2（1）× 10^-5, and αv = 7.4（1） × 10^-3 ℃ 1 in good agreement with a recent neutron powder diffraction study. On the other hand, the variation of the unit-cell angles α, β and γ of kyanite with increase in temperature is very complicated, and the agreement among all studies is poor. The thermal expansion data at ambient pressure reported here and the compression data at ambient temperature from the literature suggest that, for the kyanite lattice, the most and least thermally expandable directions correspond to the most and least compressible directions, respectively.

A novel implementation algorithm of asymptotic homogenization for predicting the effective coefficient of thermal expansion of periodic composite materials

Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization (NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element (RVE). The new algorithm can be executed easily using commercial finite element analysis (FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.

Thermal Expansion Coefficients of Thin Crystal Films

The formulas for atomic displacements and Hamiltonian of a thin crystal film in phonon occupation number representation are obtained with the aid of Green's function theory. On the basis of these results, the formulas for thermal expansion coefficients of the thin crystal film are derived with the perturbation theory, and the numerical calculations are carried out. The results show that the thinner films have larger thermal expansion coefficients.

Effect of thermal-cooling cycle treatment on thermal expansion behavior of particulate reinforced aluminum matrix composites

Two micron SiC particles with angular and spherical shape and the sub-micron Al2O3 particles with spherical shape were introduced to reinforce 6061 aluminium by squeeze casting technology. Microstructures and effect of thermal-cooling cycle treatment （TCCT） on the thermal expansion behaviors of three composites were investigated. The results show that the composites are free of porosity and SiC/Al2O3 particles are distributed uniformly. Inflections at about 300℃ are observed in coefficient of thermal expansion （CTE） versus temperature curves of two SiCp/Al composites, and this characteristic is not affected by TCCT. The TCCT has significant effect on thermal expansion behavior of SiCp/Al composites and CTE of them after 3 cycles is lower than that of 1 or 5 cycles. However, no inflection is observed in Al2O3p/Al composite, while TCCT has effect on CTE of Al2O3p/Al composite. These results should be due to different relaxation behavior of internal stress in three composites.

Novel thermal expansion of lead titanate

Lattice parameters of lead titanate were precisely re-determined in thetemperature range of-150-950 deg C by high precision XRPD measurements. It was clarified that therewas no any evidence for a new phase transition at low tempera-lures. Tetragonal distortion straindecreases with temperature increasing. A novel thermal expansion was observed, positive thermalexpansion from -150 deg C to room temperature (RT) and above 490 deg C, and the negative thermalexpansion in the temperature range of RT-490 deg C. A big jump of thermal expansion coefficient isattributed to the tetragonal-cubic phase transition. A rationalization for the negative thermalexpansion of PbTiO_3 is due to the decrease of anion-anion repulsion as polyhedra become moreregular at heating. The mechanisms of positive and negative thermal expansions were elucidated asthe same nature in the homogenous tetragonal phase at present case.

The phase transition, hygroscopicity, and thermal expansion properties of Yb_(2-x)Al_xMo_3O_(12)

Materials with the formula Yb2-xAlxMo3O12 （x = 0.1, 0.2, 0.3, 0.4, 0.5, 0.7, 0.9, 1.0, 1.1, 1.3, 1.5, and 1.8） were synthesized and their structures, phase transitions, and hygroscopicity investigated using X-ray powder diffraction, Raman spectroscopy, and thermal analysis. It is shown that Yb2-xAlxMo3012 solid solutions crystallize in a single monoclinic phase for 1.7 〈 x 〈 2.0 and in a single orthorhombic phase for 0.0 〈 x 〈 0,4, and exhibit the characteristics of both monoclinic and orthorhombic structures outside these compositional ranges. The monoclinic to orthorhonlbic phase transition temperature of A12Mo3012 can be reduced by partial substitution of A13＋ by Yb3＋, and the Yb2-zAlxMo3012 （0.0 〈 x 〈 2.0） materials are hydrated at room temperature and contain two kinds of water species. One of these interacts strongly with and hinders the motions of the polyhedra, while the other does not. The partial substitution of A13＋ for Yb3＋ in Yb2Mo3012 decreases its hygroscopicity, and the linear thermal expansion coefficients after complete removal of water species are measured to be -9.1 x 10-6/K, -5.5 x 10-6/K, 5.74 x 10-6/K, and 9.5 x 10 6/K for Ybl.sAlo.2（MoO4）3, Yb1.6Alo.4（MoO4）3, Ybo.4All.6（Mo04）3, and Ybo.2Al1.8（MoO4）3, respectively.

Effects of Chemical Treatments on Thermal Expansion Properties of Cordierite Ceramics

Cordierite honeycomb ceramics was treated with 1.5 M HNO3 , followed with 1.5 M NaOH at 93 ℃. The combination of acid treatment with alkali treatment significantly diminished the rebounding of coefficient of thermal expansion （CTE） caused by heat treatment, a phenomenon observed in samples treated solely with acid. Inductively coupled plasma （ICP） analysis results reveal that the alkali treatment preferentially dissolved ＂free＂ SiO2 left in the acid-treated samples, which is considered to be a key factor responsible for the CTE rebounding.

PREPARATION OF HIGH THERMAL EXPANSION COEFFICIENT PORCELAINS FUSED TO METALS

Usually the thermal expansion coefficients (TEC) of metals are higher than that of porcelains. In order to match the TECs in the case of coating porcelains on metals, high TEC porcelains are needed. In this research, the high TEC phase leucite (KAlSi2 O6) in the high TEC porcelain was prepared by sol-gel method. The crystal size of leucite made by sol-gel is about 77nm through controlling the process parameters. The process from xerogel to leucite was investigated by means of DSC (differential scanning calorimetry), TG (thermogravimetry), XRD ( X-ray diffraction) and IR (infrared absorption spectrum). Leucite had been detected after the gel was treated at 900℃, this formation temperature is about 250℃ lower than that of melting method. The porcelain made from 50% of the leucite powder and 50% of low fused temperature frit has an average TEC of 19.2×10-6/℃ C from room temperature to 450℃, which is much higher than the common porcelains.