Assessments of coefficients of linear thermal expansions for magnetic elements Fe, Co and Ni

The coefficients of linear thermal expansions （CLEs） of magnetic elements Fe, Co and Ni were assessed from experimental information using theoretical models combined with MATLAB calculations. Model parameters can be determined accurately, and the assessed data are in good agreement with the experimental results. To facilitate the assessments, theories of thermal expansion were applied to separate CLEs into its nonmagnetic and magnetic components. The calculations of nonmagnetic contribution to CLEs were based on the modified Gruineisen- Debye model, in which the Debye temperature was regarded as an undetermined constant. In order to put the prediction of CLEs at the magnetic transition region on a sound physical basis, two kinds of theoretical models were innovatively used to calculate the magnetic contribution to CLEs, i.e., the Bragg-Williams model and the Fermi-Dirac distribution function. Model parameters were evaluated from experimental data using least square method. Detailed comparisons were made with the published experimental data and the calculated total CLEs. A satisfactory agreement is reached.

Improvement strategy on thermophysical properties of A_(2)B_(2)O_(7)-type rare earth zirconates for thermal barrier coatings applications:A review

The A_(2)B_(2)O_(7)-type rare earth zirconate compounds have been considered as promising candidates for thermal barrier coating(TBC) materials because of their low sintering rate,improved phase stability,and reduced thermal conductivity in contrast with the currently used yttria-partially stabilized zirconia (YSZ) in high operating temperature environments.This review summarizes the recent progress on rare earth zirconates for TBCs that insulate high-temperature gas from hot-section components in gas turbines.Based on the first principles,molecular dynamics,and new data-driven calculation approaches,doping and high-entropy strategies have now been adopted in advanced TBC materials design.In this paper,the solid-state heat transfer mechanism of TBCs is explained from two aspects,including heat conduction over the full operating temperature range and thermal radiation at medium and high temperature.This paper also provides new insights into design considerations of adaptive TBC materials,and the challenges and potential breakthroughs are further highlighted for extreme environmental applications.Strategies for improving thermophysical performance are proposed in two approaches:defect engineering and material compositing.

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.

Anisotropy of Thermal-expansion for β-Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine： Quantum Chemistry Calculation and Molecular Dynamics Simulation

Molecular dynamics simulations on octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine （HMX） at 303-383 K and atmospheric pressure are carried out under NPT ensemble and COMPASS force field, the equilibrium structures at elevated temperatures were obtained and showed that the stacking style of molecules don＇t change. The coefficient of thermal expansion （CTE） values were calculated by linear fitting method. The results show that the CTE values are close to the experimental results and show anisotropy. The total energies of HMX cells with separately increasing expansion rates （100%-105%） along each crystallographic axis was calculated by periodic density functional theory method, the results of the energy change rates are anisotropic, and the correlation equations of energy change-CTE values are established. Thus the hypostasis of the anisotropy of HMX crystal＇s thermal expansion, the determinate molecular packing style, is elucidated.

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.

DEVELOPMENT OF INCONEL~ ALLOY 783，A LOW THERMAL EXPANSION，CRACK GROWTH RESISTANT SUPERALLOY

Low thermal expansion superalloys have been used for a number of years in a variety of applications, including gas turbine engines. The low thermal expansion characteristics of the most widely used class of materials are derived from the ferromagnetic characteristics of Ni, Fe, and Co-based austenitic matrices containing little or no Cr.Alloy developments have been aimed at improving the oxidation resistance and stress accelerated grain boundary oxygen (SAGBO) attack.INCONEL alloy 783 is an oxidation resistant, low coefficient of thermal expansion superalloy developed for gas turbine applications. Alloy 783 represents a culmination in the development, of an alloy system with very high alumtnum content that, in addition to forming γ′,causes βaluminide phase precipitation in the austenitic matrix.This type of structure can be processed to resist both SAGBO and general oxidation,while providing low thermal expansion and useful mechanical properties up to 700℃.Key aspects of the alloy's development are presented.

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.

Microstructure and thermal properties of copper matrix composites reinforced with titanium-coated graphite fibers

Milled form of mesophase pitch-based graphite fibers were coated with a titanium layer using chemical vapor deposition technique and Ti-coated graphite fiber/Cu composites were fabricated by hot-pressing sintering. The composites were characterized with X-ray diffraction, scanning/transmission electron microscopies, and by mea- suring thermal properties, including thermal conductivity and coefficient of thermal expansion （CTE）. The results show that the milled fibers are preferentially oriented in a plane perpendicular to the pressing direction, leading to anisotropic thermal properties of the composites. The Ti coating reacted with graphite fiber and formed a continuous and uniform TiC layer. This carbide layer establishes a good metallurgical interracial bonding in the composites, which can improve the thermal properties effectively. When the fiber content ranges from 35 vol% to 50 vol%, the in-plane thermal conductivities of the composites increase from 383 to 407 W.（m.K）-~, and the in-plane CTEs decrease from 9.5 x 10-6 to 6.3 10-6 K-1.

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.

Effects of boron on the microstructure and thermal properties of Cu/diamond composites prepared by pressure infiltration

Diamond reinforced copper（Cu/diamond） composites were prepared by pressure infiltration for their application in thermal management where both high thermal conductivity and low coefficient of thermal expansion（CTE） are important.They were characterized by the microstructure and thermal properties as a function of boron content,which is used for matrix-alloying to increase the interfacial bonding between the diamond and copper.The obtained composites show high thermal conductivity（660 W/（m·K）） and low CET（7.4×10-6 K-1） due to the formation of the B13C2 layer at the diamond-copper interface,which greatly strengthens the interfacial bonding.Thermal property measurements indicate that in the Cu-B/diamond composites,the thermal conductivity and the CTE show a different variation trend as a function of boron content,which is attributed to the thickness and distribution of the interfacial carbide layer.The CTE behavior of the present composites can be well described by Kerner＇s model,especially for the composites with 0.5wt% B.

Effects of cryogenic treatment on the thermal physical properties of Cu_(76.12) Al_(23.88) alloy

The thermal diffusion coefficient, heat capacity, thermal conductivity, and thermal expansion coefficient of Cu76.12Al23.88 alloy before and after cryogenic treatment in the heating temperature range of 25℃ to 600℃ were measured by thermal constant tester and thermal expansion instrument. The effects of cryogenic treatment on the thermal physical properties of CU76,12A123,88 alloy were investigated by comparing the variation of the thermal parameters before and after cryogenic treatment. The results show that the variation trend of the thermal diffusion coefficient, heat capacity, thermal conductivity, and thermal expansion coefficient of CU76.12Al23.88 alloy after cryogenic treatment was the same as before. The cryogenic treatment can increase the thermal diffusion coefficient, thermal conductivity, and thermal expansion coeffi- cient of Cu76.12Al23.88 alloy and decrease its heat capacity. The maximum difference in the thermal diffusion coefficient between the before and after cryogenic treatment appeared at 400℃. Similarly, thermal conductivity was observed at 200℃.

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.

Evaluation of the microstructure,thermal and mechanical properties of Cu/SiC nanocomposites fabricated by mechanical alloying

Nano-sized silicon carbide(SiC:0wt%,1wt%,2wt%,4wt%,and 8wt%)reinforced copper(Cu)matrix nanocomposites were manufactured,pressed,and sintered at 775 and 875℃in an argon atmosphere.X-ray diffraction(XRD)and scanning electron microscopy were performed to characterize the microstructural evolution.The density,thermal expansion,mechanical,and electrical properties were studied.XRD analyses showed that with increasing SiC content,the microstrain and dislocation density increased,while the crystal size decreased.The coefficient of thermal expansion(CTE)of the nanocomposites was less than that of the Cu matrix.The improvement in the CTE with increasing sintering temperature may be because of densification of the microstructure.Moreover,the mechanical properties of these nanocomposites showed noticeable enhancements with the addition of SiC and sintering temperatures,where the microhardness and apparent strengthening efficiency of nanocomposites containing 8wt%SiC and sintered at 875℃were 958.7 MPa and 1.07 vol%^(−1),respectively.The electrical conductivity of the sample slightly decreased with additional SiC and increased with sintering temperature.The prepared Cu/SiC nanocomposites possessed good electrical conductivity,high thermal stability,and excellent mechanical properties.