Linear Thermal Expansion Coefficient Research Articles

A systematic study on linear thermal expansion coefficient of metals based on interferometric measurement with Fresnel bimirror

AbstractLinear thermal expansion coefficient, which is vital for measuring the thermal expansion characteristics of metals, has been attracting considerable attention globally. Herein, a novel design based on Fresnel bimirror has been developed. In this design, when the upper end of the object to be measured comes in contact with a tilted double‐sided mirror, the temperature rises and intersection angle of the Fresnel bimirror decreases. Meanwhile, interference fringe spacing becomes narrower, while the number of fringes increases. An imaging system based on a digital microscope and smartphone is also incorporated in this design, which records the changes in the interference fringes. Then, using a self‐programmed software, the linear thermal expansion coefficients of Cu, Fe, and Al samples are determined at elevated temperatures as 17.85 ± 0.23 × 10−6/°C (), 11.8 ± 0.09 × 10−6/°C (), and 23.34 ±0.16 × 10−6/°C (), respectively, with a relative error of less than 1.6%. A cooling process is also designed, and the average value of the linear thermal expansion coefficient of metal samples during heating and cooling conditions is determined. The measurement results obtained via the finite‐method simulation demonstrate the feasibility and reliability of the system. Overall, this study provides a new idea for measuring the linear thermal expansion coefficient of metals.

Oxide ceramics of A2M3O12 family with negative and close-to-zero thermal expansion coefficients: Machine learning-based modeling of functional characteristics

Ceramic materials with negative and close-to-zero coefficients of thermal expansion may open the avenue to the technologies that have so far been constrained by physical limitations concerned with the thermal stress or with the insufficient structural stability. Two important characteristics of NTE materials which could be used for the evaluation of the possible area and limitations of the sphere of application for negative thermal expansion (NTE) materials are the linear thermal expansion coefficient and the transition temperature from monoclinic to orthorhombic phase. In this study, the machine learning methods were involved in the analysis of experimental data for NTE oxide ceramics of A2M3O12 family (where M is Mo6+, W6+, V5+ or P5+ while A position may be accommodated by the wide range of metal cations). The models are characterized by the following statistical coefficients: the determination coefficient R2 = 0.81 and prediction error RMSE = 1.170 for linear thermal expansion coefficient; the corresponding parameters for the phase transition temperature were assessed as 0.81 and 82.239, respectively. Ionic conductivity in this class of compounds has been discussed as a tandem functional characteristic, emphasizing the role of anharmonicity in both characteristics. The role of synthesis route and defect chemistry in NTE was analyzed. A conclusion on the expected enhancement of NTE resulted from the intentional introduction of cation A vacancies has been made. The principal possibility of combining two functional characteristics, - an ion conductor and a phase with negative thermal expansion, with some compromise in the characteristics of each of them is substantiated.

Structural Origins of the Anisotropic Thermal Expansion of BINOL Crystals

AbstractMeasurement of the unit cell of (R)-BINOL over a 200° temperature range (300–100 K) reveals an anisotropic contraction where the c-axis contracts ca. 2.3% compared to a ca. 0.45% contraction of the a and b axes, a ca. six-fold difference in linear thermal expansion coefficient. This contraction corresponds to a decrease in the helical pitch of the 31 screw axis in the [001] direction. The anisotropic nature of the contraction is rationalised by a thorough analysis of intermolecular contacts within the crystal and their impact on the conformation of the molecule and crystal packing. Graphical Abstract The crystal structure of (R)-BINOL exhibits a pronounced anisotropic thermal expansion.

Wood-Composite Boards with a Low Coefficient of Linear Thermal Expansion

Wood-Composite Boards with a Low Coefficient of Linear Thermal Expansion

Thermodynamics of cordierite formation during firing of water-permeable ceramics

The analysis of the influence of an increase in firing temperature on the thermodynamic possibilities of solid-phase chemical reactions in the MgO–Al2O3–SiO2 system in the direction of cordierite formation has been conducted. The thermodynamic direction of solid-phase reactions in the MgO–Al2O3–SiO2 system allows determining rational firing temperatures of materials containing cordierite for the manufacture of products for various purposes. During low-temperature firing (up to 1200 K) of finely dispersed masses based on talc-clay-alumina compositions, materials with high open porosity but low strength characteristics can be obtained. This is because the reactive sintering mainly occurs due to reactions forming intermediates for cordierite synthesis and incomplete processes of destruction in natural mineral raw materials. In the firing temperature range of 1200–1500 K, the thermodynamic probability of reactions immediately via several cordierite formation mechanisms increases, which should limit the growth of individual crystals while increasing their quantity. This should positively affect the strength and heat resistance of materials due to low values of the thermal coefficient of linear expansion. Firing temperatures of 1500–1659 K correspond to the limits for cordierite formation and contribute to the consolidation of the material with a change in the nature of porosity from open to closed. Exceeding firing temperatures above 1659 K results in the thermodynamic instability of the cordierite-corundum phase combination and can lead to the formation of defects due to the appearance of a significant amount of melt in the phase composition of the material.

First-principles study on the structure, mechanical and thermodynamic properties of (Ti, Hf, Nb, Ta)C high-entropy carbide ceramics

High-entropy carbide ceramics (HECCs) have demonstrated extraordinary properties and broad application potential. However, the action mechanisms of metallic elements on the properties have not been understood in depth. In this study, the structural stability and the mechanical and thermodynamic properties of (Ti, Hf, Nb, Ta)C HECCs across a broad composition spectrum were systematically analyzed based on the density functional theory and Debye–Grüneisen model. The crystal structure was constructed and validated through experimental testing. The mechanical properties such as elastic moduli, ductility, hardness, and Poisson's and Pugh's ratios were calculated. Furthermore, the temperature dependence of bulk moduli, thermal expansion coefficients, and heat capacities of the HECCs were investigated. To interpret the elastic and toughening mechanisms of non-equiatomic HECCs, the electronic structures were investigated. The results indicate that the HECCs with a single solid solution phase of the FCC rock-salt structure are thermodynamically stable. The HECCs containing higher Nb and Ta contents have greater strength and stiffness, and those containing higher Ti and Hf contents exhibit greater hardness and brittleness than the equiatomic HECC. In addition, non-equiatomic HECCs containing higher Nb and Ta contents have larger bulk moduli and lower linear thermal expansion coefficients, which can be attributed to the stronger covalent interaction among metallic elements and carbon. This study is expected to have an impact on designing ideal HECCs for high-temperature applications under extreme environments.

Phase diagram and physical properties anisotropy of strontianite

The physical properties and anisotropy of carbonates at high pressure are fundamental to understanding the deep carbon cycle and storage. Here, we redraw the phase diagram of strontianite (SrCO3) by first-principles calculations combined with lattice dynamics and study its physical properties and anisotropy at high pressure. The results show that there are only Pnma and Pmmn phases in SrCO3 in the entire Earth's mantle, and there is no R3m phase. The SrCO3 polymorphs have a large elastic anisotropy. SrCO3 polymorphs are a kind of carbonate with high density, low wave velocity, and low wave velocity anisotropy. The linear thermal expansion coefficient of SrCO3-Pmmn was obtained for the first time by using the linear elastic compression coefficient combined with the volume thermal expansion coefficient. The results are of great significance for understanding the high-pressure behavior of Sr-carbonates.

Valorization of Agro-Wastes as Fillers in PLA-Based Biocomposites for Increasing Sustainability in Fused Deposition Modeling Additive Manufacturing.

The use of wheat middlings (WM) and rice husks (RH) as biofillers for mixing with poly(lactic acid) (PLA) matrix to produce new 3D-printable biocomposites was assessed. Filaments containing 10 and 20 wt.% agro-waste-derived biofillers were manufactured and, for the sake of comparison, filaments of neat PLA were also produced. The obtained filaments were characterized via thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC), showing potential for further application in additive manufacturing processing. Three-dimensionally printed specimens were thus produced and characterized via: DSC, also evaluating the specific heat capacity (CP) of specific 3D-printed specimens; dynamic mechanical analysis (DMA), also applied for determining the coefficient of linear thermal expansion (CLTE) measured on 3D-printed specimens in two different directions (X and Y); and tensile tests. The latter testing campaign was carried out along three printing directions (X, Y, and Z axes) to test the intrinsic biocomposite features (X-printed samples) as well as interbead and interlayer adhesion (Y- and Z-printed specimens, respectively). All samples demonstrated acceptable properties. The inclusion of a cost-free natural material leads to a strong reduction of the whole material cost. Implementing this new class of composite material to an additive manufacturing technique can significantly reduce the environmental impact of 3D-printed products.

Measuring coefficient of thermal expansion of materials of micrometre size using SEM/FIB microscope with in situ MEMS heating stage.

A new method is proposed to measure the linear coefficient of thermal expansion (CTE) of solid metals and ceramics of micron-sized dimensions. This approach uses a focused ion beam (FIB) to extract and transfer a slab of the sample, typically (15-20) ×10 × (3-5) µm onto a Micro-Electro-Mechanical Systems (MEMS) in situ heating holder inside a scanning electron microscope (SEM). CTE is thereafter calculated by image correlating the change of length (ΔL) between the fiducial marks on the slab as a function of temperature, taking advantage of the temperature calibration of the MEMS heating holder and nanometre resolution of the scanning electron microscope. The CTE results are validated to be consistent with standard copper and silicon. We further demonstrate the method on a graphene platelet reinforced copper composite and a graphite filler phase isolated from a bulk sample, these represent materials that cannot be practically synthesised or isolated at the macro-scale. Errors associated with the measurement are discussed.

ИССЛЕДОВАНИЕ ВЛИЯНИЯ ДОБАВКИ ВЫСОКОДИСПЕРСНОЙ ФАЗЫ КАРБИДА ТИТАНА, СИНТЕЗИРОВАННОЙ В РАСПЛАВЕ, И ТЕРМООБРАБОТКИ НА СТРУКТУРУ И СВОЙСТВА СПЛАВА АМ4,5Кд

The study results are given which are devoted to finding the effect of reinforcement with fine phase of titanium carbide in the amount of 10 masses% on the physico-mechanical and tribotechnical properties of industrial aluminum AM4.5Kd alloy. The physico-mechanical (density, porosity, coefficient of thermal linear expansion, hardness, microhardness) and tribotechnical (wear rate, friction factor, self-heating temperature) properties of the composite material AM4.5Kd-10%TiC obtained by self-propagating high-temperature synthesis before and after heat treatment are analyzed. It is found out that composite samples after heat treatment have a good combination of physical and mechanical properties, namely a low level of porosity, a low value of the coefficient of thermal linear expansion, and the values of hardness and microhardness are increased twice. Special attention should be paid to the fact that reinforcement with a ceramic phase in combination with heat treatment leads to a significant increase in the level of wear resistance of the matrix alloy (by 9 times) and a decrease in the friction factor (by 4 times). Thus, according to the results of the studies conducted, the resulting composite material AM4.5Kd-10%TiC can be recommended as a material used in tribological assemblies.

Fabrication of low thermal expansion Fe–Ni alloys by in-situ alloying using twin-wire arc additive manufacturing

The binary Fe–Ni system offers alloys with notably low linear coefficients of thermal expansion (CTE), contingent upon their Ni content. In this respect twin-wire arc additive manufacturing (T-WAAM) presents the opportunity of in-situ alloying through the simultaneous feeding of two metal wires into a weld pool to obtain desired alloy compositions. This study aims to deposit a graded wall with Ni contents targeted at 42, 46, and 52 wt% in the building direction of the wall, along with a block comprising of 46 wt% Ni, employing the T-WAAM approach. The results show effective incorporation of additional Ni into the weld pool and geometrically stable weld beads in the continuous metal transfer mode during the T-WAAM process. This mode led to the defect-free and chemically stable deposition of the graded wall and the block with average Ni contents of 42.3 ± 1.1, 45.8 ± 1.4, 52.6 ± 0.8 wt%, and 46.4 ± 0.9 wt%, respectively. The measured Curie temperatures of the as-deposited alloys and the mean CTE values of alloy 46 were found to be comparable to the commercial alloys. In summary, this study validates the feasibility of in-situ deposition of low thermal expansion alloy compositions, thereby enabling the possibility of on-demand thermal expansion properties.

Investigation of the anisotropic thermal expansion of PbIn6Te10 crystal by high temperature x-ray diffraction measurements

The PbIn6Te10 crystal, an IR laser frequency conversion material, grown via the Bridgman method with dimensions ϕ35 mm × 90 mm in a four-zone furnace, was subject to the investigation of its thermal expansion behavior using high-temperature x-ray diffraction in the range of 25–450 °C. Based on the obtained data, the average thermal expansion coefficients of 15.21 × 10−6 K−1 for α a and 6.44 × 10−6 K−1 for α c were determined utilizing the least square method. The study revealed that the linear and volume thermal expansion coefficients of PbIn6Te10 crystals satisfy the relationships α a > α c > 0, α V = 2α a + α c , and α a increased while α c decreased with increasing temperature, accentuating a substantial anisotropy in thermal expansion between the crystal’s principal axes. A detailed exploration pinpointed that the variations in the PbTe6 octahedron primarily governed the changes in the PbIn6Te10 unit cells, with further investigation uncovering its association with variations in the nearest neighboring bonds, which is mainly related to Pb-Te4 and Pb-Te2 bonds. Additionally, the determination of temperature-dependent anisotropic thermal expansion coefficient α was complemented by calculating Grüneisen parameter γ using Quasi-harmonic Debye model. Remarkably, these parameters also exhibited anisotropic behaviors ( γ⊥ increases with temperature whereas γ// decreases, α ⊥ > α ∥), contributing additional insights into the crystal thermal characteristics.

Effects of (KMg)3+ co-doping and sintering temperature on the negative thermal expansion property of Sc2W3O12 ceramics

(KMg)3+ co-doped Sc2W3O12 ceramics have been prepared via co-precipitation method. Effects of (KMg)3+ co-doping amount and sintering temperature on the phase constitution, microstructure, morphology, and negative thermal expansion (NTE) performance of KxMgxSc2-xW3O12 (0 ≤ x ≤ 1.25) ceramics were studied. Results indicate that: Sc3+ cations can be substituted by (KMg)3+ dual-cations and a composition-induced structural phase transition was observed in KxMgxSc2-xW3O12. For x ≤ 0.25, orthorhombic Sc2W3O12 gradually changed into hexagonal KxMgxSc2-xW3O12 and coexisted. Single phase KxMgxSc2-xW3O12 with hexagonal symmetry can be prepared for 0.25 < x ≤ 1. When x ≥ 1.25, (KMg)3+ substitution reaches its solid solution limit in Sc2W3O12, and impurity MgWO4 formed in the samples. As co-doping amount x increased, the NTE performance of the KxMgxSc2-xW3O12 (0 ≤ x ≤ 1) ceramics gradually enhanced. The coefficient of thermal expansion (CTE) of KxMgxSc2-xW3O12 (0 ≤ x ≤ 1) ceramics enhanced from −2.14 × 10−6 °C−1 to −19.68 × 10−6 °C−1 in 30–700 °C. With the increase of sintering temperature from 800 to 1100 °C, the grains grew up and the density of the K0.75Mg0.75Sc1.25W3O12 ceramics increased as well, and the NTE performance was also improved. The linear CTE of K0.75Mg0.75Sc1.25W3O12 ceramics enhances from −2.15 × 10−6 °C−1 to −14.70 × 10−6 °C−1 in 30–700 °C.

Phase compositions and thermophysical performances for (Sm1-xYbx)3TaO7 compounds

The (Sm1-xYbx)3TaO7 compounds were prepared using high-temperature calcining technology to evaluate the impact of Yb2O3 on the crystal-type and thermal-physical performances for Sm3TaO7. Final analytical conclusions show that the synthesised compounds have a sole pyrochlore or fluorite crystal structure, and the lattice variation from pyrochlore to fluorite is found with an increase in Yb2O3 fraction. Owing to the phonon scattering caused by substituting cation and disorder atomic arrangement, the heat insulation ability of (Sm1-xYbx)3TaO7 oxides is improved, which meets the requirements for thermal barrier coatings. The synthesised (Sm1-xYbx)3TaO7 oxides also present relatively high linear thermal expansion coefficients owing to the combined influence of ionic radius and crystal lattice energy. The addition of Yb2O3 also improves the crystal constancy until 1200 °C.

Phase Transformation Temperature Prediction in Steels via Machine Learning.

The phase transformation temperature plays an important role in the design, production and heat treatment process of steels. In the present work, an improved version of the gradient-boosting method LightGBM has been utilized to study the influencing factors of the four phase transformation temperatures, namely Ac1, Ac3, the martensite transformation start (MS) temperature and the bainitic transformation start (BS) temperature. The effects of the alloying element were discussed in detail by comparing their influencing mechanisms on different phase transformation temperatures. The training accuracy was significantly improved by further introducing appropriate features related to atomic parameters. The melting temperature and coefficient of linear thermal expansion of the pure metals corresponding to the alloying elements, atomic Waber-Cromer pseudopotential radii and valence electron number were the top four among the eighteen atomic parameters used to improve the trained model performance. The training and prediction processes were analyzed using a partial dependence plot (PDP) and Shapley additive explanation (SHAP) methods to reveal the relationships between the features and phase transformation temperature.

Poly(ester imide)s with Low Linear Coefficients of Thermal Expansion and Low Water Uptake (VII): A Strategy to Achieve Ultra-Low Dissipation Factors at 10 GHz.

In this study, a series of ester-linked tetracarboxylic dianhydrides (TCDAs) with 2,6-naphthalene-containing longitudinally extended structures consisting of different numbers of aromatic rings (NAr = 6-8) was synthesized to obtain novel modified polyimides, poly(ester imide)s (PEsIs). These TCDAs were fully compatible with the conventional manufacturing processes of conventional polyimide (PI) systems. As an example, the PEsI film obtained from the ester-linked TCDA (NAr = 8) and an ester-linked diamine achieved unprecedented outstanding dielectric properties without the support of fluorinated monomers, specifically an ultra-low dissipation factor (tan δ) of 0.00128 at a frequency of 10 GHz (50% RH and 23 °C), in addition to an extremely high glass transition temperature (Tg) of 365 °C, extremely low linear coefficient of thermal expansion (CTE) of 6.8 ppm K-1, suppressed water uptake (0.24%), requisite film ductility, and a low haze. Consequently, certain PEsI films developed in this study are promising candidates for heat-resistant dielectric substrates for use in 5G-compatible high-speed flexible printed circuit boards (FPCs). The chemical and physical factors denominating tan δ are also discussed.

Anisotropic thermal expansion and themomechanic properties of α-phase group-VA monolayers

The theoretical investigations of anisotropic thermal expansion are quite few as the huge computational cost. In this work, a scheme of Taylor expansion for phonon free energy is introduced to investigate anisotropic thermal expansion, which can save lots of computational cost. The anisotropic thermal expansion and thermomechanic properties of α-phase group-VA monolayers (α-P, α-As, α-Sb and α-Bi) are investigated systematically by using the first-principles calculations. It is found all the four monolayers show remarkably anisotropic thermal expansion, and very different from each other. In α-As and α-Bi monolayers, remarkable negative thermal expansion appears along armchair direction. From α-P to α-Bi monolayer, the absolute value of linear thermal expansion coefficient becomes larger. In particular the linear thermal expansion coefficient of α-Bi is in terms of order of magnitude close to 10−4 K−1 at 300 K. The macroscopic Grüneisen parameters and elastic constants are also investigated to unveil the underlying physical mechanisms.

Anorthite ceramics: grog and clay selection for lowering the sintering temperature

ABSTRACT A research investigation was conducted on two variables that are indicative of plastic raw materials based on kaolin vs. interstratified illite-smectite clay and a non-plastic admixture including grog (quartz vs. alumina) during the sintering process of an anorthite porcelain body beginning at 950°C, up to the sintering temperature. A correlation was found between the mineralogical composition and various parameters of the fired bodies. A purely anorthic sintered body can be produced using interstratified illite-smectite clay with quartz as a grog, which has the lowest coefficient of linear thermal expansion in the temperature range of 30°C to 700°C and highest bending strength – modulus of rupture of sintered body. When alumina is present in the raw material mixture, the coefficient of linear thermal expansion is lower due to the absence of the SiO2 phases. Quartz in combination with interstratified illite-smectite clay significantly reduces the sintering temperature through the formation of an amorphous melt up to the sintering temperature.

Isotropic negative thermal expansion in ZrW2O8 and HfW2O8 from 1100 to 1275°C

AbstractZrW2O8 (ZrO2•2WO3) and HfW2O8 (HfO2•2WO3) have been the focus of thermal expansion studies due to their isotropic negative thermal expansion (NTE) measured previously at temperatures below 775°C. This work presents measurements of these materials at their thermodynamically stable temperature ranges of 1105 and 1257°C for ZrW2O8 and 1105–1276°C for HfW2O8, where they were characterized with in situ, powder X‐ray diffraction. The linear coefficients of thermal expansion were measured to be −5.52 × 10−6 and −4.87 × 10−6°C−1 for ZrW2O8 and HfW2O8, respectively. The mechanism leading to this NTE is discussed. Powder samples were synthesized by a solution‐based process called the organic–inorganic steric entrapment method. In situ characterization in air was carried out at the National Synchrotron Light Source II using a hexapole lamp, optical furnace and the Advanced Photon Source using a quadrupole lamp, optical furnace to achieve elevated temperatures.

Thermomechanical Analysis and Numerical Simulations of Fused Filament Fabricated Polylactic Acid Parts

This work aimed to investigate the thermal deformation of polylactic acid (PLA) samples 3D-printed by Fused Filament Fabrication. The irreversible thermal strain (ITS) and coefficient of linear thermal expansion (CLTE) of four sets of samples with various sizes and thicknesses of the layer in the three directions of the measurements were investigated. The thermomechanical analysis (TMA) was used for the investigation of thermal deformation. During the study, the dependencies of deformation on temperature were obtained. The samples' CLTE values at various ranges of temperatures were estimated using the obtained dependencies. ITS was observed after heating to 80 ℃ during the first TMA cycle. The values reached 8 – 9 %. The impact of layer thickness and the number of layers in the sample on ITS was noticed. Shrinkage in the X direction and expansion in the Z direction with almost the same values were observed. Finite element code ANSYS was used to simulate the distribution of temperature and accumulation of residual thermal stresses in the printed part. The correlation was obtained between the level of simulated residual thermal stresses for samples with different number of layers and layer thicknesses and measured ITS after annealing.