Anisotropic Thermal Expansion Behavior Research Articles

Anisotropic thermal expansion based on a novel metamaterial

Metamaterials exhibiting exceptional thermoelastic properties are emerging as promising candidates for scientific and engineering applications. Previous studies on mechanical metamaterials with negative thermal expansion (NTE) have primarily focused on enhancing isotropic NTE, often resulting in a high coefficient of thermal expansion (CTE) but low stiffness that characterizes bending-dominated NTE metamaterials. In this study, we proposed a novel mechanical metamaterial with significant anisotropic thermal expansion behavior and substantial stiffness based on the cross structure, re-entrant structure, and triangular structure with NTE. The programmable CTE and effective elastic modulus were analytically derived using the unit load method and stiffness matrix method, respectively, which were validated by numerical results obtained from finite element analysis (FEA). Drawing inspiration from the body-centered cubic and face-centered cubic strategies, two types of extended three-dimensional metamaterials can be obtained. The results demonstrate that a larger length ratio λ and angle θ3 can enhance the NTE effect, while reducing the Young's modulus. The maximum magnitudes of NTE and positive thermal expansion (PTE) are achieved at approximately θ2 = 90°, resulting in a decreased stiffness and slight negative Poisson's ratio (NPR). By adjusting the angles θ2 of re-entrant structures, six distinct anisotropic thermal expansion behaviors can be obtained in this planar metamaterial. Furthermore, a wider range of isotropic CTE as well as an extended range of anisotropic CTE can be achieved in the present metamaterial compared to its original metamaterials. The proposed metamaterial can be combined with traditional triangle metamaterials to enhance thermoelastic properties. The analysis also provides valuable insights into designing metamaterials with large CTE, optimal stiffness, and lightweight properties simultaneously for engineering applications.

Fundamentally intertwined: anharmonic intermolecular interactions dictate both thermal expansion and terahertz lattice dynamics in molecular crystals.

We investigate the anisotropic thermal expansion behavior of a co-crystalline system composed of 4,4'-azopyridine and trimesic acid (TMA-azo). Using variable-temperature single-crystal X-ray diffraction (SC-XRD), low-frequency Raman spectroscopy, and terahertz time-domain spectroscopy (THz-TDS), we observe significant temperature-induced shifting and broadening of the vibrational absorption features, indicating changes in the intermolecular potential. Our findings reveal that thermal expansion is driven by anharmonic interactions and the potential energy topography, rather than increased molecular dynamics. Density functional theory (DFT) simulations support these results, highlighting significant softening of the potential energy surface (PES) with temperature. This comprehensive approach offers valuable insights into the relationship between structural dynamics and thermal properties, providing a robust framework for designing materials with tailored thermal expansion characteristics.

Thermal expansion behavior of vanadium pernitride, CuAl2-type VN2, synthesized under high pressures

CuAl2-type VN2, which is synthesized under high pressure, is a recoverable material at ambient conditions and has a high bulk modulus. In this study, we investigated the thermal expansion behavior of CuAl2-type VN2 by low-temperature X-ray diffraction measurements between 109.3(5) K and 298.3(8) K. The axial thermal expansion coefficient of VN2 was determined to be αa = 2.7(9) × 10−6 K−1 and αc = 17.8(12) × 10−6 K−1 at 298.3(8) K, which has large anisotropy similar to that of compression behavior. It is found that the small coefficient of thermal expansion of the a-axis is due to the negative and positive effects on the a-axis length with increasing temperature of the bond angles and bond lengths of VN2, respectively. As a result, VN2 exhibits very large anisotropic thermal expansion behavior.

Hydrogen-bonded nickel(II)-organosulfonate framework: Thermal expansion behavior, proton conduction, and magnetic properties

Metalo Hydrogen-bonded organic frameworks are emerging supramolecular platforms for designing functional molecular materials. Herein, we reported the supramolecular structure, thermal, magnetic, and proton conduction properties of a hydrogen-bonded nickel(II)-organosulfonate framework, [Ni(H2O)6][NPS]2 (NiHOF, HNPS = naphthalene-2-sulphonic acid). Single-crystal X-ray diffraction studies reveal a two-dimensional hydrogen-bonded network sustained by multiple and charge-assisted OH···O H bonds between hexaaquanickel(II) cations and organosulfonate anions. Additionally, continuous ca. 0.47 × 0.70 nm2 windows were formed within the framework. The thermal stability of the NiHOF was confirmed by thermal gravimetric analysis and variable temperature single-crystal and powder X-ray diffraction patterns. N2 sorption isotherms suggest an ultramicroporous supramolecular framework of NiHOF with permanent porosity. The anisotropic positive thermal expansion behavior of NiHOF was evidenced by the dynamic crystallography experiments. Magnetic measurements indicate easy-axis magnetic anisotropy (D = -10.5 cm−1) of the NiHOF while no slow magnetic relaxation behavior. Electrochemical impedance spectroscopy indicates the temperature and humidity dependence of conductivities of NiHOF. At 50 °C and 70% relative humidity, the conductivity is 1.13 × 10−4 S·cm−1, revealing a supramolecular proton conductor of NiHOF. This work provides a potential way for designing novel thermal, magnetic, and electrical molecular materials through the supramolecular assembly of inorganic and organosulfonate synthons.

Single Unit-Cell Layered Bi2 Fe4 O9 Nanosheets: Synthesis, Formation Mechanism, and Anisotropic Thermal Expansion.

As an important multiferroic material, pure and low-dimensional phase-stable bismuth ferrite has wide applications. Herein, one-pot hydrothermal method was used to synthesize bismuth ferrite. Almost pure Bi2 Fe4 O9 , BiFeO3 , and their mixture were successfully obtained by controlling the KOH concentration in the hydrothermal solutions. The as-prepared Bi2 Fe4 O9 products were crystalline with Pbam space group, had nanosheet morphology, and tended to aggregate into nanofloret or random stacking. Each Bi2 Fe4 O9 nanosheet was a single crystal with (001) plane as its exposed surface. Single unit-cell layered Bi2 Fe4 O9 nanosheets had a uniform thickness of 1 nm. The surface energies of various (100), (010), and (001) planes were 3.6-4.0, 5.6-15.1, and 1.7-3.0 J m-2 , respectively, in the Bi2 Fe4 O9 crystal. The formation mechanism and structural model of the as-prepared single unit-cell layered Bi2 Fe4 O9 nanosheets have been given. The growth of Bi2 Fe4 O9 nanosheets was discussed. Thermal analysis showed that the Bi2 Fe4 O9 phase was stable up to 1260 K. The thermal expansion behavior of the Bi2 Fe4 O9 nanosheet was nonlinear. The thermal expansion coefficients of the ultrathin Bi2 Fe4 O9 nanosheets on the a-, b-, c-axes, and on the unit-cell volume V were determined, showing an anisotropic thermal expansion behavior. This study is helpful for the controllable synthesis of ultrathin Bi2 Fe4 O9 nanosheets.

Influence of Ceramic Freeze-Casting Temperature on the Anisotropic Thermal Expansion Behavior of Corresponding Interpenetrating Metal/Ceramic Composites

Influence of Ceramic Freeze-Casting Temperature on the Anisotropic Thermal Expansion Behavior of Corresponding Interpenetrating Metal/Ceramic Composites

Negative Thermal Expansion of Undulating Coordination Layers through Interlayer Interaction

The negative thermal expansion (NTE) of solid-state materials is of significance in various fields, but a very rare phenomenon. In this study, we carried out a meta-analysis for the anisotropic thermal expansion behavior of fifteen two-dimensional coordination polymers [M(salen)]2[M'(CN)4(solvent)] (M = Mn, Fe; M' = MnN, ReN, Pt, Pt(I2)x; x = 0.18, 0.45, 0.85, 1.0; solvent = H2O, MeOH, MeCN) with a newly synthesized [Fe(salen)]2[MnN(CN)4(MeCN)]. Consequently, we successfully demonstrate the unusual NTE of the undulating coordination layers by an expansion deformation of the layers via strong interlayer interaction within the layer stacking. Notably, the layer volume of [Mn(salen)]2[ReN(CN)4] with its powder form decreases with a large NTE coefficient, αlayer-volume = -27 × 10-6 K-1 (100-500 K). This is a significantly large value despite the increase in layer thickness along the layer contraction based on the anisotropic transformation of undulating layers. Conversely, the analysis demonstrates that the chemical modification of the layers to enhance intralayer interaction rather than interlayer interaction switches a direction of the layer anisotropy, yielding positive thermal expansion materials with the coefficient of the layer volume reaching +92 × 10-6 K-1.

Study on the anomalous thermal expansion behavior of cold-rolled Ti-34 Nb alloy and its novel tailoring strategy

In this study, we have investigated the anisotropic in-plane thermal expansion behavior of cold-rolled (CR) Ti-34 Nb alloy and its relationship with temperature by means of continuous heating and cyclic heating-cooling thermal expansion measurement methods. A new microscopic model including the morphology of β and martensite (α″) phases, cold rolled textures and α″ content is proposed, which successfully explains the mechanism of anomalous positive thermal expansion of transverse direction (TD) and negative thermal expansion of rolling direction (RD). It is found that the coefficient of thermal expansion (CTE) of CR-Ti-34 Nb alloy is controlled by α″ content. The instantaneous CTEs of TD and RD (absolute value) both increase first and then decrease (nonlinearity) within the temperature range of anomalous thermal expansion, which is attributed to the increase of α″→β transformation rate (temperature increases by 1 °C) with increasing temperature and the significant decomposition of α″ phase above 260 °C. Moreover, we have excluded the influence of the anisotropy of α″ and internal stress on CTE. According to the abovementioned findings, α″ content is adjusted by pre-aging treatment for the first time, and a wide range of CTEs (−33.0 × 10−6 k−1 ~ 0.4 × 10−6 k−1) are obtained in CR-Ti-34 Nb alloy, including a variety of low (−6.3 × 10−6 k−1, −3.3 × 10−6 k−1) and zero (−1.5 × 10−6 k−1, −0.9 × 10−6 k−1, 0.4 × 10−6 k−1) CTEs with a wide temperature window of 275 °C (25 °C ~ 300 °C).

Lattice dynamics and negative thermal expansion in layered mercury-based halides

Materials with negative thermal expansion are beneficial as they can be appropriately tuned to be compatible for device engineering. Here, we report our first-principles investigation on Hg2X2 and HgX2 (X= Cl, I), which exhibits negative thermal expansion behaviour along c-direction. The first-principles studies reveal an anisotropic thermal expansion behaviour in the investigated compounds over a broad range of temperature. The computed coefficients along the c-axis are found to be negative for Hg2Cl2 and HgCl2. Hg2I2 exhibits negative thermal expansion behaviour up to 100 K, while HgI2 exhibits positive thermal expansion, whose values are qualitatively in good accord with the experimentally reported ones. The Grüneisen parameters along with elastic compliance matrix are used to calculate the thermal expansion coefficients of these materials. A detailed study of vibrational spectra was also done to get a better understanding of thermal expansion.

Crystallography relevant to Mars and Galilean icy moons: crystal behavior of kieserite-type monohydrate sulfates at extraterrestrial conditions down to 15 K.

Monohydrate sulfate kieserites (M 2+SO4·H2O) and their solid solutions are essential constituents on the surface of Mars and most likely also on Galilean icy moons in our solar system. Phase stabilities of end-member representatives (M 2+ = Mg, Fe, Co, Ni) have been examined crystallographically using single-crystal X-ray diffraction at 1 bar and temperatures down to 15 K, by means of applying open He cryojet techniques at in-house laboratory instrumentation. All four representative phases show a comparable, highly anisotropic thermal expansion behavior with a remarkable negative thermal expansion along the monoclinic b axis and a pronounced anisotropic expansion perpendicular to it. The lattice changes down to 15 K correspond to an 'inverse thermal pressure' of approximately 0.7 GPa, which is far below the critical pressures of transition under hydro-static compression (Pc ≥ 2.40 GPa). Consequently, no equivalent structural phase transition was observed for any compound, and neither dehydration nor rearrangements of the hydrogen bonding schemes have been observed. The M 2+SO4·H2O (M 2+ = Mg, Fe, Co, Ni) end-member phases preserve the kieserite-type C2/c symmetry; hydrogen bonds and other structural details were found to vary smoothly down to the lowest experimental temperature. These findings serve as an important basis for the assignment of sulfate-related signals in remote-sensing data obtained from orbiters at celestial bodies, as well as for thermodynamic considerations and modeling of properties of kieserite-type sulfate monohydrates relevant to extraterrestrial sulfate associations at very low temperatures.

The role of thermodynamically stable configuration in enhancing crystallographic diffraction quality of flexible MOFs

SummarySingle-crystal X-ray diffraction (SCXRD) is a widely used method for structural characterization. Generally, low temperature is of great significance for improving the crystallographic diffraction quality. Herein we observe that this practice is not always effective for flexible metal-organic frameworks (f-MOFs). An abnormal crystallography, that is, more diffraction spots at a high angle and better resolution of diffraction data as the temperature increases in the f-MOF (1-g), is observed. XRD results reveal that 1-g has a reversible anisotropic thermal expansion behavior with a record-high c-axial positive expansion coefficient of 1,401.8 × 10−6 K−1. Calculation results indicate that the framework of 1-g has a more stable thermodynamic configuration as the temperature increases. Such configuration has lower-frequency vibration and may play a key role in promoting higher Bragg diffraction quality at room temperature. This work is of great significance for how to obtain high-quality SCXRD diffraction data.

Node Distortion Modulation for Anisotropic Thermal Expansions of Two‐dimensional Coordination Polymers

AbstractAnisotropic negative thermal expansion is a valuable property of solid‐state materials, influencing their micromechanical and functional response. Two flexible two‐dimensional (2D) cyanide‐bridged coordination polymers (CPs) of type [Fe(salen)]2[M(CN)4] (M=MnN (FeMnN) and Pt (FePt)) were synthesized. Their anisotropic negative thermal expansions was strongly linked to relaxations of node distortions in [Fe(salen)]+ units. Comparison with the [Mn(salen)]+ analogues indicated shorter bond lengths around iron(III), due to the different electronic states. These changes of node structures resulted in FeMnN and FePt exhibiting lower and higher degrees of anisotropic thermal expansion behavior, respectively, than their Mn analogues.

Spin–phonon coupling and thermodynamic behaviour in YCrO3 and LaCrO3: inelastic neutron scattering and lattice dynamics

We report detailed temperature-dependent inelastic neutron scattering and ab initio lattice dynamics investigation of magnetic perovskites YCrO3 and LaCrO3. The magnetic neutron scattering from the Cr ions exhibits significant changes with temperature and dominates at low momentum transfer regime. Ab initio calculations performed including magnetic interactions show that the effect of magnetic interactions is very significant on the low- as well as high-energy phonon modes. We have also shown that the inelastic neutron spectrum of YCrO3 mimics the magnon spectrum from a G-type antiferromagnetic system, which is consistent with previously reported magnetic structure in the compound. The pressure-dependent ab initio lattice dynamics calculations are used to calculate the anisotropic thermal expansion behaviour in orthorhombic YCrO3, which is in excellent agreement with the available experimental data in the paramagnetic phase. We identify that the low energy anharmonic phonon modes involving Y vibrations contribute maximum to the thermal expansion behaviour.

Phonons and anisotropic thermal expansion behavior of NiX (X = S, Se, Te)

Metal chalcogenides have been known for their important technological applications and have attracted continuous interest for their structural, electronic, thermal, and transport properties. Here, we present first-principles calculations of the vibrational and thermodynamic properties of NiX (X = S, Se, Te) compounds along with inelastic neutron scattering measurements of the phonon spectrum in NiSe. The measured phonon spectrum is in very good agreement with the computed result. We also report the measurement of thermal expansion behavior of NiSe using X-ray diffraction from 13 K to 300 K. The change in the hexagonal c lattice parameter in NiSe is considerably greater as compared to that in the a-parameter. The ab initio calculated anisotropic Grüneisen parameters of the different phonon modes in all the chalcogenides along with the elastic constants are used to compute anisotropic thermal expansion behavior, which is found in good agreement with experiments. The displacement pattern of phonons indicates that the difference in the amplitudes of Ni and X atoms follows the anisotropy of thermal expansion behavior along c- and a-axes.

In-situ high-temperature X-ray diffraction investigations of magnetron sputtered niobium oxide layers up to 900 °C

Niobium oxide layers with a thickness in the range of 1.0–1.4 μm were deposited on silicon single crystal wafers by magnetron sputtering using substoichiometric niobium oxide target materials. After the deposition process, the layer material was completely amorphous. The primary crystallization of the hexagonal Nb2O5 phase and the subsequent transformation to the orthorhombic phase were investigated by means of in-situ high-temperature X-ray diffraction up to a temperature of 900 °C under a reducing N2/H2 atmosphere. The precise determination of the cell parameters by Rietveld refinement enabled the determination of the anisotropic thermal expansion behavior of the crystalline Nb2O5 phase. Besides, an activation energy of the primary crystallization reaction of +460(50) kJ/mol was quantitatively determined by isothermal in-situ experiments in the temperature range of 505–545 °C.

Anisotropic Near-Zero Thermal Expansion in REAg xGa4- x ( RE = La-Nd, Sm, Eu, and Yb) Induced by Structural Reorganization.

In this work, we have discovered the anisotropic near-zero thermal expansion (NZTE) behavior in a family of compounds REAg xGa4- x ( RE = La-Nd, Sm, Eu, and Yb). The compounds adopt the CeAl2Ga2 structure type and were obtained as single crystals in high yield by metal flux growth technique using gallium as active flux. Temperature-dependent single crystal X-ray diffraction suggests that all the compounds exhibit near zero thermal expansion along c direction in the temperature range of 100-450 K. Temperature-dependent X-ray absorption near-edge spectroscopic study confirmed ZTE behavior is due to the geometrical features associated within the crystal structure. The anisotropic NZTE behavior was further established by anisotropic magnetic measurements on selected single crystals. The atomic displacement parameters, apparent bond lengths, bond angles, and structural distortion with respect to the temperature reveal that geometric features associated with the structural distortion cause the anisotropic NZTE along c-direction. The preliminary magnetic studies suggest all the compounds are paramagnetic at room temperature except LaAgGa3. Electrical resistivity study reveals that compounds from this series are metallic in nature.

Anisotropic Negative Thermal Expansion Behavior of the As-Fabricated Ti-Rich and Equiatomic Ti–Ni Alloys Induced by Preferential Grain Orientation

The present study focuses on the anisotropic negative thermal expansion (NTE) behaviors of Ti-rich (Ti54Ni46) and equiatomic Ti–Ni (Ti50Ni50) alloys fabricated by vacuum arc melting and without subsequent plastic deformation. Both alloys exhibit NTE responses in vertical and horizontal directions, and the total strains and CTEs of the NTE stage along the two mutually perpendicular measuring directions are obviously different, indicating obvious anisotropic NTE behavior of the alloys. Besides, the numerical differences between the starting temperature of NTE and austenitic transformation and between the finishing temperature of NTE and austenitic transformation are very small, which indicates that an apparent relationship exists between the NTE behavior and the phase transformation. The microstructure in the vertical cross sections shows obviously preferential orientation characteristics: Ti2Ni phases of both alloys grow along the vertical direction, and B19′ martensite of Ti50Ni50 alloy has distinct preferential orientation, which results from a large temperature gradient between the top and the bottom of the button ingots during solidification. The microstructure with preferential orientation induces the anisotropic NTE behavior of the samples.

Preparation and Anisotropic Lattice Thermal Expansion of Hexagonal Cordierite

The hexagonal cordierite was synthesized by the reverse coprecipitation-calcination method and characterized by powder X-ray diffraction. The lattice thermal expansion behavior of hexagonal cordierite was investigated by high temperature X-ray diffraction in the temperature range 298-1273 K. The lattice parameters of the hexagonal cordierite at different temperature were calculated by a least squares method. The hexagonal cordierite expressed anisotropic thermal expansion behavior with the average lattice thermal expansion coefficient were 2.13×10-6 K-1 along a or b axis and-1.03×10-6 K-1 along c axis from room temperature to 1273 K. The crystal structure of hexagonal cordierite at 298 K and 1273 K were refined by Rietveld method. The thermal expansion coefficient of the height of the [MgO6]-[AlO4] polyhedral layer is-1.8×10-6 K-1. Although the six-member ring expressed the normal positive thermal expansion along arbitrary direction, the height thermal expansion coefficient of the six-member ring is just 0.6×10-6 K-1.

Thermal Expansion of Sintered Glass Ceramics in the System BaO-SrO-ZnO-SiO2 and Its Dependence on Particle Size.

The thermal expansion behavior of sintered glass-ceramics containing high concentrations of Ba1-xSrxZn2Si2O7, a phase with very low and highly anisotropic thermal expansion behavior, was investigated. The observed phase has the crystal structure of the high-temperature phase of BaZn2Si2O7, which can be stabilized by the introduction of Sr(2+) into this phase. The high anisotropy leads to microcracking within the volume of the samples, which strongly affects the dilatometric thermal expansion. However, these cracks also have an influence on the nominal thermal expansion of the as-mentioned phase, which decreases if the cracks appear. Below a grain size of approximately 80 μm, the sintered glass-ceramics have almost no cracks and show positive thermal expansion. Hence, coefficients of thermal expansion between -5.6 and 6.5 × 10(-6) K(-1) were measured. In addition to dilatometric studies, the effect of the microstructure on the thermal expansion was also measured using in situ X-ray diffraction at temperatures up to 1000 °C.

Effect of sintering technology in β-eucryptite ceramics: Influence on fatigue life and effect of microcracks

β-eucryptite ceramics with low negative or near-zero coefficient of thermal expansion (CTE) with excellent mechanical properties, such as Young's modulus ≥100GPa, have attracted attention for many important industrial applications. The extremely anisotropic thermal expansion behavior of this material leads to thermal residual stresses, and causes spontaneous microcracking. These microcracks cause large negative CTE with mechanical weaknesses. The appearance of microcracks is due to different factors. The most important are prolonged sintering time and heating source used.The present work shows experimentally the evolution of grain microcracks and residual stresses of the sintered β-eucryptite material going through many thermal fatigue cycles (∼3600). The effect of stresses applied on β-eucryptite crystals due to the thermal cycling could be considered for explaining the small change observed of β-eucryptite to β-spodumene phase, which is higher in the samples obtained by microwave sintering. Therefore, the study of residual stresses has suggested that the heating source employed, such as conventional or microwave, has a great influence on thermal fatigue life and the final mechanical and thermal properties. The microwave heating has a significant impact on β-eucryptite materials lifetime.