Large Thermal Expansion Coefficient Research Articles

Compensation of temperature effects on imaging quality of thermal imaging objectives using deep learning techniques

Thermal imaging objectives are made from infrared materials with large thermal expansion coefficients, such as Ge, Si, and ZnSe. When the temperature changes, it leads to variations in the refractive index, curvature radius, and thickness of the lens, causing defocus shifts that degrade the image quality of the thermal imaging system. In this paper, we propose a novel method to compensate for the effects of temperature variations on the quality of thermal imaging objectives by using deep learning techniques. The temperature variations are measured using a thermal sensor. Subsequently, a U-Net network is employed to mitigate the impact of temperature on the imaging quality of the thermal imaging objectives without requiring any optical displacement or replacement of the lens. Simulation results show that the proposed method performs the effectively compensation for the influence of temperature changes on thermal imaging objective over a wide temperature range from -5 °C to 50 °C.

Assessment of the Risk of Crack Formation at a Hybrid Bonding Interface Using Numerical Analysis.

Hybrid bonding technology has recently emerged as a promising solution for advanced semiconductor packaging technologies. However, several reliability issues still pose challenges for commercialization. In this study, we investigated the possibility of crack formation caused by chemical mechanical polishing (CMP) defects and the misalignment of the hybrid bonding structure. Crack formation and thermomechanical stress were analyzed for two common hybrid bonding structures with misalignment using a numerical simulation. The effects of annealing temperature and dishing value on changes in the non-bonding area and peeling stress were systematically analyzed. The calculated peeling stresses were compared to the bonding strength of each bonding interface to find vulnerable regions prone to cracking. The non-bonding area in the bonding structure increased with a decreasing annealing temperature and an increasing dishing value. To achieve a sufficient bonding area of more than 90%, the annealing temperature should be greater than 200 °C. During the heating period of the annealing process, the SiCN-to-SiCN bonding interface was the most vulnerable cracking site with the highest peeling stress. An annealing temperature of 350 °C carries a significant risk of cracking. On the other hand, an annealing temperature lower than 250 °C will minimize the chance of cracking. The SiCN-to-SiO2 bonding interface, which has the lowest adhesion energy and a large coefficient of thermal expansion (CTE) mismatch, was expected to be another possible cracking site. During cooling, the SiCN-to-Cu bonding interface was the most vulnerable site with the highest stress. However, the simulated peeling stresses were lower than the adhesion strength of the bonded interface, indicating that the chance of cracking during the cooling process was very low. This study provides insights into minimizing the non-bonding area and preventing crack formation, thereby enhancing the reliability of hybrid bonding structures.

Internal radiation effect on semiconductor β-Ga2O3 crystals grown by the VB Method and anisotropic thermal stress

Gallium oxide crystals are semitransparent semiconductors with good optical and electrical properties, which allow their use for several technological applications. During the growth process of β-Ga2O3 crystals, internal radiation plays a crucial role that affects the growth process and then the crystal quality. In this work, the effect of the melt and the crystal transparency on the vertical Bridgman growth of β-Ga2O3 oxide is thoroughly studied. Using a global 2D/3D finite element model, temperature, melt flow, melt-crystal interface, and three-dimensional anisotropic thermal stress are computed at different growth stages. At each stage, four cases are considered, namely, opaque melt and crystal, semi-transparent melt and opaque crystal, semitransparent crystal and opaque melt, and finally semitransparent melt and crystal. The role of internal radiation in each case at different growth stages is then highlighted separately and then coupled together. It was found that the melt-crystal interface is shifted from a convex shape at the early stage to a nearly plane and then to a concave shape at the last stage. The melt flow is then changed from two rolls pattern at the beginning to a single-roll structure at the last stage. Thermal stress of the as-grown ingot is decreased during the growth due to the decrease of temperature non-linearities. Internal radiation inside the crystal acts to increase the melt-crystal interface convexity at the early and middle stages of the growth process and leads to a decrease in its concavity at the final stage. However, the melt transparency leads to the opposite effects, i.e., it decreases the interface convexity at the early stage and increases the interface concavity at the final stage. As a result, for semitransparent crystal and melt, the interface is between the two previous cases. The calculated thermal stresses are found to be more affected by the transparency of the crystal than the melt as the absorption coefficient of β-Ga2O3 crystal is smaller than that of the melt. At all stages, the thermal stresses are found to be larger for the opaque case due to the increase of temperature non-linearities in the crystal. Large values are found at the bottom and the lower part of the periphery. Furthermore, internal radiation inside the melt plays a major role during the early growth stage due to the large liquid volume. It reduces the melt flow intensity close to the free surface where the shear stress is combined with the buoyant force and leads to the flattening of the interface decreasing then the radial temperature gradients, which leads to small attenuation of the thermal stress. At the final stage, the transparency of the melt plays the opposite role due to the increase of the interface concavity which leads to an increase in both of the temperature gradients and the thermal stress inside the crystal. Due to the crystal anisotropy, and especially to the large thermal expansion coefficient in the [010] direction, the 3D thermal stress values are found to be larger in this direction, especially in the bottom part of the ingot. Comparisons with available experimental and numerical works are provided in this paper.

Thermal expansion in Prussian Blue analogs M3[Cr(CN)6]2.nH2O (M = Mn, Fe, Co, Ni)

Thermal expansion in Prussian Blue Analogs (PBAs) M3[Cr(CN)6]2.nH2O (M = Mn, Fe, Co, Ni; n = 10–16) was studied using powder X-ray diffraction (XRD) as a function of temperature in the range 123–298 K. Standard chemical precipitation was used to prepare the materials and they were characterized using standard characterization techniques XRD, X-ray fluorescence (XRF), thermogravimetric analysis (TGA) and Fourier transform infrared (FTIR) spectroscopy. All materials were found to crystallize in the cubic structure with space group Fm3‾m. Strong compositional dependence of thermal expansion is found in this series of PBAs. While Mn3[Cr(CN)6]2.12H2O and Ni3[Cr(CN)6]2.16H2O show positive thermal expansion (PTE) behavior the other two PBAs, Fe3[Cr(CN)6]2.10H2O and Co3[Cr(CN)6]2.14H2O, show strong negative thermal expansion (NTE) behavior with as large coefficient of thermal expansion (CTE) as −19.7 x 10−6 K−1 (for M = Fe) in the temperature range 123–223 K. For the PBAs showing NTE, the magnitude of NTE coefficients can be correlated with the trends for M cation size and cell (or lattice) parameter.

Investigation of the effects of rare earth element doping on the thermophysical properties of Gd2Zr2O7 by first principles

Gd2Zr2O7 is one of the most promising new generation of ceramic materials for high temperature thermal barrier coatings. However, it still has great potential of improving thermal and mechanical properties and contributing tobetter thermal cycling performance of the coating. Doping rare earth elements in Gd2Zr2O7 is an effective method to enhance its thermal and mechanical properties. In this paper, the first principles is used to calculate the thermophysical properties of doped Gd2Zr2O7 with 16 rare earth elements, including modulus of elasticity, Debye temperature, minimum high-temperature thermal conductivity, high temperature thermal expansion coefficient, and fracture toughness, by which all doped Gd2Zr2O7 ceramics were ranked using the entropy method. The results show that doping with Pr, Sm, Yb, and Nd showed superior comprehensive performance. Specially, (Gd0.875Pr0.125)2Zr2O7 has the lowest Young's modulus of 244 MPa, Pugh ratio of 0.53, Debye temperature of 523.4 K, thermal conductivity of 1.27 W/(m·K), and the largest coefficient of thermal expansion of 9.19 × 10−6 K−1, and (Gd0.875Ho0.125)2Zr2O7 has the highest fracture toughness of 2.21 MPa·m1/2.

Recent Progress in Modification of Polyphenylene Oxide for Application in High-Frequency Communication.

With the rapid development of highly integrated electronic devices and high-frequency microwave communication technology, the parasitic resistance-capacitance (RC) delay and propagation loss severely restrict the development of a high-frequency communication system. Benefiting from its low dielectric constants (Dk) and low dielectric loss factor (Df), polyphenylene oxide (PPO) has attracted widespread attention for its application in the dielectric layers of integrated circuits. However, PPO suffers from a very high melting viscosity, a larger coefficient of thermal expansion than copper wire and poor solvent resistance. Recently, many efforts have focused on the modification of PPO by various means for communication applications. However, review articles focusing on PPO are unexpectedly limited. In this article, the research progress concerning PPO materials in view of the modification of PPO has been summarized. The following aspects are covered: polymerization and design of special chemical structure, low molecular weight PPO and blending with thermosetting resin, hyperbranched PPO, thermosetting PPO and incorporating with fillers. In addition, the advantages and disadvantages of various types of modification methods and their applications are compared, and the possible future development directions are also proposed. It is believed that this review will arouse the interest of the electronics industry because of the detailed summary of the cutting-edge modification technology for PPO.

Giant electrostriction-like response from defective non-ferroelectric epitaxial BaTiO3 integrated on Si (100)

Lead-free, silicon compatible materials showing large electromechanical responses comparable to, or better than conventional relaxor ferroelectrics, are desirable for various nanoelectromechanical devices and applications. Defect-engineered electrostriction has recently been gaining popularity to obtain enhanced electromechanical responses at sub 100 Hz frequencies. Here, we report record values of electrostrictive strain coefficients (M31) at frequencies as large as 5 kHz (1.04×10−14 m2/V2 at 1 kHz, and 3.87×10−15 m2/V2 at 5 kHz) using A-site and oxygen-deficient barium titanate thin-films, epitaxially integrated onto Si. The effect is robust and retained upon cycling upto 6 million times. Our perovskite films are non-ferroelectric, exhibit a different symmetry compared to stoichiometric BaTiO3 and are characterized by twin boundaries and nano polar-like regions. We show that the dielectric relaxation arising from the defect-induced features correlates well with the observed giant electrostriction-like response. These films show large coefficient of thermal expansion (2.36 × 10−5/K), which along with the giant M31 implies a considerable increase in the lattice anharmonicity induced by the defects. Our work provides a crucial step forward towards formulating guidelines to engineer large electromechanical responses even at higher frequencies in lead-free thin films.

Biosynthesized CuO nanoparticles–coated grating sensors for temperature measurement

In this study, we demonstrate temperature sensing using a fiber Bragg grating (FBG) fixed on a Teflon substrate with a large thermal expansion coefficient. A significant enhancement in sensitivity was achieved by coating the fiber with green synthesized copper oxide nanoparticles. This improvement was characterized by UV–visible spectroscopy, scanning electron microscopy, differential scanning calorimetry, and other techniques. The behavior of the coated materials is unique in their response to thermal stability based on the mode of coating. We have examined the thermal responses of FBG sensors mounted on temperature units on and after coating. The designed sensor is compact, cost effective, and measures temperatures in the range of 25 °C–200 °C. It demonstrated a linear relationship between the wavelength shift and temperature change along with 0.59 pm/ oC enhancement in the sensitivity. However, by optimizing the materials and physical dimensions of FBG, it is possible to increase the range of temperature detection, thereby improving the sensor’s performance. It is observed that the sensitivity of the nanoparticles-coated FBG is better than that of the bare FBG for all temperature ranges.

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.

Crack-free tungsten coating on ODS plate via a modified laser-based additive technique: Offset laser cladding

A modified laser-based additive manufacturing technique, offset laser cladding was introduced to achieve dense tungsten coating on an oxide dispersion-strengthened (ODS) substrate as a plasma facing material (PFM). Different from ordinary direct energy deposition (DED) which leads to incomplete melting of tungsten and excessive melting of ODS substrate, the offset laser cladding technique can achieve complete melting of tungsten while substrate melting is suppressed. Experimental conditions (i.e., laser power, scanning speed, powder size, offset distance and injection powder nozzle setting) were carefully calculated using two validated simulation models to minimize the consumption of valuable experimental resources. Tungsten coating using the offset laser cladding in an open chamber condition showed that dense coating was achieved with a pore size of 1–2 μm. The result is comparable to that of vacuum plasma spray (VPS) tungsten coating which requires a high-level vacuum chamber. A thin interface layer (2–5 μm) was formed between the tungsten coating and ODS substrate that can alleviate thermal damage due to a large thermal expansion coefficient difference. While a small amount of surface melting was involved, the microhardness test revealed that the ODS substrate was insignificantly affected by laser heating during the offset laser cladding.

Effective Strategies for Electron Beam Additive Manufacturing of Graded Metal Interfaces between Stainless Steel and Vanadium

This work examines the feasibility of joining two dissimilar metals, vanadium (V) and wrought Nitronic 40 stainless steel, through electron beam additive manufacturing (EBAM). Depositing V on Nitronic 40 led to mixed results with some builds exhibiting microcracking and other builds exhibiting severe cracking resulting in delamination. These build failures are thought to be caused by a large coefficient of thermal expansion (CTE) mismatch and solubility issues, demonstrating the challenges associated with this material combination. The large melting temperature discrepancy between Nitronic 40 and V was thought to exacerbate the issues with CTE mismatch and solubility. Four strategies could be employed by EBAM to mitigate the observed issues to successfully deposit V on Nitronic 40: (1) adjust wire feed speed, (2) use dual wire feeders, (3) use different wire feedstocks to control composition, and (4) create a transition layer known as buttering to accommodate CTE mismatch.

Phase evolution, thermophysical and mechanical properties of high-entropy (Ce0.2Nd0.2Sm0.2Eu0.2Yb0.2)2Zr2O7 ceramic for advanced thermal barrier coatings

Single-phase high-entropy rare-earth zirconate (Ce0.2Nd0.2Sm0.2Eu0.2Yb0.2)2Zr2O7 with large thermal expansion coefficient (11.69 ×10−6 K−1, 25–1500 °C), low thermal conductivity (1.07 W m−1 K−1, 1500 °C), and high fracture toughness (1.84 ± 0.03 MPa m1/2, 25 °C) was successfully synthesized using reverse coprecipitation and high-temperature calcination. The underlying mechanism governing the observed results was analyzed by considering the ionic bond strength, crystal lattice energy, and bond length. X-ray diffraction and Raman spectroscopy results demonstrated that the pyrochlore structured sample has excellent high-temperature phase stability. Moreover, after being heated at 1600 °C for 10–30 h, the average grain size of this sample only increases from 0.95 µm to 1.47 µm, indicating a sluggish grain growth rate. The outstanding combination of thermophysical and mechanical properties of the (Ce0.2Nd0.2Sm0.2Eu0.2Yb0.2)2Zr2O7 emphasizes its enormous potential for next-generation thermal barrier coating applications.

PDMS-filled micro-spring Fabry-Perot cavity for temperature sensing.

A highly sensitive fiber-tipped temperature sensor based on polydimethylsiloxane (PDMS)-filled spring Fabry-Perot (FP) cavity has been proposed and experimentally demonstrated. The spring FP cavity is first fabricated on the fiber endface by the two-photon polymerization lithography. After that, PDMS is filled into the cavity to drive the elongation of the flexible spring and thus to functionalize high-performance temperature sensing. Benefiting from the large thermal expansion coefficient of PDMS, the proposed sensor exhibits a maximal temperature sensitivity of 704.3 pm/°C with excellent operating repeatability and stability. Besides, by selecting a proper spring constant k, the FP sensitivity can be precisely adjusted in the range of 100-700 pm/°C. Thanks to the advantages of high fabrication accuracy and designable property, the proposed sensor could promote numerous usages for customizable temperature sensing.

Exploring the negative thermal expansion and magnetocaloric effect in Fe2(Hf,Ti) Laves phase materials

The transition-metal based Laves phase materials represent an extended family of alloys with rich and fascinating physical properties. In this work, we have investigated the negative thermal expansion and magnetocaloric effect in arc-melted and melt-spun Fe2Hf1-xTix (x = 0.15, 0.27, 0.30, 0.33, 0.36, 0.40) alloys. For x = 0.30–0.40, two hexagonal phases with different compositions share the same P63/mmc lattice symmetry, but have slightly different lattice parameters. The saturation magnetization and Curie temperature both follow a decreasing trend with the average unit-cell volume. For Fe2Hf0.6Ti0.4 melt spinning improves the saturation magnetization from 48.7 to 59.6 Am2/kg and the magnetic entropy change from 0.46 to 0.54 J/kgK at a magnetic field change of 2 T. These enhanced values are attributed to an improved homogeneity caused by a suppression of phase segregation during rapid solidification. We have utilized neutron powder diffraction and Mössbauer spectroscopy to illustrate the correlation between the magnetic order and the negative thermal expansion in single-phase Fe2Hf0.85Ti0.15. The magnetic moments of Fe align below 400 K in the a-b plane and a moment change for the Fe atoms is responsible for the large volumetric coefficient of thermal expansion of −25 × 10−6 K−1 over a wide temperature range of 300–400 K.

Bioorthogonal Glycoengineering-Mediated Multifunctional Liquid Metal Nanoprobes for Highly Efficient Photoacoustic Imaging-Guided Photothermal/Chemotherapy of Tumor.

The development of a multifunctional cancer diagnosis and treatment platform offers excellent prospects for the effective eradication of malignant solid tumors. Herein, a doxorubicin hydrochloride (DOX)-loaded tannic acid (TA)-coated liquid metal (LM) multifunctional nanoprobe was synthesized and applied as a highly efficient platform for the photoacoustic (PA) imaging-guided photothermal/chemotherapy of tumor. The multifunctional nanoprobes exhibited strong near-infrared absorption, a remarkable photothermal conversion efficiency (PCE) of 55%, and high DOX loading capacity. Combined with the large intrinsic thermal expansion coefficient of LM, highly efficient PA imaging and effective drug release were realized. The LM-based multifunctional nanoprobes were specifically adsorbed into the cancer cells and tumor tissues via glycoengineering biorthogonal chemistry. The in vitro and in vivo photothermal/chemo-anticancer activity confirmed their promising potential in cancer treatment. The subcutaneous breast tumor-bearing mice completely recovered in 5 days under light illumination with clear PA imaging presentation, which showed better antitumor outcomes than single-mode chemotherapy or photothermal therapy (PTT), while keeping side effects at a minimum. Such an LM-based PA imaging-guided photothermal/chemotherapy strategy provided a valuable platform for resistant cancer precise treatment and intelligent biomedicine.

Improving Electrocatalytic Activity of Cobalt-Free Barium Ferrite-Based Perovskite Oxygen Electrodes for Proton-Conducting Solid Oxide Cells via Introducing A-Site Deficiency

Proton-conducting solid oxide cells are regarded as promising solid-state energy conversion devices to realize the high-efficiency conversion between electrical energy and chemical energy. However, the high cost, easily reducible ion characteristics, and large thermal expansion coefficient related to the valence state of the traditional high-catalytic cobalt-based oxygen electrode are unavoidable problems. Cobalt-free barium ferrite-based oxides with triple-conducting properties are considered the most promising prospective candidates for highly active oxygen electrode materials because of the increased electrochemical reaction active sites, excellent thermal stability, and low thermal expansion coefficient. In this work, by introducing 5% A-site deficiency at the atomic scale, the oxygen vacancy concentration is increased so that the catalytic reaction kinetics and proton-conduction ability of ABO3-type perovskite oxygen electrode material BaFe0.5Sn0.2Bi0.3O3−δ are improved. The effects of non-stoichiometry on the phase composition, microstructure, hydration capacity, thermal expansion characteristics, conductivity, and chemical stability are investigated. In both fuel cell and electrolysis cell operation modes, the proton-conducting solid oxide cells with the A-site-deficient Ba0.95Fe0.5Sn0.2Bi0.3O3−δ oxygen electrode demonstrate excellent electrochemical performance, giving a peak power density of 0.69 W cm–2 (increased by 19.0%) and an electrolysis current density of 1.64 A cm–2 (increased by 30.2%) at 700 °C. Moreover, even at 600 °C with 50% high steam partial pressure, electrolysis for hydrogen production is maintained for about 100 h without significant attenuation, confirming the vital role of A-site defect engineering in the design of advanced oxygen electrode materials.

Magnetoelastic transition and negative thermal expansion of Fe2Hf0.83Ta0.17 ribbons

In this work, the magnetocaloric effect and negative thermal expansion in melt-spun Fe2Hf0.83Ta0.17 Laves phase alloys were studied. Compared to arc-melted alloys, which undergo a first-order magnetoelastic transition from the ferromagnetic to the antiferromagnetic phase, melt-spun alloys exhibit a second-order transition. For Fe2Hf0.83Ta0.17 ribbons, we observed a large volumetric coefficient of negative thermal expansion of −19 × 10−6 K−1 over a wide temperature range of 197 – 297 K and a moderate adiabatic temperature change of 0.7 K at 290 K for a magnetic field change of 1.5 T. The magnetic field dependence of the transition temperature (dTt/dµ0H = 4.4 K/T) for the melt-spun alloy is about half that of the arc-melted alloy (8.6 K/T). The origin of second-order phase transition of the melt-spun alloy is attributed to the partially suppressed frustration effect, which is due to the atomic disorder introduced by the rapid solidification.

Modular Design of a Polymer-Bilayer-Based Mechanically Compliant Worm-Like Robot.

Soft earthworm-like robots that exhibit mechanical compliance can, in principle, navigate through uneven terrains and constricted spaces that are inaccessible to traditional legged and wheeled robots. However, unlike the biological originals thatthey mimic, most of the worm-like robots reported to date contain rigid components that limit their compliance, such as electromotors or pressure-driven actuation systems. Here, a mechanically compliant worm-like robot with a fully modular body that is based on soft polymers is reported. The robot is composed of strategically assembled, electrothermally activated polymer bilayer actuators, which are based on a semicrystalline polyurethane with an exceptionally large nonlinear thermal expansion coefficient. The segments are designed on the basis of a modified Timoshenko model, and finite element analysis simulation is used to describe their performance. Upon electrical activation of the segments with basic waveform patterns, the robot can move through repeatable peristaltic locomotion on exceptionally slippery or sticky surfaces and it can be oriented in any direction. The soft body enables the robot to wriggle through openings and tunnels that are much smaller than its cross-section.

Approaching the Fill Factor Limit in Dopant-Free Hole Transporting Layer-Based All-Inorganic Perovskite Solar Cells.

As an important part of perovskite solar cells (PSCs), hole transporting layer (HTL) has a critical impact on the performance and stability of the devices. In an attempt to alleviate the moisture and thermal stability issues from the commonly used HTL Spiro-OMeTAD with dopant, it is urgent to develop novel HTLs with high stability. In this study, a new class of polymers D18 and D18-Cl are applied as undoped HTL for CsPbI2Br-based PSCs. In addition to the excellent hole transporting properties, we unveil that D18 and D18-Cl with larger thermal expansion coefficient than that of CsPbI2Br could impose a compressive stress onto the CsPbI2Br film upon thermal treatment, which could release the residual tensile stress in the film. As a result, the efficiency of CsPbI2Br-based PSCs with D18-Cl as HTL reaches 16.73%, and the fill factor (FF) exceeds 85%, which is one of the highest FF records for the conventional-structured device to date. The devices also show impressive thermal stability with over 80% of the initial PCE retained after 85 °C heating for 1500 h.

Cryogenic liquid nitrogen stimulation-induced cracking in gas-enriched shale reservoirs: A numerical investigation

Cryogenic shock-induced brittle cracking has promising application prospects in reservoir stimulation. In this paper, a fully coupled thermo-hydro-mechanical (T-H-M) model combined with the statistical meso-damage theory is proposed to investigate the trans-scale progressive cracking process of shale gas reservoirs stimulated by liquid nitrogen (LN2). In this theoretical framework, shale meso-heterogeneity in both thermo-mechanical and hydraulic properties is characterized by two independent statistical distribution functions; temperature-dependent rock properties and temperature- and pressure-dependent fluid thermodynamic properties are described using some experimental and theoretical formulas. The numerical model is implemented in a finite element context and subsequently validated against existing classical coupling results. Numerical results demonstrate that LN2 fracturing accompanied by the unique cryogenic shock effect leads to a complex cracking process involving multiple-point fracture initiation, asymmetric macrofracture propagation, and primary fracture bifurcation. Sensitivity analysis indicates that approximately equidistant or equilength radial fractures may be generated at a lower stress difference, lower permeability, or higher elastic modulus; both fracture initiation pressure and induced fracture morphology are more sensitive to injected fluid temperature relative to initial reservoir temperature; a larger thermal expansion coefficient is beneficial for inducing more fractures, but not applicable to the thermal conductivity. Preferable candidates for LN2 stimulation to generate multiple fractures in shale reservoirs are recommended. It is also found that compared with H2O and supercritical CO2, fracturing using LN2 can generate fractures with lower initiation pressure and greater complexity. Preliminary results confirm the potential of using LN2 fracturing to improve the stimulation effect of shale reservoirs.