Low Thermal Conductivity Research Articles

Influence of Subvalent Twin-Rattler for High n-Type Thermoelectric Performance in Bi13S18Br2 Chalcohalide.

Metal chalcohalides, owing to their higher stability over halides and greater tunability of electronic features over chalcogenides, open new avenues for investigating properties of materials. Complex metal chalcohalides can be a good choice for thermoelectric studies for their halide-like low thermal conductivity and chalcogenide-like high electrical conductivity. Here, we have investigated the thermoelectric properties of n-type Bi13S18Br2 and utilized the concept of Fajans' polarization to describe the formation of a dimer and explained how it can help achieve high thermoelectric figure of merit (zT) of ∼1.0 at 748 K. This zT value is so far the highest-reported value for pristine metal chalcohalides. The existence of subunit in Bi13S18Br2 is experimentally verified by synchrotron X-ray pair distribution function (X-PDF) analysis. The complex structure of Bi13S18Br2 having a large unit cell exhibits simultaneous dimer-cation rattler (i.e., "twin-rattler"), which decreases the lattice thermal conductivity drastically. We observed evidence of such low-energy rattling vibrations from DFT-calculated eigen mode visualizations of the phonon dispersion. The subvalent nature of accommodates an extra electron in Bi(6pz) orbital, which helps form a weakly dispersed donor band just below the Fermi energy (EF), leading to a significant reduction in band gap (0.77 eV), which is favorable for high thermoelectric performance. Consequently, we obtained a semiconducting nature of n-type Bi13S18Br2 with moderate electrical conductivity, as well as a high Seebeck coefficient. Our investigation presents the importance of fundamental chemistry in thermoelectrics and demonstrates the influence of subvalent twin-rattler in triggering high thermoelectric performance in metal chalcohalides.

Eco-Friendly Jute-Based Hybrid Nonwoven Fabric for Packaging Applications.

Eco-friendly materials must replace pure synthetic materials to protect the environment and improve human welfare. This study uses a blow room-integrated carding machine to create a filmy web by properly mixing modified jute and polyester fibers. Jute-polyester fiber blended carded webs have been utilized to produce jute-based hybrid nonwoven fabrics (JHNFs), which are subsequently given an antibacterial treatment by spraying a solution of silver nitrate, ethanol, and ammonia. The performance of the developed JHNF is evaluated by its morphological, FTIR, antibacterial, mechanical, and thermal properties. The fiber distribution of jute and polyester fibers is shown in SEM micrographs. The JHNF showed 29 and 27.8 mm ZOI against Staphylococcus aureus bacteria and Escherichia coli, respectively. The developed sample exhibited a 2.3% extension at the break and 170.8 N of breaking force. The sample confirmed itself as a water-repellent material as water could not penetrate from one surface to another when it was tested by a moisture management tester. The thermal conductivity of the produced sample was measured at 0.0839 W/m K. The lower thermal conductivity signifies a good thermally insulative packaging material. The developed jute polyester nonwoven fabric also demonstrated higher radiative heat resistance, providing a thermal barrier of 22 °C. The porosity, thickness, and density were determined at 49.59%, 0.22 mm, and 0.40 g/cm3, respectively. The sample exhibited significant thermal stability, with polymer degradation initiating at temperatures above 280 °C. The developed nonwoven fabric proves its practical utility as a packaging material, offering a viable alternative to pure synthetic packaging materials.

Compressive Mechanical and Heat Conduction Properties of AlSi10Mg Gradient Metamaterials Fabricated via Laser Powder Bed Fusion

Metamaterials are defined as artificially designed micro-architectures with unusual physical properties, including optical, electromagnetic, mechanical, and thermal characteristics. This study investigates the compressive mechanical and heat transfer properties of AlSi10Mg gradient metamaterials fabricated by Laser Powder Bed Fusion (LPBF). The morphology of the AlSi10Mg metamaterials was examined using an ultrahigh-resolution microscope. Quasi-static uniaxial compression tests were conducted at room temperature, with deformation behavior captured through camera recordings. The findings indicate that the proposed gradient metamaterial exhibits superior compressive strength properties and energy absorption capacity. The Gradient-SplitP structure demonstrated better compressive performance compared to other strut-based structures, including Gradient-Gyroid and Gradient-Lidinoid structures. With an apparent density of 0.796, the Gradient-SplitP structure exhibited an outstanding energy absorption capacity, reaching an impressive 23.57 MJ/m3. In addition, heat conductivity tests were performed to assess the thermal resistance of these structures with different cell configurations. The gradient metamaterials exhibited higher thermal resistance and lower thermal conductivity. Consequently, the designed gradient metamaterials can be considered valuable in various applications, such as thermal management, load-bearing, and energy absorption components.

Enhanced thermoelectric performance of silicon powder arrays by remotely doping

We report improved thermoelectric (TE) properties of mesostructured silicon powder arrays simply prepared by die-pressing without sintering. In contrast to bromoethane's modest effect, the symmetric dibromoethane molecule coupling could significantly increase the conductivity of Si powder array TE device, from 12.7 S cm−1 of a silicon powder array to 62.3 S cm−1, which is possibly caused by the high electronic transmission probability of symmetric organic molecule–Si crystal coupling, and additionally enhanced by Si bandgap narrowing and defect states of an organic–inorganic interface identified by UV–vis absorption spectra and photoluminescence spectroscopy. Boosted by the very low thermal conductivity (0.58 W m−1 K−1), the dimensionless figure of merit, the ZT value of an Si powder array remotely doped by dibromoethane, ∼0.173, was obtained at 385 K, which is about 17 times higher than that of the bulk Si. An Si–organic hybrid TE device shows potentials to approach the threshold of practical applications with moderate ZT performance and low cost.

Study on Phase Change Materials' Heat Transfer Characteristics of Medium Temperature Solar Energy Collection System.

Within the next five years, renewable energy is expected to account for approximately 80% of the new global power generation capacity, with solar power contributing to more than half of this growth. However, the intermittent nature of solar energy remains a significant challenge to fully realizing its potential. Thus, efficient energy storage is crucial for optimizing the effectiveness and dependability of renewable energy. Phase-change materials (PCMs) can play an important role in solar energy storage due to their low cost and high volumetric energy storage density. The low thermal conductivity of PCMs restricts their use for energy storage, despite their immense potential. Hence, the primary goal of this study is to experimentally investigate the energy storage capacity of two blended phase-change materials (paraffin and barium hydroxide octahydrate) through integration with a medium-temperature solar heat collection system. The experimental findings reveal that the blended PCMs possess the highest cumulative charge fraction (0.59), energy capacity, and low energy loss compared to each PCM alone. Furthermore, the phase change storage tank achieves higher heat storage (27%) and exergy storage efficiency (18%) compared to the stored tank water without any PCMs. The blended PCMs enhanced their performance, exhibiting improved interaction and excellent thermal storage properties across a range of temperatures, offering an opportunity for the design of an energy-efficient, low-cost storage system.

Low-Cost Hyperelastic Fuller-Dome-Structured Nanocellulose Aerogels by Dual Templates for Personal Thermal Management.

It is critically important to maintain the body's thermal comfort for human beings in extremely cold environments. Cellulose nanofibers (CNF)-based aerogels represent a promising sustainable material for body's heat retention because of their renewability and low thermal conductivity. However, CNF-based aerogels often suffer high production costs due to expensive CNF, poor elasticity and/or unsatisfactory thermal insulation owing to improper microstructure design. Here, a facile dual-template strategy is reported to prepare a low-cost, hyperelastic, superhydrophobic Fuller-dome-structured CNF aerogel (CNF@PU) with low thermal conductivity. The combination of air template by foaming process and ice template enables the formation of a dome-like microstructure of CNF@PU aerogel, in which CNF serves as rope bars while inexpensive polyurethane (PU) acts as joints. The aerogel combines ultra-elasticity, low thermal conductivity (24mW m-1 K-1), and low costs. The as-prepared CNF@PU aerogel demonstrates much better heat retention than commercial thermal retention fillers (e.g., Flannelette and goose down), promising its great commercial potential for massively producing warming garments. This work provides a facile approach for creating high-performance aerogels with tailored microstructure for effective personal thermal management.

Electric Structure and Thermoelectric Performance in Cs2O Crystal

In this work, first principles DFT calculations has been employed with anharmonic phonon scatter theory and Boltzmann transport method to perform a exhaustive study on the thermoelectric properties as electronic and phonon transport of layered Cs2O crystal. The results indicate that Cs2O crystal represents a flat-and-dispersive type band structure, which returns a high power factor. In the other hand, low lattice thermal conductivity is discovered in Cs2O semiconductor, combined with its high power factor, the Cs2O crystal is considered a promising thermoelectric material. It is demonstrated that p-type Cs2O could be optimized to exhibit outstanding thermoelectric performance with a maximum ZT value of 0.71 at 500K. Explored by density functional theory calculations, the high ZT value is due to its high Seebeck coefficient S, high electrical conductivity , and low lattice thermal conductivity .

Construction and Properties of Ultralow Thermal Conductivity and High Strength Zirconia Aerogel Composites by Freeze-Drying.

Zirconia aerogels possess significant applications, including their use catalyst carriers, thermal insulation materials, and thermal barrier coatings. This is due to their ultrahigh temperature resistance, high porosity, and low thermal conductivity. Nonetheless, the inherent challenges associated with ZrO2 aerogels, such as high brittleness, low compressive strength, and inadequate formability, restrict their potential applications. In this paper, with ultralow thermal conductivity and high strength zirconia aerogel composites with inorganic zirconium salt zirconium carbonate as the raw material, acetic acid as the solvent, polyvinylpyrrolidone (PVP) as the viscosity builder to stabilize the structure of the aerogel during the freeze-drying process. Additionally, yttrium nitrate hexahydrate (Y(NO3)3·6H2O) is employed as a phase stabilizer. The sol-gel method, in conjunction with the freeze-drying process, is utilized to fabricate ZrO2 aerogel composites with an optimized microstructure. The findings indicate that optimal process parameters are achieved with a PVP solution concentration of 2.0 wt % and a zirconium carbonate concentration of 20 wt %. The mechanical properties of the resulting composites reach up to 550 kPa, while the thermal insulation performance exhibits a temperature difference of 207 °C/cm and a thermal conductivity of 0.0504 W/(m·K). This advancement addresses the mechanical stability issues commonly associated with traditional ceramic aerogels and widely used elastic insulating materials, thereby enhancing their applicability as thermal insulation and heat preservation materials.

Thermal performance of shell-and-tube polymeric hollow fiber heat exchangers as oil coolers

Motor oil must be appropriately treated in motors, and aluminum plate heat exchangers are used to cool it. An aluminum heat exchanger is an additional part of the oil treatment module, which increases its size and weight. Two compact plastic shell-and-tube heat exchangers were tested alongside with aluminum heat exchanger to evaluate the efficiency of the plastic cooling core inside the oil module. A total of 63 experimental points were tested on three heat exchangers with good thermal balance (discrepancy of about 1,8 %), and the data were used to evaluate the heat transfer coefficients. While plastic unit PA11 showed the heat outputs exceeding the heat output of the aluminum plate unit by about 7 %, the pressure drops were about ten times higher. The unit PEEK showed good performance and pressure drops on the oil side, but the heat transfer was limited by a small heat transfer surface. Analysis of thermal resistances confirmed that the thermal resistance between the wall and the oil is dominant due to the oil's low thermal conductivity and high viscosity. The results showed that optimization of the fiber structures is needed, aiming to increase the oil flow around the fiber structures.

2D Embedded Ultrawide Bandgap Devices for Extreme Environment Applications.

Ultrawide bandgap semiconductors such as AlGaN, AlN, diamond, and β-Ga2O3 have significantly enhanced the functionality of electronic and optoelectronic devices, particularly in harsh environment conditions. However, some of these materials face challenges such as low thermal conductivity, limited P-type conductivity, and scalability issues, which can hinder device performance under extreme conditions like high temperature and irradiation. In this review paper, we explore the integration of various two-dimensional materials (2DMs) to address these challenges. These materials offer excellent properties such as high thermal conductivity, mechanical strength, and electrical properties. Notably, graphene, hexagonal boron nitride, transition metal dichalcogenides, 2D and quasi-2D Ga2O3, TeO2, and others are investigated for their potential in improving ultrawide bandgap semiconductor-based devices. We highlight the significant improvement observed in the device performance after the incorporation of 2D materials. By leveraging the properties of these materials, ultrawide bandgap semiconductor devices demonstrate enhanced functionality and resilience in harsh environmental conditions. This review provides valuable insights into the role of 2D materials in advancing the field of ultrawide bandgap semiconductors and highlights opportunities for further research and development in this area.

Preparation and properties of a rigid hemp shiv insulation particle board using citric acid-glycerol mixture as an eco-friendly binder

Particle boards are commonly manufactured from wood-based material bound with a thermosetting adhesive based on the reaction of formaldehyde with phenol, urea, melamine, or co-condensates. The use of formaldehyde is a cause for concern due to its harmful emissions. This study investigates the use of an alternative binder combined with particles derived from a short-cycle crop as an alternative to timber derived particles. A low density particle board was developed using hemp shiv as an aggregate with a binder made with crude glycerol, derived from the waste stream of the bio-diesel industry, esterified with citric acid under heat activation. This board was characterized and found to have good mechanical properties, low thermal conductivity, and good moisture buffering. Dimensional stability was compromised by swelling when exposed to water, but it will be possible to address this shortcoming using hydrophobic additives. The acoustic properties of the board were also found to be excellent, showing potential for use as a thermally insulating acoustic separator for internal walls.

Experimental Research on Basalt Fabric-Based Composites for Protection Against Contact Heat

ABSTRACT The unique properties of basalt fibers, i.e. low thermal conductivity, thermal resistance up to 800°C, biodegradability, resistance to acids and alkalis, corrosion, ultraviolet radiation, and non-flammability, make them increasingly used in personal protective equipment. The design and production of basalt fabric-based composites were performed, and composite layers were directly modified by depositing thin coatings using the magnetron sputtering method. The designing and testing were performed in five stages. For direct basalt fabric modification and basalt fabric-based composites, resistance to contact heat was tested for contact temperatures of 100°C and 250°C. Moreover, the uncertainty budgets of the threshold time measurement results were determined and analyzed for all composites. New basalt fabric-based composites were designed to protect users from contact heat in hot work environments. As a result of the research, it was found that applying composite coatings: aluminum and zirconium dioxide or aluminum and zirconium dioxide and titanium dioxide to both composite layers proved to be effective in obtaining composites that guarantee perfect resistance to contact heat up to 250°C.

Analyzing switching variability of SiNx-based RRAM in terms of Joule heating dissipation

In this paper, the switching variability of SiNx-based RRAM with reactive metal electrodes in terms of Joule heating dissipation was analyzed. The electrode with high (low) thermal conductivity showed low LRS (HRS) variability in SiNx-based RRAM. By analyzing the I–V characteristics and the current conduction mechanism, we proposed that the thermal conductivity of reactive electrodes significantly affected the number of ions involved in the switching process and the vacancies distribution in the switching layer, resulting in the difference in the switching performance. This study suggested that attention should be paid to the influence of electrode thermal conductivity on variability, providing ideas for designing RRAM with low switching variability.

Fins-nanoparticle combination for phase change material enhancement in a triplex tube heat exchanger: A numerical approach to thermal sustainability

Many phase change materials exhibit low thermal conductivity, leading to incomplete melting and solidification processes. To address this issue, researchers have numerically explored the integration of alumina nanoparticles (Al2O3) with paraffin (RT82), a phase change material with a solidification temperature of 65 °C, in a triplex-tube heat exchanger. The phase change material model with internal longitudinal fins employed the both-sides freezing technique and was conducted using Ansys Fluent software, employing the enthalpy-porosity method within a finite-volume framework to model the phase change material behavior during both melting and solidification phases. This methodology aims to significantly improve the thermal performance of thermal energy storage systems by enhancing heat transfer efficiency within the phase change material (PCM), thereby ensuring more effective utilization of stored thermal energy. The numerical findings show that the pure PCM completely solidified in 780 min. By dispersing 1 %, 4 %, 7 %, and 10 % of Al2O3 in the PCM, thermal conductivity improved by 3 %, 12.5 %, 22.5 %, and 32.5 %, respectively. Additionally, the inclusion of nano-PCM reduced the solidification time. This research also compares the overall energy release in two different situations: PCM with and without nanoparticles. The computer-generated simulation results closely correlated with the practical experimentation results.

Multifunctional Wood Composite Aerogel with Integrated Radiant Cooling and Fog–Water Harvesting for All‐Day Building Energy Conservation

AbstractPassive radiative cooling, as a cooling technique with no energy input, can continuously radiate heat into the supercooled universe. However, the continuous cooling effect tends to cause the problem of nighttime overcooling. Moreover, non‐renewable radiative cooling materials and energy‐intensive processing methods lead to increased carbon emissions and resource consumption. Therefore, there is an urgent need to develop a renewable and environmentally friendly self‐adaption radiative cooling thermal management material. In this paper, a high‐performance self‐adaption thermal management wood composite aerogel material is designed and prepared by in situ growth of multi‐scale silicon dioxide on wood. The constructed passive radiative cooling material has a sub‐ambient cooling effect of up to 13.5 °C and 20.2 °C during daytime in winter and summer, respectively. Meanwhile, it has a certain thermal insulation performance (2.0 °C above ambient) due to low thermal conductivity (0.063370 ± 0.000329 W m−1 k−1) at night in winter. In addition, the material is also suitable for fog–water harvesting (fog–water harvesting rate of 59.27 ± 0.76 mg min−1) due to its hydrophobicity. This work can significantly promote the practical application of passive radiative cooling materials.

Cooling and Lubricating Strategies for INCONEL® Alloys Machining: A Comprehensive Review on Recent Advances

Abstract INCONEL® alloys are Ni-based superalloys with superior mechanical properties for extremely high temperature (T) applications. These alloys present significant challenges: they are difficult-to-cut materials due to the low thermal conductivity (k), severe work hardening and elevated surface hardness. They are widely used in applications that require good dimensional stability; however, built-up edge (BUE) followed by premature Tool Wear (TW) are the most common problems when applying conventional machining (CM) and hybrid machining processes, i.e. Additive Manufacturing (AM) followed by milling, resulting in a meagre final product finishing. Regarding cooling/lubricating environments, a miscellanea of methods can effectively be applied to INCONEL® alloys, depending on their advantages and disadvantages. It is imperative to refine the machining parameters to enhance the performance outcomes of the process, particularly concerning the quality and cost-effectiveness of the product. This current review intends to offer a systematic summary and analysis of the progress taken within the field of INCONEL® CM and the various cooling/lubricating methods over the past decade, filling a gap found in the literature in this field of knowledge. A Systematic Literature Review (SLR) approach was employed in this study, aiming to identify pertinent papers within the cooling and lubricating strategies for INCONEL® alloys machining. The most recent solutions found in the industry and the prospects from researchers will be presented, providing significant insights for academic researchers and industry professionals. It was found that selecting cooling methods for INCONEL® machining requires careful consideration of various factors. Each lubrication environment utilized in traditional INCONEL® machining methods offer unique advantages and challenges regarding the different outcomes: TW, Tool-Life (TL) and/or surface quality assessment; nevertheless, cryogenic cooling by CO2(l) and N2(l) highlights as the better cooling environment to improve the machined surface quality.

Enhanced Thermoelectric Performance of SnTe via Introducing Resonant Levels

SnTe has emerged as a non-toxic and environmentally friendly alternative to the high-performance thermoelectric material PbTe, attracting significant interest in sustainable energy applications. In our previous work, we successfully synthesized high-quality SnTe with reduced thermal conductivity under high-pressure conditions. Building on this, in this work, we introduced indium (In) doping to further decrease thermal conductivity under high pressure. By incorporating resonance doping into the SnTe matrix, we aimed to enhance the electrical transport properties while maintaining low thermal conductivity. This approach enhances the Seebeck coefficient to an impressive 153 μVK−1 at 735 K, marking a notable enhancement compared to undoped SnTe. Furthermore, we noted a substantial decrease in total thermal conductivity, dropping from 6.91 to 3.88 Wm−1K−1 at 325 K, primarily due to the reduction in electrical conductivity. The synergistic impact of decreased thermal conductivity and heightened Seebeck coefficient resulted in a notable improvement in the thermoelectric figure of merit (ZT) and average ZT, achieving approximately 0.5 and 0.22 in the doped samples, respectively. These advancements establish Sn1−xInxTe as a promising candidate to replace PbTe in thermoelectric applications, providing a safer and more environmentally sustainable option.

Enhanced Weighted Mobility Induced High Thermoelectric Performance in Argyrodite Ag8SnSe6.

The argyrodite family has emerged as a promising thermoelectric candidate due to its highly diffusive Ag ions and inherent low thermal conductivity. To address issues that commonly arise with hot pressing (HP) sintering, this study proposes to use the zone melting (ZM) method to synthesize high-density polycrystalline bulk Ag8SnSe6 samples. The thermoelectric properties of samples synthesized by the ZM and HP methods were thoroughly evaluated over a temperature range of 300 to 700 K. Due to the weaker scattering of electrons, the ZM-synthesized samples exhibited an ∼60% increase in weighted mobility, compared to those produced by the HP method. Despite the slight increase in thermal conductivity, the specimen synthesized by the ZM method achieves a higher peak zT value of 1.05 at 700 K. The average zT value also improves to 0.71 across the temperature range of 300 to 700 K. This work demonstrates the effectiveness of the ZM method in enhancing the thermoelectric performance of Ag8SnSe6, with great potential applicability to other argyrodite compounds.

Construction of “organic–inorganic” hierarchical structure of carbon fibers and the effect on the properties of epoxy composites

AbstractThe demand for epoxy (EP) in semiconductor, aerospace, and other applications is currently on the rise. However, pure epoxy is difficult to meet these requirements, such as low thermal conductivity and poor toughness. Therefore, in this paper, sulfonamides (SAs) and core‐shell silica (SLC‐SiO2) were grafted onto the surface of short carbon fibers (SCF) with sizes of 0.1–6 mm by the chemical grafting method. As a result, the surface activity of SCF was improved and the interfacial properties of the EP composites were enhanced. The interfacial compatibility of SCF grafted with SAs and SLC‐SiO2 in EP is greatly improved, resulting in stronger mechanical interlocking and chemical bonding ability between EP and SCF. The results showed that when the content of SCF@SAs@SLC‐SiO2/EP composites reached 0.3 wt% of SCF@SAs@SLC‐SiO2, the impact and tensile strengths were increased from 12.15 kJ·m−2 and 43.4 MPa to 16.93 kJ·m−2 and 74.97 MPa compared with the pure epoxy, which were improved 39.3% and 72.7%. In addition, the thermal conductivity of SCF@SAs@SLC‐SiO2/EP composites was also improved by 12.5% from 0.205 W·(m·K)−1 to 0.2306 W·(m·K)−1 compared with the pure EP. This is due to improved chemical interactions and mechanical interlocking at the fiber‐epoxy interface. This study provides a new method for the preparation of high‐performance SCF/EP composites.Highlights The amino group of sulfonamides was grafted with short carbon fiber to increase the surface active group of short carbon fiber. Sulfonamides react with carboxyl groups on the surface of core‐shell silica to form an “organic–inorganic” structure. Improve the surface roughness of short carbon fiber, and make it evenly dispersed in epoxy resin, so as to improve the performance of epoxy composite materials.

Synergistic effect of lone-pair electron and atomic distortion in introducing anomalous phonon transport in layered PbXSeF (X= Cu, Ag) compounds with low lattice thermal conductivity

Using first-principles calculations, self-consistent phonon theory and Boltzmann transport theory, the crystal structure, phonon and electronic transport, and thermoelectric (TE) properties of PbXSeF (X = Cu, Ag) compounds are comprehensive explored in the current work. The heterogeneous bonding characteristics along the in-plane and out-of-plane directions lead to low lattice thermal conductivities in PbXSeF (X = Cu, Ag) compounds. The low lattice thermal conductivity is primarily attributed to strong anharmonicity caused by the lone-pair electrons of Pb. Notably, the PbCuSeF compound, despite the lighter mass in comparison with PbAgSeF, exhibits relatively lower lattice thermal conductivity. Such finding can be attributed to the distortion introduced by Cu atom, which leads to strong quartic anharmonicity, and thereby suppressing the heat-carrying phonons through the rattling-like behavior of Cu atom. The lone-pair electrons of Pb2+ and the heterogeneous bonding characteristics in PbXSeF (X = Cu, Ag) compounds contribute the multi-valley band degeneracy, resulting the decoupling of Seebeck coefficient and electrical conductivity with carrier concentration while generating in a high power factor. Our current work not only illustrates the fundamental insights into the low lattice thermal conductivity and related anomaly of layered PbXSeF (X = Cu, Ag) compounds based on the four-phonon scattering and multiple carrier scattering rates, but also highlights the anisotropic feature of electronic and thermal transport properties.