Cold sintering co-firing of (Ca,Bi)(Mo,V)O4–PTFE composites in a single step

Because of large differences in the processing temperature windows between ceramics and polymers, the single-step co-sintering of microwave dielectric ceramic–polymer substrates remains challenging. In this work, a dense (Ca_0.65Bi_0.35)(Mo_0.65V_0.35)O₄ (CBMVO) ceramic was first prepared through cold sintering at 150°C, under a uniaxial pressure of 300 MPa for 60 min with Li₂MoO₄ (LMO) as a transient low-temperature solvent. Cold-sintered CBMVO–5 wt% LMO ceramic shows excellent microwave dielectric properties: ε_r ∼ 11.4, Q × f ∼ 7070 GHz, τ_f ∼ −7.4 ppm/°C. Moreover, the optimized cold sintering process enabled the preparation of a layered co-sintered (2–2 type) CBMVO–polytetrafluoroethylene composite, which maintained excellent microwave dielectric properties and showed a good heterogeneous interface bonding. The proposed cold sintering co-firing of ceramic–polymer composites in a single step shows great potential for application in the seamless integration between ceramics and polymer substrates.     

One‐ or two‐dimensional channel structures and properties of piezoelectric composites via freeze‐casting

By employing carefully tailored tert‐butyl alcohol (TBA)‐based freeze‐casting parameters, a large amount of porosity (>70 vol%) and one or two‐dimensional pore channels created were produced into alkali niobate‐based (NKN) ceramics. The relationship between processing factors and microstructures has here been studied, in terms of (i) porosities controlled by adjusting the solid loading in the initial slurry and (ii) strategically attempted freezing direction to make varied pore channels, in which two freezing directions from the bottom or side of mold can produce unidirectional elongated and radially centrosymmetric microstructures, respectively. In addition to that, NKN/epoxy composites with 3‐1 or 3‐2 type polymer channels in the NKN matrix have been fabricated by infiltration of the polymer into the porous NKN hosts. The effect of the channel directions on the mechanical and piezoelectric properties of the composites was investigated for varied volume fractions of the active ceramic phase, mechanical loading, and the poling direction, leading to very high‐piezoelectric g₃₃ coefficients at >60 mV·m/N in the composites with unique channel structures.     

A novel low permittivity microwave dielectric ceramic Sr2Ga2SiO7 for application in patch antenna

The dielectric properties of a Ga-based melilite type ceramic Sr₂Ga₂SiO₇ via theoretical prediction based on far-infrared spectroscopy and experimental measurement by the Hakki–Coleman method were studied in this work. Dense and single-phase ceramics were fabricated via solid-state reaction at 1330°C and exhibited comprehensive microwave dielectric properties (ε_r ∼ 7.6, Q × f ∼ 23 600 GHz, and τ_f ∼ −35.2 ppm/°C) at 14.3 GHz. Chemical modifications were proposed to adjust the thermal stability and reduce the densification temperature. By adding 10 mol% CaTiO₃, the negative τ_f can be compensated to a near-zero value of −3.8 ppm/°C. The densification temperature was reduced to 940°C by adding 3 wt.% LiF. A patch antenna was designed using Sr₂Ga₂SiO₇ ceramic with a high radiation efficiency of 99.1% and a gain of 2.788 dBi at the center frequency of 4.371 GHz. All results indicate that the Sr₂Ga₂SiO₇ ceramic has promising application potential for 5G wireless communication technology.     

Controlling anisotropy of porous B4C structures through magnetic field-assisted freeze-casting

Anisotropic porous boron carbide (B₄C) structures were successfully produced, for the first time, using the magnetic field-assisted freeze casting method. The effect of the magnetic field on the structure and mechanical strength of the formed porous B₄C was compared for two different magnetic field directions that were either aligned with ice growth (vertical), or perpendicular to the ice growth direction (horizontal). It was shown that applying even a weak horizontal magnetic field of 0.1–0.3 T noticeably affected the alignment of mineral bridges between lamellar walls. Both the porosity and the channel widths decreased with increasing horizontal magnetic field strength. In the case of a vertical magnetic field, a larger strength of 0.4 T was required for highly aligned lamellar walls and larger channel widths. Compression strength tests indicated that the application of magnetic fields led to more homogeneously aligned channels, which resulted in increased compression strength in the longitudinal (parallel to the ice growth) direction. Applying a vertical magnetic field of 0.4 T with a cooling rate of 2 °C/min during the freezing step of the magnetic field-assisted freeze-casting method was found to result in the best conditions for producing highly anisotropic structures with large channel widths and fewer mineral bridges, which led to an increase in the mechanical strength.     

Hierarchical Structure of Porous Silicon Nitride Ceramics with Aligned Pore Channels Prepared by Ice‐Templating and Nitridation of Silicon Powder

A unique hierarchical porous structure of silicon nitride ceramic with 76.5% porosity is fabricated by combining an ice‐templating method and nitridation for a silicon powder. The porous silicon nitride ceramics were composed of a lamellar structure with aligned pore channels and ceramic walls filled with fibrous whiskers. This study is focused on the influences of freezing rate on the microstructures and properties of the silicon nitride ceramics. The properties were characterized by compressive strength and gas permeability, which were shown to vary with controlled microstructure. The compressive strength and the permeability reached up to 32.2 MPa and 0.035^?12 m², respectively.     

Temperature-stable Na0.5Bi0.5TiO3-based ceramics with favorable low-temperature dielectric and energy storage property

In this work, (1 − x)(0.94Na_0.5Bi_0.5TiO₃–0.06BaTiO₃)–xKTaO₃ (x = 0–0.30) ceramics are developed for dielectric capacitor applications. The introduction of KTaO₃ from x = 0 to 0.30 increases the tolerance factor t from 0.984 to 1.005 and causes the decrease of ferroelectric rhombohedral phase in the ceramics. Besides, a gradual structural change toward a higher symmetry can be detected, accompanied by the obvious domain refinement. In the aspect of electrical property, the strengthened dielectric relaxation leads to the greatly enhanced thermal stability of dielectric response. The decline in T_s from 98 to −96°C causes a significant widening of the low-temperature region with temperature-stable dielectric constant ε_r and low dielectric loss tan δ. The x = 0.30 ceramic shows a high ε_r (25°C) of 1094 with the temperature coefficient of capacitance ≤±15% over −70 to 200°C, which exceeds the X9R standard. Meanwhile, tan δ is less than 0.02 in a wide temperature range of −35 to 300°C. In addition, the ultrafine grain size of 290 nm, large bandgap of 3.22 eV, and high resistance of the x = 0.30 ceramic contribute to its electrical breakdown strength. A linear-like P–E loop with the large discharged energy density W_D ∼ 3.50 J/cm³ and high energy efficiency η ∼ 90.1% is obtained under 28 kV/mm at room temperature. The thermal stability of the energy storage performance is also satisfactory with the variation of W_D less than 15% over −40 to 200°C, and the η is higher than 85%.     

Synthesis,crystal structure,and characterization of Na2SrV4O12: A low-firing dielectric vanadate

In this work, cyclotetravanadate Na₂SrV₄O₁₂ was synthesized at a relatively low sintering temperature of ∼500°C using a solid-state reaction method. X-ray diffraction and a transmission electron microscope characterization featured a tetragonal structure that was built by a 3D frame of isolated tetracyclic (V₄O₁₂)⁴⁻. Dielectric measurements demonstrated strong dependence on frequency and temperature. A low relative permittivity of ε_r ∼ 8 ± 0.2 and a dielectric (loss tanδ) ∼ 0.4 ± 0.01 was achieved at a frequency of 10 kHz and room temperature. ac impedance and conductivity analysis revealed a thermally activated migration behavior of charge carriers with a short-range hopping feature. XPS analysis validated the existence of oxygen vacancy and reduction in vanadium (from V⁵⁺ to V⁴⁺), which gave rise to charged lattice defects. The migration or hopping of such charged defects was responsible for the observed electrical behaviors. Owing to the simple composition, inexpensive raw materials and low density (2.99 g/cm³) make Na₂SrV₄O₁₂ ceramic a potential candidate for lightweight devices and in photocatalytic degradation and all-solid-state ion batteries.     

Effect of a lattice distortion strategy on the phase transition and properties in KNN-based ceramics

High performance lead-free piezoelectric ceramics are of great importance to the sustainable development of the environment. To obtain excellent comprehensive performance KNN-based lead-free piezoelectric ceramics, a lattice distortion strategy combined with domain configuration was designed in (1 − x)K_0.5Na_0.5Nb_0.95Sb_0.05O₃–xCaHfO₃ ((1 − x)KNNS–xCH) system by introduced Ca²⁺ into the A-site and Hf⁴⁺ into the B-site. The results demonstrated that the rhombohedral–orthorhombic–tetragonal polymorphic phase boundary (PPB) was constructed in 0.02 ≤ x ≤ 0.04 and significant lattice distortion occurred in R- and T-phase. Moreover, the 0.97KNNS–0.03CH sample exhibited excellent electrical performance (e.g., k_p ∼ 43.8%, d^*₃₃ ∼ 478.6 pm/V, and d₃₃ ∼ 392 pC/N) together with a high Curie temperature (T_C ∼ 295°C) profited from the PPB and domain configurations. The ceramics also showed the optimal thermal stability, which was beneficial to promote the development of KNN-based ceramics.     

Direct and indirect measurement of large electrocaloric effect in barium strontium titanate ceramics

Barium strontium titanate (Ba_1-xSr_xTiO₃-BST) ceramics, where x = 0.05, 0.15, 0.25, and 0.35, was prepared via a solid-state reaction method. The lattice structures and morphologies of the ceramic samples were analyzed using X-ray diffraction and scanning electron microscopy technologies. The dielectric and ferroelectric properties of the BST ceramics were characterized using a precision impedance analyzer and a ferroelectric polarization-electric field (P-E) hysteresis loop tester, respectively. The electrocaloric effect was indirectly calculated using the Maxwell relations and P-E loops as a function of temperature and electrical field, and also directly measured using a computer-controlled thermocouple and high-voltage power supply. An adiabatic temperature change of 1.82 K was procured, indicating a promising potential in the applications as cooling devices.     

All-inorganic flexible high-temperature strain sensor based on SrRuO3/muscovite heteroepitaxy

Design and fabrication of flexible strain sensors are still challenging for high-temperature application in the aerospace, metallurgical industry, and underground energy exploration. In the present work, an all-inorganic flexible strain sensor has been fabricated based on single-crystal SrRuO₃ (SRO) thin films epitaxially grown on muscovite. A high resistive tunability ((∆R/R₀%) ∼ 26.05%), excellent linearity (correlation coefficient of 0.93), and large gauge factor (GF ∼ 101) have been achieved in the as-prepared SRO-based sensors with great bending durability. The mechanism for the tunability of the electrical transport in flexible SRO thin films under mechanical bending is proposed based on the Raman and X-ray photoelectron spectroscopy results. The sensors have been confirmed to work properly from ambient temperatures up to ∼425 K, showing the potential application in high-temperature environments. Moreover, the flexible sensors have the ability to monitor the hand joint movements.     

Coupled CFD–DEM of particle-laden flows in a turning flow with a moving wall

The nature of the particle–solid interactions and particle–fluid interactions in rectangular duct bend geometry with/without a moving wall is studied, taking into account particle collision, colloidal, and hydrodynamic forces, and four way coupling between the fluid flow and particles. The focus is on systems where particles and fluid phase have similar length scales, fluid Reynolds number (Re_f) ∼ 1, and particle's Stokes number (St) ∼ 1. Particles move toward the walls of the channel near the bend, and have long residence times in these regions. Buoyancy force has negligible effect on particle motion, where adhesion and drag forces lead to particle motion and agglomeration patterns. The effect of a free surface on agglomeration sites in the turning flow is elucidated.     

Rheological,mechanical, and electrical properties of Sr0.7Bi0.2TiO3 modified BaTiO3 ceramic and its composites

Porous BaTiO₃-based relaxor ferroelectric ceramics with lamellar structure were achieved by ice templating method, and the rheological properties of ceramic slurry for freeze casting were deeply studied. Epoxy resin was then backfilled to generate ceramic–epoxy resin composites. Ceramic–epoxy composites with a lamellar structure were obtained when using a slurry with a ceramic content of 45 wt.%. The nanoindentation results showed that the introduction of ceramic materials into the epoxy resin can significantly improve the penetration resistance and hardness of the material. The dielectric and ferroelectric properties of the composites were also characterized. The interaction between the highly coupled dipoles in the polymers results in a decrease in the breakdown field strength of the composite. The dielectric constant reached up to ∼800. At 220 kV/cm, W_rec = 0.62 J/cm³, and η was ∼80%. At low frequencies, W_rec was ∼0.16 J/cm³, which indicated good stability.     

Effect of freezing velocity and platelet size on structural parameters and morphology of freeze-cast porous alumina scaffolds

In this article, we examine the effects of two different platelet sizes (4 and 8 μm respectively) on the architecture of freeze-cast sintered alumina scaffolds as a function of a wide range of freezing velocities, 5–57 μm s^?1. The microstructural evolution along the freezing direction has been studied a-priori, explained on the basis of ice physics and the interaction of ceramic platelets with the advancing freezing front. An array of microstructures was produced to delve into the role of platelet sizes and freezing velocities on various structural parameters, viz. wavelength (λ), lamella thickness (δ), and bridge density (ρ_b). Regarding the pore morphology, transitions from lamellar to dendritic or isotropic structures were identified for the scaffolds containing smaller and bigger platelets, triggered by an increase in freezing velocity as well as platelet size. The different microstructures are quantified with a specific dimensionless parameter m. We identify the microstructure to be lamellar with low bridge density and m > 4. The wavelengths and bridge spacing were comparable for 2 < m < 4 and led to dendritic structure. For the morphologies characterized by m < 2, the spacing among the numerous interlamellar bridges was smaller than the structural wavelength and hence, the scaffolds revealed usually isotropic structure. Finally, the specific processing conditions that yield different morphologies and the parameter m are presented together in the form of a ‘morphology map’ to establish the different microstructural regimes.     

Crystal structures and electrical properties of Sr/Fe-modified KNbO3 ferroelectric semiconductors with narrow bandgap

In the process of exploring ferroelectric semiconductors, a new system of (1−x) KNbO₃–xSrFeO_3−δ (x = 0.00-0.20) was successfully synthesized via solid-state reaction. The crystal structures, ferroelectric, dielectric, optical, and electrical properties were systematically characterized. The orthorhombic phase with Amm2 space group is detected in all the ceramics. In addition, the orthorhombic and tetragonal phases coexist in 0.80KNbO₃-0.20SrFeO_3-δ ceramic. The decrease in oxygen octahedron distortion induces a weak ferroelectric polarization. The existence of long-range ferroelectric polarization order in all the ceramics is verified and the bandgap of the ceramics can be tuned to ~2.18 eV. The improved short-circuit photocurrent density (J_sc) and open-circuit voltage (V_oc) of the poled 0.95KNbO₃-0.05SrFeO_3−δ ceramic at 30 kV/cm are ~6.90 nA/cm² and 0.04 V, respectively. The activation energies for electrical conductivity of the grains and grain boundaries from 0.90KN–0.10SF ceramic are 0.67 and 0.77 eV, respectively, which indicate the doubly ionized oxygen vacancies. This work provides a new way to tune the optical bandgap/ferroelectric properties of KNbO₃-based ceramics for potential application in ferroelectric photovoltaic and energy fields.     

Achieving both high electromechanical properties and temperature stability in textured PMN-PT ceramics

Textured piezoelectric ceramics, such as textured Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ (PMN-PT) ceramics, have attracted considerable attention from both academia and industry, as they possess crystal-like piezoelectric properties, high composition homogeneity, and low manufacturing cost. However, the main difficulty with the textured piezoelectric ceramics is the presence of BaTiO₃ (BT) templates, which greatly reduces their piezoelectricity and phase transition temperature. Thus, it is highly recommended to fabricate textured piezoelectric ceramics using as few templates as possible. Here, we successfully fabricated high-quality <001>-textured PMN-28PT ceramics (texturing degree of 99%) by using an extremely small amount of BT templates (1 vol.%) with the help of CuO/B₂O₃ sintering aids. The textured PMN-28PT ceramic exhibits 80% piezoelectric coefficient (d₃₃ ∼ 1200 pC/N), 96% electromechanical coefficient (k₃₃ ∼ 88%) and the same temperature stability (T_rt ∼ 100, T_c ∼ 150°C) when compared to its single crystal counterpart. In addition, by using an alternating current electric field poling (AC-poling), the piezoelectric coefficient d₃₃ and dielectric permittivity ε₃₃ of the textured PMN-28PT ceramics were further enhanced around 5–8%. It is believed that the advantages of high electromechanical properties, low cost, and easy mass production of textured PMN-28PT ceramic will make it a promising candidate for advanced electromechanical devices.     

Structural and Piezoelectric Properties of (1−x)Pb(Zr1−yTiy)O3–xPb(Zn0.4Ni0.6)1/3Nb2/3O3 Ceramics Near Triple Point

The crystal structure and piezoelectric properties of (1?x)Pb(Zr_1?yTi_y)O₃‐xPb(Zn_0.4Ni_0.6)_1/3Nb_2/3O₃ [(1?x)PZ_1?yT_y‐xPZNN] ceramics were investigated. The 0.665PZ_0.45T_0.55‐0.335PZNN ceramic has the triple point composition, where the rhombohedral, pseudocubic, and tetragonal structures coexist. Maximum d₃₃ and k_p values of 770 pC/N and 0.69, respectively, were observed from this specimen; it also exhibited a large ε^T₃₃/ε_o value of 3250. Although the maximum d₃₃ value was obtained from the triple point composition specimen, its g₃₃ and d₃₃ × g₃₃ values were relatively small because of its large ε^T₃₃/ε_o value. However, the 0.665PZ_0.46T_0.54‐0.335PZNN ceramic, which has a rhombohedral structure, exhibited a large g₃₃ value of 43 × 10^?3 Vm/N and a d₃₃ × g₃₃ value of 27 000 × 10^?15 m²/N. Therefore, this ceramic is a good candidate for multilayer actuators and piezoelectric energy harvesters.     

Enhancement of super-hydrophilic/underwater super-oleophobic performance of ceramic membrane with TiO2 nanowire array prepared via low temperature oxidation

A gradient porous ceramic membrane with surface super-hydrophilic and underwater super-oleophobic performance was prepared by combining hydrogel directional freezing method and low temperature oxidation process. The effects of solid contents and sintering temperature on the ceramic membrane matrix were examined. The reaction time and synthesis temperature on the TiO₂ nanowire array were also evaluated. In addition, the related effects on pore size distribution, permeation flux, contact angle, and oil-in-water emulsion separation were systematically investigated. The ceramic membrane matrix pore size changed from 0.5 μm to 25 μm gradually, indicating the gradient structure controlled by the growth of ice. The super-hydrophilic and underwater super-oleophobic performance of ceramic membrane surface was obtained with surface modification by TiO₂ nanowire array, and the surface water contact angle and underwater oil contact angle were less than 5° and over 158°, respectively. The bonding strength between TiO₂ nanowire and ceramic membrane matrix was high enough to withstand ultrasonic waves. The ceramic membrane modified with TiO₂ nanowire array was used for 1000 ppm diesel oil-in-water emulsion separation, and the stable separation efficiency and flux were about 97% and 100–200 L/(m² h bar) even after 10 filtration cycles.     

Microstructure of TiO2 porous ceramics by freeze casting of nanoparticle suspensions

During freeze casting of TiO₂ porous ceramics, the porous architecture is strongly influenced by TiO₂ particle size, solids loading, and cooling temperature. This work investigates the influences of particle size, freezing substrate, and cooling temperature on the TiO₂ green bodies prepared by freeze casting. The results show that the lamellar channel width with 100 nm particles is larger than that of 25 nm particles, yet the ceramic wall thickness is noticeably decreased. The lamellar structure is more ordered when using a copper sheet than glass as its freezing substrate. A finer microstructure results when frozen at − 50 ℃ than − 30 ℃. Such porous materials have application potentials in a wide range of areas such as photocatalysis, solar cells, and pollutant removal and should be further studied.     

Highly conductive ceramic-in-polymer composite electrolyte enabling superior electrochemical performance for all-solid-state lithium batteries

In the present work, poly (vinylidene fluoride-co-hexafluoropropylene) [P(VDF-HFP)] and various amounts of NASICON-type LiZr_1.5Sn_0.5(PO₄)₃ (LZSP) as the active filler were used to fabricate composite solid electrolytes (CSEs) by solution-casting method and their structural and electrochemical behaviour were studied. The X-ray diffraction (XRD) data showed the compatibility of the rhombohedral LZSP with P(VDF-HFP). A uniform distribution of ceramic particles in the polymer was observed from scanning electron microscopy (SEM) images and energy X-ray dispersive maps. The addition of 15% wt. ceramic filler to the polymer matrix enhanced the room temperature ionic conductivity (σ ∼ 2.87 × 10⁻⁵ S/cm), lithium-ion transference number (t_Li⁺ ∼ 0.55), and electrochemical stability window (∼4.87 V). The reversibility and endurance of lithium-ion conduction across the composite electrolyte at various current densities were confirmed through galvanostatic charge-discharge measurements on a symmetric lithium cell for more than 500 h. A full cell fabricated using a commercial grade LiMn₂O₄ cathode and the optimized CSE electrolyte showed excellent rate performance at room temperature. The cell delivered a discharge capacity of 105 mAh/g with a nominal voltage of 4.0 V and retained 93% of its initial capacity after 100 cycles at a current density of 0.1 mA/cm².     

Impact of initial moisture content levels,freezing rate and instant controlled pressure drop treatment (DIC) on dehydrofreezing process and quality attributes of quince fruits

Dehydrofreezing process involves water partial removal before freezing. This treatment has been proposed in order to reduce the negative impacts of conventional or even accelerated freezing, especially on the textural quality of high water content fruits and vegetables. Indeed, in such cases, freezing and thawing processes result in severe damage of the integrity of product’s cell structure due to the formation of ice crystals. For this purpose, quince fruits (7?g H₂O/g db) were subjected to convective air drying of 40?°C and 3m/s to reach different water content levels of 2, 1, and 0.3?g H₂O/g db. Freezing profiles obtained at various freezing rates (V₁, V₂, and V₃) for different water contents allowed the main freezing characteristics such as the Initial Freezing Temperature (IFT), the Practical Freezing time (PFt), and the Specific Freezing time (SFt) to be assessed. The impact of freezing rate was important on PFt and SFt, and more pronounced for high water contents (W between 7 and 2?g H₂O/g db (dry basis)). Furthermore, IFT decreased sharply when initial sample water content decreased. Indeed, it started at ?0.8?°C for W?=?7g H₂O/g db, while it reached a value of ?8.2?°C for samples of W?=?1g H₂O/g db. Since convective air drying normally triggers shrinkage which causes a detrimental deformation of fruit structures, instant controlled pressure drop (DIC) treatment was used to improve the texture and enhance the whole dehydrofreezing performance and the final frozen-thawed product quality. Moreover, DIC implied a slight increase of PFt compared to untreated ones. On the other hand, quality attributes were estimated through the assessment of thawed water exudate (TWE g H₂O/100?g db), color and texture (maximum puncture force as index of firmness): freezing rate and water content had great impacts on TWE. Hence, the lower the water content, the weaker the TWE. Furthermore, the TWE of the pre-dried quince (0.3?g H₂O/g db) had higher value for DIC-textured samples than for the un-treated ones. Indeed, DIC-texturing leads to a well-controlled structure expansion of the cell wall. These textural changes resulted in more lixiviation of residual water. Consequently, water becomes more available, hence more releasable after thawing. Finally, the partial removal of water by air drying before freezing remarkably reduced the negative impact of freezing/thawing processes on final quince color. Decisively, the firmness of quince fruit increased with the decrease of water content level.

Abbreviations: DMC: Dry Matter Concentration (%); DIC: Instant controlled pressure drop; W: Water content dry basis (g H₂O/g db); IFT: Initial Freezing Temperature (°C); PFt: Practical Freezing time (min); SFt: Specific Freezing time (min); TWE: Thawed Water Exudate (g H₂O/100?g db); L, a, and b: Color coordinates; (L): The degrees of lightness; (a) and (–a): The redness (a) or greenness (?a), respectively; (b) and (?b): The yellowness (b) or blueness (?b), respectively; ΔE*_ab: Total color difference; L₀, a₀, and b₀: Color coordinates of fresh or dried quince samples; SD: Standard Deviation; ANOVA: Analysis of variances; LSD: Least Significant Differences; cp: Specific Heat of the product depending on composition (dry material and water content)(KJ/kg K); cp_d: Specific Heat of the dry material (KJ/kg K); cp_W: Specific Heat of water (KJ/kg K); V₁: Freezing rate without insulation; V₂: Freezing rate with a food stretch film insulation with thickness e2?=?3?mm and thermal conductivity λ₂?=?0.17 W/m K; V₃: Freezing rate with a versatile flexible insulation (Armacell) with thickness e3?=?13mm and weak thermal conductivity λ₃?=?0.036 W/m K; v_d: Volume of dry material of quince sample (mm³); v_H2O: Volume of quince sample water (mm³); v_t: Total volume of quince sample (mm³); e₀: Quince sample thickness (mm); e₂: Insulation thickness in the case V2; = 3?mm; ; e₃: Insulation thickness in the case V3; = 13?mm; ; λ₀: Quince sample conductivity (W/m K); λ₂: Insulation conductivity in the case V2;?=?0.17 W/m K; ; λ₃: Insulation conductivity in the case V3;?=?0.036 W/m K; λ_d: Conductivity of quince sample dry material (W/m K); λ_H2O: Conductivity of water (W/m K); λ_equiv: Equivalent conductivity of quince sample versus water content (W/m K); m_i and m_f: Weights of the frozen and thawed samples, respectively