Transformation Properties Research Articles

Ca substitution effects on structure transformation and physical properties of (Eu,Ca)FeAs2 co-doped with La and Co

In this study, Ca substitution and carrier doping effect on phase formation temperature and physical/superconducting properties of (Eu0.9-xCaxLa0.1)(Fe0.97Co0.03)As2 ((Eu,Ca)112, x = 0–0.4) compounds were investigated. The best synthesis condition for obtaining pure phases vary (850–900 °C) depending on the Ca substitution amount. Ca substitution in the EuFeAs2 structure induced a structural transformation from orthorhombic I2mm to monoclinic P21/m symmetry. Single crystals of EuFeAs2 and (Eu0.9La0.1)FeAs2 were grown and their crystal structures were determined. Density functional theory calculations confirmed the transformation and stability of the La-doped Eu112 crystal structure with Ca substitution. Compared with the parent compound EuFeAs2, the effective substitution of Ca reduced the lattice constants. The magnetic and transport properties of (Eu0.9-xCaxLa0.1)(Fe0.97Co0.03)As2 compounds were studied using the temperature and field dependence of the magnetization and electrical resistivity measurements. Ca substitution suppressed the magnetic ordering of Eu and gradually reduced the Néel temperature TNEu. As determined by the magnetization and electrical resistivity data, the onset of critical temperature (Tc) values increased with Ca substitution increment from 26 K to 32.2 K and 31 K–34.8 K, respectively. Ca substitution slightly increased the upper critical field values, while the coherence length ξ values were slightly decreased. The Ca substitution and sintering temperature dependence of superconductivity, upper critical fields, lower critical fields, and Eu-related magnetic transitions were extracted. The new series of Eu-containing iron-based superconductors with high Tc provides an interesting playground in this field.

The effect of Zn doping on the structure, phase transformation and electric properties of 0.5BZT-0.5BCT materials

In the current study, an improved method of adding Zn ion doping to the 0.5BZT–0.5BCT–based films with high pyroelectric properties was designed. Under different Zn ion doping ratios, the structure, dielectric constant, phase transition relationship and other characteristics of the test product were analyzed experimentally to obtain the optimal ratio parameters. The experimental results demonstrate that the dielectric properties of the 0.5BZT–0.5BCT–xZn–based films proposed in this study can be far superior to those of other films under the optimal preparation process. The optimal dielectric properties and ferroelectric properties are obtained when the doped data are 0.008. Considering the comprehensive dielectric and energy storage capacity, the optimal doping ratio is 0.01, which can take into account dielectric data and energy storage performance. The energy storage density is 1.842 J/cm3, and the energy storage efficiency exceeds 30%. From 0 to 0.02, the properties of the material, such as the hysteresis loop and phase transition relationship are excellent. The properties of the materials studied in this study are excellent, and they are excellent candidate materials for the future application of ferroelectric materials, and provide ideas for related work.

Formation kinetics and thermodynamic stability of the Aurivillius compounds in Bi4Ti3O12–BiFeO3 system

AbstractThe Aurivillius compounds in the Bi2O3–Fe2O3–TiO2 system, combining ferroelectric, semiconducting, and ferromagnetic properties, have attracted particular interest. Formation kinetics and thermodynamic stability are the fundamental knowledge needed for modeling and predicting the temporal microstructure and property evolution during materials processing but have not yet been addressed by quantitative experimental measurement. This article focuses on the Bin+1Fen–3Ti3O3n+3 Aurivillius compounds on the Bi4Ti3O12–BiFeO3 tie‐line to elucidate the mechanisms and thermodynamic controls responsible for phase formation of compounds with various perovskite‐like layers. Five high‐purity Aurivillius compounds Bi4Ti3O12, Bi5FeTi3O15, Bi6Fe2Ti3O18, Bi7Fe3Ti3O21, and Bi8Fe4Ti3O24 with integer n = 3–7 values were synthesized and their phase transformation properties and enthalpies of formation were studied by X‐ray diffraction in situ, high temperature differential scanning calorimetry, and high temperature oxide melt solution calorimetry. Thermodynamic stability of the compounds decreases with increasing n, and formation kinetics gradually slow down, demonstrating the inherent difficulty to synthesize pure Aurivillius compounds with n larger than 8. This difficulty was confirmed by an impurity phase coexisting with Bi9Fe5Ti3O27.

A hybrid modeling approach: dynamic simulation of two-phase fluid flow in compacting gas condensate reservoirs using potential flow theory

Simulating the flow processes of complex hydrocarbon mixtures, such as gas condensate mixtures and volatile oils, in deep reservoirs is one of the most challenging problems in reservoir hydrodynamics. The challenge lies in meeting three requirements simultaneously when creating a simulator: high accuracy, low computational cost, and high reliability. These metrics determine the performance of the simulation. Meeting all these requirements at the same time necessitates a hybrid approach to solving the problem and optimizing the computational algorithm in terms of CPU time. A new technique has been developed for hybrid modeling of the development of deposits of complex hydrocarbon mixtures. This technique integrates the theory of potential flow, the Binary Flow Model (which accounts for rock compaction, PVT properties of reservoir fluids, phase transformation, and mass transfer between phases), and the material balance equations of the hydrocarbon system using time discretization. In this case, to linearize nonlinear differential equations for the flow of a gascondensate mixture, the method of averaging reservoir pressure along the radial coordinate was used. By introducing the Khrestianovich function, an algorithm was obtained to determine the rate of inflow of the gas-condensate mixture to the well. Using material balance equations for gas and condensate, it was possible to obtain differential equations that describe changes in reservoir pressure and condensate saturation over time. Based on this technique, a simulator for a gas condensate reservoir was created, enabling computer studies to be conducted. The results demonstrated the proposed technique's good accuracy compared with the results of the semi-analytical solution. Keywords: dynamic modeling; simulation; monitoring; streamline; hybrid modeling; binary model.

Phase transformation and mechanical properties of nanocrystalline Ti–2Fe-0.1B alloy processed by high pressure torsion

In this paper, nano-Ti-2Fe-0.1B alloys with different grain sizes were processed by high pressure torsion (HPT) deformation. The study examined the microstructural evolution of the Ti–2Fe-0.1B alloy during HPT and evaluated its mechanical properties through microhardness and tensile tests. The results of the microstructural observations revealed that the grain size of the Ti–2Fe-0.1B alloy progressively decreased from 3.14 μm in the as-annealed state to approximately 20 nm after 10 turns. In the initial state, the alloy consists of α-phase and β-phases, with a volume ratio of approximately 5:1. During the HPT process, transformations of α-phase and β-phase to ω-phase were observed. The primary reason for this is that the shear forces applied during the HPT process facilitated the phase transformation of the α-phase. Additionally, the presence of Fe element in the alloy altered the lattice compatibility between the grains of β-phase and ω-phase, thereby promoting the phase transformation of the β-phase, with the accumulated turns of HPT process, the fraction of ω-phase increased in the beginning gradually, then decreased, which reached to the maximum 80.8% in the 5 turns. This is higher than that of pure titanium and Ti–Fe alloys under the same conditions, because the proportion of the ω-phase increases with the increase in Fe content. Studies of mechanical properties demonstrated that HPT can substantially enhance the hardness of Ti–2Fe-0.1B alloys to as high as 483 HV, and the tensile strength of the Ti–2Fe-0.1B alloy was observed to increase from 725 MPa to 1568 MPa after 5 turns, which is much higher than Ti–6Al–4V subjected to the identical processing conditions. It can be ascribed to the exist of mass ω-phase as well as finer grain size in nanocrystalline Ti–2Fe-0.1B alloy.

Cretaceous evolution of the Lhasa-Qiangtang Orogen: insights from mafic igneous rocks

ABSTRACT The compositional changes of successively emplaced mafic magmatites provide insights into the evolution of orogenic belts, particularly the transformation processes and properties of the orogenic lithospheric mantle. Herein, we present new zircon U‒Pb ages and Lu‒Hf isotopes, as well as whole-rock major, trace element, and Sr – Nd isotope compositions from three mafic intrusions in the Asuo area, central Tibet, to clarify the evolution of the Lhasa – Qiangtang Orogenic Belt (LQOB). These mafic intrusions can be classified into calc-alkaline basalts and are enriched in large ion lithophile elements and depleted in high-field strength elements. Significant differences in the whole-rock trace element compositions, Sr – Nd isotope values, and U – Pb ages stratify them into two groups, namely Groups I and II, of which Group I rocks (ca. 105 Ma) show lower87Sr/88Sri = (0.70694–0.70701), [Sm/Yb]N = (1.51–1.54) and higher εNd (t) = (−0.74 to −0.61) than Group II (ca. 97–95 Ma) (87Sr/88Sri = 0.70759–0.70870; εNd (t) = –4.58 to −3.75; [Sm/Yb]N = 2.43–2.94). These features indicate that the mantle source exhibits a progressive increase in the proportion of garnet, along with significant addition of subduction-related components into the primary melts. One scenario for producing such trace element patterns and gradually enriched radioactive isotope signatures involves the extensive heating of an oceanic slab beneath the LQOB by upwelling asthenosphere, which leads to the extensive melting of sediments within the slab. Identification of ca. 105–95 Ma Asuo mafic rocks suggests their formation in a post-collisional setting with additional heat input from the deep mantle. These results provide new evidence supporting the occurrence of the Lhasa – Qiangtang collision within the framework of north-south bidirectional subduction.

Nanocellulose-based cobalt(II) coordinated malonic acid hybrid aerogels exhibiting reversible thermochromism and moisture sensor properties

The emergence of sustainable polymers and technologies has led to the development of innovative materials with minimal carbon emissions which find extensive applications in wearable electronics, biomedical sensors, and Internet of Things (IoT)-based monitoring systems. Nanocellulose which can be generated from abundant biomass materials has been widely recognized as a sustainable alternative for a diverse range of applications due to its remarkable properties and eco-friendly nature. By making use of the unique and easily accessible coordination transformation property of Co(II) ions and associated visible light absorption changes, we report a novel Co(II) cation-incorporated nanocellulose/malonic acid hybrid aerogel material that exhibits reversible thermochromism induced by thermal stimulus in the presence of atmospheric moisture. This effect is accentuated by the highly porous nature of the nanocellulose aerogel material we have developed. Besides the reversible thermochromic property which Co(II) ions exhibit, the metal ions act as very efficient reinforcing units contributing significantly to the structural stability and rigidity of the hierarchical aerogels by coordinative cross-linking through carboxylate moieties present in the TEMPO-oxidized cellulose nanofibers (TCNF) and additionally adding malonic acid to provide sufficient COO− for cross-linking. Thorough characterization and detailed investigation of as-prepared hybrid aerogels was conducted to evaluate their overall properties including reversible thermochromism and moisture sensor behaviour. Further, an Android mobile-based application was developed to demonstrate the real-world application of the aerogels for atmospheric humidity sensing.

Effect of Nb content and cooling rate on the microstructure transformation and mechanical properties of hot-rolled rebar

In this study, the synergistic effect of the Nb content and cooling rate on the microstructural transformation, precipitation behavior, and mechanical properties of hot-rolled rebar was studied using a Gleeble-3800 thermal simulation machine, scanning electron microscopy, transmission electron microscopy, and a universal tensile testing machine. The results showed that the synergistic effect of Nb content and cooling rate could optimize the microstructure and precipitation behavior of rebar, promote ferrite and pearlite transformation, and reduce the ferrite grain size, pearlite lamellar spacing, and precipitated phase size, thereby improving the strength and plasticity of Nb-containing rebar. When the cooling rate was 3 °C/s and the Nb content was 0.035 wt%, the ferrite grain size decreased to 21.45 μm, the pearlite lamellar spacing refined to 0.222 μm, and the particle size of the (Nb, Ti, V) C precipitates reduced to 5 nm. Accordingly, the yield and tensile strength increased to 779 ± 6 MPa and 973 ± 8 MPa, respectively, the elongation at fracture increased to 16.35%, and the microhardness increased to 311.39 ± 8.0 HV.

Soliton generation and conservation laws for vector light pulses propagating in weakly birefringent waveguides

The principal algebra Lp of coupled nonlinear Schrödinger equations describing the propagation of polarized optical pulses and involving four-wave mixing terms is obtained in terms of the three arbitrary labelling parameters of the system of equations. This algebra is found to be five-dimensional, indicating the richness in symmetries of the system. The most general symmetry group transformation by generators of Lp is found and it is shown that this transformation preserves the boundedness of solutions, and an example of transformation of a soliton solution into a completely new soliton of a different type is presented. Moreover, it is explained how an infinite sequence of bounded solutions can thus be generated, yielding new solitons. Several other important properties of solutions and symmetry group transformations of the system are also demonstrated. As the system of Schrödinger equations under study turns out to be of Lagrange type, conservation laws associated with all variational symmetries of Lp are constructed and interpreted. Some symmetry reductions of the system are also derived.

‘The ‘Vector-Model’ wavefunction: spatial description and wavepacket formation of quantum-mechanical angular momenta’

We introduce the concept of an asymptotic spatial angular-momentum wavefunction, Xmjφ,θ,χ=eimφδθ−θm eij+12χ, which treats j in the jm state as a three-dimensional entity; φ, θ, χ are the Euler angles, and θm is the Vector-Model polar angle, given by cosθm=m/j. A wealth of geometric information about j can be deduced from the eigenvalues and spatial transformation properties of the Xmjφ,θ,χ. Specifically, the Xmjφ,θ,χ wavefunction gives a computationally simple description of the sizes of the particle and orbital-angular-momentum wavepackets (constructed from Gaussian distributions in j and m ), given by effective wavepacket angular uncertainty relations for ΔmΔφ, ΔjΔχ, and ΔφΔθ. The Xmjφ,θ,χ also predicts the position of the particle-wavepacket angular motion in the orbital plane, so that the particle-wavepacket rotation can be experimentally probed through continuous and non-destructive j -rotation measurements. Finally, we use the Xmj(φ,θ,χ) to determine geometrically well-known asymptotic expressions for Clebsch–Gordan coefficients, Wigner d-functions, the gyromagnetic ratio of elementary particles, g=2, and the m -state-correlation matrix elements. Interestingly, for low j, even down to j=1/2, these expressions are either exact (the last two) or excellent approximations (the first two), showing that the Xmj(φ,θ,χ) give a useful spatial description of quantum-mechanical angular momentum, and provide a smooth connection with classical angular momentum.

Exploring the optical properties of the 1.53 μm emission in Er3+-doped glass, anti-glass and ceramic in TeO2 - Ta2O5 – Bi2O3 system

A series of 80TeO2 - 10Ta2O5 – 10Bi2O3 glasses, anti-glasses and ceramics doped with different concentrations of Er₂O₃, ranging from 0.25 % to 2 % mol, were synthesized to explore their structural transformation and optical properties. The maximum solubility of Er₂O₃ was identified at 1.25 % mol, beyond which the glass transitioned from an amorphous to a crystalline structure. The anti-glasses and ceramics obtained from the heat treatment of the parent glasses were also studied to gain insights into their optical properties. This study reveals a direct relationship between Er3+ ions concentration and full width at half maximum (FWHM) of photoluminescence spectra. The increase in Er3+ ions concentration correlates with a rise in FWHM, indicative of spectral broadening. Anti-glass exhibits a higher emission intensity, followed by ceramic and then glass, reflecting their distinct structural properties. Anti-glass doped with 1 % mol Er2O3 shows an FWHM over 130 nm under 578 mW pumping. The lifetime of the excited state 4I13/2 increases with the Er2O3 content in the anti-glass and the ceramic, with a notable decrease at 1 % mol Er2O3 ions for both materials, while in glass, the decrease is observed at 0.5 %. Emission cross-sections decrease with increasing Er3+ ions concentration and power, influenced by factors like thermal effects and saturation. The Judd-Ofelt theory highlights structural differences, with glasses having a more disordered structure and with an increase in the Ω₆ parameter across all materials, implying enhanced electric dipole line strength and spontaneous emission probability with higher Er₂O₃ content. Overall, this comprehensive study provides valuable insights into the optical behavior of Er3+ ions in these materials, essential for applications in laser design and optical amplifiers.

An SMA-based compliant adjustable constant force gripper for micro-assembly

Ensuring precise and consistent force regulation in a confined workspace is critical for high-quality micro-assembly operations. To enhance structural efficiency and reduce system complexity, this study leverages the variable stiffness properties of the shape memory alloy (SMA) and presents a novel compliant adjustable constant force microgripper. In this work, a passive variable stiffness chained pseudo-rigid-body model is established to address the coupling analysis problem arising from the mechanical and SMA’s in-homogeneous phase transformation properties, thereby facilitating the integrated design of the SMA and the mechanism. Exploiting the variable stiffness property of SMA, an improved stiffness-tunable two-beam-binding constant force mechanism is proposed for the gripper jaws, which makes adjustable constant force operation via current control can be achieved straightforwardly. Further, inspired by differential actuation mode, a compact SMA-based actuator comprising two parallel guide mechanisms and SMA drivers is developed to meet the requirement for the large working stroke of the gripper. Numerical simulations and experimental studies validate the design model’s efficiency and the proposed structures’ capabilities, and also prove the gripper’s constant operation force value can be regulated in the range of 0.152 to 0.381 N. With dimensions of 35×56.5×7 mm3 and a maximum stroke of 2.077mm, the gripper demonstrates fine compactness and potential for continuous, cross-scale micro-assembly.

Microstructural features, martensitic transformation, and functional properties of multicomponent Ti–Ni based shape memory alloys

Microstructural features, martensitic transformation, and functional properties of multicomponent Ti–Ni based shape memory alloys

Effect of heat treatment on phase transformation behavior and properties of Ni-Co-Mn-Al-Y shape memory alloy by laser direct energy deposition

Laser direct energy deposition (LDED) of Ni-Co-Mn-Al-Y magnetic shape memory alloys (MSMAs) with high elastocaloric properties has important application prospects in solid-state refrigeration. However, because the microstructure of laser non-equilibrium metallurgy does not have reversible martensitic transformation, further regulating the microstructure of deposited samples through scientific post-heat treatment to obtain better properties is still a top priority. In this work, Ni-Co-Mn-Al-Y alloy samples were prepared by an optimized LDED process, and then the deposited samples were heat-treated with different temperatures. The results showed that the sample subjected to heat treatment with 550 °C × 3.5 h + 1100 °C × 20 h had maximum entropy change of the phase transformation, compressive properties, and elastocaloric effect. The compressive fracture strength was up to 1327 MPa, the maximum compressive strain was up to 26.2%, and an adiabatic temperature change was up to −4.3 K under the condition of rapid unloading. Characterization of the microstructure changes of the alloy under 11 cycles of compression revealed that the deformation mechanism was mainly planar sliding of dislocations in the martensite and dislocation cutting the γ(Y-rich) phase. The alloy prepared by the optimizing LDED and heat treatment process had better cycle stability and preliminary refrigeration capacity.

W_{1+∞} Algebra with a Cosmological Constant and the Celestial Sphere.

It is shown that there exists a simple deformed version of Strominger's infinite-dimensional w_{1+∞} algebra of soft graviton symmetries, which we conjecture to arise in spacetimes with a nonvanishing cosmological constant. The deformed algebra contains a subalgebra generating SO(1,4) or SO(2,3) symmetry groups of dS_{4} or AdS_{4}, depending on the sign of the cosmological constant. The transformation properties of soft gauge symmetry currents under the deformed w_{1+∞} are also discussed.

Felix Klein’s early contributions to anschauliche Geometrie

Between 1873 and 1876, Felix Klein published a series of papers that he later placed under the rubric anschauliche Geometrie in the second volume of his collected works (1922). The present study attempts not only to follow the course of this work, but also to place it in a larger historical context. Methodologically, Klein’s approach had roots in Poncelet’s principle of continuity, though the more immediate influences on him came from his teachers, Plücker and Clebsch. In the 1860s, Clebsch reworked some of the central ideas in Riemann’s theory of Abelian functions to obtain complicated results for systems of algebraic curves, most published earlier by Hesse and Steiner. These findings played a major role in enumerative geometry, whereas Plücker’s work had a strongly qualitative character that imbued Klein’s early studies. A leitmotif in these works can be seen in the interplay between real curves and surfaces as reflected by their transformational properties. During the early 1870s, Klein and Zeuthen began to explore the possibility of deriving all possible forms for real cubic surfaces as well as quartic curves. They did so using continuity methods reminiscent of Poncelet’s earlier approach. Both authors also relied on visual arguments, which Klein would later advance under the banner of intuitive geometry (anschauliche Geometrie).

Effect of Mo and Cr on the Microstructure and Properties of Low-Alloy Wear-Resistant Steels.

Low-alloy wear-resistant steel often requires the addition of trace alloy elements to enhance its performance while also considering the cost-effectiveness of production. In order to comparatively analyze the strengthening mechanisms of Mo and Cr elements and further explore economically feasible production processes, we designed two types of low-alloy wear-resistant steels, based on C-Mn series wear-resistant steels, with individually added Mo and Cr elements, comparing and investigating the roles of the alloying elements Mo and Cr in low-alloy wear-resistant steels. Utilizing JMatPro software to calculate Continuous Cooling Transformation (CCT) curves, conducting thermal simulation quenching experiments using a Gleeble-3800 thermal simulator, and employing equipment such as a metallographic microscope, transmission electron microscope, and tensile testing machine, this study comparatively investigated the influence of Mo and Cr on the microstructural transformation and mechanical properties of low-alloy wear-resistant steels under different cooling rates. The results indicate that the addition of the Mo element in low-alloy wear-resistant steel can effectively suppress the transformation of ferrite and pearlite, reduce the martensitic transformation temperature, and lower the critical cooling rate for complete martensitic transformation, thereby promoting martensitic transformation. Adding Cr elements can reduce the austenite transformation zone, decrease the rate of austenite formation, and promote the occurrence of low-temperature phase transformation. Additionally, Mo has a better effect on improving the toughness of low-temperature impact, and Cr has a more significant improvement in strength and hardness. The critical cooling rates of C-Mn-Mo steel and C-Mn-Cr steel for complete martensitic transition are 13 °C/s and 24 °C/s, respectively. With the increase in the cooling rate, the martensitic tissues of the two experimental steels gradually refined, and the characteristics of the slats gradually appeared. In comparison, the C-Mn-Mo steel displays a higher dislocation density, accompanied by dislocation entanglement phenomena, and contains a small amount of residual austenite, while granular ε-carbides are clearly precipitated in the C-Mn-Cr steel. The C-Mn-Mo steel achieves its best performance at a cooling rate of 25 °C/s, whereas the C-Mn-Cr steel only needs to increase the cooling rate to 35 °C/s to attain a similar comprehensive performance to the C-Mn-Mo steel.

Compositionally graded titanium to aluminum processed by laser powder bed fusion process: Microstructure evolution and mechanical properties

A compositionally graded Ti–Al alloy with a designed composition range from pure Ti to pure Al was successfully produced by a laser powder bed fusion (L-PBF) system equipped with two powder feeders. The compositionally graded Ti–Al profile is confirmed by scanning electron microscopy, X-ray diffraction analysis, electron backscatter diffraction microscopy, and transmission microscopy. The graded material is free of macro-horizontal cracks, but micro-cracks appear at the center of the sample. Varying the Ti and Al ratio along the build direction induces microstructural changes, transforming α+β-Ti into solid solution, creating intermetallics (Ti and Al), and yielding an Al phase with diverse morphologies. Additionally, the Ti–Al ratio's influence on microstructure formation and phase evolution results in varying mechanical properties among the graded material's layers. The results demonstrate that the L-PBF process can achieve continuous compositional grading of Ti–Al materials in a single run. Moreover, this study hold the potential to facilitate the design and production of numerous compositional variants for high entropy alloys and multi-materials, enabling future investigation into microstructural evolution, phase transformation, and physical and mechanical properties.

Study of high temperature mechanical properties and damage behavior of Ni-YSZ anode/SrO–MgO–SiO2 glass-ceramic sealant/430 s.s. interconnect system in solid oxide fuel cells (SOFC)

In the sealing system of Ni-YSZ anode/SrO–MgO–SiO2 glass-ceramic sealant/430 s s. interconnect, the phase transformation and mechanical properties of interfaces are studied after operating 0 h, 100 h, and 1800 h at 750 °C. The results show that the interface fracture appears in the glass/anode and glass/interconnect interfaces after operating at 1800 h. The interface mechanical parameters within different operation times are collected to investigate the effects of crystallization, penetration, and high temperature mechanical properties on the interlayer stress and structure damage. The Sr2MgSi2O7 crystal phase increases the glass modulus from 104.5 GPa to 129.8 GPa with a runtime from 0 h to 1800 h. The modulus of the Ni-YSZ interface also increases from 82.4 GPa to 128.3 GPa with the glass penetration process. The 430 s s. modulus is reduced by 13 % at 750 °C after 1800 h to reach 191.1 GPa. The established anode/glass/interconnect interlayer stress model accurately calculates the compressive stress at the glass/anode side interface and glass/interconnect side interface, with values reaching −755.2 MPa and −587.1 MPa, respectively. The crystallization zone of the SrO–MgO–SiO2 glass-side interface near Ni-YSZ and 430 s s. become the stress damage sensitive zones and break under interlayer stress.

Matter relative to quantum hypersurfaces

We explore the canonical description of a scalar field in 1+1 dimensional Minkowski space as a parametrized field theory on an extended phase space that includes additional embedding fields that characterize spacetime hypersurfaces X relative to which the scalar field is described. This theory is quantized via the Dirac prescription and physical states of the theory are used to define conditional wave functionals |ψϕ[X]⟩ interpreted as the state of the field relative to the hypersurface X, thereby extending the Page-Wootters formalism to quantum field theory. It is shown that this conditional wave functional satisfies the Tomonaga-Schwinger equation, thus demonstrating the formal equivalence between this extended Page-Wootters formalism and standard quantum field theory. We also construct relational Dirac observables and define a quantum deparametrization of the physical Hilbert space leading to a relational Heisenberg picture, which are both shown to be unitarily equivalent to the Page-Wootters formalism. Moreover, by treating hypersurfaces as quantum reference frames, we extend recently developed quantum frame transformations to changes between classical and nonclassical hypersurfaces. This allows us to exhibit the transformation properties of a quantum field under a larger class of transformations, which leads to a frame-dependent particle creation effect. Published by the American Physical Society 2024