Scripta Materialia

Article	Citations
Control of surface inverse segregation in Al–4.5Mg strips produced by industrial twin-roll casting process	253
Schoen ACTA Biomaterialia Press Release	152
Using ab initio molecular dynamics to determine the mobility of single, di and tri self-interstitial configurations in hcp Zr	139
In situ synchrotron X-ray diffraction study: Phase evolution in transition zone of TiAl/Ti2AlNb dual alloy fabricated by laser-directed energy deposition	132
Unusual deformation behavior and the consequent emergence of Type C serrations in Fe-1.6Mn-2Ni-1.4Si-0.4C steels	117
Enhanced toughness and wear behavior of TiNbWN films via a novel microstructure of rectangular nanocrystals embedded within an amorphous matrix	102
Editorial Board	100
Three-dimensional faceted boundaries of {101¯	100
Effect of WC/WC grain boundary misorientation angle on the local hardness in WC–Co cemented carbides	91
Structural superlubricity and dislocation bending behaviors of NiCoCr medium-entropy alloys with incommensurate contact	86
Quenching induced depolarization delay and structure evolution in (1-x)Na1/2Bi1/2TiO3-xBiFeO3 ceramics	83
Melting temperature, emissivity, and thermal conductivity of rare-earth silicates for thermal and environmental barrier coatings	79
Strontium titanate modified separator regulates ion flux to stabilize aqueous zinc ion battery anodes	78
Coexistence of rod-like and lamellar eutectic growth patterns	78
Stress increase by nanoscale hcp precipitates in HfNbTaTiZr high entropy alloys	77
Achieving ultra-strong and ductile CoNi-based FCC multi-principal element alloys via alloying with refractory Mo and W	75
Investigation on the incipient plasticity of 〈001〉-oriented CoCrFeNi micropillar	73
Grain boundary sliding with diffusional accommodation enable dynamic recrystallization during hot deformation of coarse-grained body-centered cubic HfNbTaTiZr high-entropy alloys	71
Stress-induced gradient rejuvenation framework and memory effect in a metallic glass	67
Artificial neural network molecular mechanics of iron grain boundaries	65
Strain partition induced abnormal low-cycle fatigue behavior in single-phase heterostructured 316L stainless steels	64
3D mapping of orientation variation and local residual stress within individual grains of pearlitic steel using synchrotron dark field X-ray microscopy	64
Enhancement of magnetostriction in laser powder bed fusion Fe-Ga alloy by texture formation	64
The effect of pressure tuning on the structure and mechanical properties of high-entropy carbides	62
CsSn2(HPO3)2I: The first inorganic metal phosphite iodide as a promising birefringent material exhibits a large birefringence with ideally layered framework	61

Editorial Board	60
Investigating the Structural and Lithium Storage Properties of High-Entropy Oxides in the Mg-Co-Ni-Cu-Zn-O System	60
Strengthening retention and structural stability of the Al-Al3Ni eutectic at high temperatures	60
NiZnFe2O4 core-shell nanoflowers as effective EMI shielding material dedicated to the absorption of electromagnetic waves in the UHF band and wide temperature range	59
Band gap tunning to enhance photovoltaic response in NaNbO3-based bulk ferroelectrics	58
Oxygen and nitrogen effects on anelasticity and mechanical property of Ti35Zr30V10Nb25 multi-principal element alloys	58
Chemical substitution – oriented design of a new polar PbFIO3 achieving a balance between large second-harmonic generation response and wide band gap	57
Flexible design of large layer spacing V-MoS2@C cathode for high-energy zinc-ion battery storage	55
Studies of recrystallization in rhenium using positron annihilation spectroscopy	55
Tresa M. Pollock, 2023 Acta Materialia Gold Medal Recipient	55
Low modulus-yet-hard, deformable multicomponent fibrous B2-phase making a medium-entropy alloy ultra-strong and ductile	55
Editors for Scripta Materialia	54
Editors for Scripta Materialia	53
Orientation relationships in Cu/Nb bilayers deposited on (001) and (111) NaCl substrate	53
Stabilized piezoelectricity upon ferro-ferro phase transition achieved by aging induced domain memory effect in acceptor doped lead-free ceramics	53
Formation of stable equiaxial nanograined Al via combined plastic deformation	53
Editors for Scripta Materialia	52
Editors for Scripta Materialia	52
Screw dislocation mobility in a face-centered cubic solid solution with short-range order	52
Ultra-high temperature flexure and strain driven amorphization in polycrystalline boron carbide bulks	51
Compositional partitioning during early stages of oxidation of a uranium-molybdenum alloy	51
A highly sensitive MoS2/MoTe2 heterostructure enhanced by localized surface plasmon effect for broad-spectrum photodetection	50
Severe plastic deformation close to the melting point enables Mg-Fe nanocomposites with exceptional strength	50
Editors for Scripta Materialia	50
Tailoring homogeneous immiscible alloy via magneto-Archimedes levitation	49
Observation of dielectric resonance and negative capacitance in 0.65Pb(Mg1/3Nb2/3)O3-0.35PbTiO3 textured thin films	49
Recipients of the 2022 Acta Student Awards	48
Near-superplastic behavior of a body-centered cubic Zr50Ti35Nb15 multi-principal element alloy via dynamic recrystallization	48
Editors for Scripta Materialia	48
Wide tuning the carbon supersaturation within Fe-C lath martensite via high pressure martensitic transformation of Fe-0.45C alloy	48
Direct observation of grain boundary formation in bcc iron through TEM in situ compression test	47
Ultra-wide void denuded zone near composite grain boundary in micro-nano crystalline 304L steels	47
Editorial Board	47
Editors for Scripta Materialia	47
Improvement of battery performance by applying iron-containing recycled aluminum to current collector-free anode of lithium-ion batteries	46
A note on maxima and minima of dissipation in context of treatment of irreversible thermodynamic systems by application of Extremal Principles	46
Experimentally mapping the oriented-to-misoriented transition in laser powder bed fusion Ti-10%Mo alloys	46
Atomic-scale observation of strain-induced local amorphization in face-centered cubic metals	46
Iver E. Anderson, 2024 Acta Materialia Hollomon Award Medal Recipient	45
Bis (8-hydroxyquinoline) zinc complex derived ZnO@N-doped carbon composite for enhancing lithium storage performance	45
Editors for Scripta Materialia	45
Mo2N/CoN nanotube with synergistic reaction of intercalation and conversion enables high performance lithium-ion batteries	45
Microstructure and coercivity of Al-diffused Sm(Fe,Co,B)12 film	44
Editors for Scripta Materialia	44
Effect of boron segregation on bainite nucleation during isothermal transformation	43
On the influence of crystallographic texture on cyclic hardening of an AlMgSi alloy	43
Plasma-induced repair of macro-indentation formed cracks on yttria-stabilised zirconia	43
Comments about a recent publication entitled “Improving glass forming ability of off-eutectic metallic glass formers by manipulating primary crystallization reactions”	43
Origin of morphological variation of grain boundary precipitates in titanium alloys	43
Insights into photoemission origins of flash sintering of ceramics	42

Editorial Board	42
Evidence of intrinsic structural heterogeneity by monatomic metallic glass	42
Advancing electrochemical activity: Insights from Li doped Ni-MOF synthesis and performance	42
Factor which governs the feature of texture developed during additive manufacturing; clarified from the study on hexagonal C40-NbSi2	41
Exceptional fatigue life and ductility of new liquid healing hot isostatic pressing especially tailored for additive manufactured aluminum alloys	41
Direct observation of Face-centered cubic zirconium phase growth-induced stacking faults in Zr3Ge secondary phase nanoparticle	40
Enhanced high-temperature strength of austenitic steels by nanotwins and nanoprecipitates	40
Accelerated alloy discovery using synthetic data generation and data mining	40
Mechanism of DSA effect correlating to the macroscopic PLC banding in high-Mn austenitic steel	40
Identification of active slip systems in polycrystals by Slip Trace - Modified Lattice Rotation Analysis (ST-MLRA)	40
Ion exchange of glass under high pressure	39
Partially recrystallized heterostructure via Mo-doping endows CoCrNi medium-entropy alloy with exceptional strength and ductility	39
Corundum-structured AlCrNbTi oxide film grown using high-energy early-arriving ion irradiation in high-power impulse magnetron sputtering	38
Strength and ductility enhancement of high-entropy FeCoNi2Al0.9 alloy by ultrasonically refining eutectic structures	38
Electric field control of the reversible magnetocaloric effect in strain-mediated Ni37.5Co12.5Mn35Ti15/PMN-PT composite	38
Enhanced energy storage properties in BNST-based lead-free relaxor ferroelectric ceramics achieved via a high-entropy strategy	38
Achieving superior fatigue strength in a powder-metallurgy titanium alloy via in-situ globularization during hot isostatic pressing	37
Effects of Au2+ irradiation induced damage in a high-entropy pyrochlore oxide single crystal	37
Synergistic effect of twin consumption within lamellae and slip system activation at grain boundary on the formation of nano-spherical B2 phase	37
Machine Learning Approach for Evaluation of Nanodefects and Magnetic Anisotropy in FePt Granular Films	37
A rational proton compensation strategy of polyaniline-MnO2 hybrid structure for promoting dual ion storage of Zn-ion battery	36
Anisotropic grain boundary area and energy distributions in tungsten	36
Nano-twinning and uncommon α´-martensite formation as a result of very high cycle fatigue of metastable austenitic stainless steel at 573 K	36
Improvement of bulk superconducting current capability of MgB2 films using surface degradation	36
Force data-driven machine learning for defects in friction stir welding	36
Decomposition behavior in the early-stage oxidation of Sm2Co17-type magnets	36
The effect of atmosphere on the flash-sintering of nanoscale titania ceramics	36
In-situ TEM investigation of the effect of nano twins on the evolution of He bubbles under thermo-mechanical coupling conditions	36
Anomalous dislocation response to deformation strain in CrFeCoNiPd high-entropy alloys with nanoscale chemical fluctuations	36
Magnetocaloric properties of transition metal doped high entropy LaFe11Si2 alloys on Fe sites	36
Probing the fatigue enhancement in a thermally aged cast duplex stainless steel by in situ neutron diffraction	35
High strength NiMnFeCrAlCu multi-principal-element alloys with marine application perspective	35
A flow model in bulk metallic glasses	35
Modulating electronic structure of self-supported nickel-vanadium layered double hydroxide to accelerate hydrogen evolution reaction	35
New Ms-formula for exact microstructural prediction of modern 3rd generation AHSS chemistries	35
In-situ Al2O3-Al interface contribution towards the strength-ductility synergy of Al-CuO composite fabricated by solid-state reactive sintering	35
Friction stir welding of γ-fcc dominated metastable high entropy alloy: Microstructural evolution and strength	35
Oxidation mechanisms of an intermetallic alloy at high temperatures	35
Twinning mediated plasticity in high entropy CoCr1.3FeNi0.7MnNb (x = 0.3, 0.367, 0.4) ultrafine lamellar eutectic by tuning stacking fault energy	34
Porous CoP@RGO with pseudocapacitance characteristics for lithium ion storage	34
Effects of orientation on microstructure and mechanical properties of TiN/AlN superlattice films	34
Sn9O4Br9X (X = Cl, Br): Two new Sn(II) oxyhalides exhibiting large birefringence derived from highly distortive polyhedra of lone pair cations	34
Non-equilibrium thermodynamic modelling of cooling path dependent phase evolution of Li2SiO3 from Li2O-SiO2 melt by considering mixed kinetic phenomena and time-dependent concentration fields	34
Unusual martensitic strain accommodation mechanism in an electron beam processed metastable β-Ti alloy	33
In situ TEM investigation on the microstructure and phase evolution of hydrogenated Zr-4 alloy	33
Organometallic structure-based βCD@FeSe2/CoSe2 heterostructures cathodes for high-performance aluminum-ion battery	33
Tuning temperature coefficient of elastic modulus by heat treatment in a compositionally-modulated Ti-Nb-based alloy	33
Heat-affected coarsening of β grain in titanium alloy during laser directed energy deposition	33
Temperature-dependent anharmonic effects on shear deformability of Bi2Te3 semiconductor	33
Measuring the strength of ductile microparticles at extreme strain rates	33
Unveiling the thermometric sensitivity of Eu3+ doped glasses in various system from theory to experimental	33
On the migration of {101¯1} and {10	33
Solid solution strengthening of the body-centered cubic refractory complex concentrated alloy, MoNbTaW	33
Performance enhancement of Pb(In1/2Nb1/2)O3-PbTiO3 ferroelectric single crystals using pulse poling	33
On the origin of carbon supersaturation in bainitic ferrite	32
A pressure and entropy criterion for glass transition decoupling in high-entropy metallic glasses	32
Nanoscale chemistry and ion segregation in zirconia-based ceramic at grain boundaries by atom probe tomography	32
In situ observation of faceted growth and morphological instability of a complex-regular eutectic in Zn−Mg−Al system	32
Connecting processing conditions to microstructure evolution in laser powder bed fusion via defect modeling	32
Room-temperature-deformation-induced chemical short-range ordering in a supersaturated ultrafine-grained Al-Zn alloy	32
Higher Suitability of NbMoTaW over Its Elemental Metals for Laser Induced Periodic Surface Structure/Particle-Aggregate UV-to-MIR Ultrabroadband Absorber	32
Mass transport driving forces under electric current in the liquid Sn-Zn system	32
H2S gas sensing properties of ZnO–SnO2 branch–stem nanowires grown on a copper foil	31
Diffusion study by diffusion quadruple experiment and two-dimensional simulation	31
Enhanced strength-ductility synergy in brittle high borated steel by tailoring strain hardening behaviour	31
In-situ heating-stage EBSD validation of algorithms for prior-austenite grain reconstruction in steel	31
An in-situ Raman spectroscopy investigation of the oxidation of proton irradiated and cold-worked 304L stainless steel in oxygenated water at 300°C	31
Significant photovoltaic enhancement in La-doped BiFeO3 achieved by engineering crystallographic facet arrays	31
The compact-strip-produced martensitic steel possessing better resistance to hydrogen-induced delayed cracking	31
Predicting core structure variations and spontaneous partial kink formation for ½<111> screw dislocations in three BCC NbTiZr alloys	31
The effect of voids on boundary migration during recrystallization in additive manufactured samples—a phase field study	31
Discovery of a reversible redox-induced order-disorder transition in a 10-component compositionally complex ceramic	31
Polymer-assisted deposition and room-temperature ferromagnetism of amorphous Mn-doped gallium oxide films	31
The effect of annealing on kink band formation in Ag/Fe nanolaminates	31
Directionally solidified high-entropy (Y0.2Gd0.2Ho0.2Er0.2Yb0.2)3Al5O12/Al2O3 eutectic with outstanding crystallographic texture formation capability	31
Evidence for localized melting during dynamic hot compression of Ti-6Al-4V alloy	30
Planar fault transformation and unfaulting of interstitial dislocation loops in irradiated L12-Ni3Al	30
Optimizing bendability of AlSi-coated 2GPa-grade press-hardened steel by double austenitization	30
Formation of abnormal nodular ferrite with interphase precipitation in a vanadium microalloyed low carbon steel	30
Investigation of the orientation relationship between nano-sized G-phase precipitates and austenite with scanning nano-beam electron diffraction using a pixelated detector	30

High-pressure structural and transport studies of orthorhombic Sm2Ru3Ge5 compound	30
The {101¯	30
Real-time visualization of particle evolution during reactive flux-assisted processing of aluminum melts	30
Viewpoint: Can symmetric tilt grain boundaries represent polycrystals?	29
Influence of Zr element on the atomic structure of Al-Cu alloy liquid	29
Elastic strain associated with irradiation-induced defects in self-ion irradiated tungsten	29
Synthesis of Cs2TeI6 thin film and its NO2 gas-sensing properties under blue-light illumination	29
Synthesis of high-entropy alloy thin films via grain boundary diffusion–assisted solid-state alloying	29
Effect of Zr addition on metastable Liquid-Liquid Phase Separation of Cu-Fe alloys	29
An in-situ setup for simultaneous electro-chemo-mechanical characterization of electrode materials for lithium-ion battery	29
Development of ferrous-based weldable seismic damping alloy with prolonged plastic fatigue life	28
Magnetic transitions and magnetocaloric effect of Pr(Ga,Ge) compounds	28
Sharp/diffuse antiferroelectric-ferroelectric phase transition regulated by atomic displacement ordering	28
The effect of Ni and Fe on the decomposition of yttrium doped barium zirconate thin films	28
Direct observation of chemical short-range order in 25 wt% Mn steel via transmission electron microscopy	28
Regulating precipitation behavior in an ultrahigh-strength, high-molybdenum maraging steel via laser powder bed fusion	28
Secondary phase evolution of high-entropy ceramics under heavy-ion irradiation in high-temperature coupling-induced environment	28
First-principles Calculations of Bulk and Interfacial Thermodynamic Properties of the T1 phase in Al-Cu-Li alloys	28
Enhanced hardening by multiple microalloying in low carbon ferritic steels with interphase precipitation	28
Observation of Portevin-le Chatelier effect in aluminum alloy 7075-w under a heterogeneous stress field	28
Active operative heat storage application using thermoelastic martensitic transformation in TiNi-based alloy	28
Balancing data for generalizable machine learning to predict glass-forming ability of ternary alloys	28
Strong yet ductile steels via a heterogeneous phase transformation strategy	28
A unique {332}<113> twin to α″ martensite transition during twin propagation in a Ti-12wt.% Mo alloy with micro-segregation	28
Micro - and macromechanical properties of sintered steel with different porosity	27
Stimulating the inverse transformation of amorphous second-phase particles in irradiated Zr alloy to modulate the nanostructure	27
Understanding the efficacy of concentrated interstitial carbon in enhancing the pitting corrosion resistance of stainless steel; response to Comment by Martin et al.	27
“Double-yielding” behavior and progressive β → α → twins transformation in a Ti-based metallic glass matrix composite	27
Robustness of linear bands in epitaxial planar silicene heterostructure against surface doping	27
Heterogeneous yielding mechanisms of body centered cubic iron for high resistance to chemical reaction-induced deterioration in supercritical water environments: A reactive molecular dynamics study	27
Postponing the fracture strain of ultrafine-grained 316LN steel by sequential activations of deformation modes at 77 K	27
Fabrication of hierarchical porous metallic glasses decorated with Cu nanoparticles as integrated electrodes for high-performance non-enzymatic glucose sensing	27
Effect of A-site non-stoichiometry in NaNbO3 ceramics	27
An atomistic structural description of the ferrielectric polar phase involving non-coplanar cation displacements	27
Flash sintering can induce an anisotropic microstructure in ceramics. A phase field modeling insight	27
Complex irregular stacking faults within Zr3Ge secondary phase nanoparticle stimulated by face-centered cubic zirconium phase growth	27
Origin of enhanced zone lines in field evaporation maps	27
Accessing the role of Joule heating on densification during flash sintering of YSZ	27
Restrained diffusional transformation in high entropy (TiZrVNbTa)2AlC ceramic under He ions irradiation	27
Glide and mixed climb dislocation velocity in γ-TiAl investigated by in-situ transmission electron microscopy	27
Surface energy contributions to the work of infiltration in metal matrix composite processing	27
Stable nanoparticles dispersion induced an unprecedented high strength in a bulk W-TiC alloy	26
Helium partitioning to the core-shelled Ta nanoclusters in nanocrystalline Cu-Ta alloy	26
Fracture mechanism of metallic film with nano to sub-micron thickness on polycrystalline substrate	26
Domination of phononic scattering in solid solutioning and interfaces of HfB2–ZrB2 – SiC -carbon nanotube based ultra high temperature composites	26
Enhancing ductility of the TRIP aided bainitic ferrite steel by Mn heterogeneity introduced via reversion: Towards the 3rd generation	26
Towards uniform and enhanced tensile ductility of additively manufactured Ti−5Al−5Mo−5V−3Cr alloy through designing gradient interlayer deposition time	26
Electrodeposited Al mesocrystal with high thermal stability and high hardness	26
Origin of crystallization suppression in a new amorphous molecular white-light-generating material	26
Wetting of L10 twin and antiphase boundaries by nanometer-scale L12 in Fe-Pd alloys	26
Origin of twin-like {336	26
Developing neural networks to rapidly map crystallographic orientation using laser ultrasound measurements	26
In-situ investigation of tension-compression asymmetry of Ni-SiOC nanocomposites	26
Creep behavior of zirconia ceramics under a strong DC field	26
A new strategy to overcome the strength-ductility trade off of high entropy alloy	26
Revealing curvature and stochastic effects on grain growth: A thermodynamic perspective from extremal principle	26
Building a robust sulfur host for aqueous Cu-S battery by introducing nitrogen into carbon nanotubes	26
A statistical model of irradiation hardening induced by non-periodic irradiation defects	26
Novel high-entropy alloys with high-density ε-D019 and abnormal phase transformation	26
Influence of exchange coupling interaction on coercivity in 2:17-type SmCo-based high temperature permanent magnets	26
High-throughput fabrication of TiO2 nanotube arrays by 4-electrode bipolar electrochemistry	26
First-principles calculations of the temperature dependence of stacking fault energies in Mg	25
In situ synchrotron X-ray diffraction analysis of ultrasonically assisted microstructure refinement during laser melting process	25
Migration of inclusions in a matrix due to a spatially varying interface energy	25
The effect of γ matrix channel width on the compositional evolution in a multi-component nickel-based superalloy	25
Size-effects in tensile fracture of rejuvenated and annealed metallic glass	25
Multivariant Me ions design of Bi(Ni0.5Zr0.5)O3 amorphous thin film with high energy storage capability	25
Evolution of morphology and microstructure of coarsened nanoporous gold studied by automatic thresholding and image recognition algorithms	25
Unveiling the effect of vacancy defects on structural, mechanical, electronic and diffusion properties of copper (I) iodide	25
A novel durable spinel-type ZnGa2O4 transparent ceramic with wide transmission range	25
Displacive-Diffusive plasticity in nanoporous gold nanowires under tensile creep	25
Room temperature static recrystallization phenomenon in a deformed Mg96.6Zn1Y2.2Zr0.2 alloy	25
A physics-constrained neural network for crystal plasticity modelling of FCC materials	25
Tailoring deformation mechanisms in polycrystalline CoNi-base superalloys for enhanced high temperature strength	25
Structural and thermal properties and the origin of the ultralow thermal conductivity in the defect stannite CuIn2Se4	25
Overcoming high-temperature strength-ductility trade-off by combination deformation twinning of C11b and D022 superlattices in a Ni-Cr-W/Mo-based superalloy	25
Design of a cast Al-based Al-Ni-Cr-Zr eutectic alloy with excellent high temperature mechanical properties	25
Nanoprecipitates assisting subsurface cracking in high-strength steel under very high cycle fatigue	25
The rhombic hexecontahedron boron carbide microcrystals – crystal structure analysis	25
Corrigendum to “Divorced Eutectoid Transformation in High-Al Added Steels due to heterogenous nucleation of κ-carbide” [Scripta Materialia, 206 (2022)114395]	24
Superior superelasticity of laser powder bed fusion fabricated NiTi alloys achieved by post heat treatment	24
Role of Aluminum rejection from isothermal ω precipitates on the formation of α precipitates in the metastable β-titanium alloy Ti-10V-2Fe-3Al	24
Influence of microtwins on Portevin-Le Châtelier effect of a Ni-Co based disk superalloy	24
Simultaneously improving the strength and ductility of the as-sintered (TiB+La2O3)/Ti composites by in-situ planting ultra-fine networks into the composite powder	24
Corrigendum to “Effects of inclusion types on the high-cycle fatigue properties of high-strength steel” [Scr. Mater. 206 (2022) 114232]	24
Mechanistic understanding of the localized corrosion behavior of laser powder bed fused 316L stainless steel in pressurized water reactor primary water	24
Insights in improving creep resistance of low-cost 2nd-generation nickel based single crystal superalloys at intermediate temperature	24
Enhanced precipitation kinetics in non-stretched Al-Cu-Li-Mg-Ag-(Sc)-(Zr) alloys	24
“Comments on: [High temperature stability and mechanical quality factor of donor-acceptor co-doped BaTiO3 piezoelectrics]”	24
Corrigendum to “Enhancing strength-ductility synergy in a casting non-equiatomic NiCoCr-based high-entropy alloy by Al and Ti combination addition” [Scripta Materialia 200 (2021) 113898]	24
High-throughput investigation of Nb and Ta alloying effects on the microstructure and properties of a novel Ni-Co-based superalloy	24
A breakthrough in creep lifetime prediction: Leveraging machine learning and service data	24
Characteristic strengthening mechanisms in body-centered cubic refractory high/medium entropy alloys	24
Abnormal strain evolution of austenite upon martensitic transformation in FeNiCo alloy with invar effect: An in situ study	24
Computational thermodynamics-guided alloy design and phase stability in CoCrFeMnNi-based medium-and high-entropy alloys: An experimental-theoretical study	24