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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Effect of substrate temperature on sputter-deposited boron carbide films

Sputter deposition of B4C films with tailored physical properties remains a challenge. Here, we systematically study how substrate temperature influences the properties of B4C films deposited by direct current magnetron sputtering onto planar substrates held at temperatures in the range of 100-510°C. Results show that all films are amorphous stoichiometric B4C, with low O content of ~1 at. %. Films deposited onto substrates at 100°C exhibit high compressive residual stress and decreased mechanical properties. Therefore, for elevated substrate temperatures in the range of 180-510°C, film mass density, surface roughness, Young’s modulus, and hardness are weakly dependent on substrate temperature. However, in this temperature range, an increase in substrate temperature leads to larger residual compressive stress accompanied by a corresponding reduction in the concentration of nanoscale inhomogeneities. At least for the landing atom ballistics conditions studied here, a substrate temperature range of ~185-250°C is optimum for growing films with near-zero intrinsic residual stress. The overall weak substrate temperature dependence of film properties revealed in this work is favorable for the development of a robust deposition process, particularly for the case of deposition onto non-planar substrates where temperature control is often challenging.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Quasi-isentropic compression of an additively manufactured aluminum alloy to 14.8 GPa

We uniaxially and shocklessly compressed an additively manufactured aluminum alloy, laser powder bed fusion (LPBF) AlSi10Mg, to peak stresses ranging from 4.4 to 14.8 GPa at peak strain rates on the order of [Formula: see text] via a series of magnetic loading experiments to measure the principal isentrope, yield strength, and shear modulus as a function of material orientation and applied stress. We did not observe significant anisotropy in any of the measured quantities. We found that the principal isentrope, within the uncertainty and up to our peak stress, overlaps the material’s Hugoniot. We measured yield strengths and shear moduli ranging from 0.28 to 0.81 GPa and 36 to 52 GPa, respectively. Our results indicate that LPBF AlSi10Mg behaves similarly to wrought Al alloys under quasi-isentropic compression.

Brown, Nathan P.↗
DOE OSTI2023

Quantifying uncertainty in analysis of shockless dynamic compression experiments on platinum. I. Inverse Lagrangian analysis

Absolute measurements of solid-material compressibility by magnetically driven shockless dynamic compression experiments to multi-megabar pressures have the potential to greatly improve the accuracy and precision of pressure calibration standards for use in diamond anvil cell experiments. Here, to this end, we apply characteristics-based inverse Lagrangian analysis (ILA) to 11 sets of ramp-compression data on pure platinum (Pt) metal and then reduce the resulting weighted-mean stress–strain curve to the principal isentrope and room-temperature isotherm using simple models for yield stress and Grüneisen parameter. We introduce several improvements to methods for ILA and quasi-isentrope reduction, the latter including calculation of corrections in wave speed instead of stress and pressure to render results largely independent of initial yield stress while enforcing thermodynamic consistency near zero pressure. More importantly, we quantify in detail the propagation of experimental uncertainty through ILA and model uncertainty through quasi-isentrope reduction, considering all potential sources of error except the electrode and window material models used in ILA. Compared to previous approaches, we find larger uncertainty in longitudinal stress. Monte Carlo analysis demonstrates that uncertainty in the yield-stress model constitutes by far the largest contribution to uncertainty in quasi-isentrope reduction corrections. We present a new room-temperature isotherm for Pt up to 444 GPa, with 1-sigma uncertainty at that pressure of just under ±1.2%; the latter is about a factor of three smaller than uncertainty previously reported for multi-megabar ramp-compression experiments on Pt. The result is well represented by a Vinet-form compression curve with (isothermal) bulk modulus K 0 = 270.3 ± 3.8 GPa, pressure derivative K$^{'}_{0}$= 5.66 ± 0.10, and correlation coefficient $R_{K_{0},K^{'}_{0}}$= –0.843.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Egg yolk as a model for gelation: From rheometry to flow physics

Egg yolks are an excellent model for studying sol-gel transitions, particularly the power law viscoelasticity that defines the critical point of gelation. However, prior studies lack comprehensive datasets and fail to visualize flow behavior linked to temperature and time-dependent linear and nonlinear rheology. Here, we present a detailed dataset characterizing egg yolk viscoelasticity across temperature, time, and forcing amplitude using oscillatory shear, step strain, step stress, and constant high strain rate. Novel protorheology visualizations link rheological properties with observable flow behavior. Our findings highlight the nuanced determination of the critical gel point, emphasizing observation timescale dependencies. We compare methods to identify critical temperatures for gelation, including power law viscoelasticity, moduli crossover, diverging zero-shear viscosity, and emerging equilibrium elastic modulus, while visualizing flow consequences near these transitions. Egg yolk is an accessible, realistic, and nontoxic material relevant to the physicist and the chef alike, making it ideal for understanding the rheology of critical gels. By integrating protorheology photos and videos with rigorous rheometric data, we deepen the understanding of critical gels, with broader impacts for studying other materials with sol-gel transitions.

Marsh, Maxwell C. [Department of Mechanical Scienc↗
DOE OSTI2020

How cholesterol stiffens unsaturated lipid membranes

Cholesterol is an integral component of eukaryotic cell membranes and a key molecule in controlling membrane fluidity, organization, and other physicochemical parameters. It also plays a regulatory function in antibiotic drug resistance and the immune response of cells against viruses, by stabilizing the membrane against structural damage. While it is well understood that, structurally, cholesterol exhibits a densification effect on fluid lipid membranes, its effects on membrane bending rigidity are assumed to be nonuniversal; i.e., cholesterol stiffens saturated lipid membranes, but has no stiffening effect on membranes populated by unsaturated lipids, such as 1,2-dioleoyl- sn -glycero-3-phosphocholine (DOPC). This observation presents a clear challenge to structure–property relationships and to our understanding of cholesterol-mediated biological functions. Here, using a comprehensive approach—combining neutron spin-echo (NSE) spectroscopy, solid-state deuterium NMR ( 2 H NMR) spectroscopy, and molecular dynamics (MD) simulations—we report that cholesterol locally increases the bending rigidity of DOPC membranes, similar to saturated membranes, by increasing the bilayer’s packing density. All three techniques, inherently sensitive to mesoscale bending fluctuations, show up to a threefold increase in effective bending rigidity with increasing cholesterol content approaching a mole fraction of 50%. Our observations are in good agreement with the known effects of cholesterol on the area-compressibility modulus and membrane structure, reaffirming membrane structure–property relationships. The current findings point to a scale-dependent manifestation of membrane properties, highlighting the need to reassess cholesterol’s role in controlling membrane bending rigidity over mesoscopic length and time scales of important biological functions, such as viral budding and lipid–protein interactions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Active doping controls the mode of failure in dense colloidal gels

Mechanical properties of disordered materials are governed by their underlying free energy landscape. In contrast to external fields, embedding a small fraction of active particles within a disordered material generates nonequilibrium internal fields, which can help to circumvent kinetic barriers and modulate the free energy landscape. In this work, we investigate through computer simulations how the activity of active particles alters the mechanical response of deeply annealed polydisperse colloidal gels. We show that the “swim force” generated by the embedded active particles is responsible for determining the mode of mechanical failure, i.e., brittle vs. ductile. We find, and theoretically justify, that at a critical swim force the mechanical properties of the gel decrease abruptly, signaling a change in the mode of mechanical failure. The weakening of the elastic modulus above the critical swim force results from the change in gel porosity and distribution of attractive forces among gel particles, while below the critical swim force, the ductility enhancement is caused by an increase of gel structural disorder. Above the critical swim force, the gel develops a pronounced heterogeneous structure characterized by multiple pore spaces, and the mechanical response is controlled by dynamical heterogeneities. We contrast these results with those of a simulated monodisperse gel that exhibits a nonmonotonic trend of ductility modulation with increasing swim force, revealing a complex interplay between the gel energy landscape and embedded activity.

Zhou, Tingtao (ORCID:000000021766719X)↗
DOE OSTI2025

Prediction of carbon nanostructure mechanical properties and the role of defects using machine learning

Graphene-based nanostructures hold immense potential as strong and lightweight materials, however, their mechanical properties such as modulus and strength are difficult to fully exploit due to challenges in atomic-scale engineering. This study presents a database of over 2,000 pristine and defective nanoscale CNT bundles and other graphitic assemblies, inspired by microscopy, with associated stress–strain curves from reactive molecular dynamics (MD) simulations using the reactive INTERFACE force field (IFF-R). These 3D structures, containing up to 80,000 atoms, enable detailed analyses of structure-stiffness-failure relationships. By leveraging the database and physics- and chemistry-informed machine learning (ML), accurate predictions of elastic moduli and tensile strength are demonstrated at speeds 1,000 to 10,000 times faster than efficient MD simulations. Hierarchical Graph Neural Networks with Spatial Information (HS-GNNs) are introduced, which integrate chemistry knowledge. HS-GNNs as well as extreme gradient boosted trees (XGBoost) achieve forecasts of mechanical properties of arbitrary carbon nanostructures with only 3 to 6% mean relative error. The reliability equals experimental accuracy and is up to 20 times higher than other ML methods. Predictions maintain 8 to 18% accuracy for large CNT bundles, CNT junctions, and carbon fiber cross-sections outside the training distribution. The physics- and chemistry-informed HS-GNN works remarkably well for data outside the training range while XGBoost works well with limited training data inside the training range. The carbon nanostructure database is designed for integration with multimodal experimental and simulation data, scalable beyond 100 nm size, and extendable to chemically similar compounds and broader property ranges. The ML approaches have potential for applications in structural materials, nanoelectronics, and carbon-based catalysts.

Winetrout, Jordan J.↗
DOE OSTI2022

TRISO SiC Failure Probability for Reactivity Initiated Accidents in High-Temperature Gas-Cooled Reactors

This work analyzes the failure process of the silicon carbide (SiC) layer in tristructural isotropic (TRISO) during reactivity-initiated accident scenarios for a high-temperature gas-cooled reactor (HTGR) with BISON. Two cases are considered—a group control rod withdrawal (CRW) and a control rod ejection (CRE)—reproduced from a previous study. Failure probability is modeled using Weibull statistics, and worst-case scenario Weibull parameters are adopted to simulate the envelopes in BISON with a one-dimensional TRISO model. CRW scenario results are characterized by higher values of maximum energy deposition and final temperature and volumetric strain with respect to the CRE ones, but the latter have remarkably higher SiC failure probability, mainly due to the offset in strain rates between the two cases. This work also confirms the validity and conservatism of the performance envelopes produced in a previous work by replicating the envelope formulation using RELAP5-3D and RAVEN with a different sampling technique and obtaining consistent results. A sensitivity analysis using the Sobol variance decomposition method on SiC failure probability is then performed involving a set of inputs on both CRW and CRE. The two most important parameters are Weibull modulus and characteristic stress, and their relative importance depends on the specific case. The proposed interpretation of the results is that both energy deposition and strain rate influence the relative degree of importance of the failure parameters. Computation of 95% confidence intervals around worst-case scenario SiC failure probability values is also carried out for four different sets of Weibull parameters. Heren a new criterion for SiC TRISO quality classification built upon safety-based ranges of Weibull parameters is proposed to be integrated in future Fuel-Production Quality Assurance Plans.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Fabric properties and electric efficiency limits of mechanical moisture extraction from fabrics

Residential clothes drying consume about 650 TBtu of primary energy per year in the United States, equivalent to 3% of primary residential energy consumption. There is a strong impetus to reduce the energy consumption of clothes dryers by both improving existing technology and developing alternatives that use fundamentally different drying mechanisms. Clothes drying technologies are broadly classified into either evaporative or mechanical drying. The focus of this paper is on mechanical drying, including vibrational, centrifugal, and press-based methods. In this work, the physical processes involved in these mechanical fabric drying processes were analyzed to develop general theories of mechanical cloth drying energy efficiency. Quantitative evaluation of the theories requires measured fabric properties. To accomplish this, a set of experiments was conducted on samples of a standard test fabric. The fabric was a cotton-polyester blend specified by the US Department of Energy to evaluate the standardized efficiency of all residential clothes dryers in the US. Mercury porosimetry experiments were conducted to determine the fabric pore size distribution, apparent density, and porosity. Elasticity experiments were conducted to determine the fabric’s Young’s modulus. Isostatic press experiments were conducted to establish a relationship between compression force and fabric moisture content. The data resulting from these experiments were combined with mathematical models developed in this work to calculate the theoretical maximum performance limits for mechanical drying of the standard fabric. The results of the analysis are used to make recommendations for the most promising technologies that offer the greatest potential energy savings for residential clothes drying.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Equation of state for Hf, Ta, W, Re, Os, Ir, Pt, and Au to multi-terapascal pressures from density-functional theory

We present the zero-temperature equation of state (pressure dependence of compression) and phase stability predictions for the 5d-transition metals obtained from all-electron density-functional theory (DFT) calculations. The results compare favorably with experiments but extend beyond current experimental capabilities to 10 TPa. Our study reveals phase changes that are explained from the calculated electronic structure. The cubic face-centered and body-centered structures (fcc and bcc), together with two-, three-, and four-layered hexagonal structures, play major roles under compression. The results’ dependence on the electron exchange and correlation in the DFT approach is investigated, and it is shown that the impact of the choice, while significant at lower pressures, diminishes in the terapascal regime. We further illustrate that the normal parabolic trends in atomic volume and bulk modulus with atomic number, due to the occupation of bonding and anti-bonding 5d states, break down at TPa pressures, suggesting drastically different chemical bonding at these extreme conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Phase comparison and equation of state for Ta 2 O 5

Abstract Tantalum pentoxide (Ta 2 O 5 ) is among the most technologically useful heavy transition metal oxides. Unfortunately, its crystal structure is the subject of long-standing and unresolved disagreement. Among other consequences, this uncertainty has made it impossible to formulate a robust high pressure equation of state for Ta 2 O 5 . Here, we report the results of high pressure x-ray diffraction experiments indexed against a comprehensive list of proposed Ta 2 O 5 phases. Five of the proposed phases produce good matches to experimental observations, and the compressibility parameters for these phases are all consistent within uncertainty. This means that regardless of the particular phase chosen, the Ta 2 O 5 equation of state can be described with bulk modulus K 0 = 138 ± 3.68 GPa and pressure derivative K 0 ′ = 1.82 ± 0.45 . Combining these experimental results with new density-functional theory calculations allows us to identify the λ phase as the best structural model of Ta 2 O 5 at ambient conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Non-solvents as physical blowing agents in printable silicone foams

Silicone foams were produced by dispersing an incompatible liquid phase (i.e. a non-solvent) into an uncured, liquid silicone. The formulation and processing parameters were varied to see the effect on porosity and pore morphology. Specifically, two fluorosilanes were added to stabilize the inclusion of fluorinated solvents as blowing agents. As the floruosilane content increased, the void content increased up to about 44 vol. % when the fluorosilane comprised 18 wt. % of the initial formulation. Fumed silica that was treated with a fluorinated silane was also used to try to stabilize the dispersed liquid. While the fumed silica content did not have a strong effect on the total void content, the morphology changed when silica content changed. Various fluorinated solvents with distinct chemical structures were used as the non-solvent and then removed after curing of the silicone. The interaction of the internal non-solvent phase and the silicone phase was expected to influence the porosity. These insights highlight how the manipulation of formulation and processing parameters, focusing on the inclusion of fluorosilanes and fluorinated solvents, contributes to the understanding of how incompatible liquid phases interact with silicone matrices to control porosity and pore morphology. Additionally, these interactions also influenced processability, leading to formulations that could be printed. Higher content of non-solvent inclusions could increase the yield stress and storage modulus of an uncured formulation, leading to the ability to tune intrastrand porosity while a 3D printed architecture could be modified to introduce porosity between the strands. Furthermore, in addition to fluorinated solvents, we also considered non-fluorinated solvents since these may be more industrially relevant in the future. Overall, this approach provides an alternative route to producing porous foams that can be 3D printed, which could be useful for applications like cushioning and protective gear.

physical blowing agent↗
DOE OSTI2022

Tunable polyvinyl chloride (PVC) and thermoplastic polyurethane (TPU)-based soft polymer gel sensors

Abstract Polyvinyl chloride (PVC) gels have recently been found to exhibit mechanoelectrical transduction under mechanical deformation. These mechanoelectrical properties of PVC gels are largely uncharacterized and the underlying transduction mechanisms are currently unknown. These soft electroactive polymers have tunable properties such as modulus and response voltage based on physical dimensions and the amount of plasticizer content within the material making them ideal candidates for complaint sensors. This study aims to investigate PVC gels comprised of various plasticizers to further investigate underlying mechanisms of mechanoelectrical transduction and broaden possible sensing applications. Plasticizers used in this study include dibutyl adipate, dibutyl phthalate, dioctyl phthalate, otherwise known as bis(2-ethylhexyl) phthalate, diisodecyl adipate, and the environmentally friendly biodegradable plasticizer acetyl tributyl citrate (ATBC). ATBC is often used in cosmetics and food packaging applications and is even used as a food additive which may lead to future biocompatibility for these gel sensors. These plasticizers are used to produce PVC gel sensors that are experimentally tested for mechanoelectrical transduction properties and sensing performance. In this study, a Langmuir adsorptive model is fit to the collected mechanoelectrical transduction data. These results are also nondimensionalized and compared to the characteristic dimensionless Langmuir adsorptive model. This simple model agrees very well with the experimental data. Additionally, a study on the mechanoelectrical transduction of an alternative polymer lattice structure, thermoplastic polyurethane (TPU), is discussed. This is a novel electroactive polymer investigated for mechanoelectrical transduction properties. This portion of the study aims to further knowledge of underlying mechanisms of mechanoelectrical transduction as well as show feasibility of additional lattices for soft polymer gel sensors. These TPU gel sensors show strikingly similar mechanoelectrical transduction properties to analogous PVC gels, insinuating that the polymer structure has a limited role in the underlying sensing mechanism and PVC itself is not unique to polymer gel sensing. The TPU-based soft polymer gel sensors however do display some level of mechanoelectrical hysteresis which may be attributed to viscoelastic properties and display a small amount of fatigue possibly due to exudation of liquid plasticizer. This study provides further characterization of mechanoelectrical response for varying plasticizers, provides a theoretical framework for underlying mechanisms, and displays the potential for further polymeric gel sensors.

Instruments & Instrumentation↗
DOE OSTI2025

Self-assembly of wood-based shape memory composites triggered by solar-thermal energy

Transporting and assembling large, complex structures poses significant challenges due to their size, geometry, and cost. Additionally, the installation sites are often inaccessible or hazardous for humans, necessitating self-assembling capabilities in these structures. To mitigate these challenges, we propose using 3D printing materials with shape memory effect (SME) for both transport and construction. This approach involves developing 3D modular components into flat sheets for easier transportation, and then self-assembling into 3D structures on-site using solar energy. To gain a deeper understanding of the factors influencing material memory performance, we have chosen a composite PLA/WF, which is polylactic acid (PLA) with 20 wt% wood flour (WF) for this purpose, leveraging its high tensile modulus at 0.966 GPa, low cost, and sustainability. Printed shapes with this material can maintain a recovery ratio over 90% after 3 cycles. While traditional composites fillers (e.g. glass or carbon fiber) are added to enhance mechanical and thermal properties, the addition of bio-based fillers like WF accomplish similar goals without compromising sustainability. We conducted multiple experiments to demonstrate how environmental conditions (i.e. temperature) maximize the material’s SME. Although still at an early stage, this study provides initial insights into bridging the gap between the small-scale nature of shape memory polymers (SMPs) and their potential for large-scale additive manufacturing, addressing a critical need for efficient and sustainable construction. In the long term, we hope our study contributes to the design vision of utilizing SMPs for transportation, assembly, and deployment of complex structures, providing a new pathway for sustainable construction and transportation of large-scale structures to hard-to-access locations such as disaster-affected areas and remote deserts, etc.

4D printing↗
DOE OSTI2022

Early-time measure in eternal inflation

In a situation like eternal inflation, where our data is replicated at infinitely-many other space-time events, it is necessary to make a prior assumption about our location to extract predictions. The principle of mediocrity entails that we live at asymptotic late times, when the occupational probabilities of vacua has settled to a near-equilibrium distribution. In this paper we further develop the idea that we instead exist during the approach to equilibrium, much earlier than the exponentially-long mixing time. In this case we are most likely to reside in vacua that are easily accessed dynamically. Using first-passage statistics, we prove that vacua that maximize their space-time volume at early times have: 1. maximal ever-hitting probability; 2. minimal mean first-passage time; and 3. minimal decay rate. These requirements are succinctly captured by an early-time measure. The idea that we live at early times is a predictive guiding principle, with many phenomenological implications. First, our vacuum should lie deep in a funneled region, akin to folding energy landscapes of proteins. Second, optimal landscape regions are characterized by relatively short-lived vacua, with lifetime of order the de Sitter Page time. For our vacuum, this lifetime is ~ 10 130 years, which is consistent with the Standard Model estimate due to Higgs metastability. Third, the measure favors vacua with small, positive vacuum energy. This can address the cosmological constant problem, provided there are sufficiently many vacua in the entire ensemble of funnels. As a concrete example, we study the Bousso-Polchinski lattice of flux vacua, and find that the early-time measure favors lattices with the fewest number of flux dimensions. This favors compactifications with a large hierarchy between the lightest modulus and all other Kähler and complex structure moduli.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Computational exploration of biomedical HfNbTaTiZr and Hf 0.5 Nb 0.5 Ta 0.5 Ti 1.5 Zr refractory high-entropy alloys

Refractory high entropy alloys (RHEAs) have been proven to be a potential candidate in the biomedical field due to their balanced mechanical properties and biocompatible composition. Recent experimental findings show that RHEAs like HfNbTaTiZr and Hf 0.5 Nb 0.5 Ta 0.5 Ti 1.5 Zr have good mechanical properties such as high polarization and wear resistance than others which establish them as potential materials for biomedical application. In this work, we performed first-principles density functional theory calculations on the mechanical and thermal properties of HfNbTaTiZr and Hf 0.5 Nb 0.5 Ta 0.5 Ti 1.5 Zr. The predicted lattice constant, density, Young's modulus, and Vickers hardness are consistent with the available experimental report, which verifies the accuracy of the applied model. The thermal coefficient of linear expansion of both RHEAs has been investigated by utilizing the Debye theory. The present methods could be applied to study other future RHEAs on exploration of their physical properties.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Toward machine learning interatomic potentials for modeling uranium mononitride

Uranium mononitride (UN) is a promising accident-tolerant fuel because of its high fissile density and high thermal conductivity. In this study, we developed the first machine learning interatomic potentials for reliable atomic-scale modeling of UN at finite temperatures. We constructed a training set using density functional theory (DFT) calculations that was enriched through an active learning procedure, and two neural network potentials were generated. Both potentials successfully reproduce key thermophysical properties of interest, such as temperature-dependent lattice parameter, specific heat capacity, and bulk modulus. We also evaluated the energy of stoichiometric defect reactions and defect migration barriers and found close agreement with DFT predictions, demonstrating that our potentials can be used for modeling defects in UN. Additional tests provide evidence that our potentials are reliable for simulating diffusion, noble gas impurities, and radiation damage.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

A viscoelastic model for seismic attenuation using fractal mechanical networks

SUMMARY Seismic attenuation (quantified by the quality factor Q) has a significant impact on the seismic waveforms, especially in the fluid-saturated rocks. This dissipative process can be phenomenologically represented by viscoelastic models. Previous seismological studies show that the Q value of Earth media exhibits a nearly frequency-independent behaviour (often referred to as constant-Q in literature) in the seismic frequency range. Such attenuation can be described by the mathematical Kjartansson constant-Q model, which lacks of a physical representation in the viscoelastic sense. Inspired by the fractal nature of the pore fluid distribution in patchy-saturated rocks, here we propose two fractal mechanical network (FMN) models, that is, a fractal tree model and a quasi-fractal ladder model, to phenomenologically represent the frequency-independent Q behaviour. As with the classic viscoelastic models, the FMN models are composed of mechanical elements (spring and dashpots) arranged in different hierarchical patterns. A particular parametrization of each model can produce the same complex modulus as in the Kjartansson model, which leads to the constant-Q. Applying the theory to several typical rock samples, we find that the seismic attenuation signature of these rocks can be accurately represented by either one of the FMN models. Besides, we demonstrate that the ladder model in particular exhibits the realistic multiscale fractal structure of the saturated rocks. Therefore, the FMN models as a proxy could provide a new way to estimate the microscopic rock structure property from macroscopic seismic attenuation observation.

Geochemistry & Geophysics↗