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At least 325 records · Page 18

Collective Analysis of Alpha Particle Losses Due to Self-Absorption by Mass Loading on Radioactive Particulate Glass Fiber Filters

In this study, we derived a relationship between filter mass loading and the percent loss during analysis using the mass loading data collected from six previous studies of self-absorption. Components of mass loading include particulate dust, radioactive particulates, and filter material. In a research report published in 1984, Higby calculated a minimum burial depth for an alpha particle to be lost due to absorption (100% loss) of about 3.7 mg/cm 2 based on calculations for the range of 239-Pu alpha particles in glass fiber filters. From there, Higby concluded that a correction factor of 0.85 assumes approximately 15% losses in the count rate of both alpha and beta particles. In 2000, Luetzelschwab et al. recommended assuming a 40% loss at a loading of 3.3 mg/cm 2 and a 28% loss for a loading of 2.3 mg/cm 2 which included the frontal face mass of the filter. More recently, the 100% losses due to absorption were reported to be in the 10 mg/cm 2 range. Presented here is a trinomial relationship method of relating percent loss due to self-absorption to filter mass loading, based on data reported by Higby, Luetzelschwab et al., Huang et al., Barnett et al., Smith et al., and Hogue et al. Under normal operating conditions at the stacks monitored by Effluent Management, the mass loading of sample filters averages 0.09 ± 0.12 (2s) mg/cm 2 (excluding negative values and outliers) and ranges from 0 mg/cm 2 to 0.24 mg/cm 2 . Based on current mass loading results for Effluent Management stack sample filters, the forced-zero trinomial relationship method estimated self-absorption losses of less than 5%. Because American National Standards Institute/Health Physics Society N13.1-2011 guidelines indicate a correction factor should be used when the penetration of radioactive material into the collection media or self-absorption of radiation by the material collected would reduce the count rate by more than 5%, it is possible continued application of a correction factor to the Effluent Management stack samples is no longer necessary. Nevertheless, continuing to assign a correction factor at the 5% threshold (i.e., 0.95) would be a conservative approach.

36 MATERIALS SCIENCE↗

Deep Learning Reconstruction of Daily Soil CO 2 Efflux Reveals Biogeochemical Insights and Reduces Annual Estimate Uncertainty Despite Limited Daily Predictability

Soil CO 2 efflux is commonly measured monthly or seasonally, leaving daily dynamics poorly resolved and contributing to global estimation uncertainty. We trained a single Long Short-Term Memory (LSTM) model to predict daily soil CO 2 efflux across 82 globally distributed sites in COSORE, with 0.2%–46.9% daily data coverage from 2003 to 2020. Despite using far fewer sites than are typically used to train a single deep learning model, with observations biased toward temperate mesic sites, the LSTM model performed well at approximately one-third of sites, reconstructed nearly 2 decades of daily efflux, and outperformed commonly used approaches for estimating daily efflux when applied to the same data set. Performance was weakest at pronounced peaks and troughs and at non-temperate sites with <1.5 years of observations and irregular data patterns. Nevertheless, annual efflux from reconstructed daily data had <40% error even at underperforming sites, substantially improving estimates derived from monthly and seasonal sampling (maximum errors of 95% and 136%, respectively). Temperature sensitivity (Q 10 ) estimated from reconstructed daily predictions closely matched estimates from daily observations, whereas Q 10 values derived from monthly or seasonal observations deviated substantially, suggesting that coarse temporal sampling may contribute to uncertainty in reported Q 10 values. Consistent daily reconstructions further enabled trend analyses for well-performing, predominantly temperate sites and showed increasing soil CO 2 efflux at most sites from 2003 to 2020, with more variable summer trends. Despite limitations, these results demonstrate the potential of LSTM models to reconstruct daily soil CO 2 efflux and reduce estimation uncertainties from sparse observations.

Smykalov, Valerie [Pennsylvania State University, ↗

In situ aerobic methane oxidation rates in a stratified lake

Abstract Microbial aerobic methane oxidation is an important sink for aquatic methane worldwide. Despite its importance to global methane fluxes, few aerobic methane oxidation rates have been obtained in freshwater or marine environments without imposing changes to the microbial community through use of ex situ methods. A novel in situ incubation method for continuous time‐series measurements was used in Jordan Lake, North Carolina, during 2020–2021, to determine reaction kinetics for aerobic methane oxidation rates across a wide range of naturally varying methane (55–1833 nM) and dissolved oxygen (DO; 28–366 μM) concentrations and temperatures (17–30°C). Methane oxidation began immediately at the start of each of 21 incubations and methane oxidation rates were 1 st order with respect to methane. The data density allowed for accurate calculation of 1 st ‐order rate constants,k, that ranged from 0.018 to 0.462 h −1 (R 2 > 0.967). Addition of ammonium (20–45 μM) to natural concentrations ranging from 0.057 to 2.4 μM did not change aerobic methane oxidation rate kinetics, suggesting that the natural population of aerobic methane oxidizers in this eutrophic lake was not nitrogen limited. Values ofkinversely correlated most strongly with initial DO concentrations (R 2 = 0.82) rather than temperature. Values forkincreased with Julian day throughout our sampling period, suggesting seasonal influences on methane oxidation via responses to geochemical changes or shifts in microbial community abundance and composition. These experiments demonstrate a high variability in the enzymatic capacity for 1 st ‐order methane oxidation rates in this eutrophic lake that is tightly and inversely coupled to oxygen concentrations. Measurements of in situ aerobic methane oxidation rate constants allow for the direct quantification and modeling of the microbial community's capacity for methane oxidation over a wide range of natural methane concentrations.

Marine & Freshwater Biology↗

The influence of exploration activities of a potential lithium mine to the environment in Western Serbia

The proposed exploitation of the Jadar Valley lithium/borate deposit in Serbia, by the Rio Tinto Corporation, indicates that it would become large-scale processing of boron- and lithium-containing ore. It would be one of the world’s very first lithium mines in populated and agricultural area. The company claims that the envisioned mining will be in accordance with environmental protection requirements. The Jadar Valley deposits have been claimed to cover 90% of Europe’s current lithium needs. Yet, local opposition to the mining has arisen due to potential devastating impacts on groundwater, soil, water usage, biodiversity loss, and waste accumulation. Research drilling by the mining company has already produced environmental damage, with mine water containing high levels of boron leaking from exploratory wells and causing crops to dry out. Furthermore, our investigations reveal substantially elevated downstream concentrations of boron, arsenic, and lithium in nearby rivers as compared to upstream regions. Additionally, here we show that soil samples exhibit repeated breaches of remediation limit values with environmental consequences on both surface and underground waters. With the opening of the mine, problems will be multiplied by the tailings pond, mine wastewater, noise, air pollution, and light pollution, endangering the lives of numerous local communities and destroying their freshwater sources, agricultural land, livestock, and assets.

54 ENVIRONMENTAL SCIENCES↗

Endophyte mediated Populus trichocarpa water use efficiency is dependent on time of day and plant water status

Endophytes are potential partners for improving the resource use efficiency of bioenergy feedstock systems such as short rotation coppiced Populus. Endophytes isolated from members of the Salicaceae family have broad host compatibility and can improve water use efficiency (WUE) through decreases in stomatal conductance. However, the literature is inconsistent with regards to the environmental conditions and temporal patterns of these benefits. This study investigates how endophyte mediated changes in Populus trichocarpa (Torr. and Gray) ‘Nisqually-1’ stomatal conductance and WUE shift with time and scale in response to water-deficit stress. Leaf gas exchange and above-ground productivity were used to evaluate the carbon and water balances of glasshouse grown plants in response to endophyte inoculation and water-deficit. Differences in stomatal conductance between control and inoculated plants were more pronounced (39.7 % decrease, Welch’s two-sample t(14.34 dfadj) = -2.358, p-value = 0.033) under water-deficit conditions in the late morning during a period of higher light intensity. The decrease in stomatal conductance accompanied a substantial increase in intrinsic WUE (iWUE) for water-deficit inoculated plants. However, increases in iWUE did not result in improvements in aboveground productivity or shoot biomass WUE (WUEsb) for water-deficit inoculated plants. This decoupling between iWUE and aboveground productivity may be an indicator of assimilate allocation to microbial metabolism as an additional carbon sink or a shift in carbon allocation towards belowground biomass. Future work should take a whole-plant approach that accounts for diurnal patterns in incident irradiance to evaluate the impact of endophyte inoculation on host WUE and stress tolerance.

59 BASIC BIOLOGICAL SCIENCES↗

Complex deuteron NMR signals

To determine the spin polarization of deuterons, nuclear magnetic resonance (NMR) is used. This is necessary for polarized targets, such as for the upcoming A zz and b 1 experiment at Jefferson Lab. NMR measures the impedance of a solenoid around a deuterated sample. Although the impedance is a complex value, conventionally only the real part of the impedance has been used for this purpose. However, often the tune is not precisely real, meaning the signal has at least some small imaginary portion. This conventionally has been dealt with by an offset parameter, such as Dulya’s false asymmetry method. For vector polarization, this suffices, as the tuning is factored into the overall error of the results, and for a small phase angle doesn’t make much of a difference. However, for tensor polarization, the exact lineshape of the signal is quite significant, and treating the impedance as complex during analysis removes the need for an offset parameter. As a result, it also provides more accurate results, as the conventional false asymmetry method over- or underestimates polarization, depending on the sign of the phase angle.

McClellan, Michael [University of New Hampshire, D↗

Ion-Selective Scattering Studied Using the Variable-Energy Electron Irradiation in the Ba 0.2 K 0.8 Fe 2 As 2 Superconductor

Low-temperature variable-energy electron irradiation was used to induce non-magnetic disorder in a single crystal of a hole-doped iron-based superconductor, Ba $1-x$ K $x$ Fe 2 As 2 , $x$ = 0.80. To avoid systematic errors, the beam energy was adjusted non-consequently for five values between 1.0 and 2.5 MeV when sample resistance was measured in situ at 22 K. For all energies, the resistivity raises linearly with the irradiation fluence suggesting the creation of uncorrelated dilute point-like disorder (confirmed by simulations). The rate of the resistivity increase peaks at energies below 1.5 MeV. Comparison with calculated partial cross-sections points to the predominant creation of defects in the iron sublattice. Simultaneously, superconducting $T_c$, measured separately between the irradiation runs, is monotonically suppressed as expected, since it depends on the total scattering rate, hence on the total cross-section, which is a monotonically increasing function of the energy. Our work experimentally confirms an often-made assumption of the dominant role of the iron sub-lattice in iron-based superconductors.

36 MATERIALS SCIENCE↗

Hot Stars with Kepler Planets Have High Obliquities

It has been known for a decade that hot stars with hot Jupiters tend to have high obliquities. Less is known about the degree of spin–orbit alignment for hot stars with other kinds of planets. Here, we reassess the obliquities of hot Kepler stars with transiting planets smaller than Neptune, based on spectroscopic measurements of their projected rotation velocities (vsin i). The basis of the method is that a lower obliquity—all other things being equal—causes sin i to be closer to unity and increases the value of vsin i. We sought evidence for this effect using a sample of 150 Kepler stars with effective temperatures between 5950 and 6550 K and a control sample of 101 stars with matching spectroscopic properties and random orientations. The planet hosts have systematically higher values of vsin i than the control stars, but not by enough to be compatible with perfect spin–orbit alignment. The mean value of sin i is 0.856 ± 0.036, which is 4σ away from unity (perfect alignment), and 2σ away from π/4 (random orientations). There is also evidence that the hottest stars have a broader obliquity distribution: when modeled separately, the stars cooler than 6250 K have 〈sin i〉=0.928±0.042 while the hotter stars are consistent with random orientations. This is similar to the pattern previously noted for stars with hot Jupiters. Based on these results, obliquity excitation for early-G and late-F stars appears to be a general outcome of star and planet formation, rather than being exclusively linked to hot Jupiter formation.

79 ASTRONOMY AND ASTROPHYSICS↗

Ball-on-ring test validation for equibiaxial flexural strength testing of engineered ceramics

The validation of a ball-on-ring, equibiaxial flexural strength method to obtain the transverse rupture strength (TRS) of right cylindrical ceramic specimens was performed in this study. Validation of the test method was achieved using commercially available engineered high purity alumina disks and finite element (FE) model analysis. The validated fixture was then used to obtain the TRS and Weibull statistical analysis of MgO-partially stabilized zirconia (MSZ) and Y 2 O 3 -partially stabilized zirconia (YSZ) ceramic disks. TRS data for alumina, MSZ, and YSZ agreed with the TRS values reported in the literature. A statistically relevant number of samples (N > 30) for each material were tested to allow for a Weibull statistical analysis. Weibull parameters for these materials were within the expected values for engineered ceramics. The characteristic strength for alumina, MSZ, and YSZ were determined to be 289, 786, and 814 MPa, respectively. The Weibull modulus was determined between 10 and 25 for each material, which is typical of engineered ceramics. In addition, FE model results were in close agreement with experimental fracture values for the three ceramic materials tested in this study.

36 MATERIALS SCIENCE↗

(U)SAXS characterization of porous microstructure of chert: insights into organic matter preservation

This study characterizes the microstructure and mineralogy of 132 (ODP sample), 1000 and 1880 million-year-old chert samples. By using ultra-small-angle X-ray scattering (USAXS), wide-angle X-ray scattering and other techniques, the preservation of organic matter (OM) in these samples is studied. The scarce microstructural data reported on chert contrast with many studies addressing porosity evolution in other sedimentary rocks. The aim of this work is to solve the distribution of OM and silica in chert by characterizing samples before and after combustion to pinpoint the OM distribution inside the porous silica matrix. The samples are predominantly composed of alpha quartz and show increasing crystallite sizes up to 33 ± 5 nm (1σ standard deviation or SD). In older samples, low water abundances (~0.03%) suggest progressive dehydration. (U)SAXS data reveal a porous matrix that evolves over geological time, including, from younger to older samples, (1) a decreasing pore volume down to 1%, (2) greater pore sizes hosting OM, (3) decreasing specific surface area values from younger (9.3 ± 0.1 m 2 g -1 ) to older samples (0.63 ± 0.07 m 2 g -1 , 1σ SD) and (4) a lower background intensity correlated to decreasing hydrogen abundances. The pore-volume distributions (PVDs) show that pores ranging from 4 to 100 nm accumulate the greater volume fraction of OM. Raman data show aromatic organic clusters up to 20 nm in older samples. Raman and PVD data suggest that OM is located mostly in mesopores. Observed structural changes, silica–OM interactions and the hydro­phobicity of the OM could explain the OM preservation in chert.

(U)SAXS↗

Polycyclic aromatic hydrocarbons in samples of Ryugu formed in the interstellar medium

Polycyclic aromatic hydrocarbons (PAHs) contain ≲20% of the carbon in the interstellar medium. They are potentially produced in circumstellar environments (at temperatures ≳1000 kelvin), by (~10 kelvin) interstellar clouds, or by processing of carbon-rich dust grains. We report isotopic properties of PAHs extracted from samples of the asteroid Ryugu and the meteorite Murchison. The doubly- 13 C substituted compositions (Δ2× 13 C values) of the PAHs naphthalene, fluoranthene, and pyrene are 9 to 51‰ higher than values expected for a stochastic distribution of isotopes. The Δ2× 13 C values are higher than expected if the PAHs formed in a circumstellar environment, but consistent with formation in the interstellar medium. By contrast, the PAHs phenanthrene and anthracene in Ryugu samples have Δ2× 13 C values consistent with formation by higher-temperature reactions.

Science & Technology - Other Topics↗

Classification of gaseous UF 6 assay by femtosecond LIBS in the 424.4 nm spectral region using numerical HOGSVD-DTW features

This technical note presents experimental results using numerical features of fs-LIBS data to classify the assay value of a gaseous UF 6 material. Here, the data-driven feature vectors are computed by Higher Order Generalized Singular Value Decomposition (HOGSVD) and Dynamic Time Warp (DTW). The method achieves 96.97% accuracy in spectral classification testing with fs-LIBS samples obtained from a UF 6 material with five known assay values ranging from 0.287% to 61.740%, with 100% accuracy for the four largest assay values ranging from 4.615% to 61.740%.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Understanding Fracture Aperture and Permeability Evolution due to Carbonate Mineralization Utilizing 3D Printing

Caprock formations are a crucial part of subsurface-engineered systems. Composed largely of shale, caprocks act as natural barriers that prevent the upward migration of fluids, thereby ensuring the containment of stored substances in subsurface formations. Fractures in these formations are potential leakage pathways for stored fluids. Mineral precipitation reactions in these fractures, particularly calcite, can significantly restrict the fluid permeability, reducing leakage potential. However, predictive capabilities of mineral precipitation in fractures and associated permeability evolution are limited due to a lack of fundamental understanding of such reactions in natural samples, complicated by mineral heterogeneity and the complexity of the fracture structure. In this study, 3D-printed fracture samples are used to understand the impact of carbonate mineralization on fracture aperture and permeability evolution. Samples were printed using a digital light processing (DLP) 3D printer and commercial liquid resin. Calcite precipitation was first tested on printed 2D films before conducting plug flow column experiments aimed to understand fracture permeability changes due to mineral precipitation. Contact angle measurement and Fourier transform infrared (FTIR) spectroscopy on printed 2D films show evidence of a substantial amount of surface energy for calcite nucleation and precipitation. Surface topography analysis of printed fractured surfaces reveals comparable values, highlighting the high replicability of the printed samples. During the column experiments, the permeability reduces exponentially due to a decrease in fracture aperture. Reductions in fracture aperture estimated from effluent concentration and 3D X-ray computed tomography (CT) show comparable results. Moreover, 3D X-ray CT images suggest the impact of local flow velocities on precipitation. The insights gained from this research contribute to a deeper understanding of the permeability evolution due to carbonate mineralization in caprock formations.

3D printing↗

Computational study of Li3BO3 and Li3BN2 I: Electrolyte properties of pure and doped crystals

Both Li3BO3 and Li3BN2 materials have promising properties for use in all-solid-state batteries and other technologies dependent on electrolytes with significant ionic conductivity. As the first of a two-part study, this paper reports the analysis of detailed simulations of Li ion diffusion in the monoclinic forms of these materials. Using both NEB and MD methods, it is clear that Li ion migration via vacancy mechanisms provides the most efficient ion transport in each material. While the results suggest that interstitial defects in these materials do not play a direct role in Li ion migration, their relative stability seems to enhance vacancy production via the formation of Frenkel-type defects. This may partially explain why the Li ion conductivities computed from MD simulations of samples initially containing a single Li ion vacancy are in reasonable agreement with measured values of this work for Li3BO3 and those reported in the literature for poorly crystalline samples of both materials. The possibility of increasing vacancy concentrations by substitutional doping (F for O in Li3BO3 and C for B in Li3BN2) is also examined, finding simulated conductivities comparable to those of the ideal vacancy model.

Li, Yan↗

QSE 04-21-2022 ST-11 Alpha Data Report

In the California Industrial General Permit (IGP) 2014-0057-DWQ for storm water monitoring, effective July 1, 2015, there are 21 contaminants that have been assigned NAL (Numeric Action Level) values, both annual and instantaneous. For annual NALs, an exceedance occurs when the average of all analytical results from all samples taken at a facility during a reporting year for a given parameter exceeds an annual NAL value listed in Table 2 of the General Permit. For instantaneous maximum NALs, an exceedance occurs when two or more analytical results from samples taken for any parameter within a reporting year exceed the instantaneous maximum NAL value (for TSS and O&G), or are outside of the instantaneous maximum NAL range (for pH) listed in Table 2.

54 ENVIRONMENTAL SCIENCES↗

Residual resistance ratio measurement system for Nb 3 Sn wires extracted from Rutherford cables

Residual resistance ratio (RRR) of superconducting strands is an important parameter for magnet electrical stability. RRR serves as a measure of the low-temperature electrical conductivity of the copper within a conductor that has a copper stabilization matrix. For Nb 3 Sn, due to the need of a reaction heat treatment, the technical requirements for high quality measurements of strands extracted from Rutherford cables are particularly demanding. Quality of wire, cabling deformation, heat treatment temperature, heat treatment atmosphere, sample handling, and measurement methods can all affect the RRR. Therefore, as an integral part of the electrical quality control (QC) of Nb 3 Sn Rutherford cables manufactured at the Lawrence Berkeley National Laboratory, it was prudent that we established a RRR measurement system that can isolate the assessment of cable-fabrication-related impacts from sample preparation and measurement factors. Here we describe a bespoke cryocooler-based measurement system, capable of measuring RRR of over 80 samples in a single cooldown. The samples are mounted on custom-designed printed circuit boards that accommodate the shape of strands extracted from a Rutherford cable without added deformation, which we will show is critical in ensuring that the measurements accurately represent the RRR values of the conductor within the cable. Using this sample mounting solution, we routinely measure the overall RRR of the strand as well as individual intra-strand sections corresponding to both cable edges and cable broad faces with high reproducibility. Such measurements provide valuable information on the variation of RRR along the length of the strands as well as across strand productions and cable runs over time.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Experimental and Computational Studies of Stress Corrosion Cracking of Alloys 308/309 and 82/182 Weldments in Corrosive and Radiation Environment

The goal of the project was to determine factors that influence SCC and IASCC in weldments found in LWR nuclear power plants. We focused on a SA508-304L SS weldment fabricated by EPRI using gas tungsten arc welding and used an aggressive BWR normal water chemistry (NWC) immersion environment. This weldment used 309L butter and 308L groove filler material. The microstructure of the 309L butter was non-uniform, exhibiting a 20–30μm thick martensitic layer closest to the SA508 interface, a 1–4 mm thick single γ austenite phase dilution zone, and a γ–δ duplex region extending to the 308L groove filler. The 308L groove filler had an entirely γ–δ duplex microstructure. Two approximately 1-inch thick 304L and SA508 plates approximately 12 by 6 square inches were joined using standard nuclear grade welding techniques. This included a post weld heat treatment of the 309L butter after application, a 0.32 cm fit-up root opening, and 57 bead lines of 308L groove filler applied in 18 layers. A 60 degree weld bevel angle was used and the 309L butter was 1.5 cm thick. Displacement cascade damage was induced using proton irradiation at the Michigan Ion Beam Laboratory. The incident proton energy was 2 MeV, the sample temperature was 360 ºC, and the calculated dpa value at 10 μm (60% of the Bragg peak depth of ~18 μm) was 5 dpa using the quick Kinchin-Pease model. Proton irradiation to this damage level required approximately 125 hours of beam time. Two types of samples were irradiated, tensile specimens and TEM bars. Samples were selected from all regions of the weldment, including the SA508-309L butter interface, the 309L-308L interface, and 308L-304L interface. The stainless steel alloys (304L, 308L, and 309L) within the heat affected zone are characterized by a duplex skeletal morphology of δ-ferrite and γ-austenite resulting from the recrystallization associated with weld fabrication. Approximately 7 to 8 mm of length along the specimen was irradiated. The gauge volume surfaces were mechanically polished and then electro-polished to remove mechanical damage from the mechanical polishing step prior to irradiation. Immersion tests were performed in a recirculating autoclave under BWR NWC conditions (2000 ppb wt. dissolved oxygen, neutral pH, 288 ºC, 10 MPa, and inlet water conductivity <100 nS/cm) to accelerate corrosion. Constant strain rate tests were performed either to failure or to approximately 5% strain. Strain rates of 10 -7 to 10 -6 mm/mm/s were used and typical immersion testing required four to six weeks to achieve failure or strains near 5%. Analysis primarily used advanced electron microscopy techniques of FIB lift out specimens.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Structural and Thermoelectric Properties of Black Arsenic–Phosphorus

Here, we report the structural and temperature dependent transport properties of As x P 1-x (x = 0, 0.2, 0.5, 0.83, 1) alloys. It is observed that black phosphorous (BP)-related phonon modes in the alloy samples are red-shifted with increasing arsenic concentration, while black arsenic-related modes in these samples are blue-shifted with increasing phosphorus concertation. As the arsenic concentration, x increases from 0 to 1, the 4-probe resistance of the As x P 1-x alloys is found to decrease by more than 3 orders of magnitude. The transport studies reveal that samples with the highest arsenic concentration (x = 1 and 0.83) show metallic behavior in the temperature dependence of resistance with a small thermopower at room temperature with an anomalous temperature dependence. In contrast, the samples with high phosphorus concentration (x = 0, 0.2, and 0.5) show very large thermopower values at room temperature reaching a value as high as 803 μV/k for x = 0.2. The temperature dependence of the thermopower of these samples can be well described by the variable range hopping (VRH) mechanism in two-dimensions (2-d), S ~ T 1/3 . Similarly, their 4-probe resistance (R) values can be fitted with 2-d VRH mechanism, R ~ exp(T -1/3 ).

36 MATERIALS SCIENCE↗