Rapid Diffusion Rate Research Articles

Getting a Grip on Greasy Molecules

Lipids are structurally and functionally diverse biological metabolites that have long proven difficult to study, particularly as targets for molecular imaging. This challenge arises from their small size, hydrophobicity, rapid diffusion and trafficking rates, and, perhaps most critically, their status as metabolites whose structures and biosynthesis are not directly encoded in the genome, making them inaccessible to direct fusion with fluorescent proteins.

Unveiling the hydrodechlorination of trichloroethylene by reduced graphene oxide supported bimetallic Fe/Ni nanoparticles

Reduced graphene oxide (rGO) is a promising support for electrochemical and environmental applications. However, the role of rGO in dechlorination of chlorinated hydrocarbon by zerovalent iron-based nanoparticles remains unclear. Herein, the rGO-supported bimetallic Fe/Ni nanocomposites were fabricated by chemical reduction method and the microstructures as well as the electrochemical properties of rGO/Fe/Ni, were investigated to elucidate the dechlorination behaviors of trichloroethylene (TCE) under various environmental conditions. Results show that the 10–60 nm Fe/Ni nanoparticles with average particle size of 32 nm are homogeneously dispersed onto the rGO surface. The rGO/Fe/Ni exhibits excellent dechlorination efficiency and rate of TCE is 2.4 times higher than that of free Fe/Ni nanoparticles. Cyclic voltammetric curves and electrochemical impedance spectra indicate that the superior dechlorination activity is attributed to the strong interaction between Fe/Ni and rGO, low internal resistance and rapid diffusion rate of electrons and ions. In addition, the capacitive behavior of rGO can store and transfer 2.7–3.4 electrons produced from Fe0 to the adsorbed TCE more readily, and then converts TCE to non-toxic ethane via hydrodechlorination in the presence of Ni nanoparticles. The rGO/Fe/Ni can be recycled for at least 8 times to effective dechlorinate TCE. Moreover, the reaction rate of TCE dechlorination can be enhanced 1.26–1.49 times when 5–10 mg L−1 humic acid are added. Results obtained in this study have clearly unveiled the role of rGO in hydrodechlorination of TCE and can provide a new insight into the development of rGO−supported bimetallic Fe/Ni nanoparticles for the enhanced removal of chlorinated pollutants in water and wastewater treatment.

Layered-spinel capped nanotube assembled 3D Li-rich hierarchitectures for high performance Li-ion battery cathodes

We report an effective approach to fabricate layered-spinel capped nanotube assembled 3D Li-rich hierarchitectures as a cathode material for Li-ion batteries. The resultant material exhibits a reduced first-cycle irreversible capacity loss, rapid Li-ion diffusion rate and excellent cycle stability.

The Diffusion of Doctrinal Innovations in Tort Law

This article examines the diffusion of “innovations” — new ideas — in tort law. Drawing from a larger body of research into the spread of new products and ideas, this study charts and evaluates the adoption patterns associated with “successful” common-law doctrinal innovations in the law of torts. This analysis reveals recurring influences upon and tendencies within the spread of novel tort doctrines across the states, and explores the interactive qualities of the diffusion process. Furthermore, these diffusion patterns document a trend toward common-law doctrinal “stabilization” over the past quarter-century. As detailed herein, this stabilization owes in part to altered diffusion dynamics associated with the ongoing diminution and fragmentation of the common-law tort dockets entertained by state supreme courts. The structural character of these influences will make it difficult, this article concludes, for even well-received common-law doctrinal innovations of the future to match the rapid diffusion rates associated with innovations in tort law that spread during the 1960s, 1970s, and 1980s.

In-situ trace elements and Li and Sr isotopes in peridotite xenoliths from Kuandian, North China Craton: Insights into Pacific slab subduction-related mantle modification

The trace element, Li and Sr isotopic compositions of major minerals in peridotite xenoliths from Kuandian, North China Craton (NCC) were analyzed in situ to investigate Pacific slab subduction-related mantle modification beneath the eastern NCC. The 87Sr/86Sr ratios (0.70282–0.70553) are positively correlated with the La/Nb and U/Nb ratios for clinopyroxenes (Cpx). Based on the trace element distribution patterns, three types of Cpx were identified. Type 1 Cpx are characterized by significant Nb–Ta–Ti depletions and the highest Sr isotopic ratios (up to 0.70553); Type 2 Cpx display Nb (or Ta) depletions and highly variable Nb and Ta fractionation; and Type 3 Cpx show no significant Nb or Ta depletion or even weak Ta enrichment and have the lowest Sr isotopic ratios (0.70282–0.70323). Some Cpx display a pattern of increasing Ca+Mg±Si from the cores to the rims, indicating addition of Ca+Mg±Si-rich fluids derived from a serpentinized peridotite layer above the subducting slab. These features indicate an ancient mantle metasomatic event associated with the subduction of the altered Pacific oceanic crust, which may contribute substantially to the destruction of the eastern NCC.The variations in the Li contents and isotopic compositions of major minerals in the Kuandian peridotite xenoliths encode both the melt/fluid metasomatism and the cooling process. The Li contents in the Cpx (up to 34.8ppm) and orthopyroxenes (Opx) (up to 28.0ppm) are typically higher than those in the coexisting olivines (Ol) (<9.19ppm), suggesting silicate melt metasomatism. Considering the rapid diffusion rate of Li in minerals at mantle temperature, the Li enrichment and low δ7Li values in the rims of most Ol, Cpx and Opx may have arisen from diffusive fractionation due to faster diffusion of 6Li compared to 7Li during a latest Li-rich melt/fluid metasomatic process shortly before the host magma eruption. On the other hand, a few Ol grains show decreased Li contents and higher δ7Li values from the cores to the rims. This could imply Li isotope fractionation caused by cooling-induced Li redistribution during and/or after the host magma eruption, because DLiOl/Cpx decreases significantly with decreasing temperature and 6Li diffuses faster than 7Li.

The Geography of the British Motorcycle Industry, 1896–2004

Two major agglomerations or clusters (West Midlands and Greater London) have been shown to have been the driving force behind the historical geography of the British motorcycle industry (its distribution over time and the rate at which motorcycle marques entered and exited). A net positive effect on the West Midlands and a net negative effect on the Greater London area were exerted by motorcycle marque exits from the industry (shakeout). Spin-off of new companies was primarily an internal process in the West Midlands and an external process in the Greater London area. The high level of spatial concentration, The rapid rate of technology diffusion, the large number of spin-off firms and the high level of spatial concentration helped to maintain a wide variety of marques over a long time in the British motorcycle industry. However, the result was an industry that was stagnant and increasingly innovation-averse with each successive shakeout period, which eventually ended in its near total collapse.

Disappearing and reappearing differences in drug-eluting stent use by race.

Drug-eluting coronary stents (DES) rapidly dominated the marketplace in the United States after approval in 2003, but utilization rates were initially lower among African American patients. We assess whether racial differences persisted as DES diffused into practice. Medicare claims data were used to identify coronary stenting procedures among elderly patients with acute coronary syndromes (ACS). Regression models of the choice of DES versus bare mental stent controlled for demographics, ACS type, co-morbidities and hospital characteristics. Diffusion was assessed in the short run (2003-2004) and long run (2007), with the effect of race calculated to allow for time-varying effects. The sample included 381,887 Medicare beneficiaries treated with stent insertion; approximately 5% were African American. Initially (May 2003-February 2004), African American race was associated with lower DES use compared to other races (44.3% versus 46.5%, P < 0.01). Once DES usage was high in all patients (March-December 2004), differences were not significant (79.8% versus 80.3%, P = 0.45). Subsequent concerns regarding DES safety caused reductions in DES use, with African Americans having lower use than other racial groups in 2007 (63.1% versus 65.2%, P < 0.01). Racial disparities in DES use initially disappeared during a period of rapid diffusion and high usage rates; the reappearance of disparities in use by 2007 may reflect DES use tailored to unmeasured aspects of case mix and socio-economic status. Further work is needed to understand whether underlying differences in race reflect decisions regarding treatment appropriateness.

Microstructure and thermal properties of dysprosium and thulium co-doped barium titanate ceramics for high performance multilayer ceramic capacitors

Abstract The co-doping characteristics on microstructure and thermal properties of barium titanate (BaTiO3) were investigated to elucidate formation of core–shell structure by dysprosium (Dy) and thulium (Tm) addition in the BaTiO3–Dy2O3–Tm2O3 system. The dielectrics co-doped with 0.7 mol% Dy2O3 and 0.3 mol% Tm2O3 had the dielectric constant up to 2200 as a function of temperature, which was 30% higher than that of specimen containing only Tm2O3 at the room temperature. It could be explained by the fact that the increase of Dy2O3 addition contributed to the improvement of dielectric constant. On the other hand, the rapid diffusion rate of Dy3+ ions in BaTiO3 showed an adverse effect on temperature stability caused by destruction of core–shell. As the compensation for shell expansion in BaTiO3, the reinforcement of the core–shell structure through the addition of Tm2O3 was confirmed by TEM-EDS analysis and attributed the temperature coefficient of capacitance (TCC) in a reliability condition (−55 °C to 125 °C, △C = ±15% or less). The enhanced electrical properties and temperature stability could be deduced from the generation of electrons and the formation core–shell structure in co-doped BaTiO3 system respectively.

Adsorption Behavior of Metal Ions by Amidoxime Chelating Resins

AbstractIn this work, the acrylonitrile (AN) – divinylbenzene (DVB) –methylacrylate (MA) resin was synthesized via suspension polymerization in the presence of toluene as diluent, and benzoylperoxide (BPO) as initiator. The effect of MA, toluene and alkaline treatment on the exchange capacity of the resin were investigated. The results showed that the anion exchange capacity decreased with an increase in the amount of MA, while alkaline treatment had no significant effect. Also, the cation exchange capacity increased with an increase in the amount of hydrophilic agent and reached a maximum point. The sorption equilibrium was achieved relatively fast within 40 mins, and the resin exhibited affinity towards lead (II), copper (II) and in particular uranium (VI). The adsorption of uranium was directly depended up on the pH value. Furthermore, the macroreticular chelating resin, containing amidoxime group had higher adsorption of uranium (VI) in comparison to other metal ions studied. Finally, the alkaline treatment enhanced the potential for much faster adsorption characteristics and the highly porous chelating resin provided a more favorable pore structure for the rapid rate of diffusion of metal ions.

Adsorption properties of amidoxime resins for separation of metal ions from aqueous systems

In this study, the acrylonitrile (AN)–divinylbenzene (DVB)–methylacrylate (MA) resin was synthesized via suspension polymerization in the presence of toluene as diluent, and benzoylperoxide (BPO) as initiator. The effects of MA as a hydrophilic agent and toluene as a diluent on the anion and cation exchange capacity of the synthesized amidoxime resins were investigated before and after alkaline treatment. The results showed that the anion exchange capacity decreased with an increase in the amount of MA while alkaline treatment had no significant effect. Also, the cation exchange capacity increased with an increase in the amount of hydrophilic agent and reached a maximum point. The sorption equilibrium was achieved relatively fast within 40 min, and the resin exhibited affinity towards lead (II), copper (II) and in particular U(VI), and the order of adsorption affinity were UO 2 2 + > Pb 2+ ≫ Co 2+ > Cu 2+ ≫ Cd 2+. The adsorption of uranium was directly depended up on the pH value. Furthermore, the macroreticular chelating resin, containing amidoxime group had higher adsorption of uranium (VI) than other metal ions studied. Finally, the alkaline treatment enhanced the potential for much faster adsorption and the highly porous chelating resin provided a more favorable pore structure for the rapid rate of diffusion of metal ions.

Effect of coagulation temperature on the properties of poly(acrylonitrile- itaconic acid) fibers in wet spinning

A dimethyl sulfoxide (DMSO)-water system was used as the coagulation bath in the wet-spun process for poly(acrylonitrile-itaconic acid) fibers. The coagulation bath concentration of DMSO was kept constant at 65%, and the jet stretch ratio was 1. The coagulation bath temperature was varied from 40 to 70 °C. The properties of the fibers so obtained were investigated. The diffusion coefficient of solvent was calculated and the concentration profiles of solvent in a moving filament were computed by using a MOL (method of lines) method. The nascent fibers coagulated at 50 °C obtained a circular symmetrical cross section with high density and strength. The diffusion coefficients of solvent (DMSO) increase with the bath temperature increase. Simulation results show that the noncircular cross section form was the response of the rapid diffusion rate and the loose structure in the core of nascent fibers was caused by the overmuch remained solvent.

Adoption of liquid-based cervical cancer screening tests by family physicians and gynecologists.

To examine reasons for the adoption of liquid-based cervical cancer screening tests. A mailed survey of 250 family physicians and 250 gynecologists in Maryland in 2000. Additional data were obtained from the AMA Master File of Physicians. Key outcome variables in this cross-sectional survey were early adoption of a liquid-based test by the end of 1997 and overall adoption by the time of the survey. Adoption was viewed in terms of a supply and demand theoretical framework with marketing influencing physician and patient demand as well as supply by insurance companies and laboratories. Random samples of family physicians and gynecologists were selected from the AMA Master File of Physicians. The overall response rate was 61.9 percent. By 2000, 96 percent of gynecologists and 75 percent of family physicians in Maryland were using liquid-based cervical cancer screening tests, most commonly the ThinPrep Pap Test. Gynecologists were more likely than family physicians to have been early adopters (34 percent versus 5 percent, p<.01). Part of this variation in adoption was due to aggressive marketing to gynecologists, who were more likely than family physicians to receive information in the mail from the test manufacturer (89 percent versus 56 percent, p<.01) and to have been informed by the manufacturer that a patient had inquired about physicians' use of the test (22 percent versus 8 percent, p<.01). The rapid diffusion of liquid-based cervical cancer screening tests occurred despite general agreement that the Pap smear has been one of the most successful cancer prevention interventions ever. Commercial marketing campaigns appear to contribute to the more rapid rate of diffusion of technology among specialists compared with generalists.

Adsorption of an ionizable drug onto microspheres: experimental and modeling studies

The purpose of this work was to study the in vitro equilibria and the adsorption kinetics of an ionizable drug, indomethacin, onto commercially available cationic polymeric microspheres: DEAE Trisacryl LS and QA Trisacryl LS. Isotherms were fitted to theoretical equations allowing accurate predictions of drug loading at different salt concentrations. Isotherm measurements were quickly obtained by simple column breakthrough experiments. The nature of the ion exchange group of the microspheres was observed to be preponderant for adsorption, as the tertiary amine derivative exhibited 53% more capacity than its quaternary amine counterpart. The maximum equilibrium uptake capacity in a 5 mM Tris–HCl buffer at pH 7.4 is 303 mmol/ml of particle volume, for DEAE microspheres. Transport properties of indomethacin into the tertiary amine microspheres were obtained in agitated contactor. Microbeads loading was completed in a 1–6 min range and was found to be controlled by pore diffusion mechanism. Equilibrium uptake data was fitted to the Langmuir and the mass action law models. Adsorption kinetics were fitted to a pore diffusion model. Good correlation was obtained between the theoretical models and the experimental data. The methodology outlined in this work provided a simple approach of estimating adsorption behavior of drugs onto ion-exchange macroporous microspheres. Although significant indomethacin loading was obtained onto the DEAE microspheres, the rapid rate of diffusion is not compatible with sustained release properties sought for this type of microspheres.

X-ray diffraction, neutron scattering and NMR studies of hydrides formed by Ti 4Pd 2O and Zr 4Pd 2O

The oxygen-stabilized Ti 4Pd 2O and Zr 4Pd 2O alloys with the cubic E9 3-Ti 2Ni type structure have been reacted with hydrogen gas. Powder X-ray diffraction (XRD) has shown that the hydride phase retains a face-centered-cubic unit cell with an expansion of lattice parameter that is dependent on hydrogen content. The crystal structure has been solved for Zr 4Pd 2OD 3.5 by neutron diffraction. NMR measurements of proton relaxation times were made on Ti 4Pd 2OH 5.0 to assess diffusion behavior. Although the activation energy of 0.39 eV derived for Ti 4Pd 2OH 5.0 was nearly identical to the value found for hydrogen diffusion in oxygen-free Ti 2PdH 1.47, the spin-lattice ( T 1d) and rotating-frame ( T 1ρ) relaxation times minima were at much lower temperatures for Ti 4Pd 2OH 5.0, which implies more rapid hydrogen diffusion rates in the oxygen-stabilized phase. The nearest neighbor coordination sites that are involved in proposed hydrogen diffusion path ways are discussed and compared to the deuterium sites of Zr 4Pd 2OD 3.5.

Two phase morphology limits lithium diffusion in TiO(2)(anatase): a (7)Li MAS NMR study.

7Li magic angle spinning solid-state nuclear magnetic resonance is applied to investigate the lithium local environment and lithium ion mobility in tetragonal anatase TiO(2) and orthorhombic lithium titanate Li(0.6)TiO(2). Upon lithium insertion, an increasing fraction of the material changes its crystallographic structure from anatase TiO(2) to lithium titanate Li(0.6)TiO(2). Phase separation occurs, and as a result, the Li-rich lithium titanate phase is coexisting with the Li-poor TiO(2) phase containing only small Li amounts approximately equal to 0.01. In both the anatase and the lithium titanate lattice, Li is found to be hopping over the available sites with activation energies of 0.2 and 0.09 eV, respectively. This leads to rapid microscopic diffusion rates at room temperature (D(micr) = 4.7 x 10(-12) cm(2)s(-1) in anatase and D(micr) = 1.3 x 10(-11) cm(2)s(-1) in lithium titanate). However, macroscopic intercalation data show activation energies of approximately 0.5 eV and smaller diffusion coefficients. We suggest that the diffusion through the phase boundary is determining the activation energy of the overall diffusion and the overall diffusion rate itself. The chemical shift of lithium in anatase is independent of temperature up to approximately 250 K but decreases at higher temperatures, reflecting a change in the 3d conduction electron densities. The Li mobility becomes prominent from this same temperature showing that such electronic effects possibly facilitate the mobility.

Tin–lead (SnPb) solder reaction in flip chip technology

Solder reactions between SnPb and one of the four metals, Cu, Ni, Au, and Pd have been reviewed on the basis of the available data of morphology, thermodynamics, and kinetics. The reactions on both bulk and thin film forms of these metals have been considered and compared. Also the two kinds of reactions, above and below the melting point of the solder, have been considered and compared. The rate of intermetallic compound formation in wetting reactions between the molten solder and the metals is three to four orders of magnitude faster than those between the solid state solder and the metals. The rate is controlled by the morphology of intermetallic compound formation. In the wetting reaction between molten SnPb and Cu or Ni, the intermetallic compound formation has a scallop-type morphology, but in solid state aging, it has a layer-type morphology. There are channels between the scallops, which allow rapid diffusion and rapid rate of compound formation. In the layer-type morphology, the compound layer itself becomes a diffusion barrier to slow down the reaction. Similar morphological changes occur between SnPb and Au or Pd. The stability of scallop-type morphology in wetting reaction and layer-type morphology in solid state aging have been explained by minimization of surface and interfacial energies. The unusually high rate of scallop-type intermetallic compound formation has been explained by the gain of rate of free energy change rather than free energy change. Also included in the review is the use of a stack of thin films as under-bump-metallization, such as Cr/Cu/Au, Al/Ni(V)/Cu, and Cu/Ni alloyed thin films.

Episodic weakening and strengthening during synmetamorphic deformation in a deep-crustal shear zone in the Alps

Abstract The Greiner shear zone (western Tauern Window) deformed a variety of metasedimentary, metavolcanic, and plutonic lithologies at conditions of c. 525–575 °C and 30–40 km depth. Microstructural relationships point to a succession of weakening and strengthening episodes. Stage I involved softening via a change in deformation mechanism. Grain-size reduction in plagioclase-rich horizons locally produced rocks with an average grain size of &lt;30 μm microstructural features consistent with deformation via grain boundary diffusion creep (GBDC; a fluid-assisted deformation mechanism similar to pressure solution, which may result in superplastic behaviour). At constant stress, GBDC will result in a significant increase in strain rate relative to neighbouring layers. Stage II involved reaction-induced strengthening. Rapid bulk diffusion rates associated with GBDC allowed rapid growth of large (up to 20 cm) hornblende cystals. This growth of large cross-cutting crystals shut down grain-size-sensitive flow mechanisms in the plagioclase matrix and locally ‘locked’ the shear zone, shifting ductile deformation to weaker horizons. Stage III involved reaction-induced softening. Local variations in bulk composition and/or fluid availability caused large hornblende grains in some horizons to be partially replaced by biotite. These biotite-rich layers localized subsequent deformation, whereas adjacent layers with intact hornblende record minimal strain. Deformation and metamorphism together exert control on fluid availability, diffusion rates, and reaction kinetics, and these factors collectively control fabric development and rheology. The effects of interaction between small-scale deformational and metamorphic processes are difficult to predict, but can have an important influence on shear zone behaviour at depth. The resulting complexities need to be accounted for in models of crustal strength-depth relationships and shear zone rheologies.

Macrophage-enriched Myristoylated Alanine-rich C Kinase Substrate and Its Phosphorylation Is Required for the Phorbol Ester-stimulated Diffusion of β2 Integrin Molecules

An early event of beta(2) integrin activation is the increased diffusion rate of this molecule on the cell surface, thereby providing integrin molecules with a better chance to meet the ligands. The activation of protein kinase C (PKC) stimulates integrin diffusion by releasing the cytoskeletal constraint on integrin molecules. We report here that macrophage-enriched myristoylated alanine-rich C kinase substrate (MacMARCKS), a membrane-associated PKC substrate involved in integrin activation, is required for this PKC-stimulated diffusion of integrin molecules. Using the single-particle tracking technique, we observed that the activation of PKC stimulated an 11-fold increase in the diffusion rate of beta(2) integrins in wild type J774 macrophage cells but not in those expressing mutant MacMARCKS. Further evidence is provided from a MacMARCKS-deficient cell line in which phorbol esters failed to stimulate the diffusion of integrin. Transfection of wild type MacMARCKS into these cells restored the rapid diffusion rate of the beta(2) integrins. The phosphorylation of MacMARCKS is important because transfection of a nonphosphorylatable MacMARCKS mutant or the addition of staurosporine eliminates the rapid diffusion rate of integrin. Furthermore, adding cytochalasin D bypasses the MacMARCKS deficiency and stimulates beta(2) integrin diffusion, suggesting that MacMARCKS's involvement in integrin activation is prior or at the site of cytoskeleton. Therefore, we conclude that MacMARCKS is required for releasing the cytoskeletal constraint on integrin molecules during PKC-mediated integrin activation.

Oxygen bulk diffusion measurements and TEM characterization of a natural ultramylonite: implications for fluid transport in mica‐bearing rocks

Oxygen bulk diffusion rates were experimentally determined in a natural ultramylonite sample (c. 5 μm grain size; 15–20% biotite, 20% quartz, 60–65% feldspars, and minor Fe‐oxides) from the Gerrish Island shear zone, SE Maine, USA. The diffusion experiments were performed at 250–550 °C and 100 MPa water pressure. Oxygen bulk diffusion rates were determined both parallel and perpendicular to the strong foliation of the sample. The Arrhenius parameters for transport parallel to the foliation are: Dbulk0=2.0×10−11 m2 s−1 and Q=30±6 kJ mol−1. The bulk diffusivity perpendicular to the foliation is about a factor of 3.5 less than that parallel to the foliation with the same activation energy. The values of bulk diffusivity and activation energy obtained are consistent with ionic diffusion through a static aqueous fluid, suggesting that an interconnected fluid exists in the ultramylonite even under hydrostatic conditions. The microstructure of the ultramylonite was characterized using transmission electron microscopy (TEM). The nature and distribution of the interconnected fluid cannot be completely resolved from the TEM analysis; however, the low percentage of three‐grain channels and open grain/interphase boundaries suggests that the fluid resides as a thin film on the grain surfaces. The results of this study have direct applications in many important geological settings and provide valuable insights into the observed rapid diffusion rates, strong lithological control and pervasive nature of fluid transport in mica‐bearing rocks.

岩石学・地球化学・年代学のリンク 同位体地質温度計と超高温変成作用 特に方解石‐石墨同位体温度計

Isotopic geothermometry is an important tool to clarify the thermal history of the metamorphic events because of independence of pressure. When applying the thermometer, it is necessary that the temperature dependence of the fractionation factors among the rock forming minerals be well calibrated.Carbon isotopic geothermometry between calcite and graphite is the most suitable thermometer to record peak metamorphic temperatures in crystalline limestone, because of the inert property of graphite in an isotopic exchange reaction during retrograde metamorphism. Various authors and approaches have reported fractionation factors in the calcitegraphite system. There is, however, still inconsistency among experimental, theoretical, and empirical results. In particular, the slope of the fractionation curve for temperature dependence still has a discrepancy between theoretical-experimental and empirical data. The causes of this discrepancy may be due to uncertainty in individual approaches, e.g., in experimental studies, uncertainty as to the reaction mechanism due to the inert property of crystalline graphite for isotopic exchange experiments ; in theoretical studies, uncertainty caused by a deficiency of reliable data on the vibrational frequency of calcite and graphite crystals; and, in empirical studies, incomplete crystallinity of carbonaceous matter.According to empirical data on carbon isotopic systematics, in crystalline limestone that metamorphosed at temperatures higher than 400°C, isotopic equilibria have been mostly attained in many cases. At temperatures lower than 400°C, data sets show an increased disequilibrium. Because the carbon isotopic fractionation between calcite-graphite is more than 3‰ at about 700°C, this thermometer has great potential as a tool for determining ultra-high temperature metamorphism. Furthermore, because of the inert property of graphite in an isotopic exchange reaction during retrograde metamorphism, graphite-calcite assemblage is the most probable candidate for preserving the highest temperature condition. Again, carbon isotopic zonation in graphite crystal could provide another tool to clarify the thermal history of polymetamorphic terrains.Oxygen isotopic thermometry was long been widely used to determine the temperatures of metamorphic rocks. It has long been recognized that oxygen isotope thermometers often record discordant temperatures during slowly cooling retrograde metamorphism, because of a relatively rapid diffusion rate during retrograde metamorphism. Revised correction techniques for re-equilibration during a retrograde isotopic exchange reaction under the such high temperatures help in using oxygen isotopic thermometry in deducing thermal history.