Isotopic partitioning between scallop shell calcite and seawater: effect of shell growth rate

The relationship between molluscan shell growth rate and skeletal δ¹⁸O and δ¹³C was investigated in a detailed field study for the scallop, Pecten maximus. Seasonal variation in shell growth rate was found to be a governing factor influencing shell δ¹⁸O and δ¹³C. At low shell growth rates, shell δ¹⁸O were more positive (of the order +0.4‰) and δ¹³C more negative (up to −2‰) as compared with predicted values for precipitation of inorganic calcite in isotopic equilibrium with seawater. The deviations in δ¹⁸O were hypothesized as reflecting possible differences in solution carbonate chemistry at the site of mineralization in the extrapallial fluid as compared with that of the external seawater medium. The deviations in shell δ¹³C were consistent with incorporation of isotopically depleted respiratory ¹³C (i.e., a metabolic effect). A trend toward more depleted shell δ¹⁸O and δ¹³C values occurred at higher shell growth rates, with negative δ¹⁸O values as compared with predicted equilibrium at shell growth rates above 0.13 mm per day. These simultaneous negative deviations in skeletal δ¹⁸O and δ¹³C were interpreted as resulting from a kinetic effect. The implications for environmental reconstruction from molluscan isotopic records are discussed in light of a model of isotopic behavior based on the findings of the study.     

Element partitioning in calcite as a function of solution flow rate: a study on vein calcites from the Harz Mountains

A semi-empirical treatment of isothermal element partitioning caused by flow rate-dependent calcite growth from hydrothermal solutions yields element/Ca ratios that are qualitatively similar to those observed in calcite bands of the Pb-Zn banded ores from the Harz Mountains, Germany. The comparison of the calculations with the analytical results suggests that flow rates varied between episodes of calcite precipitation as well as during formation of individual bands. Based on a flow rate-dependent element partition coefficient, changing element/Ca ratios in precipitates from a hydrotherm are therefore not necessarily indicative of changing compositions of the fluid. The variations in element/Ca ratios to be envisaged could be as much as a factor of three.Notation A defined by Eq. 8 - a, b individual values of any element in Eq. 1 - c concentration in moles/m³ - C ₀ initial concentration moles/m³ - i running parameter - F area of precipitation in m² - k _p rate constant of pth order reaction in s · m³/moles^p - R linear (one-dimensional) growth rate in moles/m² · s - p order of growth reaction - s distance from entry of solution in m - s ₀ vertical extension of a vein in m - t time in s - v flow rate of hydrothermal solution in m/s - v₀ standard flow rate in m/s - _r relative flow rate in multiple of v₀ - fraction of total precipitation - ₀ fraction of precipitation under reference conditions when the hydrothermal solution leaves the vein - defining the sign in Eq. 1 for elements that are en riched (= +1) or impoverished (= -1) - logarithmic partition coefficient in Eq. 10 - (R) logarithmic partition coefficient as a function of variable growth rate - [ ], { } concentration ratios of fluids and solids, respectively - EL/Ca calculated ratio of El/Ca in the calcite surface zone after Eq. 11     

Sr,Cd, Mn and Co distribution coefficients in calcite as a function of calcite precipitation rate

Distribution coefficients, as a function of precipitation rate, were determined for the metals Sr²⁺, Co²⁺, Mn²⁺ and Cd²⁺in calcite. A pH-stat was used to maintain a constant degree of-saturation, and hence precipitation rate, during each coprecipitation run. The precipitation rate was proportional to the degree of supersaturation and the mass of seed crystal introduced. Distribution coefficients (λ) as a function of rate were determined using radioactive isotopes for solutions with saturations $\text{Ω = 1}$ to $\text{Ω = 5.5}$. Strontium distribution coefficients increased with increasing precipitation rate, while Co, Mn and Cd distribution coefficients decreased with increasing precipitation rate. The following rate expressions (at 25°C) were derived: logλ_Sr = 0.249 log R ?1.57logλ_Mn = ?0.266 log R + 1.35logλ_Co = ?0.173 log R + 0.68logλ_Cd = ?0.194 log R + 1.46 where R is the observed precipitation rate in nmoles CaCO₃ per mg seed crystal per min.In separate experiments the uptake of radioactive isotopes was monitored during the recrystallization of calcite seed crystals. Rates of recrystallization were from 100 to 10, 000 times slower than the pH-stat experiments, but yielded distribution coefficients consistent with the above rate expressions.Using gross estimates of biogenic crystal growth rates, aragonite to calcite transformation rates, and the above Sr rate expression, biogenic calcite and diagenetic calcite Sr contents are estimated. These experiments indicate that in addition to solution composition, precipitation rate is a significant factor influencing the trace metal content of naturally occurring calcite.     

The influence of temperature and seawater composition on calcite crystal growth mechanisms and kinetics: Implications for Mg incorporation in calcite lattice

The composition of carbonate minerals formed in past and present oceans is assumed to be significantly controlled by temperature and seawater composition. To determine if and how temperature is kinetically responsible for the amount of Mg incorporated in calcite, we quantified the influence of temperature and specific dissolved components on the complex mechanism of calcite precipitation in seawater. A kinetic study was carried out in artificial seawater and NaCl-CaCl₂ solutions, each having a total ionic strength of 0.7 M. The constant addition technique was used to maintain [Ca²⁺] at 10.5 mmol kg⁻¹ while [] was varied to isolate the role of this variable on the precipitation rate of calcite.Our results show that the overall reaction of calcite precipitation in both seawater and NaCl-CaCl₂ solutions is dominated by the following reaction:

     

The Effect of the CO32- to Ca2+ Ion activity ratio on calcite precipitation kinetics and Sr2+ partitioning

Background  

A proposed strategy for immobilizing trace metals in the subsurface is to stimulate calcium carbonate precipitation and incorporate contaminants by co-precipitation. Such an approach will require injecting chemical amendments into the subsurface to generate supersaturated conditions that promote mineral precipitation. However, the formation of reactant mixing zones will create gradients in both the saturation state and ion activity ratios (i.e., ). To better understand the effect of ion activity ratios on CaCO₃ precipitation kinetics and Sr²⁺ co-precipitation, experiments were conducted under constant composition conditions where the supersaturation state (Ω) for calcite was held constant at 9.4, but the ion activity ratio was varied between 0.0032 and 4.15.     

The role of magnesium in the crystal growth of calcite and aragonite from sea water

The seeded precipitation (crystal growth) of aragonite and calcite from sea water, magnesium-depleted sea water, and magnesium-free sea water has been studied by means of the steady-state disequilibrium initial rate method. Dissolved magnesium at sea water levels appears to have no effect on the rate of crystal growth of aragonite, but a strong retarding effect on that of calcite. By contrast, at levels less than about 5 per cent of the sea water level, Mg has little or no effect on calcite growth. Extended crystal growth on pure calcite seeds in sea water of normal Mg content resulted in the crystallization of magnesium calcite overgrowths, containing 7–10 mole % MgCO₃ in solid solution. This suggests that the rate inhibition by Mg is due to its incorporation within the calcite crystal structure during growth, which causes the resulting magnesian calcite to be considerably more soluble than pure calcite. The standard free energy of formation of 8.5 mole% Mg calcite calculated on this assumption is in good agreement with independent estimates of magnesian calcite stability.From the work of Katz (Geochim. Cosmochim. Acta37, 1563–1586, 1973), Plummer and Mackenzie (Amer. J. Sci. 273, 515–522, 1974), and the present paper, it can be predicted that the most stable calcite in Ca-Mg exchange equilibrium with sea water contains between 2 and 7 mole%MgCO₃ in solid solution. Likewise, calcites containing more than 8.5 mole% MgCO₃ are less stable, and those containing less than 8.5 mole% MgCO₃ are more stable than aragonite plus Ca and Mg in sea water.     

Sr/Ca and Ca/Ca fractionation during inorganic calcite formation: I. Sr incorporation

Partitioning of strontium during spontaneous calcite formation was experimentally studied using an advanced CO₂-diffusion technique. Results at different precipitation rates and T = 5, 25, and 40 °C show that at constant temperature Sr incorporation into calcite is controlled by the precipitation rate (R in μmol/m²/h) according to the individual expressions

     

The incorporation of Mg2+ and Sr2+ into calcite overgrowths: influences of growth rate and solution composition

The concentrations of Mg²⁺ and Sr²⁺ incorporated within calcite overgrowths precipitated from seawater and related solutions, determined at 25°C, were independent of the precipitation rate over approximately an order of magnitude. The saturation states used to produce this range of precipitation rates varied from 3 to 17 depending on the composition of the solution.The amount of Mg²⁺ incorporated in the overgrowths was not directly proportional to $\text{Mg}{}^{\mathrm{2+}}\text{Ca}{}^{\mathrm{2+}}$ in solution over the entire range (1–20) of ratios studied. Below a ratio of 7.5, the overgrowth was enriched in MgCO₃ relative to what is predicted by the constant distribution coefficient measured above a ratio of 7.5. This increased MgCO₃ correlates with the relative enrichment of adsorbed Mg²⁺. Above a ratio of 7.5 the concentration of MgCO₃ in the calcite overgrowths followed a classical thermodynamic behavior characterized by a constant distribution coefficient of 0.0123 (±0.008 std dev).The concentration of SrCO₃ incorporated in the overgrowths was linearly related to the MgCO₃ content of the overgrowths, and is attributed to increased solubility of SrCO₃ in calcite due to the incorporation of the smaller Mg²⁺ ions.The kinetic data indicate that the growth mechanism involves the adsorption of the cations on the surface of the calcite prior to dehydration and final incorporation. It is suggested that dehydration of cations at the surface is the rate controlling step.     

Effects of seed material and solution composition on calcite precipitation

We studied the effects of seed material and solution composition on calcite crystal precipitation using a pH-stat system. The seed materials investigated included quartz, dolomite, two calcites with different particle size and specific surface area, and two dried precipitates from precipitative softening water treatment plants. Our results indicated that, of the seed materials examined, only calcite had the ability to initiate calcite precipitation in a solution with a degree of supersaturation of 5.3 over a period of two hours, and that the precipitation rate was proportional to the available surface area of the seed. For different solution compositions with the same degree of supersaturation, the calcite precipitation rate increased with increasing carbonate/calcium ratio, which contradicts the generally accepted empirical rate expression that the degree of supersaturation is the sole factor controlling precipitation kinetics. By applying a surface complexation model, the surface concentrations of two species, >CO₃⁻ and >CaCO₃⁻, appear to be responsible for catalyzing calcite precipitation.     

方解石三维热释光特性研究

热释光的产生与晶格缺陷有关,而晶格缺陷是由晶格生长过程中的缺损,生长过程中杂质离子的混入,以及核辐射造成完整晶格的损伤等多种方式产生的.因此,天然矿物的热释光性质是矿物晶格缺陷的物性特征之一.本文选择了9个来自不同产地,化学组成略有不同的天然方解石,对其进行了化学组分和经X射线辐照的三维热释光谱测试,并对测试结果进行了分析讨论.结果 表明,方解石的热释光发光主要是由Mn2+引起的,发光的强度、峰温的数值与Mn的浓度和猝灭剂(Fe,Co,Ni)的浓度都相关.另外,文中对方解石发光曲线的热释光陷阱深度进行了定量计算,得到其可能存在的陷阱深度分别为1.0～1.1 eV、1.4 eV和1.7 eV.此外,通过对比方解石样品天然热释光和人工X射线辐照产生的热释光发现人工辐照可以使晶体结构中受俘获电子进行重新分布.     

Effect of pH on boron coprecipitation by calcite: further evidence for nonequilibrium partitioning of trace elements

The influence of pH and concentration on boron coprecipitation by calcite were evaluated under near-equilibrium conditions at 25°C. Calcite was precipitated by adding a metastable polymorph (vaterite or aragonite) to a solution of known boron concentration. This method maintains a nearly constant solution composition during the slow conversion of the metastable polymorph to calcite.Boron uptake in calcite was found to be strongly pH-dependent, increasing two orders of magnitude from pH 8.5 to pH 10.5. Boron incorporation into calcites precipitated from vaterite-saturated solutions was five times greater than in calcites precipitated from aragonite-saturated solutions. Ostensibly, these results suggest that the calcite precipitation rates were not low enough to attain equilibrium partitioning of boron into calcite. However, scanning electron micrograph analyses showed that the prevalent crystal forms of calcite generated from aragonite and those generated from vaterite were distinctly different. The different quantities of boron incorporated into these calcites may reflect different crystal growth mechanisms, consistent with face-dependent, nonequilibrium partitioning of trace elements in calcite.At a constant pH of 9.0, boron uptake increased from less than 15 to over 290 mg/kg CaCO₃ as the solution boron concentration was increased from 5 to 100 mg/kg. Our results agree with those of other investigators, despite differences in solution composition, and calcite precipitation techniques used. The agreement between the studies may be because the crystal growth morphology of the calcite was rhombohedral in both cases.     

The partitioning of trace elements between clinopyroxene and trachybasaltic melt during rapid cooling and crystal growth

We present the variation in trace element partition coefficients measured at the interface between rapidly cooled clinopyroxene crystals and co-existing melts. Results indicate that, as the cooling rate is increased, clinopyroxene crystals are progressively depleted in Si, Ca and Mg counterbalanced by enrichments in Al (mainly tetrahedral Al^iv), Na and Ti. Partition coefficients (Ds) for rare earth elements (REE), high field strength elements (HFSE) and transition elements (TE) increase with increasing cooling rate, in response to clinopyroxene compositional variations. The entry of REE into the M2 site is facilitated by a coupled substitution where either Na substitutes for Ca on the M2 site or Al^iv substitutes for Si in the tetrahedral site. The latter substitution reflects an increased ease of locally balancing the excess charge at M2 as the number of surrounding Al^iv atoms increases. Due to the lower concentration of Ca in rapidly cooled clinopyroxenes, divalent large ion lithophile elements (LILE) on M2 decrease at the expense of monovalent cations. Conversely, higher concentrations of HFSE and TE on the M1 site are facilitated as the average charge on this site increases with the replacement of divalent-charged cations by Al^vi. Although crystallization kinetics modify clinopyroxene composition, deviations from equilibrium partitioning are insufficient to change the tendency of a trace element to be compatible or incompatible. Consequently, there are regular relationships between ionic radius, valence of the trace element and D. At both equilibrium and cooling rate conditions, Ds for isovalent cations define parabola-like curves when plotted against ionic radius, consistent with the lattice strain model, demonstrating that the partitioning of trace elements is driven by charge balance mechanisms; cation substitution reactions can be treated in terms of the energetics of the various charge-imbalanced configurations.     

Inhibition of calcite growth by alginate

The kinetics of calcite precipitation in the presence of alginate was investigated using the constant composition technique. In the concentration range investigated (0.0002-0.005 g L⁻¹), alginate inhibits calcite precipitation. The extent of inhibition increased with increased alginate concentration and decreased solution supersaturation. Alginate adsorption, derived from normalized calcite precipitation rates, is described satisfactorily by the Langmuir adsorption model. At lowest supersaturation, alginate adsorption onto calcite probably reaches its maximal uptake of 7.5E-4 g m⁻², corresponding to surface coverage of one molecule for each 200-300 nm², depending on the molecular mass of alginate. This means that one alginate molecule can be bound over 100-150 Ca surface sites. Initially, on the surface of the inhibited calcite, XPS identified alginate but after further time in solution, when the system had recovered, XPS demonstrated that it disappeared from the surface, presumably buried under the newly formed calcite. The alginate affinity constant decreases with increasing supersaturation, evidence for incomplete adsorption. A simple model based on competition between growth and desorption effectively describes the observed change in the adsorption constant.     

The interaction of magnesium with calcite during crystal growth at 25–90°C and one atmosphere

Calcite crystals were grown in a closed system by recrystallization of synthetic and natural aragonite crystals, in the presence of various CaCl2-MgCl2 solutions with and without NaCl.The distribution of Mg2+ between calcite and solution at the entire temperature range is heterogeneous, closely following the Doerner-Hoskins (Doerner and Hoskins, 1925) distribution law. λMg2+C is strongly dependent on temperature, being: 0·0573 ± 0·0017 at 25°C, 0·0681 ± 0·0019 at 35°C, 0·0778 ± 0.0022 at 50°C, 0·0973 ± 0·0021 at 70°C, and 0·1163 ±0 ·0034 at 90°C. λMg2+C is independent of the absolute concentration of Ca2+ in solution as well as of the presence of NaCl.Relatively high λMg2+C values are obtained during the initial reaction stages when too-highly reactive synthetic aragonites are recrystallized. SEM micrographs show that calcite crystals grown from such aragonites are imperfect and that their earlier formed Mg-rich cores redissolve later, resulting in apparently inconsistent λMg2+C values.Calculations applying the new λMg2+C value for 25°C and the solubility data for magnesian calcites (Chaveet al., 1962) demonstrate that although no calcite should be expected to precipate directly from open sea water, its direct precipitation (or recrystallization from aragonite) is possible in closed diagenetic systems which still contain marine solutions, provided a temporary increase in the dissolved calcium concentration takes place.The λMg2+C values obtained allow for a new insight into processes of calcite cementation of reefs and a variety of other carbonate sediments, and for a more precise definition of dedolomitization chemistry.     

Rb and Sr partitioning between haplogranitic melts and aqueous solutions

Rubidium and strontium partitioning experiments between haplogranitic melts and aqueous fluids (water or 1.16-3.56 m (NaCl + KCl) ± HCl) were conducted at 750-950 °C and 0.2-1.4 GPa to investigate the effects of melt and fluid composition, pressure, and temperature. In addition, we studied if the applied technique (rapid and slow quench, and in-situ determination of trace element concentration in the fluid) has a bearing on the obtained data. There is good agreement of the data from different techniques for chloridic solutions, whereas back reactions between fluid and melt upon cooling have a significant effect on results from the experiments with water.The Rb fluid-melt partition coefficient shows no recognizable dependence on melt composition and temperature.For chloridic solutions, it is ∼0.4, independent of pressure. In experiments with water, it is one to two orders of magnitude lower and increases with pressure. The strontium fluid-melt partition coefficient does not depend on temperature. It increases slightly with pressure in Cl free experiments. In chloridic fluids, there is a sharp increase in the Sr partition coefficient with the alumina saturation index (ASI) from 0.003 at an ASI of 0.8 to a maximum of 0.3 at an ASI of 1.05. At higher ASI, it decreases slightly to 0.2 at an ASI of 1.6. It is one to two orders of magnitude higher in chloridic fluids compared to those found in H₂O experiments. The Rb/Sr ratio in non-chloridic solutions in equilibrium with metaluminous melts increases with pressure, whereas the Rb/Sr ratio in chloridic fluids is independent of pressure and decreases with fluid salinity.The obtained fluid-melt partition coefficients are in good agreement with data from natural cogenetic fluid and melt inclusions. Numerical modeling shows that although the Rb/Sr ratio in the residual melt is particularly sensitive to the degree of fractional crystallization, exsolution of a fluid phase, and associated fluid-melt partitioning is not a significant factor controlling Rb and Sr concentrations in the residual melt during crystallization of most granitoids.     

Effects of phosphate ions on intergranular pressure solution in calcite: An experimental study

Intergranular pressure solution (IPS) is a coupled chemical-mechanical process of widespread importance that occurs during diagenesis and low-temperature deformation of sedimentary rocks. Laboratory experiments on IPS in halite, quartz, and calcite have largely concentrated on the mechanical aspects of the process. In this study, we report the effects of pore fluid chemistry, specifically varying phosphate ion concentration, on the mechanical compaction by IPS of fine-grained calcite powders at room temperature and 1 to 4 MPa applied effective stress. Phosphate was investigated because of its importance as a biogenic constituent of sea and pore waters. Increasing the pore fluid phosphate concentration from 0 to 10⁻³ mol/L systematically reduced compaction strain rates by up to two orders of magnitude. The sensitivity of the compaction strain rate to phosphate concentration was the same as the sensitivity of calcite precipitation rates to the addition of phosphate ions reported in the literature, suggesting that the rate of IPS in phosphate-bearing samples was controlled by calcite precipitation on pore walls. The results imply that IPS and associated porosity/permeability reduction rates in calcite sediments may be strongly reduced when pore fluids are enriched in phosphates, for example, through high biologic productivity or a seawater origin. Future modeling of IPS-related processes in carbonates must therefore take into account the effects of pore fluid chemistry, specifically the inhibition of interfacial reactions.     

The influence of experimental design on the rate of calcite dissolution

A rotating disc system has been constructed to study calcite dissolution kinetics. The disc system is shown to obey the Levich theory and to satisfy the stringent chemical controls required by the calcite dissolution system at neutral to alkaline pH values. The errors involved in using a CO₂-free atmosphere are shown to be insignificant. It is shown that the stirring dependence of systems which are not hydrodynamically well-defined is variable and dependent on the shape of the reaction vessel. Extrapolation of such results into natural systems involves very large uncertainties.     

Experimental determination of growth rate effect on U and Mg partitioning between aragonite and fluid at elevated U concentration

Results are reported from an experimental study in which the partitioning of U and Mg between aragonite and an aqueous solution were determined as a function of crystal growth rate. Crystals, identified as aragonite by X-ray diffractometry and micro-Raman spectroscopy, were grown by diffusion of CO₂ from an ammonium carbonate source into a calcium-bearing solution at temperatures of 22 and 53 °C. Hemispherical bundles (spherulites) of aragonite crystals were produced, the growth rates of which decreased monotonically from the spherulite interiors to the edges and thus provide the opportunity to examine the influence of growth rate on crystal composition. Element concentration ratios were measured using electron microprobe (EMP) and fluid composition was determined by inductively coupled plasma-mass spectrometry (ICP-MS) and atomic absorption (AA). Growth rates were determined directly by addition of a Dy spike to the fluid during the experiment that was subsequently located in an experimentally precipitated spherulite using secondary ion mass spectrometry (SIMS). At 22 °C both U/Ca and Mg/Ca partition coefficients exhibited a strong growth rate dependence when crystal growth rates were low, and became independent of growth rate when crystal growth rates were high. The U/Ca ratios in aragonite increase between 22 and 53 °C; in contrast Mg/Ca ratios show inverse dependence on temperature.     

The impact of solution chemistry on Mytilus edulis calcite and aragonite

Magnesium/calcium, Sr/Ca, and Na/Ca atom ratios were determined in the calcite and aragonite regions of Mytilus edulis shells which were grown in semi-artificial ‘seawater’ solutions having varying Mg/Ca, Sr/Ca, and Na/Ca ratios. These ratios were measured by instrumental neutron activation, atomic absorption, and electron microprobe analytical techniques. Strontium/calcium ratios in both calcite and aragonite were linearly proportional to solution Sr/Ca ratios. Magnesium/calcium ratios in calcite increased exponentially when solution Mg/Ca ratios were raised above the normal seawater ratio; whereas in aragonite, Mg/Ca ratios increased linearly with increases in solution Mg/Ca ratios. Sodium/calcium and sulfur/calcium ratios in calcite covaried with Mg/Ga solution ratios. Conversely, in aragonite, Na/Ca ratios varied linearly with solution Na/Ca ratios.Magnesium is known to inhibit calcite precipitation at its normal seawater concentration. We infer from the results of the work reported here that Mytilus edulis controls the Mg activity of the outer extrapallial fluid, thus facilitating the precipitation of calcitic shell. Increases in sulfur content suggest that changes in shell organic matrix content occur as a result of environmental stress. Certain increases in Mg content may also be correlated to stress. Sodium/calcium variations, and their absolute amounts in calcite and aragonite, are best explained by assuming that a substantial amount of Na is adsorbed on the calcium carbonate crystal surface. Strontium/calcium ratios show more promise than either Mg/Ca or Na/Ca ratios as seawater paleochemistry indicators, because the Sr/Ca distribution coefficients for both aragonite and calcite are independent of seawater Ca and Sr concentrations.     

Influence of geometry upon crack healing rate in calcite

Crack healing experiments were conducted at 780°, 815°, and 850° C in dry carbon dioxide over periods of 0.5 to 1320 h on small penny-shaped cracks of known geometry in Stahl calcite. As observed by previous investigators, healing initiates with the formation of tubes around the leading edge of the crack, followed by the pinching off of spherical bubbles from these tubes. Pillars and peninsular structures formed and grew at cleavage steps and other surface irregularities, greatly accelerating the healing process in some cracks. The crack tip regression distance at constant temperature follows a simple power law in time; although, with the exception of one crack at 850° C, the time exponent systematically decreases from 0.59 at 780° C to 0.15 and 0.07 at 815° and 850° C, respectively. Only the largest exponent is consistent with existing theory: the two smaller time exponents are, as yet, unexplained. Healing rates are strongly inversely dependent upon crack aperture, in qualitative agreement with theory. For example, cracks with maximum apertures of less than 60 nm (6×10^?8 m) healed completely in 0.5 to 25 h at 850° C; while fatter cracks, with maximum apertures of about 700 nm, showed very little healing after up to 1320 h at the same temperature. At 780° C, the functional dependence of healing rate upon crack aperture was consistent with several aspects of the present model.