Showing papers on "Grain size published in 1980"
TL;DR: In this article, a critical review of idealized two-phase geometrical models is given, which derive expressions for the resistivity and Hall coefficient of a composite material in terms of the properties of its constituents.
Abstract: Gives a critical review of idealised two-phase geometrical models. These treatments derive expressions for the resistivity and Hall coefficient of a composite material in terms of the properties of its constituents. The authors show that these models can be applied to the interpretation of transport measurements in polycrystalline films and powder layers. Important distinctions are made depending on whether the depletion layers extend completely or partially through the grains, whether the Debye length is greater or less than the grain size and whether the mean free path is greater or less than the grain size. The authors discuss the theoretical treatment of the Hall effect in percolative systems, as geometrical models neglect percolation. The modulation of Hall coefficient and conductivity by illumination and the adsorption and desorption of ambient gases are also considered.
539 citations
TL;DR: In this paper, it was found that three deformation regimes, each with its characteristic microstructural imprint, can be established, and the grain size produced by dynamic in-situ recrystallization was found to be inversely proportional to the applied flow stress.
330 citations
TL;DR: In this article, a physically consistent physical model for transport and sorting in muddy turbidity currents has been proposed, based on textural analysis of individual silt laminae and hydraulic sorting.
Abstract: Turbidite muds in cores from the outer Scotian continental margin, off eastern Canada, contain abundant thin silt laminae. Graded laminated units are recognized in parts of this sequence. These represent single depositional events, and show a regular decrease in modal grain size and thickness of the silt laminae through the unit. A similar fining trend is shown by both silt and mud layers over hundreds of kilometres downslope. Textural analysis of individual laminae allows the construction of a dynamically consistent physical model for transport and sorting in muddy turbidity currents. Hydraulic sorting aggregates finer material to the top and tail regions of a large turbidity flow which then overspills its channel banks. Downslope lateral sorting occurs with preferential deposition of coarser silt grains and larger mud flocs. Depositional sorting by increased shear in the boundary layer separates clay flocs from silt grains and results in a regular mud/silt lamination. Estimates can be made of the physical parameters of the turbidity flows involved. They are a minimum of several hundreds of metres thick, have low concentrations (of the order of 10−3 or 2500 mg 1−1), and move downslope at velocities of 10-20 cm s−1. A 5 mm thick, coarse silt lamina takes about 10 h to deposit, and the subsequent mud layer ‘blankets’ very rapidly over this. A complete unit is deposited in 2-6 days which is the time it takes for the turbidity flow to pass a particular point. These thick, dilute, low-velocity flows are significantly different from the ‘classical’ turbidity current. However, there is mounting evidence in support of the new concept from laboratory observations and direct field measurements.
270 citations
TL;DR: In this article, a transformation of grain boundary recombination centers to a uniform distribution of such states throughout the grain was proposed, and the effective carrier lifetime was expressed in terms of grain size, allowing calculation of shortcircuit current, open-circuit voltage, and fill factor.
Abstract: Grain boundary states play a dominant role in determining the electrical and photovoltaic properties of polycrystalline silicon by acting as traps and recombination centers. The recombination loss at grain boundaries is the predominant loss mechanism in polycrystalline solar cells. Cell parameters are calculated based on a transformation of grain boundary recombination centers to a uniform distribution of such states throughout the grain. Effective carrier lifetime is expressed in terms of grain size, allowing calculation of short‐circuit current, open‐circuit voltage, and fill factor. Excellent agreement is observed between theory and experiment for almost all device parameters. It is indicated that one could fabricate 10% efficiency polycrystalline solar cells from 20‐μm‐thick material if the grain size exceeds 500 μm.
248 citations
TL;DR: In this paper, a detailed statistical theory of normal grain growth has been constructed by extending the theory of Feltham and combining it with the work of Rhines and Craig, and complete solutions are found for the grain growth kinetics of each class, as well as the transfer rates between classes.
Abstract: By extending the theory of Feltham and combining it with the work of Rhines and Craig, a detailed statistical theory of normal grain growth has been constructed. The theory exhibits all four attributes of normal grain growth: uniformity, scaling, stability, and lognormality. A prime new feature of the theory is the division of the grains into topological classes (14 planar, 34 spatial), each with a lognormal distribution of grain sizes. Growth is found to be controlled by the rate of loss of grains from the lowest topological class. Complete solutions are found for the grain growth kinetics of each class, as well as the transfer rates between classes. The latter result is used to explain how the median diameter of those classes in which grains are shrinking still manages to increase in the manner required to keep their number a constant fraction of the total population. A parabolic growth law is found for the median grain size of the whole population as well as the median grain size in each topological class. The growth constant for each class is found to increase approximately as the cube of the planar topological parameter or the square of the spatial topological parameter. The Rhines‐Craig structural gradient is shown to be independent of time and hence a basic constant of normal grain growth. Stability is due to a maximum in the grain boundary velocity with increasing grain size. The ratio of the maximum to median grain diameter is found to be e(=2.718). A comparison of the present theory is made with that of Hillert. Possible origins of the lognormality are discussed.
242 citations
TL;DR: In this article, high-temperature creep experiments were made on olivine single crystals under compressional stress to large strains, and dynamic recrystllization occurs and cellular wall dislocation structure is formed.
Abstract: High-temperature creep experiments were made on olivine single crystals under compressional stress to large strains. At strains larger than about 40 to 60%, dynamic recrystllization occurs and cellular wall dislocation structure is formed. Recrystallized grain size dg(µm) and cell wall spacing ds(µm) are dependent upon applied stress σ(MPa) as: and
239 citations
TL;DR: In this paper, the sintering behavior of binary ZnO ceramics (containing 0.01-1 mol% of added Bi2O3) was investigated and it was shown that densification in the initial stage of sinter, and grain growth of the ZnOs matrix are enhanced in the presence of a liquid Bi 2O3 phase.
Abstract: The sintering behavior of binary ZnO ceramics (containing 0.01–1 mol% of added Bi2O3) showed that densification in the initial stage of sintering and grain growth of the ZnO matrix are enhanced in the presence of a liquid Bi2O3 phase. Exaggerated grain growth of ZnO was observed above 1100 °C and in mixtures containing as low as 0.05 mol % Bi2O3. Volatilization loss of Bi2O3 during sintering affected the microstructure of the sintered ceramics and resulted in the loss of varistor property and return to Ohmic behavior and high conductivity (∼1 Ω−1 cm−1). A simple microstructural model which predicts that the minimum content of Bi2O3 required to maintain varistor behavior is proportional to the thickness of intergranular layer and inversely proportional to the average grain size of the ZnO.
148 citations
TL;DR: In this paper, a model for the superplastic deformation mechanism was presented and the fact that super-plasticity is a distinct rate-controlling mechanism in the high temperature deformation of fine-grained materials, with its own and unique dependence of strain rate on grain size, stress and temperature, was emphasized.
121 citations
TL;DR: In this article, fine intragranular carbides which are precipitated during creep are effective in lowering the creep rate during the early stages of the creep regime (within 300 h).
Abstract: Creep tests have been correlated with microstructural changes which occurred during creep of Inconel 617 at 1000 °C, 24.5 MPa. The following results were obtained: 1) Fine intragranular carbides which are precipitated during creep are effective in lowering the creep rate during the early stages of the creep regime (within 300 h). 2) Grain boundary carbides migrate from grain boundaries that are under compressive stress to grain boundaries that are under tensile stress. This is explained in terms of 1 the dissolution of relatively unstable carbides on the compressive boundaries, 2 the diffusion of the solute atoms to the tensile boundaries and 3 the reprecipitation of the carbides at the tensile boundaries. The rate of grain boundary carbide migration depends on grain size. 3) M23C6 type carbides, having high chromium content, and M6C type carbides, having high molybdenum content, co-exist on the grain boundaries. M23C6 type carbides, however, are quantitatively predominant. Furthermore, M6C occurs less frequently on the tensile boundaries than on the stress free grain boundaries. This is attributed to the difference of the diffusion coefficients of chromium and molybdenum. 4) The grain boundaries on which the carbides have dissolved start to migrate in the steady state creep region. The creep rate gradually increases with the occurrence of grain boundary migration. 5) The steady state creep rate depends not so much on the morphological changes of carbides as on the grain size of the matrix.
113 citations
TL;DR: In this article, an empirical relationship was established for the grain size resulting from sub-grain rotation in a series of peridotite xenoliths from some representative localities.
Abstract: Lithospheric stress magnitudes may be estimated through the application of geological thermobaromeo ters [Mercier, 1980] and grain size piezometers [Ross et al., 1980]. Discontinuities in grain size profiles based on series of peridotite xenoliths from some representative localities can hardly correspond to abrupt changes in stress conditions at depth, inasmuch as no geochemical difference is observed across the textural discontinuities, and no phase changes are possible. These discontinuities would thus result from reaching a critical temperature or stress beyond which the dominant recrystallization mechanism drastically changes. Indeed, the grain size piezometer is very sensitive to the recrystallization mechanism [Poirier and Guillope, 1979], and whereas recrystallization through subgrain rotation has been recognized in some natural peridotites [e.g., Nicolas et al., 1971], the experimental data available so far apply to grain boundary migration recrystallization. On the basis of two significantly different grain size profile discontinuities, an empirical relationship (o = 74.5/D) is inferred for the grain size resulting from subgrain rotation. Applying this new relationship when relevant, the stress magnitudes estimated from deep samples remain virtually unchanged relative to previous results [Ave Lallemant et al., 1980], as do their implications regarding large-scale convection. However, revised magnitudes for the uppermost mantle may be significantly increased to a value as high as 45 MPa (450 bar) for the Basin and Range Province, with stresses in the lower crust possibly reaching up to 80 MPa.
106 citations
TL;DR: In this article, the transition from single-crystal to polycrystalline fracture energies was studied as a function of the flaw-size to grain-size ratio by two methods.
Abstract: The transition from single-crystal to polycrystalline fracture energies was studied as a function of the flaw-size to grain-size ratio by two methods. The primary method was calculating fracture energies from observed flaw sizes found at fracture origins in strength-test specimens. Some measurements were also made by varying the number of grains across the web in the applied-moment DCB test. Both methods agreed and generally snowed the transition to polycrystalline fracture energies being completed at flaw-size to grain-size ratios of ∼1 to ∼ 6 for the cubic materials studied. It is estimated that cracks less than ∼½ to ¼ of the grain size cannot be arrested at grain boundaries and that single-crystal fracture energies can be applied below this limit. The grain-size range over which this fracture-energy transition occurs was shown to be a function of extrinsic factors, such as texture, as well as intrinsic factors, such as the number and multiplicity of low-energy single-crystal fracture planes.
TL;DR: In this paper, it was shown that the region of significant plastic deformation is confined by the grain boundaries, resulting in a plastic zone size that is insensitive to crack length and to external load.
Abstract: The crack tip opening displacement (CTOD) of small surface fatigue cracks (lengths of the grain size) in Al 2219-T851 depends upon the location of a crack relative to the grain boundaries. Both CTOD and crack tip closure stress are greatest when the crack tip is a large distance from the next grain boundary in the direction of crack propagation. Contrary to behavioral trends predicted by continuum fracture mechanics, crack length has no detectable effect on the contribution of plastic deformation to CTOD. It is apparent from these observations that the region of significant plastic deformation is confined by the grain boundaries, resulting in a plastic zone size that is insensitive to crack length and to external load.
TL;DR: In this article, the changes in grain size and concentration with time were studied in relatively dilute settling suspensions of varying initial concentration and constituent grain sizes and composition, and the results showed that during sing...
Abstract: The changes in grain size and concentration with time were studied in relatively dilute settling suspensions of varying initial concentration and constituent grain size and composition. During sing...
TL;DR: In this paper, the deformation of an ultrafine-grained aluminium alloy has been examined in tension and torsion, and the results show that at grain sizes below about 3 μm the alloy exhibits inhomogeneous yielding but this is absent at larger grain sizes.
Abstract: The deformation of an ultrafine-grained aluminium alloy has been examined in tension and torsion. At grain sizes below about 3 μm the alloy exhibits inhomogeneous yielding but this is absent at larger grain sizes. If the lower yield strength values are plotted versus grain size the strengths are inversely dependent on grain size whereas the usual plot versus d −½ is non-linear and shows an enhanced strength at the finer grain sizes. However, if the inhomogeneous yielding region is avoided by extrapolating the work-hardening portion of the curve back to the elastic line, all the data can be well represented by the Hall–Petch relationship. Torsion tests, which allow the investigation of a large strain range, show that. the gredient of the grain size plots decreases slowly wIth strain but that the grain boundaries remain effective barriers to flow at strains up to at least 1.0. The deformation behaviour does not appear to agree with the current models for the influence of grain size on the flow stre...
TL;DR: In this article, a group of quartz-bearing mylonitic rocks from the Coyote Mountain mylonite zone, near Borrego Springs, California, using the grain sizes and dislocation densities of quartz grains is presented.
Abstract: Several recent studies have attempted to determine the flow stresses during geological deformations from the microstructures of rocks, utilizing quantitative estimates of such structural parameters as grain size, subgrain size, and dislocation density. The basis for these stress determinations is the apparent correlation between flow stress and microstructures in experimental deformation studies of several crystalline materials. Estimates of flow stresses are presented for a group of quartz-bearing mylonitic rocks from the Coyote Mountain mylonite zone, near Borrego Springs, California, using the grain sizes and dislocation densities of quartz grains. Neglecting complexities in the geological history of the rocks, flow stresses inferred from grain sizes range from 16 to 74 MPa (160 to 740 bars), whereas those derived from dislocation densities range from 131 to 50 Mpa, respectively, for the same rocks. Stress estimates by the two methods are not well correlated and may differ by an order of magnitude for the same rock. The major causes of the inconsistencies are considered to be (1) inadequacy of the currently available experimental data and (2) complexity of the thermomechanical history of the rocks. These problems are discussed, and the potential value of the methods is assessed. It appears likely that the rocks were subjected to flow stresses (σ1–σ3) of 100 MPa (1 kbar) or more during mylonitization.
TL;DR: In this paper, the effect of grain size on the resistivity of polycrystalline silicon films has been investigated theoretically and experimentally, and it is shown that existing models do not accurately predict resistivity dependence on doping concentration as grain size increases.
Abstract: The effect of grain size on the resistivity of polycrystalline silicon films has been investigated theoretically and experimentally. It is shown that existing models do not accurately predict the resistivity dependence on doping concentration as grain size increases. A new modified trapping theory demonstrates from a good agreement with experimental results that a significant increase in grain size drastically reduces the sensitivity of polysilicon resistivity to doping concentration.
TL;DR: An extensive set of measurements on the grain growth and microstructure evolution of a series of high-density Ni•Zn ferrites annealed over periods ranging from 1/4 to 48 h is reported in this article.
Abstract: An extensive set of measurements on the grain growth and microstructure evolution of a series of high‐density Ni‐Zn ferrites annealed over periods ranging from 1/4 to 48 h is reported. A comparison of the data with predictions of the statistical multiple‐lognormal theory of normal grain growth presented in Part I is made. The time invariance of the standard deviations of both the grain size and population of individual topological classes is confirmed, demonstrating that the scaling and stability of normal grain growth are critically related to the dispersion of the grain sizes and that at least two parameters are needed to characterize a given microstructure. A parabolic growth law for the median diameter in both two and three dimensions is confirmed as well as the predicted power law dependence of the growth constants for each class on the topological index. A series of sectioning experiments verifies the near equivalence of the planar and spatial size parameters.
TL;DR: In this paper, the authors measured the kinetics of hot pressing of Al2O3 with and without MgO additives at 1475 and 1630° C and at 5 to 20 MPa using powders of different grain size and using different additive levels.
Abstract: The kinetics of hot pressing of Al2O3 with and without MgO additives have been measured at 1475 and 1630° C and at 5 to 20 MPa using Al2O3 powders of different grain size and using different additive levels. Data obtained within the solid solution regime are interpreted in terms of diffusional creep processes. MgO additions accelerate densification within this regime; the consequent reduction in pore size, and hence in pore drag, can explain the function of MgO as sintering additive for Al2O3.
TL;DR: In this article, the energy criterion is extended to predict the relationship between the temperature of microcrack initiation (TMB) caused by thermal stressing in brittle materials and the grain size, which can be extrapolated to room temperature to provide an estimate of the critical grain size.
Abstract: In this paper, the energy criterion is extended to predict the relationship between the temperature of microcrack initiation (TMB) caused by thermal stressing in brittle materials and the grain size. The relation can be extrapolated to room temperature to provide an estimate of the critical grain size. When the relation was compared to literature data, it was found that: (1) the predicted inverse square root relation of TMB to grain size is satisfied; (2) the room temperature intercept on the grain-size axis agrees well with the measured critical grain sizes. Also presented is a graphical method, based on the proposed relation, by which an engineering estimate of the critical grain size may be made from a minimal set of data.
TL;DR: In this article, the critical grain sizes for the onset of microfracture are expressed in terms of the boundary fracture energy, the elastic properties and the defect size distribution, and the results are compared with those obtained by considering the change in elastic strain energy produced on the introduction of an embryonic crack in the stress field generated by the shape change of the ensemble.
TL;DR: The thermal conductivity of polycrystalline Ge30Si70 has been determined at and above room temperature for samples having a wide range of porosity and mean grain diameter.
Abstract: The thermal conductivity of polycrystalline Ge30Si70 has been determined at and above room temperature for samples having a wide range of porosity and mean grain diameter. It has been established that the thermal conductivity at 300K is completely dominated by the lattice contribution and that its value varies linearly with the porosity. It has, therefore, been possible to calculate the lattice conductivity at zero porosity and to show how this varies with the grain size. The lattice conductivity is equal to 8.2 M m-1 K-1 for fully dense large-grained Ge30Si70 at 300K and falls to 4.3 W m-1 K-1 when the mean grain diameter is reduced to 2 mu m. It is shown that there is a significant contribution to the heat transfer from thermal radiation at 600K; when this contribution is taken into account it is found that the lattice conductivity at this temperature falls from 5.8 W m-1 K-1 when the grain size is very large to 3.7 W m-1 K-1 at a mean grain diameter of 2 mu m. Less comprehensive results are also reported for Ge70Si30.
TL;DR: Hall mobility of polycrystalline silicon was measured in the dark and under illuminated conditions as discussed by the authors, and the free carrier concentration of 5×1015 cm−3 was not affected by illumination, and the room temperature mobility in 1mm grain size material after barrier elimination with light was 900 cm2/V
Abstract: Hall mobility of polycrystalline silicon was measured in the dark and under illuminated conditions. Grain boundary potential barriers present in the dark can be eliminated with light. When the barriers are removed, the mobility between 200 and 400 K is found to vary as T−2, which is the dependence observed in single crystals for the same order of magnitude of doping. The free‐carrier concentration of 5×1015 cm−3 was not affected by illumination, and the room temperature mobility in 1‐mm grain size material after barrier elimination with light was 900 cm2/V sec. A phenomological theory of Hall mobility in polycrystallllne silicon which explains these observations is presented.
TL;DR: In this paper, a modified version of the grain theory was used to analyse the effect of temperature on the sulfation reaction and its effect on the rate of transport of SO2 and the chemical reaction.
TL;DR: In this paper, the evolution of structures has been studied in mylonitic quartzo-feldspathic rocks across a shear zone in Adrar des Iforas (Republic of Mali).
TL;DR: In this article, a study was made of quenched and tempered laboratory heats of 35 Ni-17 Cr steels doped with P, Sn, or Si in which the hardness, the grain size, and the extent of intergranular segregation of the metalloid dopents were varied by aging treatments of various times at 480 °C.
Abstract: A study was made of quenched and tempered laboratory heats of 35 Ni-17 Cr steels doped with P, Sn, or Si in which the hardness, the grain size, and the extent of intergranular segregation of the metalloid dopents were varied The segregation was accomplished by aging treatments of various times at 480 °C It was found that the increases in ductile-brittle transition temperature (ΔTT) were determined completely by the above three variables and that they can be combined in an “embrittlement equation” that permits the calculation of theΔTT that will occur from a particular degree of segregation in a steel of a given hardness and grain size The embrittlement equation contains coefficients which must be determined empirically for each type of steel and embrittling element; however, the equation is derived by a straight-forward Taylor series expansion of theTT as a function of the three variables Each term of the resulting equation can be justified from physical considerations The embrittlement equation can serve as a rational basis for analysis of a given type of steel or for comparisons between types In particular, it allows one to account for variations in hardness and grain size, and to determine the benefits to be gained from control of these two factors
TL;DR: In this article, an inverse square dependence of lifetime on current density has been verified for 2.5 cm long, 1-4 μm wide conducting stripes, and it has been shown that film composition affects the electromigration lifetime through its contribution to the grain structure.
Abstract: The electromigration behavior of Al films, deposited by the sputter gun (varian s‐gun) and ranging in alloy content from 0.5% Cu to 2% Si has been evaluated for 2.5 cm long, 1–4 μm wide conducting stripes. An inverse square dependence of lifetime on current density has been verified. Furthermore, it has been shown that film composition affects the electromigration lifetime through its contribution to the grain structure, in that, an increase in lifetime accompanies an increase in grain size and a decrease in spread of the grain size distribution. Increasing the Si content is detrimental, since it results in a reduction in grain size. Failures occur by the random growth of subsurface voids along the conductor length. The s‐gun films have a completely random orientation in contrast to electron beam evaporated Al‐0.5% Cu, which exhibits a prominent 〈111〉 fiber texture. This preferred grain orientation in the case of the latter is held responsible for its superior lifetime in comparison to the sputtered films.
TL;DR: In this article, a nonlinear version of the theory was used for boundary value problems corresponding to gravity flow in a closed vertical channel and in a channel with a free surface inclined at various angles from the vertical.
Abstract: A theory of flowing granular materials with incompressible grains is presented which is similar to one proposed by Goodman and Cowin in 1972. Using a nonlinear version of the theory, boundary‐value problems corresponding to gravity flow in a closed vertical channel and in a channel with a free surface inclined at various angles from the vertical are considered in detail. In analyzing these problems, the dependence of the free energy and viscosity on the volume fraction are specialized to agree with those proposed as a result of recent experimental work. Solutions of these problems demonstrate many of the characteristics normally assumed in other treatments of granular materials. In particular, for vertical flow, when the volume fraction is greater than (less than) the critical volume fraction, a compressive (tensile) force must be exerted on the walls to maintain isochoric flow. Pluglike regions in which the velocity is almost constant develop, and there is a relatively thin shear region near the wall. For the flow with a free surface, as grain size or angle of inclination increases, the solutions tend to two rigid motions separated by a thin shear layer.
TL;DR: In this article, fine-grained polycrystalline MgO specimens were deformed in compression at constant strain rates of ∼6.7×10−6 s−1 to 6.7 × 10−5 s− 1 at 1173 to 1423 K. Under suitable experimental conditions, superplastic strain was achieved in specimens; no change was detected in the equiaxed-grain shape configuration.
Abstract: Fine-grained polycrystalline MgO specimens were deformed in compression at constant strain rates of ∼6.7×10−6 s−1 to 6.7×10−5 s−1 at 1173 to 1423 K. Both mechanical data and microstructural observations are distinctive of a diffusion-accommodated flow, where the grain-size parameter is of prime importance in enhancing plasticity. Under suitable experimental conditions, superplastic strain was achieved in specimens; no change was detected in the equiaxed-grain shape configuration. Finally, the effect of grain growth during deformation was considered; specimens of initial grain size ∼0.1 μm showed an apparent hardening which was quasi-linear with time.
TL;DR: In this article, the influence of grain size on the fatigue lives was investigated for eight kinds of austenitic stainless steels with the grain size numbers from 9 to 1, and the fracture modes of some types of the steel were completely intergranular, and others mixed.
Abstract: The influence of grain size on the fatigue lives was investigated for eight kinds of austenitic stainless steels with the grain size numbers from 9 to 1. Fatigue tests were carried out at 600 and 700 °C under triangular wave shapes at strain rates of 6.7 × 10-3/s and 6.7 × 10-5/s, respectively, and under truncated wave shape with 30 m;n hold-time at tension side. When a strain rate was 6.7 × 10-3/s at both 600 and 700 °C, the fracture modes were always transgranular, and the fatigue lives scarcely depended on the type of steels or the grain size. When a strain rate was 6.7 × 10-5/s at 600 °C, the fracture modes changed from a dominantly transgranular mode to a completely intergranular one and the fatigue lives decreased with decreasing the grain size number. When a strain rate was 6.7 X 10-5/sVs at 700 °C, grain size dependence of the fatigue lives was divided into two groups of the steels depending on the type of steel. The fracture modes of some types of the steel were completely intergranular, and others mixed. In hold-time tests, the grain size dependence of the fatigue lives was similar to that in the tests of triangular wave shape at a strain rate of 6.7 × 10-5/s.
TL;DR: In this article, the classical theories of the formation of CaCO3 from dolomite were reexamined, and a direct formation theory was suggested on the basis of the results of X-ray analysis.