Article Cite This: Cryst. Growth Des. XXXX, XXX, XXX−XXX
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Step Patterns on {100} Faces of Diamond Crystals As-Grown in MgBased Systems Alexander F. Khokhryakov,*,†,‡ Yuri N. Palyanov,†,‡ Yuri M. Borzdov,†,‡ Anton S. Kozhukhov,‡,§ and Dmitriy V. Shcheglov§ †
Sobolev Institute of Geology and Mineralogy, Siberian Branch of the Russian Academy of Sciences, Koptyug Pr., 3, Novosibirsk 630090, Russian Federation ‡ Novosibirsk State University, Pirogova, 2, Novosibirsk 630090, Russian Federation § Rzhanov Institute of Semiconductor Physics, Siberian Branch of the Russian Academy of Sciences, Lavrentieva Pr., 13, Novosibirsk 630090, Russian Federation ABSTRACT: In this article, we report the unusual growth of diamond crystals produced in Mg−C and Mg−Ge−C systems at high-pressure, high-temperature conditions. We have found that the growth of the habit {100} faces occurs by deposition of a substance (carbon) on two nonequivalent {100} and {111} surfaces. Precipitation of carbon atoms on the (100) plane occurs by elementary layers with a thickness of about 0.1 and 0.2 nm. The change in the density of elementary steps leads to the formation of step bunches that transform into faceted macrostates with an increase in their thickness of more than 400 nm. The maximum inclination angle of macrostep ends corresponds to the {111} faces position. As a result, singular stable {111} microfacets are formed at the ends of the macrosteps, which themselves grow layer by layer. The deposition of carbon on {100} and {111} surfaces of one simple form of diamond crystals leads to the zonal structure of {100} growth sectors.
1. INTRODUCTION Step patterns are common elements of the surface morphology of natural and synthetic crystals.1,2 Usually, these are macrosteps that are bunches of elementary steps. The presence of macrosteps significantly affects the internal structure of the crystals and can result to the formation of striation, inclusions of the crystallization medium, dislocations, and other defects.3,4 In this regard, investigation of macrosteps and conditions for their formation is a topical research issue in the field of crystal growth. Depending on the macrostep end structure, two fundamentally different macrostep types are distinguished. The first type includes macrosteps that appear as dense bunches in the echelon of elementary steps of growth. These step bunches can arise for various reasons, with the main ones being temperature fluctuations, supersaturations, and impurity adsorption on a growing surface. The second type of macrosteps is “true macrosteps” or “faceted macrosteps” whose ends are formed by faces with simple crystallographic indices.3,4 True macrosteps move along the surface by layer-bylayer growth of their ends. Usually, they form on vicinal surfaces deviating from rational surfaces by a small angle. The most common cause for formation of true macrosteps on vicinal surfaces is the surface energy anisotropy.3,5 However, true macrosteps also occur on rational dense-packed surfaces with simple crystallographic indices.6−9 The conditions of their formation have been poorly explored. The nature of macrosteps on real crystals is not always recognizable. The complexity of assigning macrosteps to a certain type is associated with both instrumental capabilities for studying the microrelief at © XXXX American Chemical Society
macrostep ends and insufficient attention to these objects during research. Diamond is also not an exception, and its faces have various stepped structures. Bunches of steps with a thickness of 5−150 nm on faces of diamond crystals synthesized in metal−carbon systems at high-temperature high-pressure (HPHT diamond) conditions were detected by interference microscopy as early as the 1960s.10,11 Also, faceted macrosteps were found on {100} and {111} faces of diamond crystals.12−15 Recently, the development of atomic force microscopy (AFM) has enabled investigation of a more subtle morphology of faces. However, this method has not been extensively used for investigation of HTHP diamonds. This is apparently associated with a postgrowth relief present on the surface of many HTHP diamond crystals, which overlaps the growth relief of faces. This relief forms after completion of the growth cycle and reflects mainly the structure of a metal-catalysts (Ni, Co, Fe) in which the diamond is synthesized.16 There are only fragmentary data on investigation of the subtle surface microrelief of HTHP diamond crystals. The morphology of step bunches (thickness from 3 to 26 nm) of some diamonds synthesized in traditional metal−carbon systems were studied by AFM.17,18 It should be noted that investigation of the morphology of diamond faces in a wide range of magnifications is most informative for understanding of the growth mechanisms and potential control Received: July 23, 2017 Revised: December 5, 2017 Published: December 5, 2017 A
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of crystal properties. This is especially important for studying diamond crystallization in new systems. Recently, we published data on the growth of HPHT diamond crystals in magnesium-based systems.19−22 The crystals grown in these systems are unique by their extremely high growth rates and the presence of impurity centers in them, which are of interest for quantum optics. It is shown that the growth of the cube faces of diamond crystals occur with the formation of either an echelon of macrosteps or an unusual relief of macrolayers strongly elongated in one of the [110] directions. The ends of macrosteps (macrolayers) are composed of {111} faces, and, therefore, these are true macrosteps. In this article, we present the results of scanning electron microscopy (SEM) and AFM studies of the {100} faces microrelief of HPHT diamonds grown in Mg-based systems. The morphology of faces, from faceted macrosteps to elementary growth layers, is analyzed in a wide range of magnifications. A possible mechanism of macrostep formation and the causes for extremely high growth rates of the diamond crystals are proposed.
Figure 1. Two main types of microrelief of {100} faces of diamond crystals grown in magnesium-based systems at 1800−1900 °C: (a) echelons of macrosteps on a diamond crystal grown on a seed (optical microscopy); (b) cluster of rectangular layers - islands on a spontaneous diamond crystal (SEM).
diamond crystals but is most typical of spontaneous diamond crystals that crystallize directly in a metallic Mg0.9Ge0.1 melt. Let us first consider the first type of microrelief. Figure 1a shows the (100) face of a typical diamond crystal grown on a seed. The seed crystal is visible in the image center as a gray noncontrasted square. The largest morphological elements of {100} faces are echelons of faceted rectangular macrosteps that are seen even by optical microscopy (Figure 1a). Edges of the steps are oriented along the [110] directions. Centers of steps propagation on these crystals are either a diamond microcrystal in the twin position, as shown in Figure 2b, or outputs on the faces of the strongest dislocations, as shown previously.23 Macrosteps with a height of several hundreds of nanometers to several micrometers are clearly seen on diamond crystals using SEM (Figure 2c−f). The macrostep ends are composed of {111} facets, and the height of macrosteps increases as they move away from the growth center. Near the steps’ source, the thickness of macrosteps is less than 1 μm (Figure 1c). In the middle part of the surface, the thickness of steps is often 3−4 μm (Figure 2d,e). At the face edge, near the {111} crystal face, their thickness reaches 15 μm (Figure 2f). Near the growth center, the macrostep ends are smooth or have elements of layerwise growth along the {111} facets. Layers on the {111} facets of macrosteps have a triangular or hexagonal shape and are oriented along [110] directions (Figure 3). In addition, the ends of macrosteps with the height greater than 1 μm have additional narrow {111} facets. This additional {111} microfacet forms an incoming angle with the lower {100} terrace of the next macrostep (Figure 3b,c). On the terraces of faceted macrosteps, there are echelons of thinner rectilinear steps, also oriented in the [110] directions, parallel to the edges of the terrace (Figures 2 and 3). The smaller relief on the macrostep terraces was studied by AFM. AFM measurements demonstrated that the step heights varied in a wide range, from a few nanometers to a few micrometers. However, step echelons were built up of steps with certain heights, the most typical of which are shown in Figure 4. Figure 4 presents a series of AFM images of terraces of faceted macrosteps from an observable area of 83 × 83 μm to 2 × 2 μm. Figure 4a,b clearly demonstrates parallel steps that form step echelons. An analysis of cross sections of the step echelons shows that the height of steps ranges from 0.2 to 1.5 μm for an observable area of 83 × 83 μm and from 20 to 50 nm for an observable area of 11 × 11 μm (Figure 4a,b). The ends these thin steps in most cases do not have a constant slope. Figure 4c shows an AFM image of the macrostep terrace region with an observable area of 2 × 2 μm. Thinner steps and single layers located on the macrostep terrace are clearly seen. The thinnest layers have the form of rectangles, strongly elongated
2. EXPERIMENTAL SECTION We studied synthetic diamond crystals grown in Mg−C and Mg0.9Ge0.1−C systems at 7.0 GPa in a temperature range of 1800− 1900 °C using a multianvil high-pressure split sphere apparatus.19−21 A detailed description of the high-pressure cell design, the method for growth, and characterization of produced crystals are provided in our recent studies.19−21 We studied seed-grown diamond crystals of 0.8− 2.0 mm in size. As seed crystals, we used cuboctahedral diamonds of the SDA100+ grade with a size of 0.4−0.5 mm. Before analysis, grown diamond crystals were cleaned with an oxidizing solution (a mixture of concentrated sulfuric acid and a K2Cr2O7 solution) to remove products of experiments (magnesium alloy oxidation products, quenching graphite, etc.) that interfered with the study of the fine relief faces. Then, crystals were washed several times in hot distilled water. As we noted above, diamonds grown in traditional systems based on Fe, Ni, Mn, and Co show in most cases “a post-growth relief” on their surfaces. It is formed in the cooling process and reflects the structure of the crystallizing metal. This relief is a very fine dendritic pattern or a lamellar structure, which is independent of the crystal orientation of the diamond.16 In the Mg−C system, because of the high cooling rate (200 deg/s) and, apparently, the characteristics of carbon deposition from the melt, such a relief is not observed. Since in situ observation of diamond growth is impossible, we can assume that the observed relief of the diamond surfaces corresponds well to the relief formed in the growth process. The crystals were studied using an Axio Imager Z2m optical microscope and a Tescan MIRA3 LMU scanning electron microscope at the Analytical Center for the MultiElemental and Isotope Research of the Siberian Branch of the Russian Academy of Sciences. The topography of diamond crystals {100} with a higher resolution was investigated using AFM with a Solver P-47H device in a noncontact mode.
3. RESULTS The {100} faces are the main faces that determine the shape of diamond crystals in Mg−C and Mg0.9Ge0.1−C systems. The {111} faces are the minor faces that truncate cube vertices. The {100} faces have two types of microrelief. The first microrelief type is determined by the presence of macrostep trains propagating from one or two growth centers (Figure 1a). This type of microrelief is found only on seed-grown diamonds. The second microrelief type is characterized by the presence of clusters of rectangular macrolayers that are strongly elongated in one of the [110] directions (Figure 1b). This type of microrelief is also present on the {100} faces of seed-grown B
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Figure 2. Images of the faceted macrosteps on the {100} face of a diamond crystal grown on seed: (a) general view of the face (optical microscopy); (b) diamond microcrystal in the twin position, which is located at the steps propagation center; (c−f) fragments illustrating macrosteps on various areas of the face (SEM). T - terraces of macrosteps, E - ends of macrosteps.
terraces. Figure 5 presents an AFM images of a such surface areas of 3 × 3 μm at different locations on the same face of the
Figure 5. AFM image of the {100} face fragments with 2D islands: (a) island clusters, from isometric to elongated (the regions containing islands are outlined by a solid line); (b) numerous elongated 2D islands. The color height scale is identical for both figures.
crystal. The size of islands ranges from 10 to 50 nm. The maximum ratio of the island length to the island width exceeds 60. The second type of microrelief that is typical of the {100} faces of diamond crystals grown in Mg systems is characterized by the absence of unidirectional step echelons. Figure 1b depicts this type of topography. The {100} faces of these diamond crystals have a relief formed by clusters of highly elongated rectangular macrolayers. Previously, we performed a
Figure 3. Macrostep ends on the {100} faces of the diamond crystals: (a, b) SEM images of microrelief on the macrostep ends; (c) a schematic representation of the cross section of macrosteps.
parallel to the step train. The measured heights of steps amount to 0.08−0.1 nm, 0.17−0.2 nm, and 0.3 nm (Figure 4c, profile C). Islands and rectangular pits, from isometric to highly elongated in [110] directions, are often observed on macrostep
Figure 4. (a−c) AFM images of the step trains on the {100} face of diamond and graphs showing the profiles (A, B, C) along the lines on the upper figures. C
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HELs and the {100} plane of a terrace. The measurements were performed for step patterns with a height of 20−1500 nm. The inclination angle between slopes and the {100} plane of a terrace was calculated from the width and height of these slopes. Figure 8 shows the dependence of the inclination angle
detailed study of these structures with a height of more than 500 nm using SEM and selective etching.22 As in our previous work, these highly elongated layers will be abbreviated as HELs. Previously, the ends of HELs were demonstrated to be composed of {111} microfacets. Thinner HELs with a height of 20−500 nm were studied using AFM. The ends of these HELs were found to most often have a nonconstant inclination and profile. In this case, there were no differences in inclinations of the ends of the long and short HEL sides. Figure 6 shows a typical AFM image of HEL ends with profiles across and along the elongation.
Figure 8. Slope angle of macrostep riser as a function of macrostep height.
of steps and HELs slopes on their height. As seen from thefigure, the inclination of ends gradually increases as the step height grows. At a height of the steps and HELs of more than 400−500 nm, the inclination angle reaches a value of 54° and does not change with a further increase in the macrostep height.
Figure 6. AFM image of the 2D island fragment and its section profiles.
As seen from the figure, the HEL ends can have a constant inclination or consist of steps with a smaller height. Figure 7 shows typical AFM images of the (100) face of a diamond crystal with several HELs. The surface profile in Figure 7b clearly demonstrates different heights (from 60 nm to 1.5 μm) of these structures, as well as different angles of HEL end slopes. An AFM image of a more smooth 5 × 5 μm surface area (Figure 7c) also shows the presence of strongly elongated layers, with their height varying from 0.1 to 0.8 nm. As described above, the ends of step patterns (step echelons and “HELs”) have a nonconstant slope. However, quite often the slopes have a more constant inclination enabling measurements of inclination angles between the ends of macrosteps or
4. DISCUSSION An analysis of the {100} faces of diamond crystals grown in Mg systems by optical, scanning electron, and atomic force microscopy revealed three basic structural elements of the {100} face structure: elementary layers (steps), elementary step bunches, and faceted macrosteps (Figure 9). These step patterns form a three-level microrelief on the {100} faces. Directional step trains of three levels form in the presence of a strong source of growth: echelons of elementary steps, echelons of elementary step bunches, and echelons of faceted macrosteps. In the absence of a strong source of growth, highly elongated rectangular islands of three levels are formed on the
Figure 7. AFM images of the fragment {100} face with strongly elongated layers (islands): (a) 3D image and (b) 2D image of the same area of the face, (c) section of a flat terrace, shown in panel b. D
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in this process. Previously, we studied diamond growth in systems with a lower magnesium concentration (45−50 atom %) and did not detect similar highly elongated step patterns.15 The range of measured heights of macrosteps on {100} diamond faces is quite wide and ranges from several nanometers to hundreds of nanometers. These step bunches have different profile types and inclination. As the thickness of macrosteps increases, the inclination angle of their slopes grows, indicating a decrease in the distance between elementary steps. The maximum angle of the macrostep riser corresponds to the {111} face position (α = 54.73°). As a result, the elementary step bunches are transformed into faceted macrosteps, and singular stable {111} faces form at the macrostep ends (Figure 8). The faceted macrosteps move along {100} faces due to the layerwise growth of {111} microfacets at the steps ends. Our observations demonstrate that macrolayers (macrosteps) become more isometric, and the length to width ratio decreases as the macrolayer size increases. This can be explained by the fact that, as shown in the Results, when the thickness of the steps is more than 400 nm, their ends (both short and long sides) are faceted by {111} microfacets. Thus, layer propagation velocities in all [110] directions become nearly equal because they are controlled by the growth rates of the {111} microfacets. On the basis of purely geometric considerations, this should result in more isometric growth layers. Figure 9 presents a schematic of the types of relief elements on the {100} diamond face and their relationship to the striation of the (100) growth sector. In accordance with the schematic, the growth of {100} faces occurs by depositing a substance (carbon) along two nonequivalent surfaces. The elementary layers are formed by deposition of carbon atoms in the (100) plane. The heterogeneity of step propagation leads to periodic bunching of steps and to formation of macrosteps with a different and often variable profile. As mentioned in the Introduction, the step propagation heterogeneity causing the formation of step bunches may be associated with supersaturation fluctuations at the point at which the step emanates, adsorption of impurities, and other factors, which are described in detail in dedicated publications.3 In contrast to the elementary {100} steps, the faceted macrosteps propagate along {100} faces by depositing the substance on the {111} microfacets of step ends. The total diamond gain on the {100} surfaces is realized mainly due to the growth of {111} microfacets of the faceted macrosteps and, to a lesser extent, by layer-by-layer growth along the {100} faces on the macrostep terraces. This deposition of a substance on two different crystallographic planes should undoubtedly be reflected in the internal structure of sectors of {100} faces. Indeed, the sectors of {100} faces of diamond crystals grown at temperatures of 1800−1900 °C have different striation of colorless and brown zones alternation. As noted in our recent work,19,21 in the peripheral part of crystals, the brown zones are confined to the base of a dihedral angle between the (111) end of faceted macrosteps and the (100) terrace of a lower macrolayer. Figure 4d of the cited study clearly demonstrates that the faceted macrolayer is colorless in the crystal bulk, and the thin adjacent diamond portion that builds up the terrace of an underlying layer has an intense brown color. Figure 9 presents a schematic of the color distribution in the diamond crystal bulk. On the basis of these observations and findings of the present work, it may be concluded that the layerwise growth by elementary layers along
Figure 9. Schematic representation of the elements of the microrelief (100) face and their relationship to the structure of the growth sector. The arrows show the direction of movement of the steps.
faces as well. Previously, it was shown22 that the location of these islands (HELs) is not associated with the dislocations outputs on the {100} face, and they formed due to twodimensional (2D) nucleation. The elementary relief of the {100} faces is determined by atomic growth steps. Measured heights of the thinnest layers (steps) and 2D islands are about 0.1 and 0.2 nm. On the basis of theoretical considerations, the minimum height of an elementary monatomic layer on the (100) diamond face should be between 0.067 and 0.083 nm in accordance with the atomic structure of diamond and the type of (100) surface reconstruction.24 Accordingly, a diatomic layer can have a height of 0.146−0.178 nm. These heights of the atomic layers are in good agreement with the height of the thinnest layers (steps) obtained in our study, taking into account the accuracy of the measurement with the aid of the AFM. Growth of the {100} faces of HPHT diamonds by monatomic and diatomic layers was not previously observed. Thin atomic layers were previously observed only on {111} and {100} faces of CVD diamonds.25−27 However, unlike CVD diamonds, the shape of elementary growth layers on the {100} faces of diamond crystals grown in Mg−C and Mg0.9Ge0.1−C systems is not isometric, but highly elongated in [110] directions. In a previous study,22 we already discussed this phenomenon. The highly elongated shape of elementary layers is determined by the direction of dimeric rows formed due to the 2 × 1 reconstruction of the {100} diamond surface. Previously, it was found that single steps parallel to the dimeric rows were straight, and their propagation was slower than that of perpendicular serrated steps.28−30 Fluctuations in the rate of elementary step propagation along the (100) face causes a local change of step density. This results in the formation of macrosteps lacking a constant inclination of step riser. Macrosteps are common structures on the faces of natural and grown diamond crystals. However, in contrast to the crystals produced in magnesium-based systems, the macrostructures on {100} diamond faces have a square or octagonal shape.1,10,11,32 The transformation of elementary highly elongated layers into isometric macrostructures occurs because of the so-called “step interlacing “ with different [110] orientations.31,32 In the case of diamond growth in Mg−C and Mg0.9Ge0.1−C systems, this “step interlacing” does not occur, and macrolayers reproduce the shape of elementary layers. At present, we have no satisfactory explanation for this phenomenon. Probably, this is associated with the peculiarities of adsorption of crystallization medium components at the different ends of the steps. Apparently, the magnesium concentration in the crystallization medium plays a key role E
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ORCID
the (100) face forms brown zones, while layerwise growth along the {111} microfacets of faceted macrosteps forms colorless growth zones (Figure 9). A previous IR study of brown zones showed the presence of continuous absorption in spectra, which steadily increased toward larger wave numbers.19−21 This continuous absorption may be due to defects associated with π-bonded carbon atoms, e.g., vacancy clusters or fragments of the growth reconstructed (100) surface with CC dimers. Such defects can be formed in the volume of diamond because of the peculiarities of the structure of microlayers on {100} faces. AFM images of {100} surfaces show islands of 2D nucleation and microdepressions between layers. Growth and coalescence of the islands should lead to numerous structural inconsistencies and bulk defects in the overgrown elementary layers, which may be the cause of the brown color of the diamond. Our studies demonstrated that the brown color of diamonds grown in Mg-systems was enhanced by lowering the synthesis temperature.19−21 At the minimum synthesis temperatures (1500−1600 °C), most crystals had a very saturated red-brown color. At the same time, a decrease in the synthesis temperature is accompanied by the disappearance of faceted macrosteps on the cube faces, which grow layer-bylayer along the {111} microfacets. Bunches of thin steps form curved macrosteps on the {100} faces and rounded surfaces near edges. In this case, the linear rate of diamond growth decreases exponentially. The maximum linear rate of diamond growth in the Mg−C system at 1900 °C reached 8.5 mm/h, which was about 10-fold higher than typical growth rates for diamond synthesis in traditional metal−carbon systems.19,21 In our opinion, these extreme growth rates are associated with the speed of movement of the faceted macrosteps, i.e., with the rate of the fastest growing {111} faces under these conditions. A high rate of faceted macrosteps propagation was demonstrated in studies on in situ growth of KH2PO4 crystals in the presence of impurities.8,33 The authors found, as in our case, that crystal growth occurred via three types of layers. In this case, the faceted macrosteps, “supersteps” in the authors’ terminology, mainly contributed to the growth rate of faces. However, the authors considered these supersteps as stable bunches of elementary steps. The formation of a singular stable face at the macrostep end was not considered. However, our study demonstrates that the formation of kinetically stable faces at the macrostep end is a real phenomenon. For example, previously,6 a study of K2Gr2O7 crystal growth demonstrated a similar transition of a change of step bunches through macrosteps to faceted macrosteps (mini-faces) as step heights increased. Growth of faceted macrostep ends on K2Gr2O7 crystals, as in our case, also occurred layerwise.6 In our opinion, the phenomenon of layerwise growth of faceted macrosteps is not a unique case and more common in crystal growth. Indeed, macroscopic steps with a rectilinear shape and sharp edges are present in many cases on faces of natural and synthetic crystals.1,2 There is every reason to believe that these macrosteps may be faceted steps, and their propagation along the faces occurs in a manner similar to that considered in this paper.
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Alexander F. Khokhryakov: 0000-0002-2395-9586 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank anonymous reviewers for their constructive reviews of the manuscript and helpful comments. This work was supported by the Russian Science Foundation under Grant No. 14-27-00054. The measurements by atomic force microscope were supported by the Russian Science Foundation under Grant No. 14-22-00143.
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REFERENCES
(1) Sunagawa, I. Crystals: Growth, Morphology, & Perfection; Cambridge University Press: Cambridge, England, 2005. (2) Growth, Dissolution and Pattern Formation in Geosystems; Jamtveit, B., Meakin, P., Eds., Springer Science & Business Media: New York, 1999. (3) Chernov, A. A. Modem Crystallography III. Crystal Growth; Springer-Verlag: Berlin, 1984. (4) Akutsu, N.; Yamamoto, T. In Handbook of Crystal Growth; Nishinaga, T., Rudolph, P., Eds.; Elsevier: Amsterdam, 2015; Chapter 6, pp 266−313. (5) Akutsu, N. Adv. Condens. Matter Phys. 2017, 2017, 2021510. (6) Plomp, M.; Nijdam, A. J.; van Enckevort, W. J. P. J. Cryst. Growth 1998, 193, 389−401. (7) Schick, M.; Dabringhaus, H.; Wandelt, K. J. Phys.: Condens. Matter 2004, 16, L33−L37. (8) Thomas, T. N.; Land, T. A.; Casey, W. H.; DeYoreo, J. J. Phys. Rev. Lett. 2004, 92, 216103. (9) Mitani, T.; Komatsu, N.; Takahashi, T.; Kato, T.; Harada, S.; Ujihara, T.; Matsumoto, Y.; Kurashige, K.; Okumura, H. J. Cryst. Growth 2015, 423, 45−49. (10) Bovenkerk, H. P. Am. Mineral. 1961, 46, 952−963. (11) Tolansky, S. Proc. R. Soc. London, Ser. A 1962, 270, 443−451. (12) Palyanov, Y. N.; Kupriyanov, I. N.; Sokol, A. G.; Khokhryakov, A. F.; Borzdov, Y. M. Cryst. Growth Des. 2011, 11, 2599−2605. (13) Palyanov, Y. N.; Khokhryakov, A. F.; Borzdov, Y. M.; Kupriyanov, I. N. Cryst. Growth Des. 2013, 13, 5411−5419. (14) Palyanov, Y. N.; Kupriyanov, I. N.; Borzdov, Y. M.; Bataleva, Y. V. CrystEngComm 2015, 17, 7323−7331. (15) Khokhryakov, A. F.; Sokol, A. G.; Borzdov, Y. M.; Palyanov, Y. N. J. Cryst. Growth 2015, 426, 276−282. (16) Kanda, H.; Akaishi, M.; Setaka, N.; Yamaoka, S.; Fukunaga, O. J. Mater. Sci. 1980, 15, 2743−2748. (17) Yin, L. W.; Li, M. S.; Xu, B.; Song, Y. J.; Hao, Z. Y. Chem. Phys. Lett. 2002, 357, 498−504. (18) Gong, J. H.; Chen, Q. L.; Liu, S. N.; Yang, L. M.; Gao, J.; Li, W.; Bin, X. Mater. Res. Innovations 2015, 19, S9-32−S9-36. (19) Palyanov, Y. N.; Borzdov, Y. M.; Kupriyanov, I. N.; Khokhryakov, A. F.; Nechaev, D. V. CrystEngComm 2015, 17, 4928−4936. (20) Palyanov, Y. N.; Kupriyanov, I. N.; Borzdov, Y. M.; Khokhryakov, A. F.; Surovtsev, N. V. Cryst. Growth Des. 2016, 16, 3510−3518. (21) Palyanov, Y. N.; Kupriyanov, I. N.; Khokhryakov, A. F.; Borzdov, Y. M. CrystEngComm 2017, 19, 4459−4475. (22) Khokhryakov, A. F.; Nechaev, D. V.; Palyanov, Y. N. J. Cryst. Growth 2016, 455, 76−82. (23) Khokhryakov, A. F.; Nechaev, D. V.; Palyanov, Y. N.; Kuper, K. E. Diamond Relat. Mater. 2016, 70, 1−6. (24) Furthmuller, J.; Hafner, J.; Kresse, G. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 53, 7337−7351. (25) Watanabe, H.; Takeuchi, D.; Yamanaka, S.; Okushi, H.; Kajimura, K.; Sekiguchi, T. Diamond Relat. Mater. 1999, 8, 1272− 1276.
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(26) Tokuda, N.; Umezawa, H.; Kato, H.; Ogura, M.; Gonda, S.; Yamabe, K.; Okushi, H.; Yamasaki, S. Appl. Phys. Express 2009, 2, 055001. (27) Tokuda, N. In Novel Aspects of Diamond: From Growth to Application; Yang, N., Ed.; Topics in Applied Physics; Spring: Berlin, 2015; Vol. 121, pp 1−29.10.1007/978-3-319-09834-0_1 (28) Hoeven, A. J.; Lenssinck, J. M.; Dijkkamp, D.; van Loenen, E. J.; Dieleman, J. Phys. Rev. Lett. 1989, 63, 1830−1832. (29) Busmann, H.-G.; Zimmermann-Edling, W.; Sprang, H.; Güntherodt, H.-J.; Hertel, I. V. Diamond Relat. Mater. 1992, 1, 979− 988. (30) Bobrov, K.; Mayne, A.; Comtet, G.; Dujardin, G.; Hellner, L.; Hoffman, A. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 195416. (31) van Enckevort, W. J. P.; Bennema, P.; van der Linden, W. H. Z. Phys. Chem. 1981, 124, 171−191. (32) van Enckevort, W. J. P.; Janssen, G.; Vollenberg, W.; Schermer, J. J.; Giling, L. J.; Seal, M. Diamond Relat. Mater. 1993, 2, 997−1003. (33) Land, T. A.; Martin, T. L.; Potapenko, S.; Palmore, G. T.; DeYoreo, J. J. Nature 1999, 399, 442−445.
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