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Formation of small straight steps among large rough steps on the {1 1 0} face of cadmium mercury thiocyanate crystal
Journal of Crystal Growth 233 (2001) 318–325
Formation of small straight steps among large rough steps on the {1 1 0} face of cadmium mercury thiocyanate crystal X.N. Jiang*, D. Xu, D.L. Sun, D.R. Yuan, M.K. Lu, G.H. Zhang, Q. Fang State Key Laboratory of Crystal Materials, Institute of Crystal Materials, Shandong University, Jinan 250100, People’s Republic of China Received 12 April 2001; accepted 18 June 2001 Communicated by T. Hibiya
Abstract Rough steps generated by dislocation sources are very often observed on the {1 1 0} faces of cadmium mercury thiocyanate crystal, which is believed to result from the complex solution structures and the various growth units incorporated into the crystal lattice. Among these large rough steps, some small straight steps perpendicular to the ½1 1 3% direction are formed. The heights of the straight steps vary from 1.6 up to 8.1 nm, most of which are multiples of the elementary step height (0.81 nm). Below each small step, there exists a hole where some impurities are adsorbed. The striking feature of these small straight steps is that they are formed by bunching of part of the rough steps, which is quite different from the usual step bunches. The occurrence of these straight steps is closely related to the slopes of growth hillocks, which is explained by the BCF theory. r 2001 Published by Elsevier Science B.V. PACS: 61.72; 68.35.B; 42.70.M; 61.16.C Keywords: A1. Atomic force microscopy; A1. Step formation
1. Introduction In recent years, much interest has been focused on the investigation of crystal growth at nanometer scale, particularly, with atomic force microscopy (AFM). The previous studies by AFM have focused on two systems. One is small molecular crystals such as KH2PO4 (KDP) [1–4] and calcium carbonate [5–8], where the molecular diameters are a few angstroms. The other is the *Corresponding author. Tel.: +86-531-856-4451; fax: +86531-856-5403. E-mail address: [email protected] (X.N. Jiang).
large complex macromolecules [9–16] with dia( . Results from these meters of up to 160 A experiments have contributed to a better understanding of the growth mechanisms, growth rates, defect formation and quality of the crystals. Furthermore, some new growth theories and models have been established since the advent of AFM [1,2]. For example, investigations on KDP {1 0 0} faces by AFM showed [2] that the propagation of the macrosteps leads to the resurrection of growth out of the ‘‘dead zone’’ and a new physical model of this process, that is, completely different from the classic theory of Cabrera and Vermilyea [17] was then established.
0022-0248/01/$ - see front matter r 2001 Published by Elsevier Science B.V. PII: S 0 0 2 2 - 0 2 4 8 ( 0 1 ) 0 1 5 5 6 - 1
X.N. Jiang et al. / Journal of Crystal Growth 233 (2001) 318–325
Cadmium mercury thiocyanate (CdHg(SCN)4, abbreviated as CMTC) crystal is a two-metalcentered (Cd2+, Hg2+) semiorganic complex compound. It belongs to a tetragonal system, space group I4; with lattice parameters of a ¼ 1:1487ð3Þ nm and c ¼ 0:4218ð1Þ nm [20]. The resulting interplanar distance of the {1 1 0} faces is 0.81 nm. In our work, we chose the CMTC crystal as the study object because of its particular structural features and highly efficient nonlinear optical properties [18–20]. In a previous paper, we examined the growth modes as a function of supersaturation [21]. The results showed that, in most cases, growth occurs on elementary steps generated by either simple or complex screw dislocation sources and 2D nucleation islands are seldom observed except at high supersaturations. In this paper, we mainly describe the formation of small straight steps among large rough steps at the slopes of growth hillocks as a new discovery during crystal growth. It was investigated on the {1 1 0} faces of the CMTC crystal by an ex situ AFM.
2. Experimental procedure Recrystallized CMTC materials are dissolved in 3% NaCl aqueous solution, in which NaCl is added to increase the solubility of CMTC. Seed crystals for AFM experiments were nucleated and grown on glass substrates in a 2 ml drop of CMTC solution, filtered through a 0.2 mm membrane, in a small glass tube by using the temperature-lowering method from 301C to 181C (supersaturation s ¼ 0:35). As soon as the crystals grew into acceptable sizes for the AFM experiment, the glass substrate was taken out and the crystals on it were dried carefully and quickly with a tissue paper to minimize the shut-off effect caused by dissolved CMTC and NaCl in the mother solution. Then the glass substrate with CMTC crystals was gently placed on the AFM sample holder using a double-sided tape. CMTC crystal obtained under such growth conditions is usually formed by the prismatic faces {1 1 0} and the pyramidal faces {2 1 1} and/or {1 0 1}, which is probably due to the relatively fast crystallization rate during the
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sample preparation when only the morphologically important crystal faces are exposed. The {1 1 0} faces are parallel to the sample holder surface, in most cases, facilitating the imaging on them immediately after the crystals are prepared. Images were collected in contact mode using a Nanoscope IIIa MultiMode AFM instrument of Digital Instruments Incorporation. A J-type scanner of size 150 mm 150 mm, standard SiN cantilevers with small force constant of 0.06 N/m, integrated with OTR tips were used. Images were usually collected at a scan rate of less than 2 Hz. During imaging, care was taken to continually adjust the set point voltage to the lowest possible value to minimize the force applied to the surface.
3. Results and discussion 3.1. Formation of dense rough steps During the investigations on the {1 1 0} face of the CMTC crystal, various steps were observed, among which the dense rough steps are dominant and remarkable. The rough steps are usually generated by simple or complex dislocation sources, which are shown in Figs. 1a and b. It is seen that the steps are rough due to many dentations at the edges, which are notably oriented along the same direction. The heights of these steps vary from 0.4 to 1.0 nm, most of which are equal to the interplanar distance (0.81 nm) of the {1 1 0} faces within the experimental error. The rough steps are formed probably due to the characteristic structure of CMTC crystal. CMTC is a two-metal-centered complex compound, in which metal cations, Hg(II) and Cd(II), are coordinated with four SCN ligands through S and N ends, forming slightly flattened tetrahedra, HgS4 and CdN4, respectively. An infinite threedimensional –Hg–S ¼ C ¼ N–Cd– network structure is formed through the –S ¼ C ¼ N– bridges that connect Hg and Cd cations. As crystal growth is closely related to the growth surroundings, the growth solution structure of CMTC was investigated by using Raman spectra [22]. The results show that the most stable [Hg(SCN)4]2 complex anions (stability constant
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the complex anions with various dimensions in the growth solution adsorb and incorporate at the kinks as the growth units, the steps exhibit the roughness. Some small ligands of SCN ions will break away from the central cations (Hg(II) or Cd(II)), incorporated in the crystal, because of the unavoidable decomposition of the complex anions and the thermal motion of molecules, which is believed to aggravate the roughness of the steps. Therefore, the intense roughness of steps is regarded as a remarkable feature of the complex compound crystals. As seen in Figs. 1 and 3, the dentations at the rough step edges are almost oriented along the same direction, which is determined to be [1 1 1]. Fig. 2 is the structure of the CMTC crystal projected along the [1 1 0] direction, from which we can seen that there exists a bond chain of –Hg– S ¼ C ¼ N–Cd–N ¼ C ¼ S–Hg– along [1 1 1] direction (indicated by the dashed lines in Fig. 2). According to the well-known PBC theory, the growth rate is high in the direction where there are strong bond chains. Therefore, CMTC crystals grow fast along the [1 1 1] direction, where the growth units are preferably arranged, and the dentations are thus formed at the step edges. In the morphology of CMTC crystal, {1 1 1} faces are exposed occasionally during growth with sol–gel
Fig. 1. Rough steps generated by simple or complex dislocation sources with several small straight steps among them. Scanning areas in (a) and (b) are both 10.0 10.0 mm2.
is 1029.6) are predominant in the growth solution, while various cadmium–thiocyanate complexes with different dimensions as well as some free SCN ions coexist due to the instability of tetrathiocyanatecadmium ion (stability constant is 102.91). Therefore, it can be deduced that when
Fig. 2. Crystal structure of CMTC projected along the [1 1 0] direction. The bond chain of –Hg–S ¼ C ¼ N–Cd–N ¼ C ¼ S– Hg– along the [1 1 1] direction is indicated by the dashed lines in a unit cell of CMTC crystal represented by the frame.
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Fig. 3. Images of two small straight steps generated among dense rough steps with scan areas of 5.0 5.0 and 4.5 4.5 mm2, and scan angles of 01 and 451 for image (a) and (b), respectively.
method [23] but are never observed during growth by using solution growth method in our lab, which is also due to the fast growth rate along the [1 1 1] direction. 3.2. Formation of small straight steps On the {1 1 0} faces of CMTC crystal, many extremely straight small steps were observed among the dense rough steps, which has been observed in neither small inorganic crystals nor large macromolecular crystals so far. These straight steps were always imaged at the slopes of large growth hillocks generated by simple or complex dislocation sources. By the routine angle measurement in the AFM analysis system, we have determined that the small straight steps are perpendicular to the crystal edge formed by the ð1% 1 0Þ face and the (2 1 1) face. The crystal edge along the ½1 1 3% direction is obtained by the multiplication cross of the normal vectors ½1% 1 0 and [2 1 1] of these intersectant crystal faces. Therefore, these straight steps are perpendicular to the ½1 1 3% direction. Below each straight step, there exists a hole. In most cases, the longer the step is, the deeper the hole becomes. The heights of the straight steps vary from 1.6 up to 8.1 nm, most of which are multiples of the elementary step
height (0.81 nm). For example, the heights of the straight steps indicated by numbers 1 and 2 in Fig. 3a are 3.2 and 4.6 nm, which amount to four and six elementary steps within the experimental error, respectively. The same area was imaged again by rotating the scan direction anticlockwise 451 (Fig. 3b), which confirms the verity of the image and shows more clearly the inclusion in the hole. A series of small straight steps are arranged along the step bunches at the slope of a large growth hillock (Fig. 4a). The longest straight step observed is as long as 6.0 mm (Fig. 4b), formed probably due to the connection of two or several neighboring small straight steps as shown in Fig. 4c. It is seen in Fig. 3 that the step trains generated by the predominant dislocation source are interdicted sharply as soon as they arrive at the small straight steps. Some rough steps prolongate into the hole under the small step, and cause hyperbola-like step trains that merge with each other gradually. It was easily assumed that the straight steps are formed at the junction of three growth hillocks, the large, predominant one and two small ones generated at its slope. It seems reasonable that inclusions can easily be formed at the spot where step trains spreading in different directions converge because of their incongruity.
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Fig. 4. Images of some other straight steps. (a) small straight steps among step bunches. (b) a straight step of 6.0 mm height (the line at the right bottom of the image indicates the crystal edge). (c) Two neighboring small straight steps link up. The scan areas of (a), (b) and (c) are 20.0 20.0, 6.0 6.0 and 2.0 2.0 mm2, respectively.
Unfortunately, however, no dislocation sources are observed beside the straight steps except that of the large hillock. Furthermore, when we purposively imaged two small hillocks generated at the slope of the same large hillock, no such small straight steps were observed at the junction of their steps (Fig. 5a). Similarity was found in many other growth hillocks (Fig. 5b). Therefore, this assumption of the straight step formation among rough ones is finally precluded. It also gives
us a suggestion that the growth hillocks on crystal faces are not always generated by dislocation sources unless hollow cores are observed. The reasonable formation mechanism of the straight steps is suggested. As is discussed in another paper [22], two-dimensional (single-layer) defects are easily formed due to the roughness of the steps. Some such defects are covered by the following growth layers, while others remain at the step terraces. When impurities are adsorbed in
X.N. Jiang et al. / Journal of Crystal Growth 233 (2001) 318–325
Fig. 5. Images of some growth hillocks where no small straight steps are formed at the slopes. The scan areas of (a) and (b) are 5.0 5.0 and 19.0 19.0 mm2, respectively.
the defects, they retard the step advancement, which is known to cause the step bunching [24,25]. The straight step is formed as soon as step bunching occurs above the hole, which is confirmed by the smallest height of the straight steps (1.6 nm), corresponding to the height of two elementary steps (1.62 nm). The striking feature of these small straight steps is that they are formed
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by bunching of part of the rough steps, which is quite different from the usual step bunches. Take one of the rough steps for example. The rough step is not parallel to the straight steps, therefore, it does not arrive at the straight step simultaneously. At the moment that a part of the rough step touches the straight step, the spread of that part is hindered, while the rest continue to advance until the rough step merges with the straight step. Then, one more step is bunched at the straight step. Meanwhile, the remaining part of that rough step goes on advancing. It curves around the small straight step and takes on two curves below the straight step gradually. It is notable that when the right part of the rough step begins to curve around the straight step, the part on the left remains above the straight step, and when the step on the left begins curving, the right part of the step becomes much more curved. It is because the right part of the rough step arrives at the straight step ahead of the left part. As more rough steps are hindered by the straight step, the straight step becomes higher and more curves are caused below the straight step. It is ensured that the straight step height is consistent with the number of the curved steps. That is, if there are m curved steps, the straight step height h is h ¼ 0:81ðnmÞm; where 0.81(nm) is the height of an elementary step. For example, there are four curves below the straight step 1 in Fig. 3a, and the step is 3.2 nm (0.81 4=3.24 nm) in height. The relation between the straight step height and the number of the curved steps below it strongly confirms our conclusion that the small straight steps are formed by the bunching of part of the rough steps and that the hyperbola-like step trains below the straight step are caused by the continual advancement of the rest of the rough steps except for the part retarded. It is notable that the occurrence of the small straight steps is closely related to the slope of the growth hillocks. The slope of growth hillocks, p; is defined as p ¼ h=w; where h is the step height and w the width of step terrace. By multiple measurement and calculation, we have found that the straight steps appear at the slope higher than 1.0 103, in most cases. For CMTC crystal, the growth hillocks are often strongly anisotropic in shape, therefore, if there exist straight steps on
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them, the straight steps are always imaged at the sharper slope. According to BCF theory [26], steps advance faster when the step terraces are wider, i.e. the slope of the growth hillock is smaller in most cases. For CMTC crystal, when the slope of a growth hillock is small, the steps advance fast and can probably get across and cover the defects at the former layer due to their high kinetic energy. Therefore, step bunches cannot usually take place at small slopes and no small straight steps are accordingly formed. At sharper slopes, however, the steps advance slowly and the kinetic energy is not sufficient enough for the steps to get over the obstruction of the impurities and small straight steps are thus formed. It is determined that the straight steps are oriented perpendicular to the ½1 1 3% direction, i.e. these straight steps represent the projections of the ð1 1 3% Þ faces at the ð1% 1 0Þ face of the CMTC crystal. In the growth habit of the CMTC crystal, the ð1 1 3% Þ faces are never exposed, probably due to ( ) among the the smallest planar distance (1.39 A crystal faces of CMTC, according to the Bravais– Donnay–Harker rule [27]. Since the large rough steps are partly retarded by the impurities adsorbed, the small straight steps indicative of the ð1 1 3% Þ faces are gradually formed.
4. Conclusion On the {1 1 0} faces of CMTC crystals, we have observed dense rough steps generated by simple or complex dislocation sources by an ex situ AFM, which is considered to be a remarkable feature of complex compound crystals. Some small straight steps perpendicular to the ½1 1 3% direction are formed among the dense rough steps, which have never been observed in small inorganic crystals or complex macromolecular crystals before. The formation of these straight steps is explained from the point of view of adsorption of impurities and bunching of part of the rough steps. As the bunching takes place on some of the large steps and the rest continue to advance as elementary steps, it is quite different from the step bunches in the common sense. Besides, the occurrence of the straight steps is closely related to the slope of the
growth hillock, i.e. they usually appear at the slope higher than 1.0 103.
Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 69890230, No. 69778023 and No. 59832080), the Scientific Research Foundation for Outstanding Young Scientist of Shandong Province of China and the Foundation for University Key Teacher by the Ministry of Education.
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X.N. Jiang et al. / Journal of Crystal Growth 233 (2001) 318–325 [18] D.R. Yuan, Z.W. Zhong, M.G. Liu, D. Xu, Q. Fang, Y.H. Bing, S.Y. Sun, M.H. Jiang, J. Crystal Growth 186 (1998) 240. [19] D.R. Yuan, D. Xu, M.G. Liu, Q. Fang, W.T. Yu, W.B. Hou, Y.H. Bing, S.Y. Sun, M.H. Jiang, Appl. Phys. Lett. 70 (5) (1997) 544. [20] X.N. Jiang, D.R. Yuan, D. Xu, M.K. Lu, S.Y. Guo, W.T. Yu, G.H. Zhang, Q. Fang, Acta Chim. Sin. 59 (5) (2001) 724. [21] X.N. Jiang, D.L. Sun, D. Xu, D.R. Yuan, M.K. Lu, S.Y. Guo, Q. Fang, J. Crystal Growth.
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[22] X.N. Jiang, D. Xu, D.R. Yuan, M.K. Lu, S.Y. Guo, G.H. Zhang, Q. Fang, to be published. [23] S.Z. Blank, J. Crystal Growth 18 (1973) 281. [24] S.Yu. Potapenko, J. Crystal Growth 133 (1993) 147. [25] W.J.P. van Enckevort, A.C.J.F. van den Berg, J. Crystal Growth 183 (1998) 441. [26] W.K. Burton, N. Cabrera, F.C. Frank, Roy. Soc. London Philos. Trans. A 243 (1951) 299. [27] P. Hartman, Crystal Growth, an Introduction, NorthHolland, Amsterdam, 1973.
Formation of small straight steps among large rough steps on the {1 1 0} face of cadmium mercury thiocyanate crystal X.N. Jiang*, D. Xu, D.L. Sun, D.R. Yuan, M.K. Lu, G.H. Zhang, Q. Fang State Key Laboratory of Crystal Materials, Institute of Crystal Materials, Shandong University, Jinan 250100, People’s Republic of China Received 12 April 2001; accepted 18 June 2001 Communicated by T. Hibiya
Abstract Rough steps generated by dislocation sources are very often observed on the {1 1 0} faces of cadmium mercury thiocyanate crystal, which is believed to result from the complex solution structures and the various growth units incorporated into the crystal lattice. Among these large rough steps, some small straight steps perpendicular to the ½1 1 3% direction are formed. The heights of the straight steps vary from 1.6 up to 8.1 nm, most of which are multiples of the elementary step height (0.81 nm). Below each small step, there exists a hole where some impurities are adsorbed. The striking feature of these small straight steps is that they are formed by bunching of part of the rough steps, which is quite different from the usual step bunches. The occurrence of these straight steps is closely related to the slopes of growth hillocks, which is explained by the BCF theory. r 2001 Published by Elsevier Science B.V. PACS: 61.72; 68.35.B; 42.70.M; 61.16.C Keywords: A1. Atomic force microscopy; A1. Step formation
1. Introduction In recent years, much interest has been focused on the investigation of crystal growth at nanometer scale, particularly, with atomic force microscopy (AFM). The previous studies by AFM have focused on two systems. One is small molecular crystals such as KH2PO4 (KDP) [1–4] and calcium carbonate [5–8], where the molecular diameters are a few angstroms. The other is the *Corresponding author. Tel.: +86-531-856-4451; fax: +86531-856-5403. E-mail address: [email protected] (X.N. Jiang).
large complex macromolecules [9–16] with dia( . Results from these meters of up to 160 A experiments have contributed to a better understanding of the growth mechanisms, growth rates, defect formation and quality of the crystals. Furthermore, some new growth theories and models have been established since the advent of AFM [1,2]. For example, investigations on KDP {1 0 0} faces by AFM showed [2] that the propagation of the macrosteps leads to the resurrection of growth out of the ‘‘dead zone’’ and a new physical model of this process, that is, completely different from the classic theory of Cabrera and Vermilyea [17] was then established.
0022-0248/01/$ - see front matter r 2001 Published by Elsevier Science B.V. PII: S 0 0 2 2 - 0 2 4 8 ( 0 1 ) 0 1 5 5 6 - 1
X.N. Jiang et al. / Journal of Crystal Growth 233 (2001) 318–325
Cadmium mercury thiocyanate (CdHg(SCN)4, abbreviated as CMTC) crystal is a two-metalcentered (Cd2+, Hg2+) semiorganic complex compound. It belongs to a tetragonal system, space group I4; with lattice parameters of a ¼ 1:1487ð3Þ nm and c ¼ 0:4218ð1Þ nm [20]. The resulting interplanar distance of the {1 1 0} faces is 0.81 nm. In our work, we chose the CMTC crystal as the study object because of its particular structural features and highly efficient nonlinear optical properties [18–20]. In a previous paper, we examined the growth modes as a function of supersaturation [21]. The results showed that, in most cases, growth occurs on elementary steps generated by either simple or complex screw dislocation sources and 2D nucleation islands are seldom observed except at high supersaturations. In this paper, we mainly describe the formation of small straight steps among large rough steps at the slopes of growth hillocks as a new discovery during crystal growth. It was investigated on the {1 1 0} faces of the CMTC crystal by an ex situ AFM.
2. Experimental procedure Recrystallized CMTC materials are dissolved in 3% NaCl aqueous solution, in which NaCl is added to increase the solubility of CMTC. Seed crystals for AFM experiments were nucleated and grown on glass substrates in a 2 ml drop of CMTC solution, filtered through a 0.2 mm membrane, in a small glass tube by using the temperature-lowering method from 301C to 181C (supersaturation s ¼ 0:35). As soon as the crystals grew into acceptable sizes for the AFM experiment, the glass substrate was taken out and the crystals on it were dried carefully and quickly with a tissue paper to minimize the shut-off effect caused by dissolved CMTC and NaCl in the mother solution. Then the glass substrate with CMTC crystals was gently placed on the AFM sample holder using a double-sided tape. CMTC crystal obtained under such growth conditions is usually formed by the prismatic faces {1 1 0} and the pyramidal faces {2 1 1} and/or {1 0 1}, which is probably due to the relatively fast crystallization rate during the
319
sample preparation when only the morphologically important crystal faces are exposed. The {1 1 0} faces are parallel to the sample holder surface, in most cases, facilitating the imaging on them immediately after the crystals are prepared. Images were collected in contact mode using a Nanoscope IIIa MultiMode AFM instrument of Digital Instruments Incorporation. A J-type scanner of size 150 mm 150 mm, standard SiN cantilevers with small force constant of 0.06 N/m, integrated with OTR tips were used. Images were usually collected at a scan rate of less than 2 Hz. During imaging, care was taken to continually adjust the set point voltage to the lowest possible value to minimize the force applied to the surface.
3. Results and discussion 3.1. Formation of dense rough steps During the investigations on the {1 1 0} face of the CMTC crystal, various steps were observed, among which the dense rough steps are dominant and remarkable. The rough steps are usually generated by simple or complex dislocation sources, which are shown in Figs. 1a and b. It is seen that the steps are rough due to many dentations at the edges, which are notably oriented along the same direction. The heights of these steps vary from 0.4 to 1.0 nm, most of which are equal to the interplanar distance (0.81 nm) of the {1 1 0} faces within the experimental error. The rough steps are formed probably due to the characteristic structure of CMTC crystal. CMTC is a two-metal-centered complex compound, in which metal cations, Hg(II) and Cd(II), are coordinated with four SCN ligands through S and N ends, forming slightly flattened tetrahedra, HgS4 and CdN4, respectively. An infinite threedimensional –Hg–S ¼ C ¼ N–Cd– network structure is formed through the –S ¼ C ¼ N– bridges that connect Hg and Cd cations. As crystal growth is closely related to the growth surroundings, the growth solution structure of CMTC was investigated by using Raman spectra [22]. The results show that the most stable [Hg(SCN)4]2 complex anions (stability constant
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the complex anions with various dimensions in the growth solution adsorb and incorporate at the kinks as the growth units, the steps exhibit the roughness. Some small ligands of SCN ions will break away from the central cations (Hg(II) or Cd(II)), incorporated in the crystal, because of the unavoidable decomposition of the complex anions and the thermal motion of molecules, which is believed to aggravate the roughness of the steps. Therefore, the intense roughness of steps is regarded as a remarkable feature of the complex compound crystals. As seen in Figs. 1 and 3, the dentations at the rough step edges are almost oriented along the same direction, which is determined to be [1 1 1]. Fig. 2 is the structure of the CMTC crystal projected along the [1 1 0] direction, from which we can seen that there exists a bond chain of –Hg– S ¼ C ¼ N–Cd–N ¼ C ¼ S–Hg– along [1 1 1] direction (indicated by the dashed lines in Fig. 2). According to the well-known PBC theory, the growth rate is high in the direction where there are strong bond chains. Therefore, CMTC crystals grow fast along the [1 1 1] direction, where the growth units are preferably arranged, and the dentations are thus formed at the step edges. In the morphology of CMTC crystal, {1 1 1} faces are exposed occasionally during growth with sol–gel
Fig. 1. Rough steps generated by simple or complex dislocation sources with several small straight steps among them. Scanning areas in (a) and (b) are both 10.0 10.0 mm2.
is 1029.6) are predominant in the growth solution, while various cadmium–thiocyanate complexes with different dimensions as well as some free SCN ions coexist due to the instability of tetrathiocyanatecadmium ion (stability constant is 102.91). Therefore, it can be deduced that when
Fig. 2. Crystal structure of CMTC projected along the [1 1 0] direction. The bond chain of –Hg–S ¼ C ¼ N–Cd–N ¼ C ¼ S– Hg– along the [1 1 1] direction is indicated by the dashed lines in a unit cell of CMTC crystal represented by the frame.
X.N. Jiang et al. / Journal of Crystal Growth 233 (2001) 318–325
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Fig. 3. Images of two small straight steps generated among dense rough steps with scan areas of 5.0 5.0 and 4.5 4.5 mm2, and scan angles of 01 and 451 for image (a) and (b), respectively.
method [23] but are never observed during growth by using solution growth method in our lab, which is also due to the fast growth rate along the [1 1 1] direction. 3.2. Formation of small straight steps On the {1 1 0} faces of CMTC crystal, many extremely straight small steps were observed among the dense rough steps, which has been observed in neither small inorganic crystals nor large macromolecular crystals so far. These straight steps were always imaged at the slopes of large growth hillocks generated by simple or complex dislocation sources. By the routine angle measurement in the AFM analysis system, we have determined that the small straight steps are perpendicular to the crystal edge formed by the ð1% 1 0Þ face and the (2 1 1) face. The crystal edge along the ½1 1 3% direction is obtained by the multiplication cross of the normal vectors ½1% 1 0 and [2 1 1] of these intersectant crystal faces. Therefore, these straight steps are perpendicular to the ½1 1 3% direction. Below each straight step, there exists a hole. In most cases, the longer the step is, the deeper the hole becomes. The heights of the straight steps vary from 1.6 up to 8.1 nm, most of which are multiples of the elementary step
height (0.81 nm). For example, the heights of the straight steps indicated by numbers 1 and 2 in Fig. 3a are 3.2 and 4.6 nm, which amount to four and six elementary steps within the experimental error, respectively. The same area was imaged again by rotating the scan direction anticlockwise 451 (Fig. 3b), which confirms the verity of the image and shows more clearly the inclusion in the hole. A series of small straight steps are arranged along the step bunches at the slope of a large growth hillock (Fig. 4a). The longest straight step observed is as long as 6.0 mm (Fig. 4b), formed probably due to the connection of two or several neighboring small straight steps as shown in Fig. 4c. It is seen in Fig. 3 that the step trains generated by the predominant dislocation source are interdicted sharply as soon as they arrive at the small straight steps. Some rough steps prolongate into the hole under the small step, and cause hyperbola-like step trains that merge with each other gradually. It was easily assumed that the straight steps are formed at the junction of three growth hillocks, the large, predominant one and two small ones generated at its slope. It seems reasonable that inclusions can easily be formed at the spot where step trains spreading in different directions converge because of their incongruity.
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Fig. 4. Images of some other straight steps. (a) small straight steps among step bunches. (b) a straight step of 6.0 mm height (the line at the right bottom of the image indicates the crystal edge). (c) Two neighboring small straight steps link up. The scan areas of (a), (b) and (c) are 20.0 20.0, 6.0 6.0 and 2.0 2.0 mm2, respectively.
Unfortunately, however, no dislocation sources are observed beside the straight steps except that of the large hillock. Furthermore, when we purposively imaged two small hillocks generated at the slope of the same large hillock, no such small straight steps were observed at the junction of their steps (Fig. 5a). Similarity was found in many other growth hillocks (Fig. 5b). Therefore, this assumption of the straight step formation among rough ones is finally precluded. It also gives
us a suggestion that the growth hillocks on crystal faces are not always generated by dislocation sources unless hollow cores are observed. The reasonable formation mechanism of the straight steps is suggested. As is discussed in another paper [22], two-dimensional (single-layer) defects are easily formed due to the roughness of the steps. Some such defects are covered by the following growth layers, while others remain at the step terraces. When impurities are adsorbed in
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Fig. 5. Images of some growth hillocks where no small straight steps are formed at the slopes. The scan areas of (a) and (b) are 5.0 5.0 and 19.0 19.0 mm2, respectively.
the defects, they retard the step advancement, which is known to cause the step bunching [24,25]. The straight step is formed as soon as step bunching occurs above the hole, which is confirmed by the smallest height of the straight steps (1.6 nm), corresponding to the height of two elementary steps (1.62 nm). The striking feature of these small straight steps is that they are formed
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by bunching of part of the rough steps, which is quite different from the usual step bunches. Take one of the rough steps for example. The rough step is not parallel to the straight steps, therefore, it does not arrive at the straight step simultaneously. At the moment that a part of the rough step touches the straight step, the spread of that part is hindered, while the rest continue to advance until the rough step merges with the straight step. Then, one more step is bunched at the straight step. Meanwhile, the remaining part of that rough step goes on advancing. It curves around the small straight step and takes on two curves below the straight step gradually. It is notable that when the right part of the rough step begins to curve around the straight step, the part on the left remains above the straight step, and when the step on the left begins curving, the right part of the step becomes much more curved. It is because the right part of the rough step arrives at the straight step ahead of the left part. As more rough steps are hindered by the straight step, the straight step becomes higher and more curves are caused below the straight step. It is ensured that the straight step height is consistent with the number of the curved steps. That is, if there are m curved steps, the straight step height h is h ¼ 0:81ðnmÞm; where 0.81(nm) is the height of an elementary step. For example, there are four curves below the straight step 1 in Fig. 3a, and the step is 3.2 nm (0.81 4=3.24 nm) in height. The relation between the straight step height and the number of the curved steps below it strongly confirms our conclusion that the small straight steps are formed by the bunching of part of the rough steps and that the hyperbola-like step trains below the straight step are caused by the continual advancement of the rest of the rough steps except for the part retarded. It is notable that the occurrence of the small straight steps is closely related to the slope of the growth hillocks. The slope of growth hillocks, p; is defined as p ¼ h=w; where h is the step height and w the width of step terrace. By multiple measurement and calculation, we have found that the straight steps appear at the slope higher than 1.0 103, in most cases. For CMTC crystal, the growth hillocks are often strongly anisotropic in shape, therefore, if there exist straight steps on
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them, the straight steps are always imaged at the sharper slope. According to BCF theory [26], steps advance faster when the step terraces are wider, i.e. the slope of the growth hillock is smaller in most cases. For CMTC crystal, when the slope of a growth hillock is small, the steps advance fast and can probably get across and cover the defects at the former layer due to their high kinetic energy. Therefore, step bunches cannot usually take place at small slopes and no small straight steps are accordingly formed. At sharper slopes, however, the steps advance slowly and the kinetic energy is not sufficient enough for the steps to get over the obstruction of the impurities and small straight steps are thus formed. It is determined that the straight steps are oriented perpendicular to the ½1 1 3% direction, i.e. these straight steps represent the projections of the ð1 1 3% Þ faces at the ð1% 1 0Þ face of the CMTC crystal. In the growth habit of the CMTC crystal, the ð1 1 3% Þ faces are never exposed, probably due to ( ) among the the smallest planar distance (1.39 A crystal faces of CMTC, according to the Bravais– Donnay–Harker rule [27]. Since the large rough steps are partly retarded by the impurities adsorbed, the small straight steps indicative of the ð1 1 3% Þ faces are gradually formed.
4. Conclusion On the {1 1 0} faces of CMTC crystals, we have observed dense rough steps generated by simple or complex dislocation sources by an ex situ AFM, which is considered to be a remarkable feature of complex compound crystals. Some small straight steps perpendicular to the ½1 1 3% direction are formed among the dense rough steps, which have never been observed in small inorganic crystals or complex macromolecular crystals before. The formation of these straight steps is explained from the point of view of adsorption of impurities and bunching of part of the rough steps. As the bunching takes place on some of the large steps and the rest continue to advance as elementary steps, it is quite different from the step bunches in the common sense. Besides, the occurrence of the straight steps is closely related to the slope of the
growth hillock, i.e. they usually appear at the slope higher than 1.0 103.
Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 69890230, No. 69778023 and No. 59832080), the Scientific Research Foundation for Outstanding Young Scientist of Shandong Province of China and the Foundation for University Key Teacher by the Ministry of Education.
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