5

Surface microtopography of crystal faces

Step patterns or etch figures which represent the final stage of growth or etching after the cessation of growth, respectively, are observed on flat crystal faces comprising a polyhedral crystal. We refer to these as surface microtopographs of crystal faces; they possess information at the atomic level relating to the mechanism of growth or dissolution and perfection of the crystal. This is because we can observe the spiral growth layers, either ex situ or in situ, with step heights of nanometer order. Since crystal faces are unique places where growth or dissolution of crystals occur, the analysis is directly connected to the concept of growth forms.

5.1The three types of crystal faces

Crystal faces bounding a polyhedral crystal are broadly classified into three types according to their surface microtopographs: (i) those appearing as mirror-flat faces; (ii) those characterized by striations; and (iii) those showing rugged or rounded forms (see Fig. 5.1). If a crystal face which is large enough to control the Habitus, with a mirror-flat surface, is observed by methods capable of detecting differences in levels at the nanometer scale, step patterns, resembling the contour lines on a topographic map, can be seen. These characteristic features on crystal faces are called surface microtopographs or are referred to as the surface morphology.

Crystal faces that show only striations are called vicinal faces with high indexes. Most typically, they appear as side faces of polygonal growth hillocks developing on low-index flat crystal faces, or as high-index faces appearing between a set of neighboring flat crystal faces. These correspond to S faces in Hartman–Perdok (HP) theory. Vicinal faces grow in a vertical direction to the face

90 Surface microtopography of crystal faces

Figure 5.1. Surface microtopographs seen on three types of crystal faces (Kossel

crystal). (a) F face; (b) S face; (c) K face.

quickly enough to disappear from the surface, and they do not develop large enough to control the Habitus; also, crystal faces on which step patterns occur due to layer growth are not expected to be seen. The substrate surface called an offfacet face in epitaxial growth corresponds to this type of face.

The {hkı¯l} faces, which determine the dog-tooth (scalenohedral) Habitus of calcite crystals, and the prismatic {hkı¯l} face of tourmaline crystals show striations only, never step patterns. These faces are S faces, by PBC analysis, and they appear due to a pile up of steps developing on the neighboring F faces. Yet they develop as large as those that determine the Habitus.

There are also crystal faces that show either step patterns or striations only, depending on the growth conditions, in spite of the fact that the faces correspond to an F face in PBC analysis. For natural quartz crystals or synthetic quartz grown in NaCl solution, the {1010} faces are characterized by striations running parallel to the edge between {1011} and {1010}; however, on synthetic quartz grown from NaOH or KOH solution, the {1010} faces are characterized by polygonal growth hillocks, and no striations are observed. The {210} face of pyrite crystals is characterized by striations either running parallel to the edge with the neighboring {100} face, or running perpendicular to this direction, depending on their localities. In the former case, no growth layers are observable on the {210} face, whereas, in the latter case, striations are due to step patterns of elongated growth layers. The reason why the same crystal face behaves differently depending on growth conditions, and changes its characteristic from an F face to an S face, remains unanswered (see Chapters 10 and 11).

Crystal faces with curved or wavy surfaces, not exhibiting either striations or step patterns, are rarely encountered. In most cases, these faces appear by dissolution. Rough interfaces grow by the adhesive-type growth mechanism, their normal

5.2 Methods of observation 91

Figure 5.2. (a) Reflection-type photomicrograph showing step patterns due to growth observed on low-index (0001) face of hematite. (b) Phase contrast photomicrograph showing etch figures on (111) face of diamond.

growth rates are high, and therefore the faces soon disappear from the crystal. If such faces become large, there must be a reason why these faces have survived.

In contrast to striated or curved faces, on low-index mirror-flat crystal faces, step patterns are observed if an appropriate method of observation is applied, which indicates that the face grew by two-dimensional layer spreading or spiral-step-like spreading of growth layers parallel to the face. These steps range from elemental steps with unit cell height to thick macro-steps formed by the bunching of elemental steps; circular, polygonal, and irregular steps are also observed. Step patterns range from those with distinct spiral steps with a wide step separation at the center to those appearing as conical or polygonal pyramids (growth hillocks) due to narrow step separations. Etch figures, such as etch pits and etch hillocks, may also be seen on this type of face (Fig. 5.2).

There is a great deal of information relating to the growth or dissolution of crystals contained in surface microtopographs. They contain more direct information relating to the growth of crystals than does the bulk morphology of crystals, and they provide information that allows us to form the basis of analysis of the origin of variations in the Habitus and Tracht of polyhedral crystals. The reason for this is clear: the surfaces of crystals are unique in that they are the places where growth or dissolution may take place. In this chapter, we will summarize the information obtained from surface microtopographs of crystal faces, and the methods required to decode this information will be discussed.

5.2Methods of observation

The earliest interest in surface microtopographs observable on crystal faces developed in the 1920s; these observations were made using reflection-type microscopes on etch figures seen in natural mineral crystals [1], [2]. At that time,

92Surface microtopography of crystal faces

the main point of interest was the relationship between the symmetries of the etch figures and the crystal faces. Through these observations, etch pits (depressions formed by etching) and etch hillocks (protrusions caused by etching) were distinguished, and both were collectively called etch figures. However, a clear distinction between growth hillocks and etch hillocks was not established. Arguments as to whether trigons (triangular pits with orientation opposite to the triangle of a (111) face; see Chapter 9) commonly observed on the {111} faces of natural diamonds are due to growth or dissolution continued for many years (see Chapter 9 and Fig. 5.2 (b)). Although it has now been established that trigons are etch pits that arise due to the strain field associated with dislocations or point defects, there was at one time a strong assertion that they were of growth origin. Once dislocation theory was established, the observation of etch pits was utilized as a powerful methodology to investigate dislocation movement.

A renewed interest in the surface microtopographs of crystal faces developed after the interferometric observations by Volmer, who confirmed for the first time the two-dimensional spreading of interference fringes on a crystal face growing from the vapor phase (see ref. [10], Chapter 3). This observation introduced not only the concept of surface diffusion, but also formed a starting point for the layer growth theory later proposed by Kossel and Stranski (see refs. [8] and [9], Chapter 3). The spiral growth theory by Frank provided further stimulation in this subject (see ref. [7], Chapter 3). It was around this time that phase contrast microscopy, which can detect extremely small step heights (of nanometer order), and multiple-beam interferometry, by which differences in levels of this order can be measured, were invented. This enabled the first verification of the theory, achieved by the observa-

tion of a horse’s hoof step pattern on {1010} faces of natural beryl, Be3Al2Si6O18, whose step height was measured to be of unit cell order by multiple-beam interfer-

ometry (see ref. [18], Chapter 3).

Thus, spiral step patterns served as excellent subjects, and many observations were reported using these new techniques [3], [4]. It was also around this time that

the movement of spiral growth layers spreading on the (0001) face of CdI2 growing in aqueous solution was first observed in situ. By using these optical techniques,

spiral growth layers with monomolecular height (0.23 nm) were observed and measured on natural hematite crystals [5].

Later, differential interference microscopy was developed, enabling the detection of difference in levels as sensitively as phase contrast microscopy, and, because this technique was easier to use, it came to be used in preference to the former techniques [6]. Differential interference microscopy is superior to phase contrast microscopy in the observation of vicinal or curved surfaces, which are impossible to observe under a phase contrast microscope because the contrast is too high.

Optical microscopy, such as phase contrast or differential interference contrast,

5.2 Methods of observation 93

Figure 5.3. Spiral steps observed on the mineral kaolin using transmission electron

microscopy with the decoration method [7].

increases the resolution in the vertical direction, but the horizontal resolution is limited to the wavelength of visible light. To observe surface microtopographs of tiny crystals of micrometer order, such as clay minerals, a decoration method [7] was developed using transmission or scanning electron microscopy. This involved the evaporation of gold in a vacuum onto dispersed samples; the gold selectively nucleates along the steps, and the surface microtopographs of tiny crystals become observable. By these means, it was demonstrated that tiny muscovite or kaolin minerals also grow by the spiral growth mechanism. An example is shown in Fig. 5.3.

Powerful methods that have been developed more recently, and are currently used to observe surface microtopographs of crystal faces, include scanning tunnel microscopy (STM), atomic force microscopy (AFM), and phase shifting microscopy (PSM). Both STM and AFM use microscopes that (i) are able to detect and measure the differences in levels of nanometer order; (ii) can increase two-dimensional magnification, and (iii) will increase the detection of the horizontal limit beyond that achievable with phase contrast or differential interference contrast microscopy. The presence of two-dimensional nuclei on terraced surfaces between steps, which were not observable under optical microscopes, has been successfully detected by these methods [8], [9]. In situ observation of the movement of steps of nanometer order in height is also made possible by these techniques. However, it is possible to observe step movement in situ, and to measure the surface driving force using optical microscopy. The latter measurement is not possible by STM and AFM.