76 Morphology of polyhedral crystals

Figure 4.10. Kuroda’s model explaining the repeated Habitus change of snow crystals

[23]. Shaded areas are crystals; dotted areas are QLLs (quasi-liquid layers).

bounded by {0001} and {1010} faces. The Habitus of polyhedral snow crystals changes repeatedly with decreasing temperature from polygonal plates, to polygonal prisms, polygonal plates, and polygonal prisms. The reason for these repeated changes was unknown until Kuroda [23] solved the mystery by assuming the presence of a quasi-liquid layer (QLL) with different thicknesses on respective faces. His model is shown in Fig. 4.10.

The thickness of the QLLs is different on different faces, and becomes thinner as the temperature is decreased. Thus, the temperature at which a QLL disappears depends on the face. When the surface is covered by QLLs, crystal growth is regarded as a solution or melt phase growth, whereas on a naked surface it is due to vapor growth. Thus, the repeated Habitus change may be explained. The presence of QLLs was confirmed by ellipsometry.

4.4.5Tracht change

MAJOR FACTORS

Tracht change differs from change in Habitus in that it describes a change in the form of a crystal grown in an isotropic environmental phase through the combination of different faces and the relative sizes of respective faces. Therefore,

Trachts are forms determined by the relative ratio of the normal growth rate R of the different crystal faces present on the surface of a growing crystal. The

4.4 Growth forms 77

identification of the factors involved in the environmental phase and how they influence R form the key points in the analysis.

Since surface structures and growth mechanisms are different at rough and smooth interfaces, the effect of environmental factors will also be different. When a crystal bounded by both smooth and rough interfaces grows, the rough interface disappears as growth proceeds, unless some factors operate to suppress the growth rate of the rough interface, and the crystal takes on a Tracht bounded by a smooth interface only. If factors suppress the growth rate R of a rough interface, the crystal will temporarily take on a Tracht bounded by rough and smooth interfaces. In extreme cases, crystals may take on a Tracht bounded by rough interfaces only. The most likely factor that suppresses the growth rate R of a rough interface is impurity precipitation covering the whole surface. The growth is intercepted, leading to the development of the rough interface. But this face will disappear as soon as growth continues without the effect of impurities.

The Tracht of polyhedral crystals is, in general, the growth form of a crystal bounded by smooth interfaces and represents the expected morphology when the crystal grows under a driving force below /kT *, namely under the condition where the principal method of growth is the spiral growth mechanism, as already explained in Chapter 3. Therefore, the normal growth rates R of faces appearing on the crystal are determined by the height of the growth spiral layers, h, their advancing rates, v, and the step separation, 0 . If we could find out which factors that are involved in environmental conditions affect h, v, and 0 , we could explain the origin of the Tracht variation. This analysis will be given in Chapter 5; for now, we will just point out the following major factors.

(1)Difference in the environmental phases. Since the interface roughness will be different for the same crystal species depending on whether the crystal was grown from the melt, solution, or vapor phases, different growth forms are expected for different environmental phases. This implies that the Tracht of the same crystal species will depend on the structure of the environmental phases, the degree of condensation, and the solute–solvent interaction.

(2)In solution or vapor phase growth, the strength of the solute–solvent interaction energies, namely the species and types of solvent component and transport agent.

(3)The growth temperature and driving force, which affect interface roughness.

(4)The surface reconstruction.

(5)Impurities and the solvent component, which affect step free energy .

78 Morphology of polyhedral crystals

METHODOLOGY

Many investigations have been carried out since the seventeenth century that analyze the Tracht variations of growth forms. These investigations fall into two principal categories: (i) experiments designed to observe Tracht variations in relation to growth conditions, and (ii) the analysis of Tracht variation of mineral crystals with respect to the geological environment in which they occur.

It had been observed that drastic changes in Tracht occurred in the presence of impurities, and thus experiments were originally designed that focused on impurity adsorption. Wells, however, considered other factors, and performed systematic investigations that demonstrated that solvents, growth temperatures, and supersaturation are the main factors involved in changing the Tracht of ionic crystals growing in the solution phase [24]. However, Wells concluded that if the observations were treated statistically, the growth forms reflected either the structural or the equilibrium form. A vast amount of data relating to the crystal morphology of natural minerals were collected, based on which the order of morphological importance was correlated to lattice types, and the relationship between Tracht and the growth environment and conditions was deduced based on observations of museum samples. A further type of investigation was made in which Tracht variations were observed in situ in relation to where they occurred; these results were used as guides for use in ore prospecting and in analyzing the genesis of rocks (a scientific discipline referred to as typomorphism) [25]. We will summarize the results achieved during the twentieth century in the following sections.

IMPURITIES

It was during the late eighteenth century that Romé de l’Isle [26] observed, for the first time, the Tracht of a crystal that had changed drastically after the addition of a small amount of impurity. He saw how NaCl crystals exhibit an octahedral form when a small amount of urea is added to the aqueous solution, in contrast to the simple cubic form commonly observed in pure solution. Motivated by this observation, many investigations were carried out, from the addition of inorganic impurities to the addition of dyes having a high adsorption power, to observe the effect caused on the Tracht by the impurities [27]. It has been confirmed that Tracht changes can occur over a wide range of impurity addition, from parts per hundred to parts per million order. The following conclusions were reached.

(1)Impurity ions adsorb selectively on a particular face and cover the whole surface, leading to retardation of the growth rate R of the face and a change of Tracht.

(2)There are two cases for which selective adsorption of impurities occurs: (i) over the entire surface by epitaxy, and (ii) along the steps of growth layers on the face.

4.4 Growth forms 79

Figure 4.11. Morphodrom of KCl crystals [28]. The vertical axis is the supersaturation;

the horizontal axis is the concentration of Pb ions.

(3)Impurities may act as either a promoting or a retarding force to growth rates.

When dyes are used as the impurity component, it is seen that R is diminished by the adsorption of the impurities, since only the growth sectors of faces appearing by impurity adsorption are colored. Crystal faces that appear due to impurity adsorption are, in general, the K face (by PBC analysis), indicating that the impurities adsorb at kink sites on a rough interface, resulting in a diminished growth rate. This may, in some cases, change the growth mechanism of the face. Figure 4.11 shows a morphodrom of KCl crystals grown in aqueous solution when Pb ions are added. Changes in Tracht and surface microtopographs of crystal faces are illustrated in relation to the driving force (supersaturation) and the concentration of Pb ions. As concentration of Pb ions is increased, the Tracht changes from cubic to octahedral, and the surface microtopograph of the {111} face, which is a K face by PBC analysis, changes from a hopper form to a face showing spiral growth layers that correspond to an F face. At the same time, spiral steps on the {100} face change their form from square with 001 edges to square with 110 directions.

Figure 4.12 is a morphodrom of NaCl crystals when Fe(CN)6 is added as an impurity, and it shows the effect of impurity changes depending on the driving force.

Tracht can change, however, due to driving force alone [29]. In these examples,

80 Morphology of polyhedral crystals

supersaturation (d)

impurity concentration Fe(CN)6 (g/l)

Figure 4.12. Morphodrom of NaCl when Fe(CN)6 is added as an impurity [29].

impurities are adsorbed all over the surface, and act to reduce R. On an F face, however, impurities adsorb along steps and the advancing rate of the steps is retarded. In such cases, even a small amount of impurity may cause a significant effect.

As an important example of the impurity effect, it is necessary to give a brief explanation of the tapering phenomenon of crystals. Tapering is a phenomenon that describes how a prismatic crystal narrows in size toward the tip, and it has often been observed on piezoelectric crystals growing from the aqueous solution, such as ADP (NH4H2PO4) or KDP (KH2PO4). Tapered crystals of similar type are also observed among prismatic crystals of natural quartz. It is understood that impurity ions such as Fe3 are selectively adsorbed along a certain direction of growth layers on the prism faces of these tapered crystals, retarding the advancing rate of the growth steps, which results in a pile up of steps, so producing a high-index tapered face. The dog-tooth-like Habitus of calcite (CaCO3) crystals bounded by scalenohedral {hkı¯l} faces is possibly formed through tapering due to impurity adsorption. When calcite crystals are synthesized from pure solution, the crystals are always rhombohedral, bounded by {1011} faces, whereas a dog-tooth Habitus appears when an organic compound is added as an impurity. On {hkı¯l} faces which