Crystal Growth

Once a crystal nucleus is stable, growth proceeds by progressively adding atoms or ions to its surface. This sounds straightforward, but it involves the same kind of kinetic barriers that challenged nucleation. Each new unit added to the crystal must bond firmly enough to remain in place rather than being redissolved back into the surrounding melt or fluid. The geometry of the crystal surface turns out to be the decisive factor in how easily and how fast this happens. ^[1]

The Problem with Flat Surfaces

Adding a new unit to a perfectly flat crystal face is energetically difficult. The new unit sits proud of the surface and forms chemical bonds only where it contacts the face below it - all the bonds that would normally stabilize the unit within the interior of the crystal are missing. With so few bonds satisfied, there is a high probability that the unit simply dissolves back into the melt. In contrast, adding a new unit along the edge of a half-completed layer on the surface is much easier: bonds can form on two or three sides simultaneously, greatly increasing stability and reducing the chance of redissolution. ^[1]

This suggests that starting a completely new layer on an otherwise flat face - with no edge to add to - would require a very large degree of undercooling or supersaturation. Theoretical analysis of layer-by-layer growth predicts that crystals should be very difficult to grow except under extreme conditions. Yet real crystals grow far more easily and rapidly than this theory suggests. ^[1]

Screw Dislocations: The Growth Mechanism

The resolution to this conflict is that real crystals do not grow one complete layer at a time. Instead, growth commonly exploits screw dislocations - structural defects in which part of a crystal is displaced relative to the rest such that the displacement terminates in a line normal to the crystal face. The geometry that results is equivalent to a helix or a spiral staircase. As atoms are added to the continuously exposed edge of the screw dislocation, the step spirals upward, always providing a built-in edge at which to add the next portion of crystal. A new flat surface never needs to be started - the screw dislocation ensures that an edge is always available. ^[1]

Why Slow-Growing Faces Are the Largest

A counterintuitive but fundamental rule governs the relationship between growth rate and crystal morphology: the slowest-growing faces end up being the most prominent and the largest. Fast-growing faces grow themselves out of existence. ^[1]

The halite crystal illustrates why. Two sets of potential faces exist on halite: octahedral {111} faces and cubic {001} faces. The {111} faces are parallel to layers of alternating Na⁺ and Cl^- in the structure, so they carry a net positive or negative charge. This strong electrical charge attracts successive layers of oppositely charged ions powerfully, producing very high growth rates. The {001} faces, by contrast, expose equal numbers of Na⁺ and Cl^- and are electrically neutral - there is no net attraction for either cation or anion, and growth proceeds only by random arrival of ions at the surface. Growth rates are therefore slow. ^[1]

Because each successive growth layer on the fast {111} faces is thicker than on the slow {001} faces, the {111} faces become progressively smaller with each layer added and ultimately vanish from the crystal’s exterior. The slow {001} faces persist and grow larger. The result is that the equilibrium form of a halite crystal shows large cubic {001} faces and no {111} faces at all - the direct opposite of what the growth rates suggest at first glance. ^[1]

Surface Energy and Thermodynamics

The link between growth rate, face size, and surface energy is thermodynamic. The surface of a crystal carries a higher energy than the interior, because surface atoms have unsatisfied or distorted chemical bonds. Adding a new atom to the surface satisfies those dangling bonds and reduces the surface energy - this energy reduction is the driving force for growth. Faces with the highest surface energy release the most energy when a new layer is added, so they grow fastest. Growing fast makes them smaller in area. The net thermodynamic effect is that the total surface energy of the crystal is minimised, because high-energy surface area is continuously eliminated by rapid growth and low-energy surface area dominates. ^[1]

The Law of Bravais and Crystal Habit

The Law of Bravais provides a crystallographic framework for predicting which faces will be prominent. It holds that the most prominent crystal faces are those that intersect the greatest density of lattice nodes - that is, faces on which lattice nodes are most closely spaced. An equivalent way of stating this is that growth rate is inversely proportional to the interplanar spacing of a given face: faces with large interplanar spacings grow slowly and become large; faces with small interplanar spacings grow fast and become small or absent. ^[1]

A consequence of this rule is a seemingly counterintuitive relationship between crystal habit and unit cell dimensions: the longest dimension of a crystal typically corresponds to the shortest unit cell dimension. Sillimanite provides a clear demonstration. Its c unit cell dimension is significantly smaller than the a and b dimensions. Because the interplanar spacing along c is less than along a and b, growth proceeds fastest in the c direction, and crystals become elongate parallel to c, producing the characteristic needle-like or prismatic habit of sillimanite. ^[1] This inverse relationship between crystal elongation direction and unit cell dimension holds for many elongate minerals, including zircon, tourmaline, apatite, amphibole, and andalusite. ^[1]

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