Illusory spirals and loops in crystal growth

Abstract

The theory of dislocation-controlled crystal growth identifies a continuous spiral step with an emergent lattice displacement on a crystal surface; a mechanistic corollary is that closely spaced, oppositely winding spirals merge to form concentric loops. In situ atomic force microscopy of step propagation on pathological L-cystine crystals did indeed show spirals and islands with step heights of one lattice displacement. We show by analysis of the rates of growth of smaller steps only one molecule high that the major morphological spirals and loops are actually consequences of the bunching of the smaller steps. The morphology of the bunched steps actually inverts the predictions of the theory: Spirals arise from pairs of dislocations, loops from single dislocations. Only through numerical simulation of the growth is it revealed how normal growth of anisotropic layers of molecules within the highly symmetrical crystals can conspire to create features in apparent violation of the classic theory.B urton, Cabrera, and Frank (BCF) (1-3) launched the modern era of crystal growth (4) with the idea that screw dislocations on a crystal surface continually extrude steps to which molecules can attach. The "living ends" of these emanating spirals resolved the paradox of fast growth from solutions at low supersaturation. BCF theory, conceived originally for simple centrosymmetric cubic lattices, anticipated that one screw dislocation would generate a spiral whereas a closely spaced pair of dislocations spiraling in opposite directions would annihilate one another to form closed loops (the so-called Frank-Read source mechanism) (5). Soon thereafter, both mechanisms were demonstrated (6, 7), forever sensitizing investigators of crystal growth to the coexistence and dichotomy of spirals and loops. Later it was discovered that crystals containing screw axes normal to the growth face could exhibit interlacing step patterns that, despite having morphologies that were more complex than crystals with proper symmetry axes, were easily understood (8-10). Hexagonal L-cystine crystals studied here by real-time in situ atomic force microscopy (AFM) exhibit extremely puzzling patterns: Single dislocations apparently form closed loops whereas pairs of dislocations generate spirals. Although careful analysis has resolved this apparent contradiction and confirmed the correctness of BCF theory, these observations vividly illustrate how crystals lacking proper rotation axes and containing several translationally nonequivalent growth units can produce unusual and deceptive morphological features that can lead to incorrect conclusions about growth mechanisms.L-cystine crystals can form in the kidneys, leading to cystinuria, a painful and chronic condition. Our laboratory has used in situ AFM measurements of step growth rates on well-developed (0001) faces of hexagonal L-cystine (noncentrosymmetric space group P6 1 22, ref. 11) in the presence of additives to identify potent growth inhibitors (12). Remedies of this sort, however, must build on a ...

Dislocation-Actuated Growth and Inhibition of Hexagonal l-Cystine Crystallization at the Molecular Level

“…As reported previously, 29 the coincidence of the screw dislocation axis and crystallographic screw axis in hexagonal Lcystine results in six-threaded interlaced spirals, as observed using real-time in situ AFM. As the six minor steps are generated and advance from the dislocation core, the slowest step limits the propagation of faster-advancing steps in the layers above, resulting in bunching of the minor steps to form the 5.6 nm major steps flanking the hexagonal islands.…”

Role of Molecular Recognition in l-Cystine Crystal Growth Inhibition

“…In this respect, our laboratory reported that in situ AFM performed on the {0001} face of hexagonal l -cystine crystals in the presence of supersaturated l -cystine solutions (0.6 mM < c < 3.5 mM) revealed spiral hillocks resembling a pinwheel emanating from screw dislocations. 16 , 18 Consecutive AFM images during l -cystine crystal growth revealed a clockwise rotation of the pinwheel at the dislocation core (a left-handed screw) accompanied by continuous generation of new step edges ( Figure 1 B). Under these conditions the {0001} surface displayed hexagonal growth hillocks that resembled stacks of islands.…”

l-Cystine Diamides as l-Cystine Crystallization Inhibitors for Cystinuria

“…9–12 Real-time in situ atomic force microscopy (AFM) revealed that CDME and CME dramatically reduce the growth velocity of six symmetry-equivalent {100} steps because of specific binding to crystal growth sites, which frustrates the further attachment of L-cystine molecules. 9 CDME was found to significantly reduce stone burden in cystinuria mice compared with a water-treated group accompanied by the formation of smaller stones, but did not prevent stone formation.…”