Does Impurity-Induced Step-Bunching Invalidate Key Assumptions of the Cabrera-Vermilyea Model? Rile I. Ristic,* ,† James J. DeYoreo,* ,‡ and Chun M. Chew † Chemical Engineering Department, UniVersity of Sheffield, Mappin Street, Sheffield S1 3JD, UK, and Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720 ReceiVed October 23, 2007; ReVised Manuscript ReceiVed January 29, 2008 ABSTRACT: We show that the growth recovery mechanism of the {110} faces on crystals of the pharmaceutical paracetamol in the presence of its intrinsic impurity acetanilide occurs in the same way as in the growth of inorganic KH 2 PO 4 (KDP) crystals with Fe(III) and Al(III) impurities, by initial movement of macrosteps while elementary steps remain pinned. This suggests that the mechanism of recovery by activation of elementary step motion assumed by Cabrera and Vermilyea (C-V) is not applicable to a diverse set of common and technologically important crystal systems. Recognizing that impurity-driven macrostep formation depends on an imbalance in the concentration ahead and behind the step, we propose a general condition that must be met for a crystal-impurity system to behave according to the C-V predictions. A well-known classical theory proposed by Cabrera and Ver- milyea (C-V) 1 has been widely used to analyze growth inhibition by pinning of elementary steps due to their interaction with adsorbates. 2–4 According to this theory, the pinning effect on elementary steps spreading across the growing crystal face leads to a “dead zone” (Figure 1) in which the steps are stopped from advancing if the supersaturation σ is below a critical supersaturation σ*, since the critical radius of step curvature (r c ) γΩ/kTσ) is greater than the impurity spacing (where γ is the step-edge free energy, Ω is the effective molecular volume, k is Boltzman’s constant, and T is temperature of crystallization). If the supersaturation increases above the critical value, σ*, the C-V model assumes that the elementary steps initially pinned by the impurity molecules start to break through the “impurity fence”. As a result, the train of elementary steps on a given surface becomes mobile again. However, it was shown through in-situ atomic force microscopy (AFM) that growth on the {100} face of inorganic KH 2 PO 4 (KDP) in the presence of Fe(III), 5,3 Cr(III), 3 and Al(III) 3 recovers from impurity poisoning by propagation of macrosteps instead of elementary steps as supposed in the C-V model. Here we report that this discrepancy between the C-V model and observations of growth recovery is also exhibited by a very different crystal system: organic paracetamol (C 8 H 9 NO 2 ) crystals. On the basis of these results and observations of other crystals, we propose a condition on the relative time scales for impurity adsorption and terrace lifetime for any crystal system that must be met before the standard C-V model can be applied. Paracetamol powder of purity >99%, purchased from Merck, was recrystallized and subjected to high performance liquid chromatography to quantify the presence of unintentionally added (intrinsic) impurities. This method revealed the presence of 0.0055% w/w of acetanilide (C 8 H 9 NO), an intrinsic impurity incorporated in the system as a result of the industrial synthesis. Other impurities were not detectable. Tangential velocity, V, of growth steps spreading across the {110} paracetamol faces was measured as a function of supersaturation σ ) ln(C/C e ), where C and C e are the actual and equilibrium concentrations, using in-situ laser interferometry, 6 at constant temperature T ) 296 K, and a flow rate of 30 cm/s. This dependence (Figure 1) shows that there is indeed a pronounced “dead zone” for 0 < σ < 10.5% in which the growth was not detectable by this technique. Although this is one of the most powerful conventional tools 7 for studying the kinetics of a single crystal face, its resolution is too low to reveal detailed characteristics of elementary steps such as height, bunching, and in particular, extremely slow growth (“zero”) kinetics. Consequently, in-situ AFM imaging was per- formed over this range of supersaturation. This technique enabled us to probe any crystal growth activity in the dead zone seen by laser interferometry from nanometer to micrometer length scales and check the validity of the postulated C-V scenario for growth resurrection. The crystallization temperature was kept constant, T ) 296 K for all σ. Other experimental details are described elsewhere. 8 Figure 2a-c shows three images of the same area (10 × 10 µm 2 ) of the {110} face for three different values of σ: (a) 3%, (b) 8%, and (c) 12%. Under these conditions, the step generation at hillocks H 1 and H 2 , as well as the movement of elementary steps generated by them, was “frozen”. The identical surface topographs, with markedly roughened step morphology, confirm that acetanalide pins the steps and creates a dead zone for elementary steps over this range of σ. This dead zone seen by AFM might initially seem a satisfactory answer to the “zero” growth rate of the {110} faces observed in the interferometric dead zone (Figure 1). However, Figure 2c shows that the elementary steps are not only immobile in the interferometric dead-zone, but also slightly above it, at σ ) 12%, a supersaturation at which growth recovery of the {110} faces was previously observable by the interferometry (Figure 1). But to go above this value of σ and try to restart growth of elementary steps was a challenging task for three reasons. The first * E-mail: R.I.Ristic@Sheffield.ac.uk (R.I.R.); jjdeyoreo@lbl.gov (J.J.D.). † University of Sheffield. ‡ Lawrence Berkeley National Laboratory. Figure 1. Tangential velocity V) f(σ) for the {110} faces. σ* ≈ 10.5% is the critical supersaturation at which growth resurrection is observable by this technique (after 8). Inset: Schematic showing the region below σ* where the step speed is small but nonzero. CRYSTAL GROWTH & DESIGN 2008 VOL. 8, NO. 4 1119–1122 10.1021/cg7010474 CCC: $40.75  2008 American Chemical Society Published on Web 03/13/2008