An analysis of combined surface and volume diffusion processes in crystal growth

Gilmer, George H.; Ghez, R.; Cabrera, N.

doi:10.1016/0022-0248(71)90027-3

Cited by 223 publications

(102 citation statements)

References 15 publications

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“…Thus, the assumption of a diffusion-limited mechanism for ferritin and apoferritin allows a reasonable kinetic barrier, comparable with the effective activation energies of viscosity and diffusion in aqueous solutions (21, 34); a too-high barrier could indicate a slowly decaying transition state (2). Note that a proper determination of U max would require knowledge about the growth mechanism, i.e., whether a solute molecule directly attaches to a growth site (6,12), similar to the silver atoms during silver electrocrystallization (35), or, similar to potassium or ammonium dihydrogen phosphate (36)(37)(38), lysozyme (39), and canavalin (40), the molecules reach the growth sites after being adsorbed on the crystals surface (10).…”

Section: Resultsmentioning

confidence: 99%

“…For the intermediate case of protein solid phases, the growth kinetics largely resemble those of small molecules, and it was assumed that transition-state laws apply (8). Although rate laws reminiscent of diffusionlimited mechanisms have been postulated for small-molecule phase transitions (9-11), they were viewed as equivalent to respective transition-state expressions (10,11), and no critical tests to discriminate between the two mechanisms were suggested or performed.…”

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confidence: 99%

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Diffusion-limited kinetics of the solution–solid phase transition of molecular substances

Petsev

Chen

Gliko

et al. 2003

Proc. Natl. Acad. Sci. U.S.A.

105

131

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For critical tests of whether diffusion-limited kinetics is an option for the solution-solid phase transition of molecular substances or whether they are determined exclusively by a transition state, we performed crystallization experiments with ferritin and apoferritin, a unique pair of proteins with identical shells but different molecular masses. We find that the kinetic coefficient for crystallization is identical (accuracy <7%) for the pair, indicating diffusion-limited kinetics of crystallization. Data on the kinetics of this phase transition in systems ranging from small-molecule ionic to protein and viri suggest that the kinetics of solution-phase transitions for broad classes of small-molecule and protein materials are diffusion-limited.T he kinetics of the reactions in solutions are either limited only by the rate of diffusion of the species (1) or additionally slowed down by a transition state (2). For the kinetics of the phase transitions in solutions, it is generally accepted that colloid particles follow the diffusion-limited model, whereas the growth rates of new phases of small molecules are thought to be governed by a transition state (3-7). For the intermediate case of protein solid phases, the growth kinetics largely resemble those of small molecules, and it was assumed that transition-state laws apply (8). Although rate laws reminiscent of diffusionlimited mechanisms have been postulated for small-molecule phase transitions (9-11), they were viewed as equivalent to respective transition-state expressions (10, 11), and no critical tests to discriminate between the two mechanisms were suggested or performed.In the transition-state kinetics, the rate coefficients are (i) mass-dependent (12, 13), (ii) independent on the diffusivity (2), and (iii) faster for high-symmetry molecules because of the transition-state entropy (7). Hence, for tests of the mechanism of growth of the new phase during a solution-solid phase transition, we selected the crystallization of ferritin͞ apoferritin, a unique pair of proteins that share a nearspherical protein shell, consisting of 24 identical subunits (14, 15). The crystals of ferritin and apoferritin are typically faceted by octahedral [111] faces and have been shown to grow by the lateral spreading of layers generated by two-dimensional nucleation (16, 17). For apoferritin, it was shown that the edges of the unfinished layers, called growth steps, propagate by the incorporation of single protein molecules at the growth sites, kinks (16,18). In the face-centered cubic lattice that ferritin and apoferritin share, kinks are defined as the termination points of three independent ͗011͘ rows of molecules belonging to the unfinished layer (19). Thus, the step velocity equals the product of the molecular diameter a, mean kink density n k Ϫ1 , and net molecular f lux into a kink (j ϩ Ϫ j Ϫ ) (16, 18). Methods Characterization of the Molecular Masses and Pair Interactions ofFerritin and Apoferritin. We performed static light scattering (20) in 0.2 M NaOOCCH 3 solutions....

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Diffusion-limited kinetics of the solution–solid phase transition of molecular substances

Petsev

Chen

Gliko

et al. 2003

Proc. Natl. Acad. Sci. U.S.A.

105

131

View full text Add to dashboard Cite

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“…Theirs experiments show that the variation of the bulk growth rate increase at low velocity and high supersaturation. Prieto et al (1996) Control of crystal growth rate could be largely described by the combination of two processes: i) chemical volume diffusion within the boundary layer occurring along the crystal faces; and ii) surface processes (Gilmer et al, 1971 such gradient is dependant on the distance between the considered growthing crystal and his nearest neighbors, because, during growth, a "chemical affinity gradient will arise and persist" forming "depleted zones" that enlarge and coalesce (Carlson 1989, Carlson 1991, Skelton 1997. Carlson (1989) established at each instant a relation of proportionality between the depleted zone and the crystal radius:…”

Section: Multiscale Fluid Flow Analysismentioning

confidence: 99%

Estimating the local paleo-fluid flow velocity: New textural method and application to metasomatism

Sizaret

Branquet

Gloaguen

et al. 2009

Earth and Planetary Science Letters

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Estimating the local paleo-fluid flow velocity: New textural method and application to metasomatism. Earth and Planetary Science Letters, Elsevier, 2009, 280 (1-4) Finally, a two-stage tectono-hydrodynamic model is proposed for the metsomatism. The first stage is genetically linked to the sill injection, and the second is characterized by a wider event with hydrothermal flow passing along the leucogranite sills.

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“…A detailed analysis of the growth dynamics within the formalism of the Gilmer-Ghez-Cabrerra model [34] demonstrated that incorporation into the step, following surface diffusion, best describes PETN growth. The crystal growth occurs on monomolecular steps generated either by simple or complex screw dislocation sources, 2-D nucleating islands, or macro-clusters that sediment onto the surface before spreading laterally as step bunches.…”

Section: Resultsmentioning

confidence: 98%

Effect of zinc doping on pentaerythritol tetranitrate single crystals

Zhang

Bhattacharia

Weeks

2010

Cryst. Res. Technol.

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In this study, the effect of zinc impurity on the organic high explosive pentaerythritol tetranitrate (PETN) single crystal has been investigated with optical microscopy and ex situ atomic force microscopy (AFM). The optical images show that the crystal shape has a transition with a predictable trend from long crystal to compact one as the zinc concentration is increased. Also, the 2-dimentional (2-D) growth hillocks are observed clearly on (110) face with contact AFM. The crystal growth occurs on monomolecular steps generated by 2-D nucleation and followed by layer-by-layer expansion, and the macro-steps formed onto the surface before spreading laterally as step bunches. The zinc ions are incorporated in growth steps as the zinc concentration is increased. The mechanism of inorganic impurity on molecular crystallization growth is still unclear. However, the incorporation of impurities may significantly affect growth kinetics of defect structure, and the bulk properties of molecular crystals.

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An analysis of combined surface and volume diffusion processes in crystal growth

Cited by 223 publications

References 15 publications

Diffusion-limited kinetics of the solution–solid phase transition of molecular substances

Diffusion-limited kinetics of the solution–solid phase transition of molecular substances

Estimating the local paleo-fluid flow velocity: New textural method and application to metasomatism

Effect of zinc doping on pentaerythritol tetranitrate single crystals

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