Single-crystal AFM cantilever bending tests on needle-like beta-L-glutamic acid crystals grown under carefully controlled seeded cooling crystallization show a broad distribution of Young's modulus EE and breakage strength σB\sigma_B (the deposited accepted manuscript of Hallac et al. reports 52 broken crystals with a median σB≈22.4\sigma_B \approx 22.4 MPa and an observed range of 5.27–81.1 MPa). Hallac et al. (2019) concluded that the broad range of EE and σB\sigma_B values "suggests a significant extend of crystal imperfections, even though the crystals where carefully crystallised using a seeded cooling crystallisation", but did not identify these imperfections or quantify their influence on the measured distributions. This record states the open gap indicated by that finding: identify which defect types (inclusions, solvent occlusions, dislocations, surface flaws) underlie the scatter and what their origin is, and quantitatively relate their population statistics to the measured distributions of EE and σB\sigma_B in individual high-aspect-ratio crystals.

Background

Molecular crystals — solids built from discrete molecules held by van der Waals forces and hydrogen bonds, including most pharmaceutical actives — are grown industrially from solution by seeded cooling crystallization, in which a seed crystal is added to a supersaturated solution that is then cooled so that material deposits on it in a controlled way. Many such compounds crystallize as needles (high-aspect-ratio crystals with one dimension much longer than the others), and these needles break easily during filtration, drying, and handling, changing the particle size distribution and hindering downstream processing. Hallac, Fragkopoulos, Connell, and Muller (CrystEngComm 21(38):5738–5748, 2019) developed a method in which an atomic force microscope (AFM; a microscope whose sharp tip on a flexible cantilever both images a surface and applies measurable nano-Newton forces) bends individual needle crystals clamped as tiny cantilevers, yielding both the Young's modulus EE (the elastic stiffness relating stress to strain) and the breakage strength σB\sigma_B (the stress at fracture) of each single crystal. For beta-L-glutamic acid (beta-LGA, the stable polymorph, i.e., one of the compound's distinct crystal packing forms) cantilevers grown under carefully controlled seeded cooling crystallization they measured broad Weibull-type distributions of both quantities: the deposited accepted manuscript reports 52 broken crystals, a Weibull median σB\sigma_B of 22.4 MPa (observed range 5.27–81.1 MPa) and a Weibull median EE of 1.90 GPa, while Mahdi et al. (2020), describing the published version of record, report 63 broken cantilevers, a median σB\sigma_B of about 20 MPa, 90% of crystals at or below about 45 MPa, and a range of roughly 9–49 MPa. Brittle solids fail from flaws — the classical Griffith picture — so strength is naturally statistical, and Weibull-type extreme-value distributions (statistics of the largest flaw in a specimen) are the standard description of flaw-controlled strength scatter in ceramics and other brittle materials. What is not known for these molecular crystals is which specific flaws produce the scatter: candidates include solvent inclusions (pockets of mother liquor trapped during growth, ranging from nanometers to hundreds of micrometers), dislocations (line defects in the crystal lattice), impurity incorporation, and surface damage. Adjacent nanoindentation literature (pressing a hard tip into a crystal face to measure local modulus and hardness) has shown that defect type matters — a review by Ramamurty and Jang (CrystEngComm 16(1):12–23, 2014) surveys the technique; Gabriele et al. (Cryst. Growth Des. 20(9):5956–5966, 2020) showed that solvent occlusions are a previously overlooked source of property variation in aspirin and survey earlier work by Swift and co-workers in which dye impurities incorporated at only 0.01–0.1% lower the modulus of uric acid crystals by 25–50%, while surface preparation changes the onset of plasticity; and molecular-dynamics nanoindentation simulations by Elgengehi et al. (J. Am. Chem. Soc. 147(41):37186–37195, 2025) can now predict the properties of ideal, defect-free organic crystals. Earlier process-level work (MacLeod and Muller, Org. Process Res. Dev. 16(3):425–434, 2012) modeled needle breakage during pressure filtration by treating crystals as cantilevers but used single literature strength values, not defect-resolved distributions. None of this work connects the defect structure of individual solution-grown needles to the observed single-crystal distributions of EE and σB\sigma_B, which is exactly the gap indicated by Hallac et al.'s conclusion that the broad range of measured values suggests a significant extent of crystal imperfections.

Problem Statement

For needle-like (high-aspect-ratio) molecular crystals grown from solution — with beta-L-glutamic acid grown by seeded cooling crystallization as the model system measured by AFM single-crystal cantilever bending in Hallac et al. (2019) — determine the nature and origin of the internal imperfections and surface flaws responsible for the broad measured distributions of Young's modulus EE and breakage strength σB\sigma_B, and establish a quantitative correlation between defect structure and this variability. Concretely: (i) identify which defect types and surface flaws, if any, are present in the as-grown crystals and which of them nucleate fracture or depress the modulus; and (ii) quantitatively relate defect metrics (type, size, density, and spatial distribution) to the statistical distributions of EE and σB\sigma_B measured on individual crystals, so that the observed variability — not merely the mean values — is explained; for this correlation, take the deposited accepted manuscript's beta-LGA distributions of Hallac et al. (52 crystals; Weibull fits with shape kk and scale λ\lambda: σB\sigma_B k=1.95k=1.95, λ=27.0\lambda=27.0 MPa; EE k=1.44k=1.44, λ=2.45\lambda=2.45 GPa; Weibull (fitted) medians 22.4 MPa and 1.90 GPa; observed ranges 5.27–81.1 MPa and 0.163–12.4 GPa) as the designated reference distributions. Both parts are required: an identification of the defect types alone is not sufficient, and the quantitative relation of part (ii) must also be established. Part (ii) is satisfied by a model that relates defect metrics (type, size, density, and spatial distribution) to the designated distributions and reproduces their reported Weibull shape, scale, and observed ranges; the defect metrics may be proposed, but they must be anchored to independently checkable values (such as defect sizes or densities reported in the cited literature) rather than free parameters tuned only to fit those distributions. A model so anchored counts as a full resolution of part (ii); experimental validation against the specific beta-LGA crystal population is not required. This correlation between defect structure and the variability in EE and σB\sigma_B remains open: Hallac et al.'s conclusions attribute the broad distributions to a significant extent of crystal imperfections, but the paper neither identifies the imperfections nor quantifies their influence on the measured distributions.

References

  1. François S. Hallac, Ioannis S. Fragkopoulos, Simon D. Connell, Frans L. Muller, "Micro-mechanical properties of single high aspect ratio crystals", CrystEngComm 21(38):5738–5748, 2019. DOI: 10.1039/c9ce00819e. https://doi.org/10.1039/c9ce00819e. https://eprints.whiterose.ac.uk/id/eprint/149357/3/Hallac%20et%20al.%202019.pdf
  2. F. M. Mahdi, A. P. Shier, I. S. Fragkopoulos, J. Carr, P. Gajjar, F. L. Muller, "On the Breakage of High Aspect Ratio Crystals in Filter Beds under Continuous Percolation", Pharmaceutical Research 37(12):231, 2020. DOI: 10.1007/s11095-020-02958-x. https://doi.org/10.1007/s11095-020-02958-x. PMCID: PMC7596000
  3. Benjamin P. A. Gabriele, Craig J. Williams, Matthias Eckhard Lauer, Brian Derby, Aurora J. Cruz-Cabeza, "Nanoindentation of Molecular Crystals: Lessons Learned from Aspirin", Crystal Growth & Design 20(9):5956–5966, 2020. DOI: 10.1021/acs.cgd.0c00635. https://doi.org/10.1021/acs.cgd.0c00635. PMCID: PMC7587144
  4. Sara M. Elgengehi, Durga Prasad Karothu, Weiwei He, Rabindranath Paul, Serdal Kirmizialtin, Panče Naumov, "Accurate Prediction of Mechanical Property of Organic Crystals Using Molecular Dynamics-Based Nanoindentation Simulations", Journal of the American Chemical Society 147(41):37186–37195, 2025. DOI: 10.1021/jacs.5c09944. https://doi.org/10.1021/jacs.5c09944
  5. Claire S. MacLeod, Frans L. Muller, "On the Fracture of Pharmaceutical Needle-Shaped Crystals during Pressure Filtration: Case Studies and Mechanistic Understanding", Organic Process Research & Development 16(3):425–434, 2012. DOI: 10.1021/op200279m. https://doi.org/10.1021/op200279m
  6. Upadrasta Ramamurty, Jae-il Jang, "Nanoindentation for probing the mechanical behavior of molecular crystals – a review of the technique and how to use it", CrystEngComm 16(1):12–23, 2014. DOI: 10.1039/c3ce41266k. https://doi.org/10.1039/c3ce41266k