Tissue properties of the human vertebral body sub-structures evaluated by means of microindentation

Purpose The better understanding of vertebral mechanical properties can help to improve the diagnosis of vertebral fractures. As the bone mechanical competence depends not only from bone mineral density (BMD) but also from bone quality, the goal of the present study was to investigate the anisotropic indentation moduli of the different sub-structures of the healthy human vertebral body and spondylophytes by means of microindentation. Methods Six human vertebral bodies and five osteophytes (spondylophytes) were collected and prepared for microindentation test. In particular, indentations were performed on bone structural units of the cortical shell (along axial, circumferential and radial directions), of the endplates (along the anterio-posterior and lateral directions), of the trabecular bone (along the axial and transverse directions) and of the spondylophytes (along the axial direction). A total of 3164 indentations down to a maximum depth of 2.5 µm were performed and the indentation modulus was computed for each measurement. Results The cortical shell showed an orthotropic behavior (indentation modulus, Ei, higher if measured along the axial direction, 14.6±2.8 GPa, compared to the circumferential one, 12.3±3.5 GPa, and radial one, 8.3±3.1 GPa). Moreover, the cortical endplates (similar Ei along the antero-posterior, 13.0±2.9 GPa, and along the lateral, 12.0±3.0 GPa, directions) and the trabecular bone (Ei= 13.7±3.4 GPa along the axial direction versus Ei=10.9±3.7 GPa along the transverse one) showed transversal isotropy behavior. Furthermore, the spondylophytes showed the lower mechanical properties measured along the axial direction (Ei=10.5±3.3 GPa). Conclusions The original results presented in this study improve our understanding of vertebral biomechanics and can be helpful to define the material properties of the vertebral substructures in computational models such as FE analysis.

Anisotropic diffusion at the field scale in a 4-year multi-tracer diffusion and retention experiment – I: Insights from the experimental data

Abstract Claystones are considered worldwide as barrier materials for nuclear waste repositories. In the Mont Terri underground research laboratory (URL), a nearly 4-year diffusion and retention (DR) experiment has been performed in Opalinus Clay. It aimed at (1) obtaining data at larger space and time scales than in laboratory experiments and (2) under relevant in situ conditions with respect to pore water chemistry and mechanical stress, (3) quantifying the anisotropy of in situ diffusion, and (4) exploring possible effects of a borehole-disturbed zone. The experiment included two tracer injection intervals in a borehole perpendicular to bedding, through which traced artificial pore water (APW) was circulated, and a pressure monitoring interval. The APW was spiked with neutral tracers (HTO, HDO, H2O-18), anions (Br, I, SeO4), and cations (Na-22, Ba-133, Sr-85, Cs-137, Co-60, Eu-152, stable Cs, and stable Eu). Most tracers were added at the beginning, some were added at a later stage. The hydraulic pressure in the injection intervals was adjusted according to the measured value in the pressure monitoring interval to ensure transport by diffusion only. Concentration time-series in the APW within the borehole intervals were obtained, as well as 2D concentration distributions in the rock at the end of the experiment after overcoring and subsampling which resulted in �250 samples and �1300 analyses. As expected, HTO diffused the furthest into the rock, followed by the anions (Br, I, SeO4) and by the cationic sorbing tracers (Na-22, Ba-133, Cs, Cs-137, Co-60, Eu-152). The diffusion of SeO4 was slower than that of Br or I, approximately proportional to the ratio of their diffusion coefficients in water. Ba-133 diffused only into �0.1 m during the �4 a. Stable Cs, added at a higher concentration than Cs-137, diffused further into the rock than Cs-137, consistent with a non-linear sorption behavior. The rock properties (e.g., water contents) were rather homogeneous at the centimeter scale, with no evidence of a borehole-disturbed zone. In situ anisotropy ratios for diffusion, derived for the first time directly from field data, are larger for HTO and Na-22 (�5) than for anions (�3�4 for Br and I). The lower ionic strength of the pore water at this location (�0.22 M) as compared to locations of earlier experiments in the Mont Terri URL (�0.39 M) had no notable effect on the anion accessible pore fraction for Cl, Br, and I: the value of 0.55 is within the range of earlier data. Detailed transport simulations involving different codes will be presented in a companion paper.

Calculation of crystal optical properties from molecular electron density

We have recently developed a method to obtain distributed atomic polarizabilities adopting a partitioning of the molecular electron density (for example, the Quantum Theory of Atoms in Molecules, [1]), calculated with or without an applied electric field. The procedure [2] allows to obtained atomic polarizability tensors, which are perfectly exportable, because quite representative of an atom in a given functional group. Among the many applications of this idea, the calculation of crystal susceptibility is easily available, either from a rough estimation (the polarizability of the isolated molecule is used) or from a more precise estimation (the polarizability of a molecule embedded in a cluster representing the first coordination sphere is used). Lorentz factor is applied to include the long range effect of packing, which is enhancing the molecular polarizability. Simple properties like linear refractive index or the gyration tensor can be calculated at relatively low costs and with good precision. This approach is particularly useful within the field of crystal engineering of organic/organometallic materials, because it would allow a relatively easy prediction of a property as a function of the packing, thus allowing "reverse crystal engineering". Examples of some amino acid crystals and salts of amino acids [3] will be illustrated, together with other crystallographic or non-crystallographic applications. For example, the induction and dispersion energies of intermolecular interactions could be calculated with superior precision (allowing anisotropic van der Waals interactions). This could allow revision of some commonly misunderstood intermolecular interactions, like the halogen bonding (see for example the recent remarks by Stone or Gilli [4]). Moreover, the chemical reactivity of coordination complexes could be reinvestigated, by coupling the conventional analysis of the electrostatic potential (useful only in the circumstances of hard nucleophilic/electrophilic interaction) with the distributed atomic polarizability. The enhanced reactivity of coordinated organic ligands would be better appreciated. [1] R. F. W. Bader, Atoms in Molecules: A Quantum Theory. Oxford Univ. Press, 1990. [2] A. Krawczuk-Pantula, D. Pérez, K. Stadnicka, P. Macchi, Trans. Amer. Cryst. Ass. 2011, 1-25 [3] A. S. Chimpri1, M. Gryl, L. H.R. Dos Santos1, A. Krawczuk, P. Macchi Crystal Growth & Design, in the press. [4] a) A. J. Stone, J. Am. Chem. Soc. 2013, 135, 7005−7009; b) V. Bertolasi, P. Gilli, G. Gilli Crystal Growth & Design, 2013, 12, 4758-4770.

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.

Nickel(II)-, cobalt(II)-, copper(II)-, and zinc(II)-phthalate and 1-methylimidazole coordination compounds: synthesis, crystal structures and magnetic properties

Three new coordination polymers [M(Pht)(1-MeIm)2]n (where M=Cu (1), Zn (2), Co (3); Pht2−=dianion of o-phthalic acid; 1-MeIm=1-methylimidazole) and two compounds [M(1-MeIm)6](HPht)2 · 2H2O (M=Co (4), Ni (5)) have been synthesized and characterized by X-ray crystallography. The structures of 1–3 (2 is isostructural to 3) consist of [M(1-MeIm)2] building units connected by 1,6-bridging phthalate ions to form infinite chains. In complex 1, each copper(II) center adopts a square coordination mode of N2O2 type by two O atoms from different phthalate ions and two N atoms of 1-MeIm, whereas in 3 two independent metal atoms are tetrahedrally (N2O2) coordinated to a pair of Pht ligands and a pair of 1-MeIm molecules. There are only van der Waals interactions between the chains in 1, while the three-dimensional network in 3 is assembled by C–H⋯O contacts. In contrast to polymers 1–3 the structures of 4 and 5 (complexes are also isostructural) are made up of the [M(1-MeIm)6]2+ cation, two hydrogen phthalate anions (HPht−) and two H2O solvate molecules. The coordination around each metal(II) atom is octahedral with six nitrogen atoms of 1-MeIm. Extended hydrogen bonding networks embracing the solvate water molecules and a phthalate residue as well as the weak C–H⋯O interactions stabilize the three-dimensional structures. Magnetic studies clearly show that the magnetic ions do not interact with each other. Furthermore, in compound 4 we have another example of a highly anisotropic Co2+ ion with a rhombic g-tensor and large zero-field-splitting. The complexes were also characterized by IR and 1H NMR spectroscopy, thermogravimetric analysis, and all data are discussed in the terms of known structures.

Physical properties and neutron texture measuerments of deep-sea carbonates of DSDP Holes 62-463 and 62-465A

In weakly indurated, nannofossil-rich, deep-sea carbonates compressional wave velocity is up to twice as fast parallel to bedding than normal to it. It has been suggested that this anisotropy is due to alignment of calcite c-axes perpendicular to the shields of coccoliths and shield deposition parallel to bedding. This hypothesis was tested by measuring the preferred orientation (fabric) of calcite c-axes in acoustic anisotropic, calcareous DSDP sediment samples by X-ray goniometry, and it was found that the maximum c-axis concentrations are by far too low to explain the anisotropies. The X-ray method is subject to a number of uncertainties due to preparatory and technical shortcomings in weakly indurated rocks. The most serious weaknesses are: sample preparation, volume of measured sample (fraction of a mm3), beam defocusing and background intensity corrections, combination of incomplete pole figures, and necessity of recalculation of the c-axis orientations from other crystallographic directions. Goniometry using thermal neutrons overcomes most of these difficulties, but it is time consuming. We test the interferences made about velocity anisotropy by X-ray studies about the concentration of c-axes in deep-sea carbonates by employing neutron texture goniometry to eight DSDP samples comprising mostly nannofossil material. Fabric and sonic velocity were determined directly on the core specimens, thus from the same rock volume and requiring no preparation. The c-axis orientation is obtained directly from the [0006] calcite diffraction peak without corrections. The fabrics are clearly defined, but weak (1.1 to 1.86 times uniform) with the maximum about normal to bedding. They have crudely orthorhombic symmetry, but are not axisymmetric around the bedding normal. The observed c-axis intensities, although higher than determined by the X-ray method on other samples, are by far too low to explain the observed acoustic anisotropies.

Anelastic strain recovery and elastic properties of ODP Leg 123 oceanic basalt samples

A knowledge of rock stress is fundamental for improving our understanding of oceanic crustal mechanisms and lithospheric dynamic processes. However, direct measurements of stress in the deep oceans, and in particular stress magnitudes, have proved to be technically difficult. Anelastic strain recovery measurements were conducted on 15 basalt core samples from Sites 765 and 766 during Leg 123. Three sets of experiments were performed: anelastic strain recovery monitoring, dynamic elastic property measurements, and thermal azimuthal anisotropy observations. In addition, a range of other tests and observations were recorded to characterize each of the samples. One common feature of the experimental results and observations is that apparently no consistent orientation trend exists, either between the different measurements on each core sample or between the same sets of measurements on the various core samples. However, some evidence of correspondence between velocity anisotropy and anelastic strain recovery exists, but this is not consistent for all the core samples investigated. Thermal azimuthal anisotropy observations, although showing no conclusive correlations with the other results, were of significant interest in that they clearly exhibited anisotropic behavior. The apparent reproducibility of this behavior may point toward the possibility of rocks that retain a "memory" of their stress history, which could be exploited to derive stress orientations from archived core. Anelastic strain recovery is a relatively new technique. Because use of the method has extended to a wider range of rock types, the literature has begun to include examples of rocks that contracted with time. Strong circumstantial evidence exists to suggest that core-sample contractions result from the slow diffusion of pore fluids from a preexisting microcrack structure that permits the rock to deflate at a greater rate than the expansion caused by anelastic strain recovery. Both expansions and contractions of the Leg 123 cores were observed. The basalt cores have clearly been intersected by an abundance of preexisting fractures, some of which pass right through the samples, but many are intercepted or terminate within the rock matrix. Thus, the behavior of the core samples will be influenced not only by the properties of the rock matrix between the fractures, but also by how these macro- and micro-scale fractures mutually interact. The strain-recovery curves recorded during Leg 123 for each of the 15 basalt core samples may reflect the result of two competing time dependent processes: anelastic strain recovery and pore pressure recovery. Were these the only two processes to influence the gauge responses, then one might expect that given the additional information required, established theoretical models might be used to determine consistent stress orientations and reliable stress magnitudes. However, superimposed upon these competing processes is their respective interaction with the preexisting fractures that intersect each core. Evidence from our experiments and observations suggests that these fractures have a dominating influence on the characteristics of the recovery curves and that their effects are complex.

Seismic velocities and elastic properties of gabbroic rocks from ODP Hole 118-735B

The nearly continuous recovery of 0.5 km of generally fresh, layer 3 gabbroic rocks at Hole 735B, especially near the bottom of the section, presents scientists an unusual opportunity to study the detailed elastic properties of the lower oceanic crust. Extending compressional-wave and density shipboard measurements at room pressure, Vp and Vs were measured at pressures from 20 to 200 MPa using the pulse transmission method. All of the rocks exhibit significant increases in velocity with increasing pressure up to about 150 MPa, a feature attributed to the closing of microcrack porosity. Measured velocities reflect the mineralogical makeup and microstructures acquired during the tectonic history of Hole 735B. Most of the undeformed and unaltered gabbros are approximately 65:35 plagioclase/clinopyroxene rocks plus olivine or oxide minerals, and the observed densities and velocities are fully consistent with the Voigt-Reuss-Hill (VRH) averages of the component minerals and their proportions. Depending on their olivine content, the predominant olivine gabbros at 200 MPa have average Vp = 7.1 ± 0.2 km/s, Vs = 3.9 ± 0.1 km/s, and grain densities of 2.95 ± 0.5 g/cm3. The less abundant iron-titanium (Fe-Ti) oxide gabbros average Vp = 6.75 ± 0.15 km/s, Vs = 3.70 ± 0.1 km/s, and grain densities of 3.22 ± 0.05 g/cm3, reflecting the higher densities and lower velocities of oxide minerals compared to olivine. About 30% of the core is plastically deformed, and the densities and directionally averaged velocities of these shear-zone tectonites are generally consistent with those of the gabbros, their protoliths. Three sets of observations indicate that the shear-zone metagabbros are elastically anisotropic: (1) directional variations in Vp, both vertical and horizontal and with respect to foliation and lineation; (2) discrepancies among Vp values for the horizontal cores and the VRH averages of the component minerals and their mineral proportions, suggesting preferred crystallographic orientations of anisotropic minerals; and (3) variations of Vs of up to 7%, with polarization directions parallel and perpendicular to foliation. Optical inspection of thin sections of the same samples indicates that plagioclase feldspar, clinopyroxene, and amphibole typically display crystallographic-preferred orientations, and this, plus the elastic anisotropy of these minerals, suggests that preferred orientations are responsible for much of the observed anisotropy, particularly at high pressure. Alteration tends to be localized to brittle faults and brecciated zones, and typical alteration minerals are amphibole and secondary plagioclase, which do not significantly change the velocity-density relationships.

Structure of intermediate shocks in collisionsless anisotropic Hall-magnetohydrodynamics plasma models

The existence of discontinuities within the double-adiabatic Hall-magnetohydrodynamics (MHD) model is discussed. These solutions are transitional layers where some of the plasma properties change from one equilibrium state to another. Under the assumption of traveling wave solutions with velocity C and propagation angle θ with respect to the ambient magnetic field, the Hall-MHD model reduces to a dynamical system and the waves are heteroclinic orbits joining two different fixed points. The analysis of the fixed points rules out the existence of rotational discontinuities. Simple considerations about the Hamiltonian nature of the system show that, unlike dissipative models, the intermediate shock waves are organized in branches in parameter space, i.e., they occur if a given relationship between θ and C is satisfied. Electron-polarized (ion-polarized) shock waves exhibit, in addition to a reversal of the magnetic field component tangential to the shock front, a maximum (minimum) of the magnetic field amplitude. The jumps of the magnetic field and the relative specific volume between the downstream and the upstream states as a function of the plasma properties are presented. The organization in parameter space of localized structures including in the model the influence of finite Larmor radius is discussed

Anisotropic magnetoresistance in single electron transport

We study the effect of magnetic anisotropy in a single electron transistor with ferromagnetic electrodes and a non-magnetic island. We identify the variation δμ of the chemical potential of the electrodes as a function of the magnetization orientation as a key quantity that permits to tune the electrical properties of the device. Different effects occur depending on the relative size of δμ and the charging energy. We provide preliminary quantitative estimates of δμ using a very simple toy model for the electrodes.

Magnetic properties of ODP Site 191-1179 sediments

As reported by Shipboard Scientific Party (2001b, doi:10.2973/odp.proc.ir.191.104.2001) in the Site 1179 chapter of the Initial Reports volume, Leg 191 Site 1179 is located on abyssal seafloor northwest of Shatsky Rise, ~1650 km east of Japan. This part of the Pacific plate was formed during the Early Cretaceous, as shown by northeast-trending M-series magnetic lineations that become younger toward the northwest (Larson and Chase, 1972, doi:10.1130/0016-7606(1972)83[3627:LMEOTW]2.0.CO;2; Sager et al., 1988, doi:10.1029/JB093iB10p11753; Nakanishi et al., 1989, doi:10.1029/1999JB900002). The site is situated on magnetic Anomaly M8 (Nakanishi et al., 1999, doi:10.1029/1999JB900002), corresponding to an age of ~129 Ma and the Hauterivian stage of the Early Cretaceous (Gradstein et al., 1994, doi:10.1029/94JB01889; 1995). The sediments recovered at Site 1179 are split into four lithostratigraphic units based on composition and color (Shipboard Scientific Party, 2001b, doi:10.2973/odp.proc.ir.191.104.2001). Unit I (0-221.52 meters below seafloor [mbsf]) is a dominantly olive-gray clay- and radiolarian-bearing diatom ooze. Unit II (221.52-246.0 mbsf) is a yellowish brown to light brown clay-rich and diatom-bearing radiolarian ooze. Unit III (246.0-283.53 mbsf) is composed of brown pelagic clay. Unit IV (283.53-377.15 mbsf) is composed of chert and some porcellanite; any softer sediments present were washed out of the core barrel by the fluid circulating during the coring process.

Dynamical properties of a strongly correlated model for quarter-filled layered organic molecular crystals

The dynamical properties of an extended Hubbard model, which is relevant to quarter-filled layered organic molecular crystals, are analyzed. We have computed the dynamical charge correlation function, spectral density, and optical conductivity using Lanczos diagonalization and large-N techniques. As the ratio of the nearest-neighbor Coulomb repulsion, V, to the hopping integral, t, increases there is a transition from a metallic phase to a charge-ordered phase. Dynamical properties close to the ordering transition are found to differ from the ones expected in a conventional metal. Large-N calculations display an enhancement of spectral weight at low frequencies as the system is driven closer to the charge-ordering transition in agreement with Lanczos calculations. As V is increased the charge correlation function displays a collective mode which, for wave vectors close to (pi,pi), increases in amplitude and softens as the charge-ordering transition is approached. We propose that inelastic x-ray scattering be used to detect this mode. Large-N calculations predict superconductivity with d(xy) symmetry close to the ordering transition. We find that this is consistent with Lanczos diagonalization calculations, on lattices of 20 sites, which find that the binding energy of two holes becomes negative close to the charge-ordering transition.

Anisotropic scattering and anomalous normal-state transport in a high-temperature superconductor

The metallic state of high-temperature copper-oxide superconductors, characterized by unusual and distinct temperature dependences in the transport properties(1-4), is markedly different from that of textbook metals. Despite intense theoretical efforts(5-11), our limited understanding is impaired by our inability to determine experimentally the temperature and momentum dependence of the transport scattering rate. Here, we use a powerful magnetotransport probe to show that the resistivity and the Hall coefficient in highly doped Tl2Ba2CuO6+delta originate from two distinct inelastic scattering channels. One channel is due to conventional electron electron scattering; the other is highly anisotropic, has the same symmetry as the superconducting gap and a magnitude that grows approximately linearly with temperature. The observed form and anisotropy place tight constraints on theories of the metallic state. Moreover, in heavily doped non-superconducting La2-xSrxCuO4, this anisotropic scattering term is absent(12), suggesting an intimate connection between the origin of this scattering and superconductivity itself.

Three-dimensional finite element analysis of the effects of anisotropy on bone mechanical properties measured by nanoindentation

A three-dimensional finite element analysis (FEA) model with elastic-plastic anisotropy was built to investigate the effects of anisotropy on nanoindentation measurements for cortical bone. The FEA model has demonstrated a capability to capture the cortical bone material response under the indentation process. By comparison with the contact area obtained from monitoring the contact profile in FEA simulations, the Oliver-Pharr method was found to underpredict or overpredict the contact area due to the effects of anisotropy. The amount of error (less than 10% for cortical bone) depended on the indentation orientation. The indentation modulus results obtained from FEA simulations at different surface orientations showed a trend similar to experimental results and were also similar to moduli calculated from a mathematical model. The Oliver-Pharr method has been shown to be useful for providing first-order approximations in the analysis of anisotropic mechanical properties of cortical bone, although the indentation modulus is influenced by anisotropy.

Anisotropic surface energetics and wettability of macroscopic form I paracetamol crystals

Advancing (θA) and receding (θR) contact angles were measured with several probe liquids on the external facets (201), (001), (011), and (110) of macroscopic form I paracetamol crystals as well as the cleaved (internal) facet (010). For the external crystal facets, dispersive surface energies γd calculated from the contact angles were found to be similar (34 ± 1 mJ/m2), while the polar components varied significantly. Cleaving the crystals exposed a more apolar (010) surface with very different surface properties, including γd = 45 ± 1 mJ/m2. The relative surface polarity (γp/γ) of the facets in decreasing order was (001) > (011) > (201) > (110) > (010), which agreed with the fraction of exposed polar hydroxyl groups as determined from C and O 1s X-ray photoelectron spectroscopy (XPS) spectra, and could be correlated with the number of non-hydrogen-bonded hydroxyl groups per unit area present for each crystal facet, based on the known crystal structures. In conclusion, all facets of form I paracetamol crystals examined exhibited anisotropic wetting behavior and surface energetics that correlated to the presence of surface hydroxyl groups.  © 2006 American Chemical Society.