Quantitative textural analysis of packings of elongate crystals

Rudge, John F.; Holness, Marian B.; Smith, Graham C.

doi:10.1007/s00410-008-0293-1

Cited by 27 publications

(30 citation statements)

References 55 publications

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“…If we compare these results with the modeling example presented by Rudge et al (2008), in their Figure 4, page 42, we find some striking similarities despite that there are two differences. In Rudge et al (2008), spherocylinders are used instead of ellipsoids, and instead of performing random 2D cuts on one spherocylinder, a random close packing of cylinders is used, and then a single 2D cut is performed.…”

Section: Examples Of 3d To 2d Transformation Of Aspect Ratiossupporting

confidence: 61%

“…In Rudge et al (2008), spherocylinders are used instead of ellipsoids, and instead of performing random 2D cuts on one spherocylinder, a random close packing of cylinders is used, and then a single 2D cut is performed. Despite this, we see that as the aspect ratio is increasing, the Figure 1.…”

Section: Examples Of 3d To 2d Transformation Of Aspect Ratiosmentioning

confidence: 99%

“…However, for real samples, they state that it might be more challenging to achieve similar results. Rudge et al (2008) present a quantitative study of elongated crystals. They use spherocylinders (if you split a sphere in two identical parts and glue a cylinder of an arbitrary length and with the same radius as the sphere, you have a spherocylinder).…”

Section: Introductionmentioning

confidence: 99%

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Aspect ratio histograms of 3D ellipsoids and 2D ellipses — Analytical relations and numerical examples

Landrø

2015

GEOPHYSICS

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A typical way of characterizing rocks, composite materials, or human tissue is to extract aspect ratio histograms. A common assumption for this type of analysis is that the sample is composed of several grains or building elements that have a similar shape. Among various shapes, the ellipsoid is very common. In practice, such detailed analysis is performed on 2D cuts or slices through the material. It is intuitive that there is a difference between a 2D aspect ratio histogram and the corresponding 3D histogram. I have derived simple equations that can be used to transform from 3D to 2D and also from 2D to 3D, assuming that the two shortest axes in the ellipsoid were equal. For the general case, when all axes were different, an approximate equation was derived. All equations were compared with stochastic numerical simulations of cutting a 3D ellipsoid by an arbitrary random number of planes. It was determined that in the general case, the shortest aspect ratio would dominate the 2D histograms and that it was practically impossible to detect the highest aspect ratio from 2D planar cuts.

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Section: Examples Of 3d To 2d Transformation Of Aspect Ratiossupporting

confidence: 61%

Section: Examples Of 3d To 2d Transformation Of Aspect Ratiosmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Aspect ratio histograms of 3D ellipsoids and 2D ellipses — Analytical relations and numerical examples

Landrø

2015

GEOPHYSICS

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“…The random rod packing is a valuable reference for packed granular matter composed of elongated particles as can be found in fiber-reinforced and other fibrous materials [1][2][3][4], and anisotropic powders [5,6]. This reference packing is a stacking of randomly oriented, rigid rods with a maximum particle volume-fraction uniquely determined by the rod aspect ratio [5].…”

Section: Introductionmentioning

confidence: 99%

On contact numbers in random rod packings

2009

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Random packings of non-spherical granular particles are simulated by combining mechanical contraction and molecular dynamics, to determine contact numbers as a function of density. Particle shapes are varied from spheres to thin rods. The observed contact numbers (and packing densities) agree well with experiments on granular packings. Contact numbers are also compared to caging numbers calculated for sphero-cylinders with arbitrary aspect-ratio. The caging number for rods arrested by uncorrelated point contacts asymptotes towards γ = 9 at high aspect ratio, strikingly close to the experimental contact number C ≈ 9.8 for thin rods. These and other findings confirm that thin-rod packings are dominated by local arrest in the form of truly random neighbor cages. The ideal packing law derived for random rod-rod contacts, supplemented with a calculation for the average contact number, explains both absolute value and aspect-ratio dependence of the packing density of randomly oriented thin rods.

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“…), ceramic bulk powders, catalyst pellets, and reinforcing fibers in industry. [1][2][3][4][5][6] On the sub-micron length scale anisometric colloids such as rods and platelets form dense random packings and glasses, 4,[7][8][9][10][11][12][13] while protein filaments may randomly pack in animal cells.…”

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confidence: 99%

Isochoric ideality in jammed random packings of non-spherical granular matter

et al. 2011

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Randomly packed particles in granular matter, ubiquitous in nature and industry, usually defy simple predictions for the optimal amorphous packing density because jammed granules are strongly correlated. While mixing different granular shapes seems to be a further complication, we discovered in simulations that binary rodsphere mixtures harbor a surprisingly simple dependence of packing volume fraction on mixture composition. This isochoric ideality covers the entire composition range and is experimentally validated by mixtures of sphero-cylindrical TicTac sweets and spherical beads: their joint random packing volume is indeed independent of the segregation state. Isochoric ideality occurs in a rod-shape range that includes the unique aspect ratio, which universally maximizes rod-sphere packing densities and suggests a novel amorphous analog of a plastic crystal, namely rod-sphere mixtures with completely uncorrelated particle orientations.The puzzle of dense amorphous particle packings has caught the close attention of mathematicians and scientists from many different disciplines. In particular, non-spherical particles and their mixtures, jammed into random packings, are abundant and occur on widely different length scales. Macroscopic instances of anisotropic granular matter, among many others, are the grains in solidifying igneous rocks, various grains in food (rice, pasta's, TicTac sweets, etc.), ceramic bulk powders, catalyst pellets, and reinforcing fibers in industry.1-6 On the sub-micron length scale anisometric colloids such as rods and platelets form dense random packings and glasses, 4,7-13 while protein filaments may randomly pack in animal cells.14 Essential questions are how tight one can pack particles in jammed amorphous packings and how to optimize the corresponding random close packing (RCP) density. In quest of the optimal or densest random packing, particle non-sphericity has proven to be an effective means to maximize the RCP density. Recent studies on random packing of sphero-cylinders 15 and ellipsoids 16,17 revealed an intriguing non-monotonic dependence of the RCP density on the particle elongation. Starting from the Bernal random sphere packing, the RCP density first raises to a maximum for nearly spherical particles and only beyond this maximum the random packing density monotonically decreases with particle aspect ratio. So far, this peculiar maximum has only been observed for monodisperse granules 15-17 and colloids. 9 As polydispersity in size and shape is often unavoidable, one important question is how to optimize packing densities of granular mixtures, which ideally could be predicted from densities of the monodisperse components. It is therefore of fundamental and practical interest to investigate for such mixtures the existence of a density maximum and the universality, if any, in its location or magnitude.We uncover the universality in jamming of rather short spherocylinders of length L (including two hemi-spherical caps at both ends) and diameter D by investigating the RCP of...

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Quantitative textural analysis of packings of elongate crystals

Cited by 27 publications

References 55 publications

Aspect ratio histograms of 3D ellipsoids and 2D ellipses — Analytical relations and numerical examples

Aspect ratio histograms of 3D ellipsoids and 2D ellipses — Analytical relations and numerical examples

On contact numbers in random rod packings

Isochoric ideality in jammed random packings of non-spherical granular matter

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