On the anisotropic elastic properties of hydroxyapatite

Katz, J. Lawrence; Ukraincik, K.

doi:10.1016/0021-9290(71)90007-8

Cited by 230 publications

(114 citation statements)

References 12 publications

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“…The bottom of the conduction band mainly consists of Ca s-states and shows free electron like behavior with the anisotropic mass at the Γ point. Our results for the vibrational eigenmodes at the Γ point are within ±10% of available experiment [41,42], and calculated elastic constants agree well with the experimental results reported by Katz [52] and Mostafa [53].…”

Section: Discussionsupporting

confidence: 90%

“…Our results are summarized in table 3. For C 11 , C 33 and the bulk modulus B we find agreement within ~6% of the values previously reported by Katz and Mostafa [52,53]. Our C 12 , C 13 and C 44 are within ~21% of Katz's and Mostafa's results indicating overall good qualitative agreement.…”

Section: E Elastic Constants Of Hasupporting

confidence: 89%

“…Although, the quality of the results fluctuates depending on the material in question, upper and lower bounds of the effective moduli of composites can be found rigorously [51]. Previously, Katz and Ukraincik [52] calculated a set of pseudo-single crystal elastic constants extracted from the measured elastic constants of fluorapatite. The validity of such a calculation is somewhat justified by a strong similarity of the crystal structures of these two materials.…”

Section: E Elastic Constants Of Hamentioning

confidence: 99%

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First-principles study of the biomineral hydroxyapatite

2011

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The biomineral hydroxyapatite Ca 10 (PO 4 ) 6 (OH) 2 is the main mineral constituent of mammal bone. Hydroxyapatite crystallizes in the hexagonal and monoclinic phases, the main difference between them being the orientation of the hydroxyl groups. Using density functional theory we study the energetics of the hexagonal and monoclinic phases along with the several hypothetical crystal structures of hydroxyapatite. The monoclinic phase has the lowest energy, with the hexagonal phase being only 22meV/cell higher in energy. We identify a structural transition path from the hexagonal to monoclinic phase with the activation energy of 0.66 eV per hexagonal cell. At room temperature the transition occurs on a millisecond time scale. The electronic structures of the monoclinic and hexagonal phases are compared. For the hexagonal phase we calculate the phonon frequencies at the Γ-point and elastic constants. Both are in good agreement with available experiment.

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Section: Discussionsupporting

confidence: 90%

Section: E Elastic Constants Of Hasupporting

confidence: 89%

Section: E Elastic Constants Of Hamentioning

confidence: 99%

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First-principles study of the biomineral hydroxyapatite

2011

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“…In more detail, we employ the four-step elastic homogenization scheme reported in [Fritsch and Hellmich, 2007;Fritsch et al, 2009a], see Figure 7, based on the tissue-independent 'universal' elastic properties of the elementary building blocks of extracellular bone material, namely hydroxyapatite, collagen, and water with some insignificant amount of non-collagenous organics. These properties, given in [Hellmich et al, 2004;Fritsch and Hellmich, 2007], are accessible through ultrasonic techniques [Katz and Ukraincik, 1971;Cusack and Miller, 1979] or ab initio simultations [Ching et al, 2009]. The aformentioned multilevel homogenization scheme relates the stiffness of material phases (i.e.…”

Section: 'Universal' Relations Between Extracellular Mass Density Andmentioning

confidence: 99%

“…The mass density-elasticity relationship of Figure 9 can be suitably approximated through higher order polynomials with mean relative errors below 0.25% (with respect to the micromechanical estimates). In a dimensionless form based on the normal elastic stiffness and the mass density of hydroxyapatite, C HA 1111 = 137 GPa [Katz and Ukraincik, 1971] and ρ HA = 3 g/cm 3 [Lees, 1987], such polynomials read as…”

mentioning

confidence: 99%

Bone fibrillogenesis and mineralization: Quantitative analysis and implications for tissue elasticity

Vuong

Hellmich

2011

Journal of Theoretical Biology

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Data from bone drying, demineralization, and deorganification tests, collected over a time span of more than eighty years, evidence a myriad of different chemical compositions of different bone materials. However, careful analysis of the data, as to extract the chemical concentrations of hydroxyapatite, of water, and of organic material (mainly collagen) in the extracellular bone matrix, reveals an astonishing fact: it appears that there exists a unique bilinear relationship between organic concentration and mineral concentration, across different species, organs, and age groups, from early childhood to OLD AGE: During organ growth, the mineral concentration increases linearly with the organic concentration (which increases during fibrillogenesis), while from adulthood on, further increase of the mineral concentration is accompanied by a decrease in organic concentration. These relationships imply unique mass density-concentration laws for fibrillogenesis and mineralization, which -in combination with micromechanical models -deliver 'universal' mass density-elasticity relationships in extracellular bone matrix -valid across different species, organs, and ages. They turn out as quantitative reflections of the well-instrumented interplay of osteoblasts, osteoclasts, osteocytes, and their precursors, controlling, in a fine-tuned fashion, the chemical genesis and continuous transformation of the extracellular bone matrix. Considerations of the aformentioned rules may strongly affect the potential success of tissue engineering strategies, in particular when translating, via micromechanics, the aformentioned growth and mineralization characteristics into tissue-specific elastic properties.

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Bone and Teeth, Properties of

Lakes

Katz

2006

Encyclopedia of Medical Devices and Instrumentation

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Bone has a variety of functions in the body of which some of the most important are structural in nature: protection of vulnerable body parts, support of the body, and to provide muscle attachments. A knowledge of the mechanical and adaptive properties of bone is useful in the design and use of prostheses that replace a bone or a portion of a bone. Mechanical properties of bone are also of interest in trauma biomechanics and in efforts to prevent injury to the body. As for teeth, they also are replaced by artificial materials which are called upon to perform the mechanical functions of the original tooth. This article contains a survey of known properties of bone and teeth and their components collagen and apatite, with an emphasis on bone and its mechanical properties.

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On the anisotropic elastic properties of hydroxyapatite

Cited by 230 publications

References 12 publications

First-principles study of the biomineral hydroxyapatite

First-principles study of the biomineral hydroxyapatite

Bone fibrillogenesis and mineralization: Quantitative analysis and implications for tissue elasticity

Bone and Teeth, Properties of

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