Crystal network microstructures

As shown in Section 2.4.6, natural hydroxy/carbonate apatite in human bones and teeth structures exhibits a needleshaped habit. It has been a longstanding objective in the development of biomaterials to reproduce these 

Another significant difference between needlelike apatite in glass-ceramics and other apatites is found in the fluoride content. The crystal structure of fluoroapatite compared with other apatites is shown in Section 1.3.2. The crystal structure of fluoroapatite is shown in Appendix Fig. 19. 

Ways in which the findings related to the formation of needlelike apatite have been used in the development of restorative dental biomaterials are presented on the basis of two materials, IPS Empress 2, IPS ERis for E2, and IPS d.SIGN , in Section 4.4.2. 

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Adam-Berret M, Boulard M, Riaublanc A, Mariette F. Evolution of fat crystal network microstructure followed by NMR. J Agric Food Chem. 59(5) (2011) 1767-1773. 

Based on this description of a fat crystal network, it makes sense that its macroscopic properties should depend significantly on the nature of the microstructures since this level of structure is closest to the macroscopic world. 

The fractal dimension of a crystal network is an important parameter in terms of its relation to mechanical strength. However, the values of the pre-exponential term, A, (and the solid fat content) are equally important. For spherical microstructures (Narine and Marangoni, 1999c Marangoni, 2000 Marangoni and Rogers, 2003),... 

The fractal dimension of the fat crystal network in milk fat decreased from 2.5 to 2.0 when the cooling rate was increased. Concomitantly, the particle-related constant, A, increases. These results demonstrate how a faster cooling rate leads to a less ordered spatial distribution of mass within the microstructural network, which would result in a lower value of D, and a decrease in the average particle diameter, which would result in a higher value of A, as predicted by our model. These microstructural changes were correlated with a much higher yield force value for the rapidly cooled milk fat (64.1 3.3N versus 33.0 3.9N for the samples cooled at 5.0°C/min and 0.1°C/min, respectively). 

There are several techniques used to image the microstructure of fat crystal networks. (See Chapter 11 on Imaging. ) The most commonly used imaging method is polarized light microscopy (PLM) since fat crystals are birefringent and appear white, while the liquid oil is not and thus appears black. 

Large deformation tests for fat samples are correlated to sensory tests (Rousseau and Marangoni 1998). It is, however, difficult to relate the large deformation experiments to fundamental characteristics of the microstructure of the fat crystal network due to the fact that the networks are destroyed during testing. 

The structure within the microstructure is fractal in nature therefore the diameter of the micro structure (or aggregates) is related to the particle volume fraction of the fat crystal networks Ot as ... 

Table 17.7 summarizes the effects of the microstructural factors on the microscopy fractal dimensions, Dj, y, and Zlpr- Different fractal dimensions reflect different aspects of the microstructure of the fat crystal networks and thus have different meanings. It is necessary to define which structural characteristic is most closely related to the macroscopic physical property of interest (mechanical strength, permeability, diffusion) and then use the fractal dimension that is most closely related to the particular structural characteristic in the modeling of that physical property. 

To obtain the fractal dimension of a network of particles, acquiring images of the microstructure is necessary. Many forms of microscopy can be used, including brightfield microscopy, confocal laser scanning microscopy, scanning electron microscopy, and in the case of fat crystal networks, polarized light microscopy. 

Assuming a statistically constant microstructural element (or particle) size, the relationship between radius and mass (Equation 2) can be used to determine the fractality of crystal networks from two-dimensional PLM images (54). 

In conclusion, exact relationships between the Young s modulus and the microstructure of particulate aggregate networks have been obtained. The elastic properties of such materials are a function of the total amount of solid material present, the properties of the particles which make up the solid, and the spatial distribution of solid particles within the network. This model can be utilized to better understand and modify the macroscopic rheological properties of soft materials and fat crystal networks in particular. 

Figure 3-21 SEM image after etching (2.5% HF, 10 sec) showing high content of iithium disilicate crystals of 70 vol% crystallinity in a network microstructure.

The microstructural level of the fat crystal network may be defined as those structures in the length range between 1 and 120 pm. At the lower range of the micro-structural level, one may encounter crystallites, whereas at the upper ranges, one... 

Now that all levels of the structural hierarchy within a fat crystal network are quantifiable (to various extents), as well as the amounts of solid fat within the network (by use mainly of pulsed nuclear magnetic resonance), it is important to relate these quantifiable parameters to rheological indicators such as the shear elastic modulus. One model to relate the microstructure to the shear elastic modulus was developed in colloidal physics by Shih et al. [57]. A brief chronology of the adaptation of this theory to the study of fat networks follows. 

It was shown experimentally by Vreeker et al. [56] and by Rousseau and coworkers [38,58-64,76] that the elastic properties of fat crystal networks at low and high solid fat contents, respectively, are highly dependent on the fractal nature of the microstructure. For the shear elastic modulus G ... 

As described in a recently published article in Physical Review E [2], we constructed a mechanical and structural model of fat crystal networks. In this model, the microstructural elements were assumed to be spherical, and the forces between the microstructures were attributed to the forces of interaction between neighboring microstructural elements at the interface between two microstruc-... 

In conclusions, we must reiterate that fat crystal networks demonstrate distinct structural hierarchies. A consideration of the microstructural level and constrac-tion of models based on elastic rheological measurements implicate all levels of structure in the determination of the macroscopic elastic moduli. Consideration of the fractal arrangement of the microstructural elements is integral to the construction of models that fit well with experimental data. Furthermore, it is seen that the fractal dimension and other network characteristics such as microstructural element size and microstructural size are indicators of macroscopic hardness, and that these factors can be manipulated by processing conditions to achieve tailored elastic characteristics of fat crystal networks. 

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