So I came across a study about bone biomaterial and it started talking about lattice structure and such and I figured it was good information to share, regardless of some of you already knowing what’s what 
5.3 Molecular and microstructural properties
The microstructure of a material contributes a great deal to its overall properties. Atomic structure and chemical composition play a key role in determining the mechanical properties and the way in which the body interacts with the material. Pore size, grain characteristics (in the case of crystalline materials) and phase distribution also affect material properties. in the case of amorphous or semi-crystalline polymers, small changes in attributes like molecular weight, thermal transition temperatures and cross-linking can have a profound effect on the behaviour of a material.
5.3.1 Atomic structure
Atoms and molecules in a material can be oriented and packed in different ways. in the case of glasses and some types of polymers, the orientation is random and is referred to as amorphous. Metals and ceramics, on the other hand, are crystalline. this means that their atoms are linked together in an ordered, repeating fashion. Other polymers have some regions of order and are thus semi-crystalline. the crystal structure is made up of the repeating pattern of atoms overlaid on a lattice of repeating points in three dimensions. A unit cell can then be thought of as a box containing a significant enough portion of the crystal structure to describe the bulk arrangement of atoms. it may be one of several shapes, including cubic, tetragonal or hexagonal. the arrangement of atoms within the unit cell results in crystal structures such as face-centred cubic (named for atoms located at the centre of each cube face and the cube corners), body-centred cubic (atoms located on the cube corners and one at the centre) and hexagonal close packed. the packing efficiency of a structure depends on the amount of space taken up by atoms in the unit cell relative to empty space.
For more detailed information on crystal structures, see Cullity and Stock (2001). (I’m gunna look for this)
A crystalline material may consist of a single crystal or, more often, it may be polycrystalline, consisting of many crystals or grains. the orientation of the grains is typically random, although they can also have a preferred orientation. Amorphous and polycrystalline materials are normally isotropic, meaning their properties are the same in every direction. Anisotropy occurs in single crystals which have directionally dependent chemical bond strengths (in the case of polycrystalline materials, the crystals’ random orientation evens out this effect) and in some composites, such as those reinforced with long, oriented fibres (see Section 5.5.4). As a composite material of long collagen fibrils intermixed with hydroxyapatite-like crystals, bone is anisotropic. In this case, mechanical properties will be better along the longitudinal fibre axis. Processing conditions can also create anisotropy in a material by orienting crystals. Polymers, for example, when drawn or extended in one direction, can have higher strength and stiffness in the drawing direction.
Despite what might seem like a perfect, infinitely repeating structure, all polycrystalline materials contain defects on several possible dimensional levels. On the 0-D level, crystal structures may contain vacancies, where an atom is missing, or interstitials, where smaller atoms force themselves in an empty space between larger atoms. On the 1-D level, an interruption in the normal alignment of atomic planes results in a dislocation. the 2-D level encompasses grain boundaries, where a mismatch occurs as two crystals meet. And finally, pores are an example of a 3-D defect.
Strengthening mechanisms
Manipulation of microstructural characteristics can alter the mechanical properties of materials. the effect of pores and grains will be discussed in following sections. Additionally, some materials can be strengthened by other mechanisms. Work hardening or cold working is a room-temperature process in which a metal is rolled or drawn. this produces more dislocations in the metal’s crystal lattice, which, when they meet, form immovable jogs which stop dislocation motion. Solution hardening involves the addition of impurities or alloying to make it more difficult for dislocations to propagate. the different sized atoms of impurities or another metal in an alloy distort the original lattice, making dislocation motion more difficult. Semi-crystalline polymers can be strengthened by drawing or pulling a specimen uniaxially. this aligns the molecular chains in the structure, making the polymer stronger in the drawing direction.
Density
the term density can apply to a material on several levels. At the most basic level, density is related to the atomic weight of chemical elements in a structure and their tightness of packing. Skeletal density (also known as theoretical or true density), which can be measured by pycnometry, also includes second phases (an alloying phase or another phase of a composite) and crystallographic defects in its calculation. Pycnometry uses small gas molecules, such as he, to compare the volume of a reference container with one filled with a sample in order to give a value for skeletal density. Bulk density uses a volume calculated from the outer dimensions of a sample divided by its mass, thus accounting for micro- and macropores and giving a lower value of density than for skeletal density if any pores are present. For non-porous materials with complex geometries, their volume can be measured by the amount of liquid they displace, provided the material is not soluble in that liquid (Archimedes’ principle). Relative density is then the percentage ratio of bulk to true density. Ceramics, for instance, are considered ‘dense’ if their relative density is at least 95%.
5.3.2 Phase composition
the chemical and crystallographic identities of the phases present in a material, along with their relative amounts, distribution and orientation, determine the material’s intrinsic properties. therefore it is very important to be able to identify these phases precisely. Phases may be distinguished in a number of different ways. if crystalline, the structure will have unique lattice parameters and an arrangement of atoms identifiable by X-ray diffraction (XRD). In the case of polycrystalline materials, Rietveld analysis applied to XRD data can determine the relative amounts of phases present in a specimen (Will, 2006). Infrared (IR) spectroscopy can identify the chemical bonds present in a material, their relative quantity, and any changes in the character or quantity of the bonds over time (Stuart, 2004). This technique is particularly useful for polymers, which are not crystalline.
the locations of different phases in a material can sometimes be determined by microscopy. Grains in metals can usually be seen in light microscopy and different phases in an alloy will reflect light differently. Scanning electron microscopy (SeM) is also useful, although sometimes phases might appear similar. In this case, an attached X-ray beam can be used for energy dispersive spectroscopy (EDS) to pinpoint an elemental analysis of a specific location in the specimen. this method is not as sensitive for determining elemental ratios as some other methods, however. When knowing the exact composition of a material is very important, such as in the case of calcium phosphates which have different dissolution behaviour depending on their Ca/P ratio, more sensitive methods like X-ray fluorescence (XRF) spectrometry are a better choice (Buhrke et al., 1997).
5.3.3 Porosity
the porosity of a material contributes greatly to both its mechanical properties and the way in which it behaves in vivo. Pores in a material act as stress concentrators, decreasing mechanical properties, while increased surface area provides a greater means of environmental interaction. in some cases a material is made intentionally porous, namely in the case of scaffolds in which interconnected macropores of 100–400 μm in diameter are placed in the material to allow bone ingrowth (Fig. 5.4a). the increased surface area may then allow the degradable scaffold slowly to dissolve away as bone replaces it. Owing to inhibited mechanical properties, however, these scaffolds can only be used in non-major load-bearing situations.
Much smaller pores will also be detrimental to mechanical properties. A material may have microporosity as a result of incomplete densification during sintering of a ceramic powder (Fig. 5.4b) or defects remaining after casting a metal, for example. in this case, the micropores will decrease the mechanical properties of a material, limiting its use in load-bearing applications.
the size and distribution of pores can be measured by a variety of techniques. Mercury porosimetry characterises porosity by forcing mercury into the pores of a material. the pressure required to intrude mercury into the pores is inversely proportional to the size of the pores. Using this technique can give a complete set of information about pore size, distribution, and surface area and bulk and skeletal density (Lowell et al., 2006c). However, it can only be used with stronger samples able to withstand the pressures involved in mercury intrusion.
in addition to knowing the surface area of a material that is evident to the naked eye, it is important to know the full surface area available for environmental interactions, such as aqueous dissolution. this includes the entire surface area of a geometrically complex implant like a scaffold, the surface area of a filler powder, or the sum of the external and ‘internal’ surface areas of a material which may be riddled with micropores owing to incomplete densification during sintering. One of the standard techniques for doing this, as just mentioned, is mercury porosimetry. Another option, for more delicate materials, is nitrogen adsorption, in which gas molecules are physically adsorbed onto a solid surface. Using Bet theory, one can use the data from nitrogen adsorption to calculate the specific surface area (Braunauer et al., 1938), measured in units of m2g–1. A green (unsintered) ceramic powder may have a surface area of hundreds of square metres per gram, while a sintered powder may be in the low tens of square metres per gram. Pore size distributions can also be calculated from nitrogen adsorption data with BJh theory (Barrett et al., 1951). Adsorption mechanisms are described in more detail in (Lowell et al., 2006a).
5.3.4 Grain structure
As mentioned previously, the term ‘grain’ refers to a crystal in a polycrystalline material. Normally these grains are randomly oriented, but they can also have a preferred orientation, referred to as ‘texture’. Where two grains meet, there is atomic mismatch, creating a grain boundary (Fig. 5.4b). Boundaries are areas of high energy, making them more chemically reactive than their surroundings. they also serve to improve mechanical properties by inhibiting dislocation motion. heat treatments cause grains to grow in size, with the driving force being the reduction in boundary energy. however, mechanical properties are increased most when grains are smaller, as there are more grain boundaries to stop the propagation of dislocations. Additionally, fine-grained ceramics tend to have lower porosity since pores are removed by the easy vacancy transport that can occur along grain boundaries. Lower porosity, of course, means higher strength.
A smaller grain size improves many different mechanical properties. Surface wear has been found to improve in ceramics with fine grain size (Wang et al., 2005) as well as strength and fracture toughness in ceramics and metals (DeWith et al., 1981; takaki et al., 2001). The shape of grains also has an influence on the mechanical properties, as discussed in more detail by (Lee and Rainforth, 1994). At the same time, however, smaller grain size and increased grain boundary area has been found to increase corrosion of metal implant materials and increase dissolution of bioceramics in vivo (Placko et al., 1998; Porter et al., 2003).
Grain size can be measured from micrographs showing the grain structure. in some cases a sample may have to be etched with acid, which preferentially attacks grain boundaries, to reveal the grain structure. By drawing a line across the image and counting the number of times it intersects a grain boundary, the grain size can then be calculated by comparing this result with the scale bar.
5.3.5 Polymer structure and properties
Starting from the smallest structural level, characteristics like molecular weight, tacticity, chain configuration, degree of polymerisation and crosslinking can affect the behaviour of polymers. Properties such as crystallinity, melting temperature and glass-transition temperature are determined by these molecular-level characteristics. these, in turn, affect mechanical properties and in vivo response.
Molecular-level structural characteristics
During the polymerisation process, single, repeating units (mers) combine to form long chains of varying lengths. the molecular weight then represents the average total molar mass for one chain in a polymer. there are several ways in which to calculate molecular weight, including a number-average molecular weight and a weight-average molecular weight, the details of which can be found elsewhere (Campbell et al., 2000a). The degree of polymerisation is a related concept and represents the number of mers in a polymer chain. During synthesis of a polymer, the degree of polymerisation can be followed over time using iR spectroscopy to measure the chemical bonds present and their relative quantity over time (Stuart, 2004). Molecular weight can be measured experimentally by osmotic pressure, gel permeation chromatography and light scattering, among other techniques (Campbell et al., 2000a). The higher the molecular weight, the more rigid is the polymer. Soft waxes or resins have molecular weights on the order of 1000 g mol–1, while solid, hard polymers have molecular weights on the order of 10 000–1 000 000 g mol–1. One of the most widely used polymers in orthopaedic applications, ultra-high-molecular-weight polyethylene (UhMWPe), has a molecular weight of 4 × 106 g mol–1.
Chains can arrange themselves in a variety of ways. Linear chains are simply long chains of monomers joined end-to-end. Branched chains, on the other hand occur when shorter chains grow off the longer chain. in an extreme example, a network polymer consists of many chains and many branches, bonded together at various points by crosslinks. tacticity refers to the arrangement of side groups around a chain. An isotactic arrangement has all side groups on the same side, a syndiotactic alternates sides, whereas an atactic arrangement is completely random. When more than one type of monomer is present in the polymer structure, it is called a copolymer. the locations of the different monomers relative to one another results in different types of structures, including alternating (the monomers alternate back and forth), block (several monomers of each type join together and then alternate with a group of another monomer type) and random (completely random arrangement of monomer types).
the various components of the chemical structure of a polymer can be determined experimentally by a wide array of characterisation techniques. iR spectroscopy can identify the types of bonds present, while nuclear magnetic resonance can determine chemical groups. Wide-angle X-ray scattering determines the local structure of semi-crystalline polymers, while small-angle X-ray scattering can identify if a polymer is multi-phase, a copolymer, or an ionomer.
Degree of crystallinity
When polymer chains are arranged in a particularly compactable way, say a linear chain with small side groups in an isotactic configuration, they are better able to align and pack into an ordered structure. Secondary bonding can then occur between adjacent chain segments and regions of crystallinity can form. the complexity of the chain affects this, including the size of side groups, any branching, and the tacticity. While both isotactic and syndiotactic arrangements allow for crystallisation, atactic structures cannot crystallise. Owing to the size and complexity of all polymer chains, it is virtually impossible for them to be completely crystalline. thus polymers are either amorphous or semi-crystalline.
The degree of crystallinity can be determined by the density of the material. the more crystalline, the more compact the structure is and thus the more dense the polymer is. in general, ductile semi-crystalline polymers have a crystallinity of about 50%, whereas very brittle ones are 90–95% crystalline. The degree of crystallinity can also be influenced by processing conditions. A slower cooling rate can allow for more crystallisation, as the chains have more time to arrange themselves in an orderly fashion. Along with the more ordered, dense structure comes an improvement in both tensile modulus and tensile strength.
Thermal transitions
Many polymers undergo two important thermal transitions – melting and glass transition. A melting temperature ™ is only present in semi- crystalline polymers. it occurs when the solid material with ordered, aligned chains turns into a randomly oriented viscous liquid. Owing to the range of molecular weights in the structure, it actually takes place over a range of a few degrees rather than at one, clearly-defined temperature. Like the degree of crystallinity, chain properties, like the size of side groups and ease of rotation, affect the melting temperature. it takes more energy to unpack a well-packed chain, resulting in a higher Tm. Branching, on the other hand, decreases Tm, as branching leads to defects in crystallinity. the rate at which the polymer is heated also affects the Tm; a higher rate results in a higher melting temperature.
the glass transition temperature (Tg) marks the point at which a polymer goes from rubbery behaviour to a rigid solid as it cools. As temperature decreases, the motion of large segments of polymer chains is reduced. All types of polymers experience a glass transition. the same molecular characteristics that affect Tm affect Tg in a similar way. the two temperatures are typically linked, as well; a change in one affects the other by the relationship Tg = 0.5–0.8Tm (Kelvin).
Several techniques can measure thermal transition temperatures in polymers. Differential scanning calorimetry (DSC) is perhaps the most widely used. DSC monitors heat flow to determine Tg and Tm (if present). Other techniques include thermomechanical analysis and dynamic mechanical analysis and are described in more detail elsewhere (Campbell et al., 2000b).
Strengthening polymers
While polymers do not have a grain structure in the same way that metals and ceramics do, they can be strengthened in a number of different ways. As previously mentioned, increasing the crystallinity and molecular weight of a polymer will strengthen it. in the same way that grain boundaries impede dislocation motion, anything in a polymer’s structure that will impede the slippage of segments of molecular chains will strengthen it. Crosslinking, mentioned briefly before, involves forming strong bonds between molecules previously only linked by weak Van der Waals forces. these strong bonds then stop chains from moving. Drawing, as mentioned before, strengthens semi-crystalline polymers in the drawing direction by aligning the molecular chains in the structure through uniaxial force.