Micro-inhomogeneous material

The material parameters encountered in these governing equations are determined through experiments. However, more recently, molecular simulation-based computational methods have been applied even for cases with extremely difficult physical and chemical conflgurations, we can obtain a set of material properties if we have the correct molecular model. For example, we can determine the material properties (at each point, if desired) for a micron-order (1 p,m = 10 m) or nanoorder (Inm = 10 m) material, which is referred to as a micro-inhomogeneous material. Then we can introduce a mathematical procedure that gives a perspective of the microscale and macroscale characteristics. 

In the framework of continuum mechanics, the material properties have mainly been determined through experiments using specimens of sufficiently large dimensions in comparison to the dimensions of any inherent fabric. This is particularly true for micro-inhomogeneous materials where the specimen is large compared to the size of this local structure. This procedure, which provides the system of governing equations and the experiment-based material properties, is referred to as the macro-phenomenological scheme. 

If we use the macro-phenomenological approach, we do not include the intrinsic properties, which represent the movement at a molecular-level. In this sense it is a difficult procedure to establish a correct system of governing and constitutive equations. For example, if we consider the experimental results for a micro-inhomogeneous material, we frequently observe differences if the specimen size is changed. The experimental results are only intrinsically true for the size range of that experiment. In this sense, the macro-phenomenological scheme is interpolation-based. 

A mathematical scheme that can treat a micro-inhomogeneous material uniformly at the microscale and the macroscale is referred to as Homogenization Analysis (HA) (see Sanchez-Palencia 1980 Bakhvalov Panasenko 1984). In the HA method, we introduce a perturbation scheme by using both a macroscale coordinate system and a microscale one, and derive a microscale equation, which represents the geometry and material properties in the micro-domain. Then, using the solution of the microscale equation, we determine the macroscale equation (Fig. 1.2). However, since the HA method is implemented within a framework of continuum mechanics, it also experiences difficulties when the material properties of micro-inhomogeneous materials need to be obtained. 

We have recently developed a new scheme that combines the MD simulation and the HA method to account for the behavior of bentonite clay, which is a nano-scale micro-inhomogeneous material (Ichikawa et al. 1998 Fig. 1.3). 

We can simulate the micro-Zmacro-behaviors of micro-inhomogeneous materials on the solid basis of physical and chemical laws. 

At the microscale level bentonite is a micro-inhomogeneous material, which consists of smectic clay minerals and macro-grains, mainly quartz, water and air (Fig. 1.5). The composition of Kunigel VI , which is a candidate buffer material for the Japanese proposals for HLW disposal, and its purified Kunipia F , is shown in Table 1.1. 

Application. Micro- and nanobeam optics are used to demagnify the cross-section of the primary beam. By means of the respective setups structure variation in inhomogeneous materials can be studied with micrometer or nanometer size resolution, respectively. For this purpose the sample is moved through the beam while... 

Before examining the conditions under which conductive polymers exhibit a more or less high level of fi, it is necessary at first to define which types of application can be concerned with the use of micro-wave properties. In parallel, the physics of the interaction of the plane wave with homogeneous or inhomogeneous material will be examined briefly. 

Classically, XRF has been considered a bulk analysis technique because standard EDXRF and WDXRF systems have analysis spot sizes with a diameter in the mm-cm range, depending on the system. This requires a relative large volume of sample, with inhomogeneous materials requiring a great deal of sample preparation, discussed in Section 8.2.7. Developments in X-ray optics now permit the analysis of discrete microscopic particles, and the creation of elemental maps of a sample with high spatial resolution. The systems are variously called micro-XRF spectrometers, p-XRF... 

Depending on the resolution they provide, balances are classed as semimicro- (10 p.g), micro- (1 fxg) or ultramicro- (0.1 p.g) balances. Besides resolution, the (continuously measurable) maximum capacity of the balance is also an important factor. This is particularly the case when measuring inhomogeneous materials where a few milligrams are often hardly representative and a larger sample mass is desirable. 

Inhomogeneous media with micro- and nanosized structural features are known to strongly alter the character of various physical processes compared to common homogeneous materials. For example, photonic band gap (PBG) structures and metamaterials can be used for subwavelength light control [1]. Similarly, quantum heterostructures such as quantum dots and quantum wells have shown great promise in nano- and optoelectronics, as well as in quantum computing. 

Type III stresses These micro-stresses are inhomogenous and exist inside a grain of the material as a result of crystal imperfections within the grain. 

Micro calorimetric measurements of ammonia, pyrrole, dimethylether, and acetonitrile adsorption unveiled various strength distributions among the acid sites population of Y-type zeoUtes with various Si/Al ratios [85]. Ammonia proved to be a reliable probe when only BrOnsted acid sites were investigated. Dimethylether, a very weak base, did not appear to be any better than ammonia to reveal the inhomogeneity of one particular acid sites population, whereas pyrrole appeared as a rather acidic probe which helped visualize the basicity difference between the parent material and the dealuminated samples. Acetonitrile proved to be a reUable probe to monitor quantitatively and qualitatively Lewis acidity. 

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