A Logical Introduction to the Notion of Heterogeneity

Heterogeneity is a primary structural property of all materials and we cannot ignore it without taking considerable risks that are almost always economically detrimental to any research performed on these materials. There are many examples in various industries using materials of mineral origin such as metallurgy, cements, coal, glass, ceramics, nuclear energy, and so on. There are other examples such as agricultural, food, paper, chemical, and pharmaceutical industries that use mineral, organic, vegetal, and synthetic materials. Without exception, all these industries, and the research programs associated with them, should be affected and extremely concerned by the notion of heterogeneity, The assessment of the quality of a product and also of the feasibility of a process depend on experimental estimates that always have a certain amount of uncertainty. Two factors contribute to this uncertainty: The measurement or analytical errors Sampling errors All people involved in research, development, production, quality assurance, and quality control deal directly or indirectly, conscientiously or unconscientiously with sampling problems. These sampling problems exist because all materials are essentially heterogeneous.