February 2002 Ž . Materials Letters 52 2002 394–398 www.elsevier.comrlocatermatlet Rational mineralogical analysis of ceramics C. Coelho ) , N. Roqueiro, D. Hotza Federal UniÕersity of Santa Catarina-UFSC, Graduation Program on Materials Science and Engineering-PGMAT PO Box 476, 88040-900, Florianopolis, SC, Brazil ´ Received 7 September 2000; received in revised form 28 May 2001; accepted 1 June 2001 Abstract Combining quantitative chemical composition and qualitative mineralogical analysis, enough information can be obtained to solve the problem of quantitative determination of mineralogical phases. This concept is usually known as Rational Mineralogical Analysis. In this paper, a method using the nonnegative least squares routine for solving a system of linear Ž . equations is proposed, as a fast and reliable alternative to the quantitative analysis by X-ray diffraction XRD . q 2002 Elsevier Science B.V. All rights reserved. Keywords: Ceramic raw materials; Clay minerals; Phase composition; Quantitative mineralogical analysis; Non-clay minerals; Rational analysis 1. Introduction There are numerous possibilities of combining two, three, or more elements into chemical com- pounds, whose specific physical properties depend on the chemical composition, type of bond between the atoms, and structure of the compound. A quanti- tative analysis of these compounds can be obtained only if the chemical composition of the component phases is known, if the system is sufficiently stable, wx and if the equilibrium phase diagram is known 1 . Most of the technologically important materials, such as metal alloys, ceramics, and cements, are ) Corresponding author. Tel.: q 55-48-331-9415; fax: q 55-48- 234-1519. Ž . E-mail address: coelho@unisul.br C. Coelho . multiphase materials, and quantification is essential for the understanding of these materials. The physi- cal and chemical properties of multiphase materials Ž . strength, toughness, corrosion resistance depend on the quantitative phase composition. The intensity of a diffraction peak from a particular mineral seems to be simply related to the abundance of that mineral in a mixture. But the quantitative analysis by X-ray Ž . Diffraction XRD is a complicated and slow proce- wx dure, requiring attention to many details 2 . The mineralogical composition of a given mate- rial is defined by the type and quantities of minerals that constitute such material. Through the combi- nation of quantitative chemical and qualitative mi- neralogical analyses, enough information can be obtained to solve the problem of quantitative deter- mination of mineralogical phases. This concept is usually called Rational Mineralogical Analysis. There are two well-known procedures for these calcula- wx w x tions: the conventional 3 and IRTEC 4,5 methods. 00167-577Xr02r$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. Ž . PII: S0167-577X 01 00429-3