High-throughput experimentation is effective in systematically producing large and diverse data sets. The marriage of combinatorial materials science and informatics is a natural one, and results are beginning to emerge from the integration of elements of materials informatics with data from combinatorial libraries. We discuss data management issues in high-throughput experimentation and highlight recent examples where data-mining tools are being implemented for extracting knowledge and predicting new compounds, with an emphasis on electronic materials.

Combinatorial methods are high-efficiency methods to create large composition “libraries” of materials, for example, continuous composition variations, and test those compositions systematically in parallel for specific properties of interest, in contrast to the time-consuming one-composition-at-a-time approach. These methods have captured the attention of the materials industry with the promise of providing new discoveries “faster, better, and cheaper.” However, in the academic community, combinatorial methods often meet with less enthusiasm, perhaps due to the perception of combinatorial methodology as an Edisonian approach to science. The facts are quite to the contrary. In addition to impressive successes arising from the application of combinatorial methods to materials discovery, results coming out of systematic high-throughput investigations of complex materials phenomena (which would be too time-consuming or expensive to undertake) provide data leading to improvement in theories and models of materials chemistry and physics. Indeed, combinatorial methods provide a new paradigm for advancing a central scientific goal—the fundamental understanding of structure–property relationships of materials behavior.

Novel phases of functional inorganic chemical systems can be efficiently explored using high-throughput thin-film fabrication techniques coupled with rapid characterization schemes. High-throughput investigation of thin-film materials has already led to the discovery of new dielectric and magnetic materials. In this article, we review various high-throughput thin-film synthesis/evaluation techniques and discuss examples of exciting discoveries and new applications of combinatorial techniques.

The rapid development of modern photonic technologies—for example, mercury-free lamps, flat-panel displays, and solid-state lamps—demands the timely discovery of advanced phosphors. A combinatorial process has been developed to dramatically accelerate the experimental search for such phosphors. High-density phosphor “libraries” containing from 100 to over 1000 discrete chemical compositions on a 1 in. × 1 in. substrate have been made in thin-film or powder form using selective vapor deposition and liquid-dispensing techniques, respectively. In this article, the existing methods of combinatorial synthesis and screening of phosphors will be reviewed with examples. These methods may also be used to screen organic-based solid-state materials and optimize their device properties. In this regard, combinatorial and spreading techniques have been utilized to study and rapidly optimize organic light-emitting devices (OLEDs).

High-throughput and systematic studies of complex materials systems using the approach of “continuous phase diagramming” (CPD) are described in this article. The discussions focus on the techniques of epitaxial film synthesis of CPD and mapping physical and structural properties, using two different material systems as examples: doped perovskite manganese oxides and magnetic alloys. In doped perovskite manganese oxides, a highly correlated system, mapping the optical, electrical, and magnetic properties, reveals surprising evidence of electronic phase transitions that correlate with the low-temperature magnetic order. In magnetic alloys, application of CPD, particularly using real-time characterization during epitaxial growth, makes it possible to examine structure–property relations systematically.

A diffusion multiple is an assembly of three or more different metal blocks, in intimate interfacial contact, that is subjected to a high temperature to allow thermal interdiffusion. The power of using a diffusion multiple approach in the efficient mapping of phase diagrams and materials properties for multicomponent alloy systems is illustrated in this article using several examples. It is now possible to map phase diagrams and materials properties at an efficiency some 3 orders of magnitude higher than the conventional one-alloy-at-a-time approach. With this high efficiency, many critical materials data that otherwise would be too time-consuming and expensive to acquire can be obtained and employed to accelerate our understanding of a system's materials physics and chemistry. It is postulated that coupling the diffusion multiple approach with the CALPHAD (calculation of phase diagrams) method will have a significant impact on the computational design of materials.

In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

In this paper we present a simple combinatorial approach for the derivation of zero-avoiding transition probabilities in a Markovian r-node series Jackson network. The method we propose offers two advantages: first, it is conceptually simple because it is based on transition counts between the nodes and does not require a tensor representation of the network. Second, the method provides us with a very efficient technique for numerical computation of zero-avoiding transition probabilities.

This paper is a survey of the solutions of various first-passage time problems in the theory of queues.