High Power Factor vs. High zT—A Review of Thermoelectric Materials for High-Temperature Application

entropy Review High Power Factor vs. High zT—A Review of Thermoelectric Materials for High-Temperature Application Mario Wolf * , Richard Hinterding * and Armin Feldhoff * Institute of Physical Chemistry and Electrochemistry, Leibniz University Hannover, Callinstraße 3A, D-30167 Hannover, Germany * Correspondence: (M.W.); (R.H.); (A.F.) Received: 27 September 2019; Accepted: 25 October 2019; Published: 29 October 2019



 Abstract: Energy harvesting with thermoelectric materials has been investigated with increasing attention over recent decades. However, the vast number of various material classes makes it difficult to maintain an overview of the best candidates. Thus, we revitalize Ioffe plots as a useful tool for making the thermoelectric properties of a material obvious and easily comparable. These plots enable us to consider not only the efficiency of the material by the figure of merit zT but also the power factor and entropy conductivity as separate parameters. This is especially important for high-temperature applications, where a critical look at the impact of the power factor and thermal conductivity is mandatory. Thus, this review focuses on material classes for high-temperature applications and emphasizes the best candidates within the material classes of oxides, oxyselenides, Zintl phases, half-Heusler compounds, and SiGe alloys. An overall comparison between these material classes with respect to either a high efficiency or a high power output is discussed. Keywords: thermoelectric materials; energy harvesting; energy materials 1. Introduction At a time when raw fossil materials are becoming scarcer and the demand for regenerative energies is relentlessly rising, the use of energy harvesting systems has gained an ever-increasing interest [1]. Regardless of whether it is from industrial processes, mechanical processes, or the transportation sector, the amount of wasted energy currently remains enormous. In 2017, the estimated energy consumption in the U.S. was shown to be approximately 67% wasted energy [2]. At this point, energy harvesting comes into play, converting even small amounts of wasted energy in the form of heat, light, vibration, or movement into usable energy [3]. Since most of this wasted energy is in the form of heat, the conversion of thermal energy to electrical energy via thermoelectric generators is an attractive solution. The associated energy conversion is based on the thermoelectric effect, which is the simplest way for direct energy conversion from dissipated heat into electrical energy. Discovered by T.J. Seebeck in 1821, the first thermoelectric effect (Seebeck effect) describes the direct conversion of thermal energy into electrical energy, which Seebeck demonstrated by thermally inducing an electrical current by heating two different electrical conductors. Together with the Peltier effect (1834), which describes the heating or cooling effect of an electrical current in a thermocouple, and the work of W. Thomson on the thermoelectric effect in homogeneous conductors (Thomson effect), the basis of thermoelectricity was laid [4]. In the first half of the 20th century, the term ‘figure of merit’ was introduced, and the first theoretical approaches were made in designing a material with a high energy conversion efficiency. In 1957, A.F. Ioffe defined the figure of merit zT as a Entropy 2019, 21, 1058; doi:10.3390/e21111058 www.mdpi.com/journal/entropy Entropy 2019, 21, 1058 2 of 32 function of the electrical conductivity, the Seebeck coefficient, and the thermal conductivity of the material [5]. However, thermoelectric energy conversion has been too inefficient for most applications for a long time. Theoretical descriptions of nanostructural engineering and superlattice structures paved the way to significantly improved zT values, which strongly increased research on thermoelectric materials in the mid 1990s [6]. Today, the improvement and development of thermoelectric materials still have the goals of gaining higher efficiencies and power outputs. Within this research field, various materials from wide-ranging material classes, such as metallics and intermetallics [7,8], oxide-based ceramics [9–11], chalcogenide compounds [12], and polymers [13] have been investigated. It is important to compare the efficiencies and resulting power outputs of these materials to draw the correct conclusions when actual generators for applications are manufactured. The purpose of this review is to convey descriptive comparisons, which is realized by two different types of Ioffe plots. These plots allow a direct comparison of the thermoelectric properties of different materials, which is vital for prospective research [14]. 1.1. Thermoelectric Parameters Discussing thermoelectricity requires an understanding of some fundamental parameters, which are briefly described in the following. Thermoelectric energy conversion is based on local coupling of fluxes of charge carriers and entropy. When a thermoelectric material is simultaneously exposed to µ̃ local gradients of temperature (i.e., ∇T) and an electrochemical potential of charge carriers (i.e., ∇ q ) the local flux densities of charge jq and entropy js are given by the following transport equation [15]: jq js ! = σ σ·α σ·α σ · α2 + Λ ! ! −∇ µ̃q . · −∇ T (1) The thermoelectric material tensor, which appears here, is characterized by three material parameters: the isothermal electrical conductivity σ, the Seebeck coefficient α, and the electrically open-circuited entropy conductivity Λ. The latter is linearly related to the traditionally used heat conductivity λ via the absolute temperature T as described in Equation (2) [15–17]. In the context of this review, thermal conductivity is a generic term, that covers both entropy conductivity and heat conductivity. Here, it is advantageous to address the thermal conductivity by the more fundamental entropy conductivity, as we will see when comparing materials. Considering entropy as a central primitive quantity of equal rank to electric charge comes with the benefit of an easy understanding of the physics of thermoelectricity. A local coupling of the fluxes of these substance-like quantities is described by Equation (1) [15]; this is in contrast to the cumbersome traditional approach, which introduces generalized forces and a kinetic matrix [18] instead of thermodynamic potential gradients and a material tensor. Naturally, for each substance-like quantity, a conductivity is assigned to the material. The material tensor is symmetric by principle, and an elaborate discussion of the reciprocity of Onsager coefficients is superfluous [15]. A further advantage is that the currents of thermal energy (heat) and electrical energy (or electrochemical energy), which accompany the fluxes of entropy and charge, can be treated separately. The entropy and charge fluxes allow us to consider energy conversion and its efficiency in a thermo (...truncated)