Research Highlights

Research Highlights

Henry group develops more accurate method to predict thermal conductivity

February 26, 2016

Vibrations of atoms in solids can be described by a summation of contributions from individual normal modes, which are called phonons. The transfer of heat in all condensed matter generally originates from the contributions of both electrons and phonons. However for non-electrically conductive materials, the atomic vibrations (phonons) dominate the heat conduction. Describing the theory of heat conduction in condensed matter based on the individual phonon contributions has been a topic of intense study for many years, and the most prevalent theory is that of the phonon gas model (PGM), which was proposed by Peierls in 1929. The reason it has become so prevalent is because it exhibits excellent agreement with experimental measurements of thermal conductivity for crystalline materials and nanostructures. However, when it comes to disordered solids, such as amorphous materials and random alloys, the applicability of the PGM becomes highly questionable. Another class of systems where the PGM has become problematic are interfaces between materials. Many modifications to the PGM model have been introduced over the last 60 years, but the core of the theory has remained unchanged in the sense that all vibrational modes are still treated as though they propagate and carry energy at a certain velocity like a gas particle – hence the name phonon gas model.

Over the last 3 years researchers in the Atomistic Simulation & Energy (ASE) research group, under the supervision of Prof. Asegun Henry have developed two new methods for understanding heat conduction in any material or at any interface involving phonons (e.g., a single formalism that can simultaneously treat ordered/crystalline and disordered solids or their interfaces). The key to the generality of the two methods is that they were derived completely independently of the prevalent paradigm, namely the PGM. The two methods attempt solve the basic problem of how to extract information from molecular dynamics (MD) simulations, and facilitate determination of which phonons/modes interact and contribute to thermal conductivity or thermal interface conductance. The key step forward in these methods is that they fully include temperature dependent anharmonicity and can treat any structure without the requirement of periodicity.

The first published paper, co-authored by Kiarash Gordiz and Dr. Henry, presents a modal analysis technique to study the heat transfer across interfaces, which is termed Interface Conductance Modal Analysis (ICMA) method. The results using this method indicate that when two materials are joined a new set of vibrational modes are required to correctly describe the transport across the interface. The new set of vibrational modes is inconsistent with the physical picture described by the PGM, because some of the most important modes are localized and non-propagating and therefore do not have a well-defined velocity nor do they impinge on the interface. Among these new modes, certain classifications emerge, as most modes extend at least partially into the other material. Localized interfacial modes are also present and exhibit the highest conductance contributions on a per mode basis by strongly coupling to other types of vibrational modes. Fig. 1 shows examples of the atomic vibration mode shapes associated with each class of vibration. Fig1

The second published paper, co-authored by Wei Lv and Dr. Henry, presents a modal analysis technique to study the phonon transport in disordered materials, which is termed Green Kubo Modal Analysis (GKMA). Due to the lack of structural periodicity in amorphous materials, there is no rigorous way to define the wave-vector or group velocity for the non-propagating modes, which comprise the overwhelming majority of the vibrations. Therefore, the application of the PGM to amorphous materials is highly questionable. Lv and Henry developed GKMA which is a natural extension of the widely used Green-Kubo approach, but with the addition of mode level analysis. The results using GKMA method have produced the best agreement with experiments for several amorphous materials and a random alloy to date as shown in Fig. 2.

Fig2