Outline for the Manual

1. Background : Introduction to thermal conductivity, of materials
2. NEMD simulations : Calculation of using molecular dynamics simulations
3. System size scaling : Effect of simulation cell size on calculated
4. Temperature scaling : Effect of system temperature on calculated
5. Thermal conductivity plugins : Calculating of MoS₂
6. Quantum corrections : Beyond classical thermal conductivity simulations
   • Velocity autocorrelation in equilibrium simulations
   • Phonon density of states
   • Specific heat of materials
   • Quantum-corrected thermal conductivity
7. Summary and take-away messages : Things to remember when you do your own thermal conductivity simulations
8. Current research applications : Engineering thermal conductivity of materials. Brief look at thermal conductivity of fractal and alloyed systems
9. Downloads/Documentation : Thermal conductivity plugin downloads, Plugin manuals and contributing to software development
10. References

1. Background

Introduction to thermal conductivity

• Thermal conductivity (denoted by the symbol ) is a fundamental property of materials that determines their ability to conduct (i.e. transmit) heat (See Refs 1,2). Materials with a higher values conduct heat well and low- materials are more insulating (Ref 9.).

Table 1: Thermal conductivity of common materials

Material	(W/m-K)
Diamond	1000
Silver	406
Copper	401
Water	0.591
Wood	0.12
Wool	0.0464
Air	0.025
Silica Aerogel	0.003

• High- materials are commonly used in heat-sink and thermal-dissipation applications and materials with low thermal conductivity are used primarily for insulation. Low insulating materials are also used for thermoelectric energy harvesting applications (See Section 8).

• Both high and low materials are extremely useful for engineers.

2. NEMD Simulations

Theory and Equations

As described previously, thermal conductivity is calculated by measuring the temperature gradient along the material. We establish the thermal gradient by adding and removing a predefined quantity of heat, E₀, at and respectively. Since we can control the amount, E₀ and frequency of heat input, , we effectively control the heat flux in the system. Once the steady-state temperature profile is established in the simulation cell, we combine the temperature profile with the known heatflux to calculate the thermal conductivity.

Specifically,

Heat Flux,

The factor comes from the fact that heat conduction happens along both the +x and -x directions away from the heat source at .

Also, from Fourier's law of thermal conduction, we have , where A is the cross sectional area of heat transfer. (Ref 6)

Putting these equations together, we have

Note here that the thermal conductivity goes as the inverse of the temperature gradient. More conducting material will have 'flatter' temperature profiles.

Image 3: Schematic of NEMD simulations for measuring thermal conductivity of 2D materials