<P> Phonon (quantized lattice vibration wave) is a central thermal energy carrier contributing to heat capacity (sensible heat storage) and conductive heat transfer in condensed phase, and plays very important role in thermal energy conversion . Its transport properties are represented by the phonon conductivity tensor K (W / m-K, from the Fourier law q = - K ⋅ ∇ T) for bulk materials, and the phonon boundary resistance AR (K / (W / m)) for solid interfaces, where A is the interface area . The phonon specific heat capacity c (J / kg - K) includes the quantum effect . The thermal energy conversion rate involving phonon is included in s _̇ i - j (\ displaystyle (\ dot (s)) _ (i (\ mbox (-)) j)). Heat transfer physics describes and predicts, c, K, R (or conductance G) and s _̇ i - j (\ displaystyle (\ dot (s)) _ (i (\ mbox (-)) j)), based on atomic - level properties . </P> <P> For an equilibrium potential ⟨ φ ⟩ of a system with N atoms, the total potential ⟨ φ ⟩ is found by a Taylor series expansion at the equilibrium and this can be approximated by the second derivatives (the harmonic approximation) as </P> <Dl> <Dd> ⟨ φ ⟩ = ⟨ φ ⟩ o + ∑ i ∑ α ∂ ⟨ φ ⟩ ∂ d i α o d i α + 1 2 ∑ i, j ∑ α, β ∂ 2 ⟨ φ ⟩ ∂ d i α ∂ d j β o d i α d j β + 1 6 ∑ i, j, k ∑ α, β, γ ∂ 3 ⟨ φ ⟩ ∂ d i α ∂ d j β ∂ d k γ o d i α d j β d k γ +...+ (\ displaystyle \ qquad \ qquad \ langle \ varphi \ rangle = \ langle \ varphi \ rangle _ (\ mathrm (o)) + \ sum _ (i) \ sum _ (\ alpha) (\ frac (\ partial \ langle \ varphi \ rangle) (\ partial d_ (i \ alpha))) _ (\ mathrm (o)) d_ (i \ alpha) + (\ frac (1) (2)) \ sum _ (i, j) \ sum _ (\ alpha, \ beta) (\ frac (\ partial ^ (2) \ langle \ varphi \ rangle) (\ partial d_ (i \ alpha) \ partial d_ (j \ beta))) _ (\ mathrm (o)) d_ (i \ alpha) d_ (j \ beta) + (\ frac (1) (6)) \ sum _ (i, j, k) \ sum _ (\ alpha, \ beta, \ gamma) (\ frac (\ partial ^ (3) \ langle \ varphi \ rangle) (\ partial d_ (i \ alpha) \ partial d_ (j \ beta) \ partial d_ (k \ gamma))) _ (\ mathrm (o)) d_ (i \ alpha) d_ (j \ beta) d_ (k \ gamma) +...+) </Dd> <Dd> ≈ ⟨ φ ⟩ o + 1 2 ∑ i, j ∑ α, β Γ α β d i α d j β, (\ displaystyle \ qquad \ qquad \ \ \ \ \ \ \ \ \ \ approx \ langle \ varphi \ rangle _ (\ mathrm (o)) + (\ frac (1) (2)) \ sum _ (i, j) \ sum _ (\ alpha, \ beta) \ Gamma _ (\ alpha \ beta) d_ (i \ alpha) d_ (j \ beta),) </Dd> </Dl> <Dd> ⟨ φ ⟩ = ⟨ φ ⟩ o + ∑ i ∑ α ∂ ⟨ φ ⟩ ∂ d i α o d i α + 1 2 ∑ i, j ∑ α, β ∂ 2 ⟨ φ ⟩ ∂ d i α ∂ d j β o d i α d j β + 1 6 ∑ i, j, k ∑ α, β, γ ∂ 3 ⟨ φ ⟩ ∂ d i α ∂ d j β ∂ d k γ o d i α d j β d k γ +...+ (\ displaystyle \ qquad \ qquad \ langle \ varphi \ rangle = \ langle \ varphi \ rangle _ (\ mathrm (o)) + \ sum _ (i) \ sum _ (\ alpha) (\ frac (\ partial \ langle \ varphi \ rangle) (\ partial d_ (i \ alpha))) _ (\ mathrm (o)) d_ (i \ alpha) + (\ frac (1) (2)) \ sum _ (i, j) \ sum _ (\ alpha, \ beta) (\ frac (\ partial ^ (2) \ langle \ varphi \ rangle) (\ partial d_ (i \ alpha) \ partial d_ (j \ beta))) _ (\ mathrm (o)) d_ (i \ alpha) d_ (j \ beta) + (\ frac (1) (6)) \ sum _ (i, j, k) \ sum _ (\ alpha, \ beta, \ gamma) (\ frac (\ partial ^ (3) \ langle \ varphi \ rangle) (\ partial d_ (i \ alpha) \ partial d_ (j \ beta) \ partial d_ (k \ gamma))) _ (\ mathrm (o)) d_ (i \ alpha) d_ (j \ beta) d_ (k \ gamma) +...+) </Dd>

Is the transport of heat by collisions between atoms and molecules