Liquid heat capacity in the approach from the solid state: Anharmonic theory

Calculating liquid energy and heat capacity in general form is an open problem in condensed matter physics. We develop a recent approach to liquids from the solid state by accounting for the contribution of anharmonicity and thermal expansion to liquid energy and heat capacity. We subsequently compare theoretical predictions to the experiments results of five commonly discussed liquids, and find a good agreement with no free fitting parameters. We discuss and compare the proposed theory to previous approaches.

Figure 1

As temperature increases, the low-frequency oscillatory shear motion of the highlighted atom between the two dashed lines is lost, as the restoring force for low-frequency shear vibrations becomes weak. Instead, the atom “slips” and diffuses to another position defined by the solid arrow. (Schematic illustration.)

Figure 2

Experimental and theoretical $c_v$ for liquid Hg. Experimental $c_v$ is shown in square symbols. Calculated harmonic and anharmonic $c_v$ are shown in the bottom and thick black curves, respectively. ${\tau }_{\mathrm{D}}{G}_{\infty }=5.5\times {10}^{-4}$ Pa s and $6.272\times {10}^{-4}$ Pa s for theoretical harmonic and anharmonic $c_v$, respectively. $\alpha =1.60\times {10}^{-4}$ K${}^{-1}$.

Figure 3

Experimental and theoretical $c_v$ for liquid In. Experimental $c_v$ is shown in square symbols. Calculated harmonic and anharmonic $c_v$ are shown in the bottom and thick black curves, respectively. ${\tau }_{\mathrm{D}}{G}_{\infty }=4.04\times {10}^{-4}$ Pa s and $4.88\times {10}^{-4}$ Pa s for theoretical harmonic and anharmonic $c_v$, respectively. $\alpha =1.22\times {10}^{-4}$ K${}^{-1}$.

Figure 4

Experimental and theoretical $c_v$ for liquid Cs. Experimental $c_v$ is shown in square symbols. Calculated harmonic and anharmonic $c_v$ are shown in the bottom and thick black curves, respectively. ${\tau }_{\mathrm{D}}{G}_{\infty }=1.19\times {10}^{-4}$ Pa s and $2.07\times {10}^{-4}$ Pa s for theoretical harmonic and anharmonic $c_v$, respectively. $\alpha =4.92\times {10}^{-4}$ K${}^{-1}$.

Figure 5

Experimental and theoretical $c_v$ for liquid Rb. Experimental $c_v$ is shown in square symbols. Calculated harmonic and anharmonic $c_v$ are shown in the bottom and thick black curves, respectively. ${\tau }_{\mathrm{D}}{G}_{\infty }=1.46\times {10}^{-4}$ Pa s and $1.914\times {10}^{-4}$ Pa s for theoretical harmonic and anharmonic $c_v$, respectively. $\alpha =4.52\times {10}^{-4}$ K${}^{-1}$.

Figure 6

Experimental and theoretical $c_v$ for liquid Sn. Experimental $c_v$ is shown in square symbols. Calculated harmonic and anharmonic $c_v$ are shown in the bottom and thick black curves, respectively. ${\tau }_{\mathrm{D}}{G}_{\infty }=4.67\times {10}^{-4}$ Pa s and $5.67\times {10}^{-4}$ Pa s for theoretical harmonic and anharmonic $c_v$, respectively. $\alpha =1.11\times {10}^{-4}$ K${}^{-1}$.