# Sign of ∆S in conversion of diamond to graphite

It is said that ∆S is positive as randomness is increasing from diamond to graphite as in diamond molecules are tightly packed together but we know that ∆S=∆H/T for phase transition and that conversion of diamond to graphite is exothermic which indicates ∆H as negative so shouldn't ∆S be negative? (Correct me if I am wrong.)

The standard expressions for the Gibbs free energy of carbon are found in Per Gustafson, Carbon 24(2) 169-176 (1986), and collected (with many other elements) in AT Dinsdale, Calphad 15(4) 317-425 (1991). In general they are in the form of a power series in temperature $$T$$,

$$G = a + bT + cT\ln(T) + \sum dT^n$$

Then, using

$$S = -b -c -c\ln(T)-\sum ndT^{n-1}$$

one can evaluate $$S$$ from the expression for $$G$$.

In Dinsdale the Gibbs free energy for diamond relative to graphite is

$$1009 + 4.88T -0.01 T \ln(T) +135400T^{-1} +33.0\times 10^5 T^{-2} -9\times 10^8 T^{-3}$$

Then the difference in entropy $$S$$ is given by

$$-4.88 + 0.01 + 0.01\ln(T) +135400T^{-2} +66.0\times 10^5 T^{-3} -27\times 10^{8} T^{-4}$$

Plotting this in your favorite plotting program will show that the entropy of diamond is less than that of graphite at all reasonable temperatures at standard pressure.