docs: def alphakt_pth(v, temp, v0, alpha0, k0, n, z, t_ref=300.,
                  three_r=3. * constants.R):
      """
      calculate thermal pressure from thermal expansion and bulk modulus
  
      :param v: unit-cell volume in A^3
      :param temp: temperature in K
      :param v0: unit-cell volume in A^3 at 1 bar
      :param alpha0: thermal expansion parameter at 1 bar in K-1
      :param k0: bulk modulus in GPa
      :param n: number of atoms in a formula unit
      :param z: number of formula unit in a unit cell
      :param t_ref: reference temperature
      :param three_r: 3R in case adjustment is needed
      :return: thermal pressure in GPa
      """
      return alpha0 * k0 * (temp - t_ref)