.3 Impurity effects Impurity effects are usually the most significant source of uncertainty in fixed-point realisations. Recent improvements in the accuracy and limits of detection in the chemical analysis of impurities in fixed-point substances have made it feasible to model and correct for some impurities. This has had a considerable impact on both the realization technique and uncertainty analysis). Throughout this section, we refer only to impurity effects. However, the same observations and models apply to dilute isotopic effects ). Before discussing the assessment of uncertainties due to impurities, we provide background discussion on the melting phenomenon, the effect of impurities, and a short derivation of Van’t Hoff’s relation. Princeprovides a tutorial description of all aspects of the problem and the interpretation of phase diagrams, Lambert provides good background reading on the understanding of the thermodynamic potential and entropy, and the derivation of Van’t Hoff’s relation comes from Ubbelohde Melting and freezing All chemical reactions and phase transitions involve a balance between the tendency for systems to occupy the lowest energy state, and for the thermal energy in the system to be dispersed as far as possible. The dispersal of thermal energy (i.e., atomic and molecular kinetic energy) is maximised when the system has access to as many microscopic (quantum-mechanical) states as possible. The number of microscopic states is measured by the entropy. The balance between the two tendencies is described in terms of the thermodynamic potential of the system (in this case, the Gibbs’ free energy) GH TS=−, ) where H is the enthalpy, T is thermodynamic temperature, and S is the entropy. The enthalpy is the total energy of the system, H = E + PV, comprising the internal energy plus the potential energy due to volume and pressure. Systems tend to reorganise themselves spontaneously to minimise the thermodynamic potential. In the solid phase, atoms are constrained to move in potential wells (a small volume centred on positions in the crystal lattice) with relatively few microscopic states available. In the liquid phase, atoms are able to move within a large volume with access to a large number and high density of microscopic states. Liquids therefore have higher entropy than solids. For atoms to move from the solid phase to the liquid phase they require energy to lift themselves out of the potential wells, and this change in potential is the origin of the enthalpy of fusion. The liquid phase therefore has both higher entropy and higher enthalpy than the solid phase. Figure 2.1 plots the typical thermodynamic potentials for solid and liquid phases. Note that the two curves cross so that the minimum thermodynamicdiscussion on the melting phenomenon, the effect of impurities, and a short derivation of Van’t Hoff’s relation potential is achieved with the system in different phases depending on the temperature. Thermodynamic potential, GTemperature SolidLiquidFreezingpointSolidLiquidFigure 2.1: The variation of thermodynamic potential with temperature for the solid and liquid phases. At the freezing point, Tf, the thermodynamic potentials of the solid and liquid phases are equal, that is