If large temperature gradients will be present in the sample as will take place during fire the NMR signal has to be corrected in order to obtain a quantitative
moisture content. In principle the nuclear magnetisation M of a material placed and thereby the NMR signal depends on the external
magnetic field B0 and on the absolute temperature of the material:

Hence the signal will be inverse proportional to the absolute temperature.
However the magnitude of the measured signal is not only determined by the nuclear magnetisation, but also by the relaxation times. Both spin–spin T2 as spin–lattice T1 relaxation are temperature dependent, and can cause a change in the observed signal.The transverse magnetisation M in a Hahn spin-echo experiment with a repetition time tr and an echo time te is given by:

provided that T1>>T2.
In a porous material the relaxation times will be a function of the poresize. In the case in which there is a fast exchange in the timescale of the experiment
between water close to the surface and the centre of a pore, which is the so-called fast diffusion regime, the relaxation rate is given by:

where  ρ is the surface relaxivity, S/V is the surface to volume ratio of the pore, and T2,B the bulk relaxation time which can be neglected because for water T2,B>>T2,S.
The temperature dependent factor in the fast diffusion regime is the surface relaxivity. Without going into the details of the chemical composition of the surface, one can describe the temperature influence on the surface relaxivity by an Arrhenius type equation:

where ρ2,0 is the surface relaxivity at a certain reference temperature and E is the effective surface interaction energy. The effective interaction energy is a combination of the energies involved in surface diffusion and surface relaxation, respectively.
The surface relaxivity therefore decreases with temperature.However, the energy corresponding to the surface interactions is different for each of the pore systems. So the relaxation times T2,i all have a different temperature dependence.Therefore, each pore system which is contributing to the total signal should be corrected separately. To obtain a quantitative moisture content a temperature and pore system dependent correction factor is applied:

To illustrate this we have plotted in Fig. 1a the correction factor as a function of temperature for concrete. Three different corrections are shown: the correction for the nuclear magnetisation (solid line),the total correction including relaxation for the gel pores, and the total correction for the capillary pores.In case of the gel pores the relaxation time correction results in a significantly different correction factor of about half of the initial correction. Note that the total correction of the gel pores is effectivelysmaller since the relaxation time correction for the gel pores is larger than one. For the capillary pores, this correction at 100 oC amounts to 1%, which is negligible. As an example the influence of these corrections is shown in Fig. 1b. Here, the uncorrected signal profile (solid line), the magnetisation corrected (M, dash-dotted line), and the total corrected (M + R, dashed line) are shown. The magnetisation correction increases the measured signal at a position of 40 mm from 1.1 to 1.6. Although the temperature, and thus correction, is higher close to the surface, no significant change of the moisture profile upon correction (correction indicated by bold curve Fig. 1a).



Figure 1: The first three contributions to the overall temperature correction as a function of temperature. The temperature correction factor for the nuclear magnetisation (1/T, solid line). The extra contribution of the surface relaxation for the concrete gel pores (dashed line). The extra contribution of the capillary pores (dash-dotted line). (b) Corrections applied to the raw signal profile in concrete after 42 min (solid line). The signal profile which is corrected for the temperature dependence of the magnetisation is indicated by M. The moisture profile which is corrected the temperature dependence of both magnetisation and relaxation is indicated by M + R. The total correction factor is shown by the bold curve.