## 1 Introduction  
NMR Relaxation (NMRR) is an extremely useful quantitative technique for material science, particularly for studying polymers and porous materials [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13]. The measurement of NMR relaxation amplitudes and decay times enables the measurement of both the mass and qualities which are variously described as mobility, dynamics, stiffness, viscosity or rigidity, for hydrocarbons and polymers, both in the bulk and in pores, Section 4. NMR relaxation can be used directly to measure micron-sized pore-sizes [11; 14; 15; 16], provided one knows the surface relaxation properties of the porous material [17; 12]--often termed NMR Relaxometry. NMR Relaxometry is of limited use for nano-metric sized pores. Alternatively, NMR Cryoporometry (NMRC) [10; 18; 19; 20] is a powerful technique for the measurement of nano-metric pore-size distributions and total porosities, based on the lowered melting temperature of liquids in the pores--the Gibbs-Thomson effect [21; 22; 18; 23], Section 3.2. This paper discusses the use and application of the Lab-Tools Mk3 precision compact NMR time-domain spectrometer for both NMRR, Sections 3.1 and 4, and NMRC, Sections 3.2 and 5. This NMR spectrometer is based on a Field Programmable Gate Array (FPGA). Other examples of FPGA based instruments appear in the literature, for instance [24; 25; 26], but do not appear to be such rather compact and yet complete and easy to use NMR time-domain spectrometers. This instrument is an NMR time-domain spectrometer that auto-tunes and is immediately ready for research measurements, under control of a Graphical User Interface (GUI). Data fitting and parameter extraction is performed online during the measurements, and can also be performed offline using the same Graphical User Interface or another copy elsewhere. A particular feature of this spectrometer is that it is fast recovery and so can measure NMR Relaxation both in the bulk and in sub-nano-meter and upward sized pores, for materials that may be liquid, gel, waxy, tarry...[13], and an example is given of it measuring T\({}_{2}\)s in brittle ice (and hence the mobility of the ice molecules), see Figures 1 and 2. This is highly useful for studying the properties of hydrocarbons in both recovered porous rock samples from oil reservoirs, and in fired biochar porous carbon samples, for example [27]. A more detailed discussion of NMR Relaxation, and specific application examples, are given in Section 4. Some applications of the Lab-Tools Peltier thermo-electrically cooled variable-temperature (V-T) probe [28; 29] are also discussed, Section 2.1, which enables this spectrometer to make NMRC measurements of pore-size distributions in porous materials on the unusually wide pore scale range of sub 1 nm to over one micron [18]. Specific application examples are discussed in detail, Section 5. All of these techniques are suitable for a wide range of polymers [18; 20] and porous materials [18], including porous glass [30; 31], zeolites [32], cement [33], clays [18], rock [27; 34], wood [35], and biochar and other porous carbons [18; 27; 36; 37]. In polymers, crystalline/amorphous ratios may be measured. By swelling rubbers and polymers by adding liquids to them, cross-link density and nano- to micro-porous properties of the polymer may be obtained [18; 20; 38]. In biochar, progressive changes to the quantity and mobility of hydrocarbons, as well as changes in pore-blocking, as a function of preparation temperature, have been demonstrated [27]. All these measurement techniques can be implemented using this recently developed highly compact Spectrometer, based on a Field Programmable Gate array (FPGA) module and custom surface mount low-noise NMR receiver and NMR linear transmitter. This instrument has a high proportion of the R.F. circuitry in a digital form, implemented as firmware in the FPGA, which aids long-term stability. The FPGA module is credit-card sized, and the NMR receiver and NMR transmitter are each even smaller.