It is proposed to use angular descriptors (in polar and Euler coordinates or quaternions), as well as radiation patterns of many variables, in HF radiofrequency and microwave thermal analysis of anisotropic systems.  

Combining thermal analysis with monitoring of electrical properties in the radio frequency range in contactless cells has long been a canonical direction of physicochemical analysis – orthodox / conventional from both thermodynamic and electrochemical positions. Having begun more than half a century ago in the USSR [1], research in the field of high-frequency thermoelectrometry (as recorded by JCTA) demonstrated applicability in dozens of different applications of the analysis of binary and ternary systems [2-4] and eutectic anomalies [5], solubility polytherms [6,7], crystallization and dehydration of crystallohydrates [8], melting and solidification processes [9], as well as thermal decomposition reactions [10,11]. This method was also used to study polymorphism [12] and isomerism [13], including cis-trans isomerism and cis-trans transitions [14]. By probing a cell (or rather its contents) with a field with a frequency from units to hundreds of megahertz, or by scanning this range when switching from one mode to another, a thermographer inevitably passes the ranges of effective HF (high frequency) / radio frequency and microwave absorption by the substances being analyzed. With sufficient power, it is possible not only to identify, but also to modify processes in a cell with an external field. This shifts the problem of controlling such processes from the area of competence of high-frequency thermal analysis to the area of microwave calorimetry [15], in contrast to microwave measurements in thermal analysis [16], which not only probes a heated body with a field, but also heats it as a detector with a field.

Microwave thermal analysis [17] includes methods of differential thermal analysis [18], adapted to the microwave region, and can be implemented on a chip for calorimetric measurements directly during the processes of phase transformations on the chip. The principle of coupling thermal analysis in situ with microwave irradiation inducing phase transitions or reactions in the system cannot be considered non-canonical: there are known works from twenty years ago on the determination of sol-gel transitions and gelification under the influence of a microwave field using differential scanning calorimetry methods [20], as well as the experiments on thermal analysis of vegetable oils during heating and biodiesel precursors during microwave-mediated technology for its production [21,22]. In the work of Schick [23], the methods of fast scanning and high-frequency or alternating-current thermal analysis are equated to the “temperature-modulated calorimetry” (it should be noted that the standard methods of thermal modulation in scanning calorimetry are not high-frequency; even in multi-frequency methods implemented on a chip, except from the very special cases, the upper limit of modulation is in the region of hundreds of hertz or even less [24]). The improvement of the mesurement capabilities in scanning fluid calorimeters, nanocalorimeters, and on-chip calorimeters is a consequence of the peculiarities of the heat transfer in the laminar (microfluidic) layer and capillary / size effects, as well as the subcritical heat capacity phenomena [25-27]. However, the question arises: the effect of which of the modulation variables in the microwave field is critical for microwave modulation [28] calorimetry and microwave heating in it?

It is known that due to the uneven distribution of waves in space, the heating in devices for microwave sample preparation is uneven. It is also known that the amplitude of these waves is different at different distances from the sample and depends on the angle from the center of the direction of propagation of the wave packet (if we take its directionality as the coordinate axis). The directivity coefficient (as the ratio of the square of the field strength of a given directionality to the average value of its "isotropic" strength) clearly affects the efficiency of the effect at the projection point of a given axis. In this case it is possible to reduce the problem of optimization and spatial-angular normalization of measurements in radio-frequency or microwave thermal analysis to the problem of determining and taking into account the radiation patterns of the radiation sources affecting the sample and the radiation patterns of its own surface as a so-called "detector" on the one hand, and the reference microwave detector, using which the metrological accounting of the microwave power is carried out (in agreement or not with the sample location as a “detector”) on the other hand. Neglecting the non-thermal effects of microwaves, one can use a smaller set of variables than when analyzing them during the measurements. When taking into account the thermal effects, we should inevitably make a correction for the energy dissipation in a medium that can be heterogeneous and anisotropic or texture-oriented in space. If in the general case it seems obvious that the effect is proportional to the microwave energy contribution to a given zone, then in the case of reaction-diffusion effects in microwave-induced self-organization [29,30] (as well as in the analysis of heterogeneous biological structures with their inherent compensation and adaptation effects) this simplified scheme is not optimal, and much depends on the electrical and magnetic properties of the sample itself [1,4].

Thus, it is firstly necessary to find out, what types of radiation patterns are physically adequate to the induced and measured processes. By the field strength or by power / power flux density does the process occur, and are they suitable criteria in the case of comparative in situ microwave thermal analysis? In some cases it is advisable to consider separately from the amplitude radiation pattern, but in colocalization with it, its equiphase visualizations - phase radiation patterns representing the dependence of the initial field phase on the spatial angles. It is obvious that the processes will occur synchronously only at the points at which at a given time moment the field phase is the same (they form the equiphase surface - visualization of the wave front). We propose to consider the difference in the directional factors / variables acting on the processes in the system and characterizing it in situ simultaneously as: the difference in the mechanisms induced in the system; differentiation of the methodological approaches (for example, high-frequency thermal analysis can analyze the phase and electrical properties at high frequencies without heating the medium, and in microwave thermal analysis microwave heating at certain frequencies is inevitable, and the task of analyzing electrophysical properties is not set); the difference in the analysis descriptors, which are the field strength or its density, the directivity coefficient, the surface utilization coefficient, as well as the phase and angular characteristics. From the formal mathematical point of view, the directivity coefficient is a dimensionless value determined in decibels, therefore, the radiation pattern is invariant to the analyzed variables. It is also possible to compare the directogram or radiation pattern with the susceptibility diagram of the analyte material or detector, so that their topological overlap will determine the areas of analysis efficiency and the areas of intensity of microwave-induced processes in the medium, and the metrological variables or analysis descriptors and the influencing factors must coincide.