The organic constituents that make up the heterogeneous coal mass are called macerals. Vitrinite and pseudovitrinite are two of the most abundantly occurring macerals in North American coals. Photoacoustic microscopy using piezoelectric detection offers a useful technique for probing the thermal-elastic properties of these coal macerals. The experimental and theoretical conditions under which photoacoustic microscopy can be used to characterize the in situ thermal-elastic properties of macerals, as a function of the percentage of carbon or "rank" of coal, are investigated in this paper. Existing piezoelectric photoacoustic theory has been applied to our sample–transducer configuration to arrive at an expression for the voltage measured from the piezoelectric transducer. The theory indicates that the photoacoustic signal is related to the following sample properties: coefficient of thermal expansion a, bulk modulus B, density ρ, and specific heat c. These properties are coupled together into a dimensionless parameter given by aB/ρc, to which the measured voltage is proportional. Some experimental results used to test the validity of the theoretical predictions are presented. Photoacoustic data gathered on 10 Appalachian Basin coals are plotted as a function of the coal rank. These results are shown to compare favourably with a calculated curve, constructed using independently measured values of a, B, ρ, and c.
Mathematical model of photoacoustic microscopy with piezoelectric detection
