Although plasma spray processing has been used for several decades, understanding of all the physical and chemical processes involved is rather limited often due to the lack of detailed enough experimental and diagnostic techniques supplying the necessary data. All coatings produced by plasma spraying have in common their fine microstructure. with features often of nanometer scale, as a result of rapid solidification. This work reports on transmission electron microscopy (TEM) studies of plasma sprayed yttria stabilized zirconia (YSZ) ceramic. A modified wedge polishing technique of TEM cross-sectional sample preparation was engaged to prepare high quality samples without the need for extensive ion milling. This paper explains observed microstructural features (e.g. grain size, cracks) and phase composition of the very first layer (splat) on a smooth hot substrate. A rapid solidification model is proposed for the observed narrow columnar grain microstructure of the first YSZ splat. Based on the model, an estimate of liquid undercooling is calculated from the grain size. The solidification of a subsequent splat and more detailed description of splat/substrate and splat/splat interfaces will be discussed in a second paper.