This diploma thesis deals with the X-Ray crystallography study of structural changes within lithium-ion cells. First part consists of the theoretical discussion about the structural changes in commerce lithium-ion cells with focus on X-Ray crystallography. Then the ex situ, in situ and operando terms are discussed. Verification of the XRD usage is realized on the LiFePO4 material. Experimental part deals with the optimization and preparation of electrochemical cells and the measurements. Finally, results of the Rietveld analysis are discussed.

The thesis deals with the design of a suitable length standard for nanometrology. This length standard will be used for metrological traceability of the Rigaku nano3DX located at CEITEC Brno and the SIOS NMM-1 device which is located at ČMI Brno. The first part is focused on the description of these measuring instruments, the analysis of their metrological traceability requirements and the requirements for the material length standard. The second part is devoted to the concrete possibilities of the etalon design, 3D printing of the prototype of the standard and verification of its dimensional compatibility. At the end of the thesis, the evaluation and selection of the appropriate standard design is made.

The diploma thesis deals with the design of three length standards, which will serve to ensure metrological traceability between Rigaku nano3DX, SIOS NMM-1, Zeiss UPMC Carat 850 and other devices located at ÚVSSR BUT and CEITEC Brno. The first part of the thesis focuses on the theoretical acquaintance with concepts closely related to the issue of ensuring metrological traceability. In addition, this section deals with computed tomography and the description of individual devices. The second part of the thesis is devoted to design, production process and testing of individual standards. The last part describes the ensuring the calibration of the smallest standard, the so-called Nano standard and the calculation of the uncertainty of measuring its calibrated length. At the end of the thesis, the outputs of these activities are evaluated.