The deflection signal of a thermally excited force sensor of an atomic force microscope can be analyzed to gain important information about the detector noise and about the validity of the equipartion theorem of thermodynamics. Here, we measured the temperature dependence of the thermal amplitude of a tuning fork and compared it to the expected values based on the equipartition theorem. In doing so, we prove the validity of these assumptions in the temperature range from 140 K to 300 K. Furthermore, the application of the equipartition theorem to quartz tuning forks at liquid helium temperatures is discussed. Over the last decades, quartz tuning forks have been used to build self-sensing sensors in many research fields, for example, hydrodynamics of quantum fluids, 1,2 spectroscopic gas sensing, 3,4 and scanning probe microscopy. [5][6][7] In this paper, we focus on quartz tuning forks used in frequency modulation atomic force microscopy (FM-AFM), although the results are also applicable to other fields utilizing quartz tuning forks. FM-AFM with quartz tuning forks has put forth a number of impressive results, [8][9][10] e.g., FM-AFM was used to resolve the chemical structure of a molecule.10 In FM-AFM, the frequency shift Df of an oscillator measures the local interaction of the microscope tip with the sample. The force between tip and sample can be calculated from the frequency shift Df if the sensor's resonance frequency, stiffness, and oscillation amplitude are known.11,12 Thus, for determining relevant physical quantities out of the observed frequency shift, those properties must be well-characterized.A tuning fork is a cut piezoelectric quartz crystal with two prongs and gold electrodes along the prongs. When one or both prongs are deflected, charge accumulates on the electrodes. The sensitivity describes the relation between the piezoelectric output signal and the deflection of a tuning fork. It is therefore essential to know in order to determine the deflection amplitude. One method to determine the sensitivity is to compare the output of the tuning fork due to thermal excitation with the expected result based on the equipartition theorem and the assumption that the first harmonic mode is the only mode significantly excited. The equipartition theorem is also used in FM-AFM to calculate the fundamental noise limits in force detection due to thermal excitation. 13,14 Understanding the fundamental noise limits is very important for judging and improving a system's performance. In this paper, we show the validity of using the equipartition theorem in the temperature range from 140 K to 300 K and discuss its application at liquid helium temperatures.The equipartition theorem states that each degree of freedom holds a thermal energy of 1 2 k B T, where k B is Boltzmann's constant and T is the temperature in Kelvin. For a coupled oscillator like the tuning fork with one degree of freedom, this leads to the relationwhere k is the spring constant and A EqT th is the thermal deflection amplitude of one prong.Exper...