Temperature validation for non-ambient X-ray diffraction (NA-XRD) determines the relation between the temperature of the temperature sensor in the heating attachment and the true temperature on the surface of the sample. Besides others, two main methods for temperature validation are used in NA-XRD:
This method makes use of substances with known temperatures of crystallographic (solid-solid) phase transition or melting points, and compares the tabulated values from the literature with the measured values.
Reference materials for temperature validation by phase transition have to fulfill certain requirements to be suitable for this method. They should have a well-established and reliable phase transition temperature, and the transition should occur fast for precise results. Materials with reversible phase transition are preferable, since this allows multiple validation experiments on the same sample. Lastly, the material must be stable and must not react with the attachment or the sample holder materials.
The stepwise procedure for validation by phase transformation is given below:
| Material | Transition Temperature / °C | solid-solid / melting point | Literature |
| KNO₃ | 128.7 | s.s. | [2] |
| KCIO₄ | 299.4 | s.s. | [2] |
| Ag₂SO₄ | 430 | s.s. | [2] |
| SiO₂ | 573 | s.s. | [3] |
| K₂SO₄ | 583 | s.s. | [3] |
| NaCl | 804 | m.p. | [4] |
| Cu | 1083 | m.p. | [4] |
In the graph below (Figure 1) the results for KNO3, measured in a heating attachment for XRD, are shown.
The measured phase transition temperature from the orthorhombic to the trigonal structure of KNO3 was 129 °C. According to the literature, the phase transition temperature for this phase transition is 130 °C. This means that the deviation between displayed and real temperature is only 1 °C.
Figure 1: Stacked scans of the phase transition of KNO₃
Figure 2: Temperature validation curve with several phase transitions / melting points
One disadvantage of the validation by using phase transitions is that a single substance has only a limited number of phase transitions. In order to have a more complete picture of the thermal behavior of the heating attachment, several substances have to be measured. (Depending on the temperature range, this can be quite time consuming.)
An example of such an extensive validation is shown in Figure 2.
This method can be applied if a material with accurately known thermal expansion behavior is available. The thermal expansion curve of a certain material relates the size increase of a lattice parameter to the applied temperature. It can be calculated using the following formula:
\[ \frac{\Delta L}{L_0} = a_0 + a_1 T + a_2 T^2 + a_3 T^3 \]
∆L=L(T)- L0
L(T) … length of lattice axis at temperature T
L0 … length of lattice axis at 293 K
T … temperature in K
a1-3 … coefficients of thermal expansion
The thermal expansion curve for the c-axis of corundum looks, e.g., as follows:
\[ \frac{\Delta L}{L_0} = -0.192 + 5.927 \times 10^{-4} T + 2.142 \times 10^{-7} T^2 - 2.207 \times 10^{-11} T^3 \]
∆L=L(T)- L0
L(T) … length of c-axis at temperature T
L0 … length of c-axis at 293 K
T … temperature in K
Reversely, the determination of the lattice parameter allows the calculation of the temperature. As axis dimensions are available from Rietveld refinement, the true temperature on the surface of the sample can be determined.
Reference materials for temperature validation by thermal expansion have special requirements. Most importantly, the thermal expansion coefficients of the material must be well-known. To make analysis easier, and reduce statistical errors, it is also helpful to use materials that show high thermal expansion. The material should also display stable lattice parameters with no phase transitions or chemical reactions occurring during the heating process.
The step-wise procedure for validation by lattice expansion is given below:
Results of this type of temperature validation will be shown in chapter 1.3.
The influence of different gas atmospheres on the temperature accuracy is discussed for a strip heater. The following conditions were evaluated: He (atmospheric pressure), N2 (atmospheric pressure) and vacuum. It is expected that the temperature deviation between the measured temperature of the temperature sensor (spot-welded to the bottom side of the heating strip) and the temperature on the sample surface should be highest under vacuum. The reason is that convection, which would help to transfer heat from the strip to the sample, is completely missing. As the thermal conductivity of He (5.193 KJ/kgK) is much higher compared to N2 (1.040 KJ/kgK), He should give the best results.
In the following figure (Figure 3) the effect of different gas atmospheres on temperature accuracy is shown for a measurement of the thermal expansion of MgO.
Figure 3: Validation results for a direct heater depending on gas atmosphere
Figure 4: Validation results for an environmental heater depending on gas atmosphere
It can be easily seen in Figure 3 that the assumptions from above are confirmed.
One can observe the same trends for environmental heaters, but in that case the absolute deviations are much smaller due to the better temperature homogeneity in environmental heaters. In this case the thermal expansion of the c-axis of Al2O3 was used for the validation (Figure 4).
Figure 5: Influence of sample thickness on temperature accuracy in a direct heater
One big advantage of environmental heaters is that the thermal properties of the sample are not that important for the temperature deviation. This is especially true for the sample thickness. For direct heaters the sample thickness has a big impact on the temperature deviation as can be seen from Figure 5. In this example the thermal expansion of Al2O3 was measured with a strip heater (=direct heater) under helium atmosphere.
It can be clearly seen that the thickness of the sample has a significant influence on the temperature deviation. Therefore, for direct heaters the best way of sample preparation is as follows: the sample should be applied as thinly as possible, but still covering the complete heating strip. Otherwise additional signals from the heating strip are visible in the diffractogram and make data interpretation more difficult.
