A thermal-gradient approach to variable-temperature measurements resolved in space

Abstract

Temperature is a ubiquitous environmental variable used to explore materials structure, properties and reactivity. This article reports a new paradigm for variable-temperature measurements that varies the temperature continuously across a sample such that temperature is measured as a function of sample position and not time. The gradient approach offers advantages over conventional variable-temperature studies, in which temperature is scanned during a series measurement, in that it improves the efficiency with which a series of temperatures can be probed and it allows the sample evolution at multiple temperatures to be measured in parallel to resolve kinetic and thermodynamic effects. Applied to treat samples at a continuum of tem-peratures prior to measurements at ambient temperature, the gradient approach enables parametric studies of recovered systems, eliminating temperature-dependent structural and chemical variations to simplify interpretation of the data. The implementation of spatially resolved variable-temperature measurements presented here is based on a gradient-heater design that uses a 3D-printed ceramic template to guide the variable pitch of the wire in a resistively heated wire-wound heater element. The configuration of the gradient heater was refined on the basis of thermal modelling. Applications of the gradient heater to quantify thermal-expansion behaviour, to map metastable polymorphs recovered to ambient temperature, and to monitor the time- and temperature-dependent phase evolution in a complex solid-state reaction are demonstrated.

Keywords: X-ray scattering; negative thermal expansion; powder X-ray diffraction; sample environments; variable temperature.

Figure 1

CAD and photographic representations of the flow-cell/furnace-equipped gradient heater (a) and (d), (b) the ceramic bar that guides the spacing of the resistive wire, and (c) a single gradient heater. Black-body radiation from the resistive wires serves as an intuitive indicator of the thermal gradient. (e) A thermal image of the gradient heater overlaid on a photograph of the heating zone (colour bar shows the temperature in °C).

Figure 2

(a) An example of a thermal gradient generated by variable spacing of resistive wire (indicated as blue lines). (b) The deviation in the temperature from a polynomial fit (black line) for a series of measurements separated by 15 min (circles, triangles, squares).

Figure 3

For a given gradient-heater configuration the temperature range spanned by the gradient heater increases linearly with the maximum temperature. The relationships are given as or . For the present gradient-heater configuration (shown in Fig. 2 ▸) a = 0.54, b = 44°C.

Figure 4

(a) The model geometry. As drawn, the top and bottom heating elements show views of the two different element edges (i.e. they are related by a 180° rotation about the x axis). Grooves that face the sample are aligned parallel to the y direction. (b) The simulated (red) and experimental (blue) temperature profiles. The edges of the heating elements are indicated by the vertical dashed lines.

Figure 5

The simulated temperature profile of the sample between two ends of the resistive wire comparing (a) different winding configurations, (b) different widths of the heating elements (Mark 2C), and (c) the effect of the sample being offset in the y direction (Mark 2A).

Figure 6

The temperature dependence of the lattice parameters in Zn(CN)₂, measured using the gradient heater, and the corresponding coefficients of thermal expansion.

Figure 7

Diffraction data corresponding to the oxidation of NbO₂ to different Nb₂O₅ polymorphs. Position-dependent data were obtained following recovery of the capillary treated at 200–700°C.

Figure 8

Variable-temperature synchrotron X-ray diffraction data documenting the ternary metathesis reaction collected after ca 20 min at a continuum of temperatures: LiMnO₂ + YOCl YMnO₃ + LiCl (middle). The series of variable-temperature data can be described by five components (left), derived from an NMF analysis, with the weightings of the five components changing as a function of temperature, reflecting different states of the metathesis reaction (right). Conventional phase identification and Rietveld refinement applied to the NMF components (left) can identify the multiple phases that contribute to each NMF component and their relative abundance. For example, component A contains 23% t-YOCl, 22% LiMnO₂, 7% r-YOCl, 13% Y₃O₄Cl, 6% Mn₃O₄, 12% LiMn₂O₄, 10% LiCl, 4% h-YMnO₃ and 2% o-YMnO₃.

Figure 9

Phase composition identified at each position along the gradient as a function of dwell temperature, measured at three reaction times: (a) 20 min, (b) 40 min and (c) recovered.