**Accurate measurements of the quantum yields of powder samples as well as exact measurements of the spectral dependence of absorption and/or reflection of the samples require an integrating sphere. This eliminates ambiguities caused due to angular dependences, amplifies the alignment repeatability while changing samples, and proves advantageous for overall reproducibility.**

Moreover, powder samples can be suitably determined by positioning the powder on a tray and making the excitation beam to point downwards, in the usual manner towards the sample. The integrating sphere is designed such that particular requirements for measuring absorption, spectral reflection, and quantum yield of powders are satisfied.

The standard sample holder equipped in the sample chamber is replaced with the integrating sphere by removing the two standard lens assemblies and inserting a special lens into the excitation path. The entire procedure takes less than 3min. There is no need for using lens in the emission channel.

The integrating sphere is made of two halves. For exchanging the sample, the upper half of the sphere is removed and is equipped with a small elliptical mirror for beam steering and a baffle plate for protecting from the detected light. Two thumb screws are utilized to tightly secure the lower half of the sphere to the sample holder base. A pillar with a small dish used as an exchangeable powder tray is equipped in this lower half.

## Theory of Reflectance, Absorbance, and Quantum Yield

Figure 1 shows a graphical representation of two spectral scans obtained by scanning the emission monochromator, and fixing the excitation monochromator at 450 nm. The first scan (blue) is obtained from a reference scatterer, which must exhibit a diffuse reflectance of 100%, while the second scan (red) is obtained by scanning the sample that is being studied.

This sample displays emission (red, solid) and reflection (red, hatched). The area represented by the blue graph (from the base line) is denoted as E_{Ref}. The red hatched area is E_{Sam} and the red solid area is L_{Sam}.

**Figure 1. **Graphical representation of spectral scans from the emission monochromator

Using ERef, E_{Sam} and L_{Sam}, we can calculate the following values:

Here, R is the reflectance, which indicates the ratio of the signal scattered from the sample and the total diffuse reflecting standard. A is the Absorbance, which is calculated as a logarithmic value (log_{10}) of the inverse of R.

The definitions mentioned in the table over the area under both the curves were used for computation. Given that the shapes of both the curves are Gaussian-like and identical, the values R and A can be obtained from individual data points of the curves. Consequently, measurement of the absorbance and reflectance spectra can be performed by synchronous scanning of the emission and excitation monochromators at zero wavelength offset.

Quantum Yield, denoted by η, is referred to the total number of emitted photons divided by the total number of absorbed photons. The difference of the two scattered curves gives the number of photons absorbed. This method for calculating the quantum yield is known as the absolute method for deducing the Emission Quantum Yield.

Another method, known as the relative method, for measuring quantum yield involves the comparison of a reference standard with a known emission quantum yield. To calculate the quantum yield, accurate spectral correction is important.

## Measurements of the Spectral Reflectance and Spectral Absorbance

Synchronous spectral scans are employed for making reflectance measurements through the emission and excitation monochromators stepping via the pre-set spectral range.

This is carried out by setting the offset between the excitation and emission wavelengths in the synchronous scans to zero, which means that the number of photons is documented for similar wavelength setting of the two monochromators. Detection of the Rayleigh (diffuse) scattered light is thus performed using this method.

We need two measurements, namely, a spectral scan of the diffuse reflected light from the sample being studied and another measurement performed by replacing the sample with a reference scatterer under similar conditions. The reference scatterer is normally BaSO_{4} which is used for coating the inner surface of the integrating sphere.

Care should be taken to ensure that the signal intensities are limited to roughly 2 million counts per second at any point in the spectrum for preventing count rate saturation. The higher signal is generated by the reference BaSO_{4} sample, so tests ought to be made by taking this reference material to precisely set the spectral band width of the monochromators such that the overall signal intensity is controlled. Usual values of the spectral band widths for the emission and excitation channels are 0.2nm and 10nm, respectively.

Uncorrected spectra are adequate for calculating the reflectance curve since the correction falls out by dividing both the curves, but for correcting the probable fluctuation in the xenon lamp light intensity, it is advisable to carry out simultaneous correction by employing the reference detector. (The gain of the reference signal amplifier should be reduced since the spectral band width of the excitation is relatively broader.) Figure 2 depicts typical measurements carried out with the reference scatterer (BaSO_{4}) and a sample (YAG:Ce).

**Figure 2. **Measurements of the reference scatterer (BaSO_{4}) and a sample (YAG:Ce ).

The spectral absorbance and reflectance can be computed in a simplified manner by means of the F900 spectrometer software using the two curves in the graph depicted in Figure 3.

**Figure 3. **Spectral reflectance and absorbance curves

## Determination of the Emission Quantum Yield

For absolute determination of the emission quantum yield for sample of unknown origin, it is important to accurately measure the emission spectrum as well as the number of absorbed photons. The number of absorbed photons can be measured by performing two spectral/emission scans: scanning across the Rayleigh scattered light emitted from the sample and scanning from a 100% diffuse reflecting reference with the emission monochromator.

Figure 4 illustrates the measurements of scattered light from BaSO_{4} (red), emission from YAG:Ce (green), and scattered light from the sample YAG:Ce (blue). It can be observed from Figure 4 that spectra have been recorded via simultaneous detection of the reference detector signal. However, the spectra have not been spectrally corrected in relation to the spectral function of the emission channel.

**Figure 4. **Scattered light of BaSO_{4} (red), scattered light of the the sample YAG:Ce (blue), and the emission of YAG:Ce (green).

The spectral emission scans were performed with narrow spectral bandwidth for the emission spectra (0.2 nm) and a broad spectral band width for the excitation spectra (10 nm). This is because (1) the narrow spectral band width for emission enables controlling signal intensity to prevent detector saturation and (2) there is a need to “over-sample” the scattered light spikes, i.e. measurements need a huge number of closely spaced data points, permitting accurate calculation of the areas with relatively narrow spikes.

Normally, spectral data cannot be viewed on a logarithmic scale, but some virtue of this exists for the determination of quantum yield. This enables a user to assess the low amplitude emission spectrum as well as the impact of the background level in a better way. Following background subtraction, spectral correction is applied to the raw data, and the quantum yield is computed from the spectrally corrected curves by means of a F900 software wizard.

Assuming that there are no systematic errors, this absolute method enables calculating the emission quantum yield with an estimated error of ±5%, whereas the repeatability yields an error of ±3%. These systematic errors are mostly caused due to count rate saturation and inaccuracy of the data file utilized for spectral correction of the raw data. For liquid sample measurement, Edinburgh Instruments supplies an integrating sphere.

This information has been sourced, reviewed and adapted from materials provided by Edinburgh Instruments.

For more information on this source, please visit Edinburgh Instruments.