7.2: Classroom Activity
- Page ID
- 46487
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Mineral Identification of Cuneiform Clays Using X-ray Diffraction Data
| Mineral identified | Clay cone 1913.132 | Leg-shaped clay artefact 1983.286 | Diffraction angle, \(2\theta (^\circ)\) | Lattice spacing, \(d (\AA) \) | Atomic plane, (hkl) |
|---|---|---|---|---|---|
| albite (example) | No | Yes | 2.97 | 3.99 | (101) |
| analcime | |||||
| aragonite | |||||
| calcite | |||||
| illite | |||||
| diopside | |||||
| quartz |
In this activity, we will use XRD data from Fig. \(\PageIndex{1}\) of the paper to identify the major minerals comprising the clay clone and leg-shaped artefacts. In XRD, a ray of X-rays is incident on the sample crystal and are scattered by the atoms in the crystal; the angles of the scattered X-rays are related to the orientation of the sets of atomic planes in the crystal. Bragg's law relates the lattice spacing \(d\) of a set of atomic planes and the diffraction angle \(\theta\):
\[2d\sin\theta = \lambda\]
where \(\lambda= 0.207 \AA\) is the wavelength of the X-rays from the synchrotron; note that \( 1\AA = 0.1 {\rm nm} = 10^{-10}{\rm m}\). By determining several sets of atomic planes \(d\) from several diffraction peaks, one can identify of the mineral. Here, we will only determine one strong diffraction peak for each mineral. For example, for the mineral albite, one strong diffraction peak is observed in the X-ray diffraction data for the leg-shaped clay (purple line) at the diffraction angle of \(2\theta= 2.97^\circ\). From Bragg's law, \( 2\times d\sin(2.97/2) = 0.207 \), which can be solved to give the lattice spacing of \(d=3.99 \AA \); this d-spacing matches the spacing of the (101) atomic planes of albite.
- Locate one strong, distinct (not mixed) diffraction peak for each of the listed minerals in the table above. From the angle of diffraction of these peaks, use Bragg's law to identify the corresponding atomic plane lattice spacing. Verify that all four lattice spacings belong to the crystal calcite.
- Based on the X-ray diffraction intensity counts relative to the standards (the colored lines), identify the presence or absence of the minerals for the clay cone and the leg-shaped clay artefact.
- Which mineral found among these two sample artefacts are most common and found in all clay artefacts examined in this study?
- Which mineral found among these two sample artefacts are likely to represent the result of decomposition due to thermal treatment (i.e., baking)?
- Which minerals are silicates?
- Which minerals are clays, the weathering products of silicates?
- Which minerals are carbonates?