diff --git a/mkdocs.yml b/mkdocs.yml index e9132bb93dd88d720f8662c9b4f015045d81978a..f6c5f293bde89971367c98b22d57653d919b71dd 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -44,7 +44,7 @@ nav: - Tight-binding model: '7_tight_binding_model_solutions.md' - Many atoms per unit cell: '8_many_atoms_solutions.md' - Crystal structure: '9_crystal_structure_solutions.md' - # - X-ray diffraction: '10_xray_solutions.md' + - X-ray diffraction: '10_xray_solutions.md' # - Nearly free electron model: '11_nearly_free_electron_model_solutions.md' # - Band structures in 2D: '12_band_structures_in_higher_dimensions_solutions.md' # - Basic principles: '13_semiconductors_solutions.md' diff --git a/src/10_xray_solutions.md b/src/10_xray_solutions.md index 031ee8f293c4e5bdcb193ee969f0d9398a3b8032..3f6a4d65dd8d77d657d51a87f4e4fe0761fbd1c3 100644 --- a/src/10_xray_solutions.md +++ b/src/10_xray_solutions.md @@ -77,7 +77,7 @@ Since $\rho=d / V$, we must maximize $d$. To do that, we must minimize $|G|$ (Su ## Exercise 3: X-ray scattering in 2D ### Subquestion 1 -``` +```python def reciprocal_lattice(N = 7, lim = 40): y = np.repeat(np.linspace(-18.4*(N//2),18.4*(N//2),N),N) x = np.tile(np.linspace(-13.4*(N//2),13.4*(N//2),N),N) @@ -103,7 +103,7 @@ $k = \frac{2 \pi}{\lambda} = 37.9 nm^{-1}$ Note that $|k| = |k'| = k $ since elastic scatering -``` +```python reciprocal_lattice() # G vector plt.arrow(0,0,13.4*2,18.4,color='r',zorder=10,head_width=2,length_includes_head=True) @@ -144,15 +144,9 @@ $$ ### Subquestion 4 -For FCC, the structure factor is the following: +Due to bcc systematic absences, the peaks from lowest to largest angle are: +$(110),(200),(211), (220), (310)$ +### Subquestion 5 -$S_\mathbf{G} = $ -$$ -\begin{cases} - 4f & \text{if $h,k,l$ are all odd or even}\\ - 0 & \text{if otherwise} -\end{cases} -$$ - -Since $(110)$ have mixed odd and even indices, no diffraction peak will be observed on FCC. For BCC, however, $(110)$ gives $1+1+0 = 2$ even number, so there will be diffraction. +$a = 2.9100 \unicode{xC5}$