How to add math on your blog : MathJax + Blogger

This tip is useful for engineering and science bloggers who want to share their knowledge on the web. Here is the way I found. I recently tested it on the blogger system,  the purpose is to share science tutorials with you using the correct math way.

Let's do it!

Draft on paper of the Debye-Scherrer equation for crystal size calculation 

Step 1: Add a new gadget to your blog and copy and paste the following script.

<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>

Step 2: Write code in a new post following using latex language inside:

• Inline \( latex code here \)
• Paragraph  \[ latex code here \]

Step 3: Equation test: Debye -Scherrer  for crystal size calculation
$$D(\text{nm})=\frac{0.9\lambda }{\beta \cos \theta }$$

• D: Crystal size 
• $\lambda$ : 0.15406 nm  X-Ray wavelength 
• $\beta$ :  FWHM in radians (Full width at half maximum)  
• $\theta$ : Angle location of the peak in radians. 

If you have any questions, please comment on the post.

Samples from : https://www.mathjax.org/#samples

• The Quadratic Formula

$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

• Cauchy's Integral Formula

$$f(a)=\frac{1}{2\pi i}\oint \frac{f(z)}{z-a}dz$$

• Angle Sum Formula for Cosines

$$\cos (\theta +\varphi )=\cos (\theta )\cos (\varphi )-\sin (\theta )\sin (\varphi )$$

• Gauss' Divergence Theorem

$${\int }_D(\mathrm{\nabla }\cdot F)dV={\int }_{\partial D}F\cdot ndS$$

• Curl of a Vector Field

$$\overrightarrow{\mathrm{\nabla }}\times \overrightarrow{F}=(\frac{\partial F_z}{\partial y}-\frac{\partial F_y}{\partial z})\mathbf{i}+(\frac{\partial F_x}{\partial z}-\frac{\partial F_z}{\partial x})\mathbf{j}+(\frac{\partial F_y}{\partial x}-\frac{\partial F_x}{\partial y})\mathbf{k}$$

• Standard Deviation

$$\sigma =\sqrt{\frac{1}{N}\sum _{i=1}^N(x_i-\mu {)}^2}$$

• Definition of Christoffel Symbols

$$({\mathrm{\nabla }}_{X}Y{)}^k=X^i({\mathrm{\nabla }}_{i}Y{)}^k=X^i(\frac{\partial Y^k}{\partial x^i}+{\mathrm{\Gamma }}_{im}^k{Y}^m)$$

How to read a scientific paper in just three steps

Reading on paper is an old school way to annotate
and highlight the most interesting elements

For a scientist, reading is a must responsibility in the modern world of information, this task allows us to update the state of the art of the current research. For example, the objective of my work is to reproduce and improve antimony sulfo-selenide thin-film solar cells. Therefore, the first thing I did before experimental research It was to read the updated literature. As I am in touch with the author of the paper of interest I asked him about it's last published paper where their group develops Sb-S-Se photovoltaic mini-module prototypes. 

P.K. Nair*, J.D.G. Sánchez, L.G. Martínez, P.Y.G. Ayala, A.K.M. Peñaloza, A.B. León, Y.C. García, J. Campos Álvarez, M.T.S. Nair, Chemically Deposited Antimony Sulfide Selenide Thin Film Photovoltaic Prototype Modules, ECS J. Solid State Sci. Technol. 8 (2019) Q89–Q95. doi:10.1149/2.0101906jss.

To fully understand, I almost read a scientific paper three times:

• First: Print it or read it on PDF (Mendeley could help), the important thing here is to read from the beginning to the end as soon as possible.
• Second: Make annotations for later discussion and highlights from the most important elements you can find on the text.
• Third: Write a resume, this will allow you to save the essential information in the same notebook of literature review. I prefer to write it on the Blogspot or a note on the Evernote app following the next template.

Read more, to discover the structure or template for paper review, here you are going to write just the notes and highlighted parts. This is my way to learn fast. If you have an alternate strategy please feel free to share it in the comments section.

Fabrication of Titanium dioxide as a compact layer for Perovskite and thin-film solar cells

Special thanks for Dra Hailin Zao Hu at IER-UNAM who let me collaborate and learn from their group the methodology for TiO2 compact layer deposition.  All the training was possible with the assistance of Ph.D. student Fabian and undergraduate  Ing. Gabriela Abrego from UTEZ.

Preparing TCO with magic tape  for HRT layer deposition 

Spin coater  and micropipette are the essential tools for TiO2 deposition 

First heating of the compact layer over a hot plate : low temperature

Second and final heating - Sintering TiO2 on a muffle furnace : high temperature

Compact TiO2 layer deposited over a TCO for thin-film chalcogenide or Perovskite solar cells.