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

\[ x = {-b \pm \sqrt{b^2-4ac} \over 2a} \]

• Cauchy's Integral Formula

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

• Angle Sum Formula for Cosines

\[ \cos(\theta+\phi)=\cos(\theta)\cos(\phi)−\sin(\theta)\sin(\phi) \]

• Gauss' Divergence Theorem

\[ \int_D ({\nabla\cdot} F)dV=\int_{\partial D} F\cdot ndS \]

• Curl of a Vector Field

\[ \vec{\nabla} \times \vec{F} = \left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right) \mathbf{i} + \left( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \mathbf{j} + \left( \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \mathbf{k} \]

• Standard Deviation

\[ \sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2} \]

• Definition of Christoffel Symbols

\[ (\nabla_X Y)^k = X^i (\nabla_i Y)^k = X^i \left( \frac{\partial Y^k}{\partial x^i} + \Gamma_{im}^k Y^m \right) \]

Exploring the XRD system at IFUAP

A scientist is continuously seeking the truth of nature. There is a jungle of fields to explore from material science to the universe, a scientist could be doing experiments at the laboratory, or maybe they just need a comfortable place to think and create new theories which will explain new phenomena. 

Training day: XRD System  and software High Score Plus, BUAP

Today I was able to explore the XRD system at IFUAP (shown in the above picture). The purpose of this visit was to analyze a previous measured XRD pattern. Gratefully the responsible researcher allows me to manipulate the software High Score Plus to perform a qualitative analysis to identify the phases in the material.

High Score plus, performing phase analysis, and calculation of crystal size.

To identify the phase three steps should be performed in the following sequence:

1. Background determination: This is a must step due phase analysis depends on it.
2. Peak search: Automatic + Manual is the best
3. Phase analysis: Should be restricted to the constitutive elements to gain time. In my case, the restriction increase using just inorganic materials and star quality powder diffraction files (PDFs) from the database.

Once these three steps are done, the analysis gives you three important values: 

• Background: This information is necessary to make a good report where the background should be extracted from the observed XRD measurement.
• Constitutive phases: This data confirms if your material is pure or is mixed
• Crystal size: This parameter gives the size domain D < 100 nm makes you think in the nanoworld.

If you want to know how the XRD system works  watch the following video: 

Have you ever seen an XRD system with your own eyes?

Challenge: Share your ride !

Downtown Puebla street - Callejon del Sapo

A month ago, I was traveling by bus from Morelos to Puebla city during the night. When I ask for my stop around 21-22 hours, more people get down too. It was a scary scene due there were just two local taxi units and no more transportation. Therefore, there was no other choice than ask for an Uber ride.  I observe the situation. Almost everybody was using their cellphone to call their friends or families.

Two cars get immediately and lift three persons. Then a young boy and I kept there a little bit more. We were waiting for a better tariff of the Uber.  As the price was elevated, I decided to ask him. Do you want to share the ride? When he said, I already pick one. And it will get here in a minute. Suddenly he surprises me, asking back, "If you want, I can pick you up to a safer place." I accept and think:  

If you break the ice you will be able to offer or get a ride 

Last weekend during midday I was standing at the bus stop an older man was there too.  We wait for 10-15 minutes, and the bus did not appear.  What was happening with public transportation?  I did not know, but I felt it was unsafe to keep in one place for an extended period.  Then I proceed to get an Uber and remember the last day when the young guy offers me a ride. This DejaVu makes me think: Its time to get back, Let's share my ride. 

I know it is difficult to open a conversation with somebody you don't know, but if there is a purpose where you can help somebody else. Then there is an excellent opportunity to show gratitude.  I think this challenge will promote kind gestures, like the movie Pay it Forward when somebody receives the support he must pay it forward and create a change.  It is a great movie, I can give you the link if you want to watch in old ways DVD.

Pay it forward movie: https://amzn.to/2FjgkXR 

This challenge its a way to give something. Have you ever share something like a ride, a book, a cup of coffee? Well, you can share your story in the comments below.  Have a great day, and remember. Small things make a bigger difference.