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Archive for December, 2010

Ijolite

Today I am going to discuss a rock that was presented to me at school; though when I first looked at it, I knew nothing about it. This specimen was part of my last lab assignment for Mineralogy, where I was given a sample and told to describe everything about it. I spent by far the most amount of time on this assignment, but also enjoyed it the most. The lab was the culmination of every diagnostic tool we had learned throughout the semester.

The rock itself was given to us in both hand sample and thin section so we could compare and combine our microscope work with the hand sample testing techniques like testing for hardness or describing luster.

Let me start by showing you the rock (please excuse the blurry photo, it looked sharper when I first took the photo):


The rock contains about 80% dark, large-grained (~3 mm), minerals that have a vitreous luster seen through the hand lens. While I was able to scratch the mineral with an iron nail some pressure had to be applied, so I called the hardness a 5 on the Mohs Scale. The same mineral leaves a gray-brown streak when rubbed against an unpolished porcelain plate. The other 20% of the rock is made up of a dark-brown/black mineral and a white/colorless mineral. The black/brown mineral has a hardness of 3 and exhibits one distinct cleavage plane, while shows a vitreous luster through the hand lens and a prismatic habit.

Sorry for the lack of scale.

In hand sample I saw three minerals and this was confirmed through thin section work. The dark mineral seen in hand sample showed a yellowish-green color, with slight pleochroism, two good cleavage planes, moderate high relief and second order birefringence in thin section. Comparing these observations with the HS work I felt comfortable calling this mineral clinopyroxene.

The brown/black mineral seen in HS showed a tan-brown color, with one good cleavage plane, distinct pleochroism, high relief, and bird’s eye extinction. The mineral is biotite.

The colorless mineral in both HS and TS had no cleavage or pleochroism, had low relief, and first order gray birefringence. I called this mineral nepheline and ended up being very important in my final decision.

Since the rock’s main two constituents were clinopyroxene and nepheline the original thought was that it could be a nephelenite, but since the mineral grains were larger it leads to the assumption that this igneous rock was plutonic. Though in HS the clinopyroxene was dominant the presence of the nepheline kept me from calling it mafic as there was a significant amount and no zonation between the two minerals. For these reasons I feel good to quite-good about calling this rock an ijolite, an igneous rock containing mostly nepheline and augite (clinopyroxene).

I was planning on showing a picture of ijolite, but I am not up to date on my copyright laws so you’ll have to do your own Google-ing. Sorry.

 

 

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As of Monday morning I am done with school for the semester. This has been a taxing few months, and I am ready for a break. Hopefully the time off will give me an opportunity to blog more often, as it has clearly been lacking. To celebrate the end of the semester I decided to compile a blog post that would include some aspect from each of the three classes I took: Calculus, Physics, and Mineralogy.

Here is a problem I created to acknowledge the three in harmony. Test me to see if I solved it correctly, and if not, please feel free to solve it yourselves and share your answer. (It took me awhile to come up with a problem that included all three, and while it makes sense in my head, it may not translate well to people outside of it. Thanks for your understanding)

If a calcite crystal is thrown vertically down from a cliff 50 meters high with an initial velocity of 5 m/s, and a horizontally projected lamp is placed at a height of 20 meters and 8 meters from the base of the cliff. What speed is the calcite travelling when it passes its critical angle (the angle at which light cannot refract in a medium)?


The first step was to determine at what height the critical angle of calcite would be reached, and I did so using Snell’s Law (n2/n1 = sinϴ1/sinϴ2) and the understanding that the critical angle for all minerals is when sinϴ2 = 1. Also needed were the refractive indices of calcite which are found easily enough in any of my textbooks or at handbookofmineralogy.org.

n1 = 1.658 and n2 = 1.486.


From the math above the critical angle of calcite was found to be 63.7° by solving for the sin-1 of (n1/n2). Now that we have the angle we can determine the height of the calcite by using a little trigonometry. But, before we do that it is best to point out that the calcite will pass the angle twice in its path, and therefore we will be solving for two different velocities.

With the help of a handy triangle and SOHCAHTOA I found the height by solving 8 * tan (63.7) which happens to be ~16 meters. Therefore the calcite passes the critical angle at 20 m (height of the lamp) ± 16 meters, so, 4 and 36 m.

By jumbling a bunch of physics and calculus formulas together I surmised the path of the calcite to follow the function:

f(t) = 4.9t2 + 5t – 50


By setting this function equal to the two determined heights and solving for t with the quadratic formula I found the time it took for the calcite to reach the critical height after being thrown. (Also by understanding time cannot be negative).

t = 2.8 and 3.7 seconds

Here is where the calculus really kicked in as finding the derivative of the position function gives the velocity function.

f(t) = 4.9t2 + 5t -50
f ‘(t) = 9.8t + 5

Dropping the two values for time into the velocity function allowed me to solve for how fast the calcite was traveling at those particular moments.

f ‘(2.8) = 9.8(2.8) +5
f ‘(2.8) = 32.4 m/s

f ‘(3.7) = 9.8(3.7) + 5
f ‘(3.7) = 41.3 m/s

So, if my calculations are correct that calcite was really flying at 32.4 m/s and 41.3 m/s!

Let me know what you think. Does my math hold up? Is the problem viable? Chime in!

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