Students gain experience using a spreadsheet and working with others to decide how to conduct their model 'experiments' with the NASA GEEBITT (Global Equilibrium Energy Balance Interactive Tinker Toy). This activity helps students become more familiar with the physical processes that made Earth's early climate so different from that of today. Students also acquire first-hand experience with a limitation in modeling, specifically, parameterization of critical processes.

In this activity, learners use the STELLA box modeling software to determine Earth's temperature based on incoming solar radiation and outgoing terrestrial radiation. Starting with a simple black body model, the exercise gradually adds complexity by incorporating albedo, then a 1-layer atmosphere, then a 2-layer atmosphere, and finally a complex atmosphere with latent and sensible heat fluxes. With each step, students compare the modeled surface temperature to Earth's actual surface temperature, thereby providing a check on how well each increasingly complex model captures the physics of the actual system.

Show Caption
Hide This diagram shows the relationship of Gibbs Free Energy to composition. In this diagram there are two minima represented for free energy which is achieved by unmixing of two distinct phases each with definite composition. The dashed line, which is tangential to the two minima in the free energy curves, gives the composition of the coexisting minerals at a specific temperature. From: Klein, C., and Dutrow, B., Manual of Mineral Science, 23rd ed., J. Wiley and Sons. Used with permission. The phenomenon of solid solution is common in many rock-forming minerals. At high temperatures, thermal vibrations permit accomodation of ions with size differences on the order of 15-30%. However, as physical conditions change, ions no longer fit into similar sites which creates internal (lattice) strain energy. Consequently, the mineral composition must adjust to relieve this strain energy and minimize the Gibbs Free Energy of the system. One possible response of the system is for elements in a crystal to move from one chemical site to another via intracrystalline diffusion. This results in segregated domains that are enriched in one element or another--this is a process called exsolution.
A good example of this process can be seen in the alkali feldspar mineral group. At high temperature the mineral anorthoclase (K,Na)AlSi3O8 shows complete solid solution, i.e. there is a random distribution of K and Na in the alkali sites of the crystal. Upon cooling, Na and K segregate into more ordered domains creating areas that are rich in albite NaAl Si3O8 and microcline KAlSi3O8(see Figure 1).
The purpose of this exercise is to provide a number of activities to demonstrate how exsolution works and to demonstrate complex-system behavior in this relatively common natural phenomenon.

Part I: Images of naturally occurring perthite.
The following images show minerals that have undergone exsolution at different scales. The image on the top left shows exsolution as viewed with a Transmission Electron Microscope (TEM; field of view is 10 microns). The image on the top right is a photomicrograph of exsolution in microcline as seen in thin section (cross-polarized light, field of view is 2 mm). The picture on the bottom left is a hand sample of perthitic microcline as seen in hand sample (field of view is 10 cm). The picture on the bottom right is a picture of plagioclase feldspar showing the "schiller" effect. This is caused by sub-microscopic unmixing of two distinct plagioclase phases in the compositional range of labradorite (An50 - An70) which results in the beautiful play of colors seen in this photo; (field of view of 20 centimeters). This series of pictures is a good example of scale invariance of this physical phenomenon.
Examine perthite textures from hand samples and thin sections from your own mineralogy collection. We can easily envision unmixing of two immiscible fluids--for example oil and vinegar salad dressing. The same thing happens when we unmix (i.e. exsolve) solid phases--the process just takes a bit longer as atoms have to migrate in the crystal lattice by intracrystalline diffusion! How can such a common feature as perthite be understood in terms of complex-system behavior?

Exsolution observed on a sub-microscopic scale in this TEM picture; this microstructure shows unmixing of labradorite in very fine essentially parallel lamellae. From Champness, P.E., and G.W Lorimer, 1976. Exsolution in silicates. Chapter 4.1 in Electron Microscopy in Mineralogy. H.R. Wenk, ed. Springer-Verlag, New York. Field of view is 10 microns.

Perthite observed in thin section. Field of view is 2 mm.

Perthite observed in hand sample. Field of View is 10 cm.

Unmixing of parallel lamellae, as observed in a hand specimen of labradorite from Madagascar. These lamellae act as diffraction grating for white light, producing spectral colors known as labradorescence or the "schiller effect"; the field of view is 20 cm. Photo by B. Dutrow; used by permission.]

Part II: Exsolution Puzzle Exercise.
This exercise is done in groups of 2-3 students. Coins are initially randomly distributed on a chessboard, and are then subsequently moved to create domains of increasing order (regions that are dominated by either pennies or nickels). This is a kinesthetic learning exercise that creates a physical model that simulates how the exsolution process works. (Inspired by Greg Marfleet, Carleton College)

Randomly distribute 20 pennies and 20 nickels on the attached 7x7 chessboard (Microsoft Word 33kB Dec1 10). The random distribution of pennies and nickels is analogous to the random distribution of Na and K in the high temperature alkali feldspar, anorthosite. (See Figure 1)
The goal is to have a given coin completely surrounded by similar neighbors (i.e. 8 nearest neighbors of the same type of coin located on adjacent edges and the diagonal squares. Each student will sequentially move a coin into an adjacent open position (horizontal, vertical and diagonal moves are allowed) to achieve this desired configuration. Perfect ordering of nickels and pennies into discrete domains is analogous to perfectly ordered crystals of albite and microcline. [NOTE: in this exercise we are modeling the diffusivity of only the alkali elements, Na and K. The ordering of Si and Al in the tetrahedral sites of a feldspar crystal is a related, but entirely different process].
Systems tend to minimize Gibbs Free Energy (see Figure 2) on their way towards a state of equilibrium. In this example, the surface area surrounding domains of the segregated compositions (nickels/Na and pennies/potassium) is proportional to the excess Gibbs Free Energy of those domains. As clusters of similar coins evolve (segregate) and get bigger, the bounding surface areas are minimized and the energetics of the system are decreased.

INSTRUCTIONS

For the initial random state, determine the area surrounding each type of element; do this by assuming the unit length along each edge is 1 and add all the surfaces surrounding Na/nickel and K/potassium coins or aggregates of coins. Count any edges that are not adjacent to another similar coin (i.e. count all nickel-penny interfaces, and any edge where a nickel or penny is adjacent to an open space. Do not count the external edges on the outer border of the chessboard).
Make 10 moves of the coins (always moving into an adjacent open space either right, left, up, down, or on a diagonal) and again determine the bounding surface areas. Record these surface area values for pennies and nickels. Repeat after 20, 30, 40, 50, and 100 moves.
After each set of moves, report your surface area measurements for both pennies and nickels to your instructor; record these values on a spread sheet for later plotting and analysis.
This part of the exercise should take about 45 minutes to complete the sets of movements and measurement of the surface areas.

Here is an example experiment showing the progressive ordering of pennies (potassium) and nickels (sodium). Show pictures of the 2-D distribution of pennies and nickels after 10,20, 30, 40, 50 and 100 successive moves
Hide

Original random distribution of coins.

Distribution of coins after 10 moves.

Distribution of coins after 20 moves.

Distribution of coins after 30 moves.

Distribution of coins after 40 moves.

Distribution of coins after 50 moves.

Distribution of coins after 100 moves; perfect order.

Plot your results. Assume that each move requires 1 unit of time.

Plot your data on a X-Y plot with surface area on the Y axis and time on the X-axis. What is the distribution of your data? (Try plotting data for pennies, nickels, their sum, and their averages). Create a "best fit" curve through the data as plotted on this X-Y diagram (easily done with functions programmed into Excel). . What type of mathematical function is represented by a curve that has a steep slope to begin (left side of the plot), and becomes asymptotic to the X-axis away from the origin? Did you notice that the first set of coin moves produced the largest change in surface area, and that subsequent sets of moves produced smaller and smaller changes to the surface area?
Have you seen other plots with similar profiles from your other studies in Earth Science?
Show Answer:
Hide radioactive decay; longitudinal profile of rivers.... It appears that many processes in Earth Science may follow the same mathematical laws.
Now plot your data on a log-log plot with surface area on the ordinate (Y-axis) and time on the abscissa (X-axis). Create a "best fit" curve through these data (easily done with functions programmed into Excel). What is the shape of this curve? Does this relationship demonstrate a) an exponential function? b) a power law?
Here is an example dataset (Excel 74kB Dec1 10) for 12 experiments completed by the spring 2010 Mineralogy class at Montana State University. Raw data and corresponding graphs are presented in the attached spreadsheet file. Compare your results with those shown in this example exercise.

Intracrystalline Diffusion and Fick's Law
The rate of transport of mass (and energy) through a fixed medium can be described mathematically by Fick's Law of Diffusion. Show details about Fick's Law of Diffusion
Hide.
The fundamental expression of Fick's First Law of Diffusion can be written as:

J = -D( -- c/ -- x)

Jis the flux of a material along a compositional gradient (e.g. mol / length2time1 ), the amount of material (e.g. atoms or moles) that will flow through a small area during a fixed time interval.
Dis the diffusion coefficient (length2 time -1);
c is the concentration (amount of material per volume, mol/m3), and
x is the length (m)
Fick's Law shows that the flux of an ion diffusing through a stationary medium (like the crystalline lattice in our example) is proportional to the concentration gradient ( -- c/ -- x). As diffusion proceeds, the concentration is always changing, and thus, the flux is always changing. Can you see why this process exhibits non-linear behavior and must be represented as a power law?
Note that The diffusivity, D, scales with temperature:

D ~ (kT/h) exp(-Q*/RT)

where k is Boltzmann's constant, h is Planck's constant, and Q* is an activation energy. This means that the rate of diffusion decreases with temperature. Consequently, exsolution will ultimately grind to a halt as temperature decreases. This is why we can observe perthite development in alkali feldspars in a wide variety of igneous and metamorphic rocks...the perthite texture gives us information about the cooling history of the mineral up to a point, but then exsolution will slow to a stop and the perthite will continue to exist in a metastable state at the surface of the earth.
Different types of diffusion pathways include: intragranular (volume) diffusion, grain boundary diffusion, diffusion in a bulk fluid, and diffusion related to crystal defects. In our example of perthite exsolution, intragranular (volume) diffusion is the operative process. This process is most effective at high temperatures.

Note that generally material tends to move in a direction from high to low concentrations, and thus, compositional gradients tend to be minimized by diffusion. However, in the case of exsolution and perthite development during cooling of a high-temperature, homogeneous alkali feldspar (anorthite), just the opposite effect happens--segregated domains of albite and microcline become more stable at lower temperatures. Why is this the case? The answer lies in the overall energetics of the system. It turns out that lattice strain that is induced upon cooling of anorthite results in large excess energy in the system. To minimize this excess energy, a single homogeneous grain of anorthite (stable at high temperature), will undergo "spinodal" decomposition upon cooling. This results in two energy minima, one for each phase, as illustrated in Figure 2. Upon further cooling, these energy minima continue to separate, thus resulting in two stable phases whose compositions increasingly approach the end member compositions of albite and microcline. A more complete description of this process can be found in Chapters 5 and 7 of Putnis A. and McConnell J.D.C. Principles of Mineral Behaviour 258pp. Blackwell Scientific Publications. Oxford. 1980.
Part III: Computer Simulation

Model output from the NetLogo "segregation"program; 2000 objects achieved 70% similarity.The computer program NetLogo can be used to model complex system behavior. This computer program was developed by Uri Wilensky (1999) at the Center for Connected Learning and Computer-Based Modeling, Northwestern University. Evanston, IL. For this exercise, we will use the pre-programmed function for Segregation

Experiment with this program by changing the input parameters to try to reproduce a) the pattern you developed in the puzzle model above, and b) perthite patterns observed in the natural microcline crystals.

Part IV: Visualization of the Development of Exsolution

The binary solvus phase diagram for the alkali feldspar system at low pressure. Figure provided by Dexter Perkins, used with permission.The binary "solvus" phase diagram (showing the relation of temperature to composition) is typically used to show the phase relations for alkali feldspars. A single homogeneous alkali feldspar occurs at high temperatures (Figure 1a), but as the system cools eventually the phase boundary (solvus) is intersected and the exsolution (unmixing) process begins. "Underneath" the solvus a single feldspar is no longer thermodynamically stable, and the system begins to separate into two phases that become increasingly Na-rich or K-rich upon further cooling. This visualization demonstrates the cooling history of an alkali feldspar, including use of the "lever rule" to calculate phase composition (mineral) and relative proportions. Examine the accompanying illustrations and track the "state" of the system as temperature changes. Binary Solvus for the Alkali Feldspar System. The accompanying illustrations on the right show the "state of the system" in terms of the relative proportions of the phases present for each assigned temperature.
Relate these products and processes to natural occurrences of perthite, and think about the changes that have to take place on the atomic scale to produce the mesoscopic features that are visible in hand samples.

Part V: Thought Questions

Driving forces: in equilibrium thermodynamics, the system always drives towards the lowest Gibbs Free Energy. At equilibrium, chemical potential is zero. This typically means there are no compositional gradients. Why does this system drive towards segregated domains that are rich in Na and K?
Consider entropy "in the system". What do we mean by "the system"?
Refer to Ilya Prigogine's (winner of the 1977 Nobel Prize for Chemistry) classic work on this subject: Order out of Chaos, Man's New Dialogue with Nature (1984, Bantam Books, 394 pp.)

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This is the first instructional sequence in a teacher's guide built with the purpose of helping students build a deeper understanding of the Structures and Properties of Matter standard.Students have the opportunity to engage with interactive simulations, create poetry, drawing scientific diagrams, read complex text, develop evidence based explanations and design a model . The instructional sequence described in the lesson uses the 5 E learning model and includes a variety of online simulations, polls and model drawings.

A collaboration between the National Aeronautics and Space Administration (NASA) and the CK-12 Foundation, this book provides high school mathematics and physics teachers with an introduction to the main principles of modeling and simulation used in science and engineering. An appendix of lesson plans is included.

Through class discussion and think-pair-share questions, this activity helps students come to understand the difference between emf and potential difference in electrical circuits. These concepts are broached within the context of internal resistance of batteries.

In this interactive lecture, models of the hydrogen atom are explored using an online Java applet. The exploration leads to qualitative and quantitative analysis of energy transitions.

How did scientists figure out the structure of atoms without looking at them? Try out different models by shooting light at the atom. Check how the prediction of the model matches the experimental results.

This activity is an indoor lab for use with Vernier gas pressure sensors that allows students to experimentally determine the molar volume of a gas and ideal gas constant.

This activity is a stand-alone problem set that involves converting mineral formulas to mole and weight %. The results are plotted on diagrams, some of which require projections. Students are asked to consider when they would use such diagrams, and also the shortcomings of projections.

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In this activity, students interact with 12 models to observe emergent phenomena as molecules assemble themselves. Investigate the factors that are important to self-assembly, including shape and polarity. Try to assemble a monolayer by "pushing" the molecules to the substrate (it's not easy!). Rotate complex molecules to view their structure. Finally, create your own nanostructures by selecting molecules, adding charges to them, and observing the results of self-assembly.

Created by the Concord Consortium, the Molecular Workbench is "a modeling tool for designing and conducting computational experiments across science." First-time visitors can check out one of the Featured Simulations to get started. The homepage contains a number of curriculum modules which deal with chemical bonding, semiconductors, and diffusion. Visitors can learn how to create their own simulations via the online manual, which is available here as well. The Articles area is quite helpful, as it contains full-text pieces on nanoscience education, quantum chemistry, and a primer on how transistors work. A good way to look over all of the offerings here is to click on the Showcase area. Here visitors can view the Featured simulations, or look through one of five topical sections, which include Biotech and Nanotechnology. Visitors will need to install the free Molecular Workbench software, which is available for Windows, Linux, and Mac.

Do you ever wonder how a greenhouse gas affects the climate, or why the ozone layer is important? Use the sim to explore how light interacts with molecules in our atmosphere.

This reference is a series of assessment items that require that the students think through momentum conceptually, analyze graphs related to impulse and momentum, and work through calculations using momentum and impulse. There are energy and momentum problems mixed together in this set. Due to the large number of assessment items, the instructor will want to select a portion of the questions rather than use the entire set as a single assessment. The webpage is formatted in a straight forward text so it is easy to copy and paste the items for use in classroom tests and quizzes.

Students learn the physical properties of sound, how it travels and how noise impacts human health—including the quality of student learning. They learn different techniques that engineers use in industry to monitor noise level exposure and then put their knowledge to work by using a smart phone noise meter app to measure the noise level at an area of interest, such as busy roadways near the school. They devise an experimental procedure to measure sound levels in their classroom, at the source of loud noise (such as a busy road or construction site), and in between. Teams collect data using smart phones/tablets, microphones and noise apps. They calculate wave properties, including frequency, wavelength and amplitude. A PowerPoint® presentation, three worksheets and a quiz are provided.

In this activity, students compute the strengths of the gravitational forces exerted on the Moon by the Sun and by the Earth, and demonstrate the actual shape of the Moon's orbit around the Sun. The lesson begins with students' assumptions about the motions of the Moon about the Earth and the Earth about the Sun, and then test their understanding using an experimental apparatus made from a cardboard or plywood disk and rope. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.

These two activities are just a small part of overall fun students will have in discovering the wonders of magnets and how they apply to us every day.

Students learn why and how motion occurs and what governs changes in motion, as described by Newton's three laws of motion. They gain hands-on experience with the concepts of forces, changes in motion, and action and reaction. In an associated literacy activity, students design a behavioral survey and learn basic protocol for primary research, survey design and report writing.

?What is Motion Diagrams in one dimension هذه المحاكاة تتحدث عن الحركة في بعد واحد

In this activity students analyze the motion of a student walking across the room and predict, sketch, and test distance vs. time graphs and velocity vs. time graphs.