Determination of the Composition of Fayalite-Forsterite Crystals
Sarah North and Jaren Strandlie
Abstract
Olivine crystals from San Carlos, Arizona were ground and tested for their composition
using X-ray diffraction. Data showed the composition was found to be one hundred percent
forsterite. The ground crystals were then tested again for composition by examining the Becke
lines when immersed in fluids of known refractive indexes. This method showed the crystals to
have a composition greater than eighty percent forsterite.
Introduction
Olivine has four end members. However, this project is only concerned with two of these
end members, fayalite (Mg2SiO4) and forsterite (Fe2SiO4), which are the most common. Olivine
is an orthorhombic neosilicate, meaning the silicon to oxygen ratio is one to four and is
composed of isolated tetrahedra. Layers of the isolated tetrahedra are symmetrical, but each is
offset by b/2, in a hexagonal closets packing array. The crystal structure has one eighth of its
tetrahedral sites filled with silicon and one half of its octahedral sites filled with Mg2+ and Fe2+.
Both the tetrahedral and the octahedral sites experience distortion due to edge sharing with other
sites. The tetrahedral sites share three edges with octahedral sites, causing an elongation along
the a axis. There are two types of octahedral sites in the crystal, M1 and M2. Each M1 site
shared six edges, and each M2 site shares three edges. Both sites exhibit shortened edges due to
this sharing. The number of these distortions increases as the crystal becomes more Mg-rich
(Papike and Cameron, 1976).
North and Strandlie: Composition of Fayalite-Forsterite Crystals
2
(Papike and Cameron, 1976)
The optical properties of olivine are also important when determining the composition.
Olivine is biaxial (+) or (-) mineral. However, the refractive index is dependant both on the
composition of the crystal and the orientation of the crystal. The standard ranges of the
refractive indexes for olivine are given as: alpha = 1.641 – 1.835, beta = 1.651 – 1.877 and
gamma = 1.670 – 1.886 (Perkins and Henke, 2000). The forsterite end member has a lower
refractive index in each orientation than the fayalite end member (Deer and Wager, 1939).
The samples were obtained in the San Carlos Apache Indian Reservation, Arizona. This
area is located mainly within the Basin Range province, which underwent major extension and
includes a great variety of geology. A section of the reservation in the North extends into the
Colorado Plateau. The San Carlos reservation includes rocks from Precambrian to Quaternary
age. Olivine usually occurs in mafic rocks, and there are several different formations of volcanic
rocks within the reservation where olivine could occur. One such region is an area of exposed
North and Strandlie: Composition of Fayalite-Forsterite Crystals
3
quaternary age basalt. This region lies southwest of the city of San Carlos, where a mine named
Peridot Mesa is in operation (Brown, 1989).
(Brown, 1989)
Methods
Two methods were used to test the composition of the olivine crystals. X-Ray diffraction
was the first of these two. To complete this task, a Rigaku Miniflex machine was used. X-Ray
diffraction tests a powdered sample by sending an X-Ray beam at the sample in specific
directions. Each atom acts as an individual unit and when the X-Ray enters the field in-phase, it
is scattered off electrons. Most of these waves interfere destructively, but at certain angles they
will interfere constructively. This constructive interference is known as diffraction. Because
diffraction only occurs at certain angles, simple calculations can be used to find the distance
between atoms in each plane, using the angle of diffraction. The Bragg equation is used to
calculate this distance: nλ = 2dsinθ, where n equals an integer, λ is the wavelength, d is the
North and Strandlie: Composition of Fayalite-Forsterite Crystals
4
distance between atoms and θ is the incident angle (Klein, 2002). Using the Bragg equation in
coordination with the miller indices of the peak positions, the lattice cell parameters of the
crystal can be calculated.
A second method used to determine the composition of the olivine was to examine the
refractive index. The refractive index is the value of the velocity of light through air divided by
the velocity of light through the mineral (Klein, 2002). Liquids with known refractive indexes
were placed onto a slide and a small amount of the powered crystal was added. Then the slides
were examined under a microscope at high magnification. By moving slowing moving the stage
down and out of focus Becke lines were observed. Becke lines are white lines that appear to
either move in towards, or out from a crystal when a stage is moved down and out of focus. If the
Becke lines move in the refractive index of the grain is greater than that of the liquid and if the
lines move out the refractive index of the grain is less than that of the liquid.
Results
Using refractive index fluids, we determined that the refractive index of the olivine
crystals was about 1.67. In the fluid with a refractive index of 1.67, Becke lines could be
observed moving both into and out of crystals when the stage of the microscope was lowered.
This occurred because refractive index varies with orientation, and the crystals were randomly
oriented. When the olivine crystals were placed in fluids of higher refractive index the Becke
lines produced when the stage was lowered moved out of the crystals. When places in fluid of
lower refractive index, the Becke lines moved into the crystals.
North and Strandlie: Composition of Fayalite-Forsterite Crystals
5
Using XRD, the lattice parameters of the olivine sample were calculated to be a=4.75 Å,
b=10.19 Å, c=5.98 Å. The volume of the lattice cell would thus be 289.45 Å3.
Discussion:
The values obtained using refractive index fluids correlate to a composition of 90 percent
forsterite when compared to chart below. This value includes an error of less than 10 percent due
to the random orientation of the crystals that were immersed in the refractive index fluids.
North and Strandlie: Composition of Fayalite-Forsterite Crystals
The white circles represent naturally occurring olivine samples, while the black circles represent synthetic olivine.
(Deer and Wager, 1976)
The XRD values correlate to nearly 100 percent forsterite, when compared to the tables
below, with our results shown in green. The b and c parameters correspond to compositions of
greater than 100 percent forsterite, but the three lattice parameters are at least consistent in their
proximity to 100 percent forsterite.
6
North and Strandlie: Composition of Fayalite-Forsterite Crystals
7
The white circles represent naturally occurring olivine samples, while the black squares represent synthetic olivine.
(Tarantino, Carpenter and Domeneghetti, 2003)
Both methods used to analyze the olivine crystal gave the result that the sample is
Magnesium rich. In addition to having a lower refractive index, lower specific gravity (Deer and
Wager, 1976), and a smaller unit cell (Tarantino, Carpenter and Domeneghetti, 2003), the
structure of olivine with this composition has more distortion in the octahedral sites, M1 and M2,
than fayalite (Papike and Cameron, 1976). Forsterite is also optically positive, while fayalite is
optically negative. The lighter green color of our crystals is also characteristic of forsterite,
fayalite having a browner in its color (Klein, 2002). The composition we determined would also
be a typical result for olivine crystals found in San Carlos, an area where peridot, the gem variety
of forsterite, is mined.
North and Strandlie: Composition of Fayalite-Forsterite Crystals
8
Conclusion:
The results of the two methods used were consistent and provide a certain degree of
precision, but if a greater degree of accuracy were required, further experimentation would be
necessary. This could include refinement of the methods used in this project, or new methods
such as the use of a microprobe.
Greater precision could have been obtained using refractive index fluids by determining
the orientation of the crystals. In order to do this, one could find crystals that remain extinct
under crossed polarizers while the stage is rotated 360 degrees. This would mean that
microscope is pointing down an optic axis, and the relief in the beta direction could be measured.
One could also find crystals that can generate and optic axis figure. Because forsterite is optically
positive, this would mean you are looking down the c axis, thus the relief of the gamma and beta
directions would be observable (Klein, 2002). If the orientation of a crystal was determined, its
composition could be measured about 5-10 percent more accurately.
Another method would be to use a variety of index fluids carefully to find the maximum
and minimum refractive index for the randomly oriented crystals. These maximum and minimum
values would correspond to the alpha and gamma values. For more accuracy, fluids could be
combined and the resulting fluid would have an index that is the average of the two original
fluids. This method could increase result in up to a 10 percent more accurate figure for the
composition of the crystal.
Dr. Youxue Zhang of the University of Michigan also analyzed this sample of olivine.
His results indicated that the sample was 90 percent forsterite, using a microprobe, which is a
more accurate method than those used in this project. Dr. Zhang’s figure of 90 percent forsterite
North and Strandlie: Composition of Fayalite-Forsterite Crystals
is consistent with the results of this project, and provides further evidence that the sample is
forsterite.
9
North and Strandlie: Composition of Fayalite-Forsterite Crystals
10
References
Brown, J.G., Geology and ground-water resources of the San Carlos Indian Reservation; Gila,
Graham, and Pinal counties, Arizona, U.S. Geological Survey Water-Resource Investigations
Report, 89-4152, 1989.
Deer W. A. and L.R. Wager, Olivines from the Skaergaard Intrusion, Kangerdlugssuak, East
Greenland, American Mineralogist, 24, 18-25, 1939
Papike J.J and M. Cameron, Crystal Chemistry of Silicate Minerals of Geophysical Interest,
Reviews of Geophysics and Space Physics, 14, 37-39, 1976.
Perkins D. and K. Henke, Olivine, Minerals in Thin Section, 70, 2000.
Tarantino S.C, M.A. Carpenter and M.C Domenghetti, Strain and local heterogeneity in the
forsterite – fayalite solid solution, Phys. Chem. Minerals, 30, 495-502, 2003.
Klein C., Analytical Methods in Mineral Science, 22nd Edition of the Manual of Mineral Science,
309-321, 2002.