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Nature (London), 1993, 363, 603-605.
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         M.C. Nature Nanotechnology, 2006, 1, 60.
     5. Tan, Y.; Resasco, D.E. J. Phys. Chem. B, 2005, 109, 14454.
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         M.A. Phys. Rev. B, 2005, 72, 075207.
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Jorio, A.; Dresselhaus, G.; Dresselhaus, M.S. (Eds.). Carbon Nanotubes, Topics in
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Trademarks : SWeNT and CoMoCAT and registered trademarks
                              ®                    ®




of Southwest Nanotechnologies, Inc. HiPCo is a registered®




trademark of Carbon Nanotechnologies, Inc.
     13.


Conclusion
Despite early excitement about SWNT materials and the
extraordinary amount of research inspired by their discovery, to
date, commercial exploitation of the technology has been
disappointing. Perhaps there is insufficient understanding of the
practical hurdles to their commercialization. However, momentum
seems finally to be building, driven by substantial recent progress
in these fundamental areas:

Metrology and Quality Control: The concept of “if you can measure
it, you can improve it” applies here. The means are now available
to adequately characterize SWNTs and to assure consistency of
the materials needed for commercialization. Supporting this is the
soon to be available offerings by NIST of Standard Reference
Materials for calibration purposes.

Improved selectivity: Driven by applications that require more than
a near-random distribution of tube chiralities, there has been a
demonstration of the means to substantially narrow the ‘as
produced’ chirality distributions of commercial scale production
products. There is also promising work toward achieving further
selectivity through secondary processing.

Dispersion: Recent years have seen the emergence of improved
aids to disperse SWNTs for formulation in inks and composites.

Scale-up of manufacturing process: The last five years have seen
development and a maturing of scalable SWNT manufacturing
processes, which can provide commercial quantities of SWNT with
high purity, controlled properties and consistent quality




SWNT Applications
The numerous unique properties of SWNTs have led to their
application in a wide range of technological problems. Their
                                                       12




extraordinary mechanical strength is exploited in enhanced carbon
fiber and reinforced resins and elastomers; their highly conductive
    13




nature and large surface areas are utilized to prepare conductive
polymer blends and films, improved lithium ion batteries, and super
capacitors. Unique optical properties allow for their use as
electrodes in displays, solarcells, and emerging solid state lighting
technologies. The semiconducting nature of some SWNT species
allow their adaptation to logic devices, non-volatile memory
elements, sensors and security tags. It seems that new SWNT
applications emerge regularly, limited only by the creativity of
scientists and engineers working in the fiel




The field emission characteristics of the body for single-walledcarbonnanotubes (SWNTs) are investigated by use of the first-principles calculations.
We find that field emission property, chemical stability and binding energy of the tube body with the practical diameter are less sensitive to the tube
diameter, morphology, and conductive characteristic, and conclude the emission features of the body film: consistence in emission sites, uniformity in
emission energy distribution, predictability in emission effects and high emission stability, which are similar to those of graphite sheet or diamond film.
These unique features guarantee the tube body to be applicable to flat panel displays with the same picture quality, cylindrical cathode and linear
emitter.




Structure of Carbon Nanotubes
Single walled carbon nanotubes are an allotrope of sp hybridized                                                            2




carbon, similar to fullerenes. The structure can be thought of as a
cylindrical tube comprised of 6-membered carbon rings, as in
graphite. The cylindrical tubes may have one or both ends capped
with a hemisphere of the buckyball or fullerene structure.
An understanding of SWNT structure requires familiarity with the
concept of nanotube chirality, since the chirality of a SWNT
dictates many of its properties. A concept known as a Chirality
Map, illustrated in Figure 1, has been developed as a tool for
understanding chirality and its implications.
A SWNT can be envisioned as a sheet of graphite one atom thick
rolled into a tube (see inset in Figure 1). The chirality describes
both the orientation and diameter to which the sheet is rolled. Each
SWNT on the chirality map is defined by two integers, (n,m). As
indicated previously chirality defines many of the properties of the
individual SWNT. For example, SWNT shown on the chirality map
in blue are metallic in nature. These are tubes where n=m
(armchair) or n - m = 3i, (where i is any integer.) Those depicted in
yellow are semiconducting, displaying different band gaps
depending on the length of the chiral vector.




Figure 1. A graphic displaying a Chirality Map which shows the various types of SWNTs that can be forfmed.The properties are governed by the way
in which they are rolled as shown in the insert. The SWNT will be metallic in the armchair configuration, or when m-n is a multiple of 3.
Cvd method
The catalytic vapor phase deposition of carbon was reported in 1952[68] and 1959,[69] but it was not until 1993[70] that carbon nanotubes were formed by
this process. In 2007, researchers at the University of Cincinnati (UC) developed a process to grow aligned carbon nanotube arrays of 18 mm length
on a FirstNano ET3000 carbon nanotube growth system.[71]

During CVD, a substrate is prepared with a layer of metal catalyst particles, most commonly nickel, cobalt,[72] iron, or a combination. [73] The metal
nanoparticles can also be produced by other ways, including reduction of oxides or oxides solid solutions. The diameters of the nanotubes that are to
be grown are related to the size of the metal particles. This can be controlled by patterned (or masked) deposition of the metal, annealing, or by
plasma etching of a metal layer. The substrate is heated to approximately 700°C. To initiate the growth of nanotubes, two gases are bled into the
reactor: a process gas (such as ammonia, nitrogen or hydrogen) and a carbon-containing gas (such as acetylene, ethylene, ethanol or methane).
Nanotubes grow at the sites of the metal catalyst; the carbon-containing gas is broken apart at the surface of the catalyst particle, and the carbon is
transported to the edges of the particle, where it forms the nanotubes. This mechanism is still being studied. The catalyst particles can stay at the tips
of the growing nanotube during the growth process, or remain at the nanotube base, depending on the adhesion between the catalyst particle and the
substrate. Thermal catalytic decomposition of hydrocarbon has become an active area of research and can be a promising route for the bulk
production of CNTs. Fluidised bed reactor is the most widely used reactor for CNT preparation. Scale-up of the reactor is the major challenge. [74] [75]

CVD is a common method for the commercial production of carbon nanotubes. For this purpose, the metal nanoparticles are mixed with a catalyst
support such as MgO or Al2O3 to increase the surface area for higher yield of the catalytic reaction of the carbon feedstock with the metal particles.
One issue in this synthesis route is the removal of the catalyst support via an acid treatment, which sometimes could destroy the original structure of
the carbon nanotubes. However, alternative catalyst supports that are soluble in water have proven effective for nanotube growth.[76]

If a plasma is generated by the application of a strong electric field during the growth process (plasma enhanced chemical vapor deposition), then the
nanotube growth will follow the direction of the electric field.[77] By adjusting the geometry of the reactor it is possible to synthesize vertically aligned
carbon nanotubes[78] (i.e., perpendicular to the substrate), a morphology that has been of interest to researchers interested in the electron emission
from nanotubes. Without the plasma, the resulting nanotubes are often randomly oriented. Under certain reaction conditions, even in the absence of a
plasma, closely spaced nanotubes will maintain a vertical growth direction resulting in a dense array of tubes resembling a carpet or forest.

Of the various means for nanotube synthesis, CVD shows the most promise for industrial-scale deposition, because of its price/unit ratio, and because
CVD is capable of growing nanotubes directly on a desired substrate, whereas the nanotubes must be collected in the other growth techniques. The
growth sites are controllable by careful deposition of the catalyst. In 2007, a team from Meijo University demonstrated a high-efficiency CVD technique
for growing carbon nanotubes from camphor.[79] Researchers at Rice University, until recently led by the late Richard Smalley, have concentrated upon
finding methods to produce large, pure amounts of particular types of nanotubes. Their approach grows long fibers from many small seeds cut from a
single nanotube; all of the resulting fibers were found to be of the same diameter as the original nanotube and are expected to be of the same type as
the original nanotube.[80]

[edit]Super-growth CVD




Procedure PROCEDURE

**Do not open the chamber while the alarm red light is on
**Never touch the detector (may result in signal off).

      1. Obtain a sample from your instructor, place it onto the double-side tape
         which is then placed on an aluminum sample holder; if you are preparing
         a powder sample, use a spatula to spread the powder onto the double-
         side tape.
      2. Read the instructions for the Miniflex X-ray diffractometer, which are on
         the wall above the instrument. Your instructor will explain the operation.
      3. Set the instrument at optimum setting as follows
time constant 2
                                         range ?
                                    chart speed: Low

   4. Slide in the sample holder and adjust the beginning 2theta at 70 degree
      (It scans from high degrees to low degrees)
   5. Switch on the start knob and chart recorder (slow) simultaneously, run
      your sample on slow chart speed.
   6. Once scan gets down to 3 degree of 2theta , stop (switch start knob to
      off) and chart. TURN OFF X-ray.
   7. Locate all peaks on the chart and corresponding 2theta values and write
      their values into the data chart below. Perform the necessary calculations
      in the table a

                      Data Table of X-ray Diffraction Peaks
                                                                lattice spacing
        2theta theta sin(theta) n d=n x wavelength/sin(theta)
                                                                    =nxd
                              1
                              2
                              3
                              4
                              5
                              6
                              7
                              8

Wavelength = 1.5418 Å for Cu Ka

   8. nd calculate the repeat distance in your unit cell.




X-Ray Diffraction Experiment

INTRODUCTION

X-rays are electromagnetic radiation of wavelength about 1 Å (10-10 m), which
is about the same size as an atom. They occur in that portion of the
electromagnetic spectrum between gamma-rays and the ultraviolet. The
discovery of X-rays in 1895 enabled scientists to probe crystalline structure at
the atomic level. X-ray diffraction has been in use in two main areas, for the
fingerprint characterization of crystalline materials and the determination of
their structure. Each crystalline solid has its unique characteristic X-ray powder
pattern which may be used as a "fingerprint" for its identification. Once the
material has been identified, X-ray crystallography may be used to determine
its structure, i.e. how the atoms pack together in the crystalline state and what
the interatomic distance and angle are etc. X-ray diffraction is one of the most
important characterization tools used in solid state chemistry amd materials
science.
We can determine the size and the shape of the unit cell for any compound
most easily using the diffraction of x-rays.




Fig. 1 Reflection of x-rays from two planes of atoms in a solid.

The path difference between two waves:

                          2 x wavelength= 2dsin(theta)



For constructive interference between these waves, the path difference must be
an integral number of wavelengths:


                               n x wavelength= 2x
This leads to the Bragg equation:


                         n x wavelength = 2dsin(theta)

Figure 2 shows the x-ray diffraction pattern from a single crystal of a layered
clay. Strong intensities can be seen for a number of values of n; from each of
these lines we can calculate the value of d, the interplanar spacing between the
atoms in the crystal.




Fig. 2 X-ray diffraction pattern from a layered structure vermiculite clay.


EXAMPLE 1 Unit Cell Size from Diffraction Data

The diffraction pattern of copper metal was measured with x-ray radiation of
wavelength of 1.315Å. The first order Bragg diffraction peak was found at an
angle 2theta of 50.5 degrees. Calculate the spacing between the diffracting
planes in the copper metal.

The Bragg equation is

                         n x wavelength = 2dsin(theta)

          We can rearrange this equation for the unknown spacing d:

                         d = n x wavelength/2sin(theta).

theta is 25.25 degrees, n =1, and wavelength = 1.315Å, and therefore
                      d= 1 x 1.315/(2 x 0.4266) = 1.541 Å
In this lab you will measure the x-ray powder diffraction pattern from a single
crystal. Your TA will give you the sample to be measured and show you how to
set up the Miniflex x-ray diffractometer.
You should measure all the values of 2theta from the chart, and after converting
them into d values calculate the repeat distance in your unit cell. In your lab
note book list all the 2theta values with their corresponding values of n and d.
Then calculate the mean and median values of the unit cell.


INSTRUMENTATION

The X-ray diffraction experiment requires an X-ray source, the sample under
investigation and a detector to pick up the diffracted X-rays. Fig 3 is a
schematic diagram of a powder X-ray diffractometer.




Fig. 3. Schematic of an X-ray powder diffractometer


The X-ray radiation most commonly used is that emitted by copper, whose
characteristic wavelength for the K radiation is =1.5418Å. When the incident
beam strikes a powder sample, diffraction occurs in every possible orientation
of 2theta. The diffracted beam may be detected by using a moveable detector
such as a Geiger counter, which is connected to a chart recorder. In normal use,
the counter is set to scan over a range of 2theta values at a constant angular
velocity. Routinely, a 2theta range of 5 to 70 degrees is sufficient to cover the
most useful part of the powder pattern. The scanning speed of the counter is
usually 2theta of 2degrees min-1 and therefore, about 30 minutes are needed to
obtain a trace.
Reference

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Reference

  • 1. 1. S. Iijima, Helical microtubules of graphitic carbon, Nature (London), 1991, 354, 56-58. 2. S. Iijima, and T. Ichihashi, Single-shell carbon nanotubes of 1-nm diameter, Nature (London), 1993, 363, 603-605. 1. 3.R.S. Ruoff et al. Carbon 33(7), 925 (1995). Iijima, S. Nature, 1991, 354, 56. 2. Meo, M.; Rossi, M. Composite Science and Technology, 2006, 66,1597. 3. Tans, S.J.; Devoret, H.; Thess, A.; Smalley, R.E.; Geerligs, L.J.; Dekker, C. Nature, 1997, 386, 474. 4. Arnold, M.S.; Green, A.A.; Hulvat, J.F.; Stupp, S.I.; Hersham, M.C. Nature Nanotechnology, 2006, 1, 60. 5. Tan, Y.; Resasco, D.E. J. Phys. Chem. B, 2005, 109, 14454. 6. Miyata, Y.; Yanagi, K.; Maniwa, Y.; Tanaka, T.; Kataura, H. J. Phys. Chem. C, 2008, 112, 15997. 7. Jorio, A.; Santos, A.P.; Ribeiro, H.B.; Fantini, C.; Souza, M.; Viera, P.M.; Furtado, C.A.; Jiang, J.; Balzano, L.; Resasco, D.E.; Pimenta, M.A. Phys. Rev. B, 2005, 72, 075207. 8. Bachilo, S.M.; Strano, M.S.; Kitrell, C.; Hauge, R.H.; Smalley, R.E.; Weisman, R.B. Science, 2002, 298, 2361. 9. Lolli, G.; Zhang, L.; Balzano, L.; Sakulchaicharoen, N.; Tan, Y.; Resasco, D.E. J. Phys. Chem. B, 2006, 110, 2108. 10. Itkis, M.E.; Perea, D.E.; Jung, R.; Niyogi, S.; Haddon, R.C. J. Amer. Chem. Soc., 2005, 127, 3439. 11. Nair, N.; Usrey, M.; Kim, W-J.; Braatz, R.D.; Strano, M.S. Anal. Chem., 2006, 78, 7589. 12. Rensselar Polytechnic Institute. Ajayan and Zhou. http://www.rpi.edu/locker/38/001238/pdfs/applications%20of %20nanotubes. pdf. (accessed Mar 03 2009). Jorio, A.; Dresselhaus, G.; Dresselhaus, M.S. (Eds.). Carbon Nanotubes, Topics in Applied Physics.,: Springer-Verlag, New York (2008).. Trademarks : SWeNT and CoMoCAT and registered trademarks ® ® of Southwest Nanotechnologies, Inc. HiPCo is a registered® trademark of Carbon Nanotechnologies, Inc. 13. Conclusion Despite early excitement about SWNT materials and the extraordinary amount of research inspired by their discovery, to date, commercial exploitation of the technology has been disappointing. Perhaps there is insufficient understanding of the practical hurdles to their commercialization. However, momentum
  • 2. seems finally to be building, driven by substantial recent progress in these fundamental areas: Metrology and Quality Control: The concept of “if you can measure it, you can improve it” applies here. The means are now available to adequately characterize SWNTs and to assure consistency of the materials needed for commercialization. Supporting this is the soon to be available offerings by NIST of Standard Reference Materials for calibration purposes. Improved selectivity: Driven by applications that require more than a near-random distribution of tube chiralities, there has been a demonstration of the means to substantially narrow the ‘as produced’ chirality distributions of commercial scale production products. There is also promising work toward achieving further selectivity through secondary processing. Dispersion: Recent years have seen the emergence of improved aids to disperse SWNTs for formulation in inks and composites. Scale-up of manufacturing process: The last five years have seen development and a maturing of scalable SWNT manufacturing processes, which can provide commercial quantities of SWNT with high purity, controlled properties and consistent quality SWNT Applications The numerous unique properties of SWNTs have led to their application in a wide range of technological problems. Their 12 extraordinary mechanical strength is exploited in enhanced carbon fiber and reinforced resins and elastomers; their highly conductive 13 nature and large surface areas are utilized to prepare conductive polymer blends and films, improved lithium ion batteries, and super capacitors. Unique optical properties allow for their use as electrodes in displays, solarcells, and emerging solid state lighting
  • 3. technologies. The semiconducting nature of some SWNT species allow their adaptation to logic devices, non-volatile memory elements, sensors and security tags. It seems that new SWNT applications emerge regularly, limited only by the creativity of scientists and engineers working in the fiel The field emission characteristics of the body for single-walledcarbonnanotubes (SWNTs) are investigated by use of the first-principles calculations. We find that field emission property, chemical stability and binding energy of the tube body with the practical diameter are less sensitive to the tube diameter, morphology, and conductive characteristic, and conclude the emission features of the body film: consistence in emission sites, uniformity in emission energy distribution, predictability in emission effects and high emission stability, which are similar to those of graphite sheet or diamond film. These unique features guarantee the tube body to be applicable to flat panel displays with the same picture quality, cylindrical cathode and linear emitter. Structure of Carbon Nanotubes Single walled carbon nanotubes are an allotrope of sp hybridized 2 carbon, similar to fullerenes. The structure can be thought of as a cylindrical tube comprised of 6-membered carbon rings, as in graphite. The cylindrical tubes may have one or both ends capped with a hemisphere of the buckyball or fullerene structure. An understanding of SWNT structure requires familiarity with the concept of nanotube chirality, since the chirality of a SWNT dictates many of its properties. A concept known as a Chirality Map, illustrated in Figure 1, has been developed as a tool for understanding chirality and its implications. A SWNT can be envisioned as a sheet of graphite one atom thick rolled into a tube (see inset in Figure 1). The chirality describes both the orientation and diameter to which the sheet is rolled. Each SWNT on the chirality map is defined by two integers, (n,m). As indicated previously chirality defines many of the properties of the individual SWNT. For example, SWNT shown on the chirality map in blue are metallic in nature. These are tubes where n=m
  • 4. (armchair) or n - m = 3i, (where i is any integer.) Those depicted in yellow are semiconducting, displaying different band gaps depending on the length of the chiral vector. Figure 1. A graphic displaying a Chirality Map which shows the various types of SWNTs that can be forfmed.The properties are governed by the way in which they are rolled as shown in the insert. The SWNT will be metallic in the armchair configuration, or when m-n is a multiple of 3.
  • 5. Cvd method The catalytic vapor phase deposition of carbon was reported in 1952[68] and 1959,[69] but it was not until 1993[70] that carbon nanotubes were formed by this process. In 2007, researchers at the University of Cincinnati (UC) developed a process to grow aligned carbon nanotube arrays of 18 mm length on a FirstNano ET3000 carbon nanotube growth system.[71] During CVD, a substrate is prepared with a layer of metal catalyst particles, most commonly nickel, cobalt,[72] iron, or a combination. [73] The metal nanoparticles can also be produced by other ways, including reduction of oxides or oxides solid solutions. The diameters of the nanotubes that are to be grown are related to the size of the metal particles. This can be controlled by patterned (or masked) deposition of the metal, annealing, or by plasma etching of a metal layer. The substrate is heated to approximately 700°C. To initiate the growth of nanotubes, two gases are bled into the reactor: a process gas (such as ammonia, nitrogen or hydrogen) and a carbon-containing gas (such as acetylene, ethylene, ethanol or methane). Nanotubes grow at the sites of the metal catalyst; the carbon-containing gas is broken apart at the surface of the catalyst particle, and the carbon is transported to the edges of the particle, where it forms the nanotubes. This mechanism is still being studied. The catalyst particles can stay at the tips of the growing nanotube during the growth process, or remain at the nanotube base, depending on the adhesion between the catalyst particle and the substrate. Thermal catalytic decomposition of hydrocarbon has become an active area of research and can be a promising route for the bulk production of CNTs. Fluidised bed reactor is the most widely used reactor for CNT preparation. Scale-up of the reactor is the major challenge. [74] [75] CVD is a common method for the commercial production of carbon nanotubes. For this purpose, the metal nanoparticles are mixed with a catalyst support such as MgO or Al2O3 to increase the surface area for higher yield of the catalytic reaction of the carbon feedstock with the metal particles. One issue in this synthesis route is the removal of the catalyst support via an acid treatment, which sometimes could destroy the original structure of the carbon nanotubes. However, alternative catalyst supports that are soluble in water have proven effective for nanotube growth.[76] If a plasma is generated by the application of a strong electric field during the growth process (plasma enhanced chemical vapor deposition), then the nanotube growth will follow the direction of the electric field.[77] By adjusting the geometry of the reactor it is possible to synthesize vertically aligned carbon nanotubes[78] (i.e., perpendicular to the substrate), a morphology that has been of interest to researchers interested in the electron emission from nanotubes. Without the plasma, the resulting nanotubes are often randomly oriented. Under certain reaction conditions, even in the absence of a plasma, closely spaced nanotubes will maintain a vertical growth direction resulting in a dense array of tubes resembling a carpet or forest. Of the various means for nanotube synthesis, CVD shows the most promise for industrial-scale deposition, because of its price/unit ratio, and because CVD is capable of growing nanotubes directly on a desired substrate, whereas the nanotubes must be collected in the other growth techniques. The growth sites are controllable by careful deposition of the catalyst. In 2007, a team from Meijo University demonstrated a high-efficiency CVD technique for growing carbon nanotubes from camphor.[79] Researchers at Rice University, until recently led by the late Richard Smalley, have concentrated upon finding methods to produce large, pure amounts of particular types of nanotubes. Their approach grows long fibers from many small seeds cut from a single nanotube; all of the resulting fibers were found to be of the same diameter as the original nanotube and are expected to be of the same type as the original nanotube.[80] [edit]Super-growth CVD Procedure PROCEDURE **Do not open the chamber while the alarm red light is on **Never touch the detector (may result in signal off). 1. Obtain a sample from your instructor, place it onto the double-side tape which is then placed on an aluminum sample holder; if you are preparing a powder sample, use a spatula to spread the powder onto the double- side tape. 2. Read the instructions for the Miniflex X-ray diffractometer, which are on the wall above the instrument. Your instructor will explain the operation. 3. Set the instrument at optimum setting as follows
  • 6. time constant 2 range ? chart speed: Low 4. Slide in the sample holder and adjust the beginning 2theta at 70 degree (It scans from high degrees to low degrees) 5. Switch on the start knob and chart recorder (slow) simultaneously, run your sample on slow chart speed. 6. Once scan gets down to 3 degree of 2theta , stop (switch start knob to off) and chart. TURN OFF X-ray. 7. Locate all peaks on the chart and corresponding 2theta values and write their values into the data chart below. Perform the necessary calculations in the table a Data Table of X-ray Diffraction Peaks lattice spacing 2theta theta sin(theta) n d=n x wavelength/sin(theta) =nxd 1 2 3 4 5 6 7 8 Wavelength = 1.5418 Å for Cu Ka 8. nd calculate the repeat distance in your unit cell. X-Ray Diffraction Experiment INTRODUCTION X-rays are electromagnetic radiation of wavelength about 1 Å (10-10 m), which is about the same size as an atom. They occur in that portion of the electromagnetic spectrum between gamma-rays and the ultraviolet. The discovery of X-rays in 1895 enabled scientists to probe crystalline structure at
  • 7. the atomic level. X-ray diffraction has been in use in two main areas, for the fingerprint characterization of crystalline materials and the determination of their structure. Each crystalline solid has its unique characteristic X-ray powder pattern which may be used as a "fingerprint" for its identification. Once the material has been identified, X-ray crystallography may be used to determine its structure, i.e. how the atoms pack together in the crystalline state and what the interatomic distance and angle are etc. X-ray diffraction is one of the most important characterization tools used in solid state chemistry amd materials science. We can determine the size and the shape of the unit cell for any compound most easily using the diffraction of x-rays. Fig. 1 Reflection of x-rays from two planes of atoms in a solid. The path difference between two waves: 2 x wavelength= 2dsin(theta) For constructive interference between these waves, the path difference must be an integral number of wavelengths: n x wavelength= 2x
  • 8. This leads to the Bragg equation: n x wavelength = 2dsin(theta) Figure 2 shows the x-ray diffraction pattern from a single crystal of a layered clay. Strong intensities can be seen for a number of values of n; from each of these lines we can calculate the value of d, the interplanar spacing between the atoms in the crystal. Fig. 2 X-ray diffraction pattern from a layered structure vermiculite clay. EXAMPLE 1 Unit Cell Size from Diffraction Data The diffraction pattern of copper metal was measured with x-ray radiation of wavelength of 1.315Å. The first order Bragg diffraction peak was found at an angle 2theta of 50.5 degrees. Calculate the spacing between the diffracting planes in the copper metal. The Bragg equation is n x wavelength = 2dsin(theta) We can rearrange this equation for the unknown spacing d: d = n x wavelength/2sin(theta). theta is 25.25 degrees, n =1, and wavelength = 1.315Å, and therefore d= 1 x 1.315/(2 x 0.4266) = 1.541 Å In this lab you will measure the x-ray powder diffraction pattern from a single crystal. Your TA will give you the sample to be measured and show you how to set up the Miniflex x-ray diffractometer.
  • 9. You should measure all the values of 2theta from the chart, and after converting them into d values calculate the repeat distance in your unit cell. In your lab note book list all the 2theta values with their corresponding values of n and d. Then calculate the mean and median values of the unit cell. INSTRUMENTATION The X-ray diffraction experiment requires an X-ray source, the sample under investigation and a detector to pick up the diffracted X-rays. Fig 3 is a schematic diagram of a powder X-ray diffractometer. Fig. 3. Schematic of an X-ray powder diffractometer The X-ray radiation most commonly used is that emitted by copper, whose characteristic wavelength for the K radiation is =1.5418Å. When the incident beam strikes a powder sample, diffraction occurs in every possible orientation of 2theta. The diffracted beam may be detected by using a moveable detector such as a Geiger counter, which is connected to a chart recorder. In normal use, the counter is set to scan over a range of 2theta values at a constant angular velocity. Routinely, a 2theta range of 5 to 70 degrees is sufficient to cover the most useful part of the powder pattern. The scanning speed of the counter is usually 2theta of 2degrees min-1 and therefore, about 30 minutes are needed to obtain a trace.