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Adsorption is a process where a solid or liquid substance is attracted and held onto the surface of another material. It is an essential process in many industries, including water treatment, food processing, and pharmaceuticals. The effectiveness of adsorption depends on the properties of the adsorbent material, such as its surface area, pore size distribution, and chemical composition. Therefore, finding an optimum adsorbent material is crucial to achieving efficient and cost-effective adsorption processes.

One of the most powerful tools for determining the properties of an adsorbent material is the BET analysis. The BET (Brunauer-Emmett-Teller) analysis is a technique used to measure the specific surface area of a material by measuring the amount of gas adsorbed onto its surface at different pressures. The data obtained from BET analysis can be used to calculate the pore size distribution and other critical parameters that determine the adsorption capacity and efficiency of the material.

BET analysis can be used to evaluate various types of materials, including activated carbon, zeolites, silica gels, and metal-organic frameworks. By using BET analysis, researchers can determine the optimum conditions for preparing and using these materials as adsorbents. Here are some ways BET analysis can help in finding an optimum material for using as an adsorbate:

1. Determining the Specific Surface Area

The specific surface area of an adsorbent material is one of the most critical parameters that affect its adsorption capacity. BET analysis can accurately measure the specific surface area of a material by analyzing the amount of gas adsorbed onto its surface at different pressures. The higher the specific surface area, the more adsorption sites are available for attracting and holding onto target molecules.

2. Calculating Pore Size Distribution

The pore size distribution of an adsorbent material is another crucial factor that affects its adsorption capacity. BET analysis can provide information about the pore size distribution of a material by analyzing the adsorption isotherm data. The pore size distribution can be used to determine the optimum pore size range for the target molecules to be adsorbed.

3. Evaluating Adsorption Capacity

BET analysis can also be used to evaluate the adsorption capacity of an adsorbent material. By measuring the amount of gas adsorbed onto the material at different pressures, researchers can determine the maximum amount of target molecules that can be adsorbed onto the material. This information can be used to optimize the adsorption process and determine the most effective operating conditions.

4. Comparing Different Materials

BET analysis can also be used to compare the properties of different adsorbent materials. By analyzing the specific surface area, pore size distribution, and other parameters, researchers can determine which material is most suitable for a specific application. This information can help in selecting the best material for a particular adsorption process and improve its efficiency and cost-effectiveness.

In conclusion, BET analysis is a powerful tool for evaluating the properties of adsorbent materials and finding an optimum material for using as an adsorbate. By analyzing the specific surface area, pore size distribution, and other parameters, researchers can determine the most effective operating conditions and select the best material for a specific application. BET analysis can help in improving the efficiency and cost-effectiveness of adsorption processes in various industries, making it an essential technique for researchers and engineers working in this field.

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1. Introduction

Today several instruments for fast spectra recording are available. In most cases the difficulty
is to process and analyze the data quickly in a reliable way. The Maud program, in one of its
many undocumented features, can be used to process a list of analyses in batch mode from the
console without requiring the interface. This is useful to process quickly similar spectra or launch
a slow/time consuming refinement in a remote computer without recurring to the interface that
would need to open a session involving the remote display setting.

The overall procedure is to prepare the analysis locally using the interface or to prepare a starting point for a series of spectra
(one common starting point) also using the interface, then to prepare an instruction file in CIF like
format to specify the analyses, the spectra and the kind of refinement to conduct and finally to run
Maud in batch mode providing the instruction file previously prepared. The program will run and
process one analysis at time and prepare an output file extracting some key information (either the
default or some to be specified) in a format suitable to be imported in spreadsheet or graphical
programs to analyze the results.
As an example we will show the procedure to analyze a series of ball milled Cu-Fe mixed powders
in which two different phases may form with a different composition. By an automatic Rietveld
analysis performed in batch mode we will extract information about phase content [2, 1], crystallite
and microstrain for each sample/spectrum. The analysis is further complicated from the fact that
the powders milled at higher energy show the presence of planar defects [5] and texture arising
from sample preparation and the platelet like shape of the grains [3].

2 Analysis and procedure
In this section we will present the procedure to analyze 25 spectra of Cu-Fe different samples. The
spectra has been collected by a Philips X-pert system in Le Mans at the LPEC laboratory of the
1
University du Maine, thanks to A. Gibaud.
2.1 Analysis preparation through the interface
We start the Maud program and load all the datafiles together to check their integrity and to prepare
a common starting analysis file. A plot of all spectra and their differences is available in Figure 1.

We load the two possible phases, bcc iron and fcc copper, from the Maud database. By computing
the spectra once and comparing them visually with the experimental spectra we may notice that
for some samples, milled at longer time, an alloyed fcc phase form (out of equilibrium) and the
bcc iron disappears. Unluckily we could not use the copper rich phase cell parameter to monitor
the Fe content in it as the cell parameter tends to growth as a result probably of oxygen entrapping.
In a first attempt we discovered the spectra were affected by texture, anisotropic crystallite sizes
and microstrain as well as planar defects (especially on the Cu like phase). So we decide here
to include also texture and anisotropic/planar defects effects in the analysis. For both the bcc
and fcc phases we select in the proper panel the Popa model for anisotropic broadening [4], the
Warren model for planar defects and the harmonic model for texture (specifying cylindrical sample
symmetry and Lmax = 6 in the options; it is required by the experiment geometry).
Next step was to adjust the cell parameters for both bcc and fcc phases in order to get a mean
starting value good for all spectra (especially for the fcc); and to adjust the crystallite value to a
good starting point (around 200 angstrom) obtaining peak shapes a little sharper than in the less
broadened spectrum. The background constant parameter was also adjusted to the value of the
spectrum with the lower background. Actually only the cell parameter adjustment is critical, the
background one is even not necessary.
Finally we remove all the spectra (we will specify which datafile to use for each analysis later in an
instruction file) and save the analysis containing everything except the spectrum/a. For the purpose
of this article we save the analysis with the name: FeCustart.par.
2.2 Preparation of the instruction file and batch processing
To run Maud in batch we need to write an instruction file containing the list of analyses to execute
one at time. The file is in CIF format but containing some terms not available in the official CIF
dictionary, but that Maud recognize. All the analyses to be performed are specified through the
loop CIF instruction. The first term of the loop must be the one specifying the starting analysis
file to be loaded (full path in unix convention) and then the others to instruct Maud for the kind
of analysis to perform, iterations and eventually datafile to load and name of the file were to save
the analysis. Additional keywords can be used to append specific results to a file for spreadsheet
analysis. The simplest instruction file is something containing the following:
First example (paths for windows):
loop
riet analysis file
riet analysis iteration number
2
´//C:/mypathfortheanalysis/analysis1.par´ 5
´//C:/mypathfortheanalysis/analysis2.par´ 3
´//C:/mypathfortheanalysis/analysis3.par´ 7
The analysis1.par (or 2 or 3) are some analyses files prepared with Maud, containing also
the datafile/spectrum, already set for the parameters to be refined and saved just ready for the refinement step. Maud will load each analysis, starts the refinement with the number of iterations
specified and save the analysis with the refined parameters under the same name. The analyses can
be loaded at end in Maud (with the interface) to see the result of the refinement.
In the case of the Cu-Fe we need to perform some more steps: first we start from one common analysis point (the FeCustart.par analysis file) but we want to specify different datafiles; second
we want to perform a full automatic analysis in which Maud performs different cycles deciding
which parameters to refine at each step and third we will specify the name of each analysis for the
saving process and a file name were to append some selected results in a tab/column format for
subsequent easy loading in a spreadsheet program.
Cu-Fe example:
loop
riet analysis file
riet analysis iteration number
riet analysis wizard index
riet analysis fileToSave
riet meas datafile name
riet append simple result to
´//mypath/FeCustart.par´ 7 13 ´//mypath/FECU1010.par´ ´//mypath/FECU1010.UDF´
´//mypath/FECUresults.txt´
´//mypath/FeCustart.par´ 7 13 ´//mypath/FECU1011.par´ ´//mypath/FECU1011.UDF´
´//mypath/FECUresults.txt´
…………(lines with all the other 23 datafiles omitted for brevity)
´//mypath/FeCustart.par´ 7 13 ´//mypath/FECU1038.par´ ´//mypath/FECU1038.UDF´
´//mypath/FECUresults.txt´
With this instruction file (that we save under the name: fecu.ins) we specify for example that
as a first analysis, Maud has to load the FeCustart.par file, then to load in the analysis the
FECU1010.UDF datafile, to perform the automatic analysis number 13 (in the wizard panel of
Maud the automatic analysis number 13 is the texture analysis; we need to refine also the texture
parameters along with phase analysis and microstructure) and to use 7 iterations for each cycle (the
texture automatic analysis is composed by 4 cycles) to ensure sufficient convergence. At the end
the analysis is saved with the name FECU1010.par and simple selected results will be appended
in the file FECUresults.txt. The simple results saved in the spreadsheet like file are some of
the most used parameters and results. It is possible to specify the parameters we want in output
using the CIF word riet append result to (in addition or as an alternative), but in the
preparation of the starting analysis file in the Maud interface, the parameters to be added to the
results must be specified by turning to true the switch in the output column of the parameter list
window or panel.
Now to run Maud in batch in the console (
where the Maud.jar is located the following:
DOS (everything in the same line): java -mx512M -cp
“Maud.jar;lib\miscLib.jar;lib\JSgInfo.jar;lib\jgaec.jar;lib\ij.jar”
it.unitn.ing.rista.MaudText -f fecu.ins
Unix (everything in the same line): java -mx512M -cp
Maud.jar:lib/miscLib.jar:lib/JSgInfo.jar:lib/jgaec.jar:lib/ij.jar
it.unitn.ing.rista.MaudText -f fecu.ins
For Mac OS X, it is advised to use the generic Unix Maud installation (or to change the path to
the jar files). Before to run Maud in batch mode it is important to run Maud interactive (with the
interface) at least once to create and extract the databases, examples and preferences folder.

2.3 Analysis of results
After running Maud in batch mode, we can check quickly the results by loading the results file
FECUresults.txt in a spreadsheet program. The results are arranged in rows and separated
by tabs. The first row contains the column titles, each subsequent row a different analysis. The
Rwp value for each analysis is reported in the second column and the biggest value found was
5.6% as an indication of the success of the analysis. As an example we report in Figure 2 the
graphical correlation of the copper-rich phase percentage and its mean crystallite value as found
in the analysis versus the sample number. The files and examples used in this articles will be
uploaded in a tutorial in the Maud web page along with some additional files with the batch mode
commands for an easier use.

3 How to get Maud 2.0 and further informations
For this analysis we need Maud version 2.037 or later and it can be freely downloaded from the
Maud web page at http://www.ing.unitn.it/ maud for the preferred platform. There are two archives
for Windows and Mac OS X plus a generic unix version that can be used for Linux, Solaris or
every unix based system with a Java 2 virtual machine installed. The new version 2.0 has a new
interface focused on reducing the effort of a new user and simplifying the most common tasks.
Some particularity of the new version respect to the previous one are (most of them to provide
some useful routines for ab-initio structure solution):
• Different minimization/search algorithms selectable: Marquardt least squares, Evolutionary
algorithm, Simulated annealing, Metadynamic search algorithm. As an example the evolutionary algorithm can be used in the early steps of the refinement to select the proper starting
solution and the Marquardt to drive it to convergence.
4
• Possibility to use crystallites and microstrain distributions for peak shape description instead
of analytical fixed shape functions.
• Maximum Entropy Electron Map full pattern fitting. An electron map can be used for fitting
instead of atoms.
• Full pattern fitting by a list of peaks. Either an arbitrary list of peaks (each one with its own
position, intensity and shape), or simply a list of structure factors to be imported, instead of
a list of atoms.
• Indexing directly on the pattern, selecting the Le Bail fit and the evolutionary algorithm for
the cell search. This may be used to improve a difficult indexing or a partly done one.
• Introduction of fragments. So fragment search can be done directly on the pattern or on a
list of extracted structure factors.
• Energy minimization. At the moment only the simple repulsion energy is completed. Other
energy principles are under completition.
• Spectra integration from image plate or CCD transmission/reflection 2D images. Center,
tilting errors and distance from sample can be refined in the spectra fitting.
Bugs and errors should be reported to the author through the bug reporter web page; questions in
the Maud forum accessible from the Maud web page.
In a future article we will report the instructions on how to modify/extend the program by little Java programming or provide a new alternative model/plugin for the instrument or the structure/microstructure or datafiles importing.
References
[1] D. L. Bish and S. A. Howard. J. Appl. Cryst., 21, 86–91, 1988.
[2] R. J. Hill and C. J. Howard. J. Appl. Cryst., 20, 467–474, 1987.
[3] L. Lutterotti and S. Gialanella. Acta Mater., 46(1), 101–110, 1998.
[4] N. C. Popa. J. Appl. Cryst., 31, 176–180, 1998.
[5] B. E. Warren. X-ray Diffraction. Addison-Wesley, Reading, MA, 1969

Author: Luca Lutterotti
Dipartimento di Ingegneria dei Materiali e delle Tecnologie Industriali
Universita di Trento, 38050 Trento, Italy `
E-mail: Luca.Lutterotti@ing.unitn.it
WWW: http://www.ing.unitn.it/ maud

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1- DTSA-II

DTSA-II is a multi-platform software package for quantitative x-ray microanalysis. DTSA-II was inspired by the popular Desktop Spectrum Analyzer (DTSA) package developed by Chuck Fiori, Carol Swyt-Thomas, and Bob Myklebust at NIST and NIH in the ’80’s and early ’90’s.

DTSA-II has being designed with the goal of making standards-based microanalysis more accessible for the novice microanalyst. We want to encourage standards-based analysis by making it as easy as possible to get reliable results. Many operations which had previously required user intervention under DTSA now are performed entirely by the software. Furthermore, the software attempts to guide the user step-by-step through common processes while performing quality control sanity checks. While this might not provide the flexibility that some sophisticated users may desire, we feel that this philosophy is more consistent with the way laboratories are moving towards technicians responsible for multiple techniques and away from experts in single techiques. We encourage users who desire the additional power and flexibility available in the EPQ library to learn to script using Jython or to create their own alternative user interface. EPQ is much more capable than the fraction exposed via DTSA-II.

DTSA-II is based on an entirely new code base written by Nicholas W. M. Ritchie. The codebase has been carefully divided into a shared algorithm library which forms the basis for a handful of software products and a user interface shell. DTSA-II is the user interface shell and the EPQ library is the algorithm library.

DTSA-II remains under active development. Many features – some fairly basic – remain unimplemented. Other features have not been tested as much as the developer might like. The program made available to the public via this web site represents the current best available version in the judgement of the developer. DTSA-II remains experimental software and no representations are made regarding the suitability of the product for any particular application.

Major features:

• Basic IO and Display
  • Read energy dispersive x-ray spectra in a variety of different commercial and non-commercial formats including the industry standard EMSA format
  • Display and overlay spectra with various scaling options on linear/log/sqrt axes
  • Copy/save/print the spectrum display as a bitmap/PNG file
  • Output the spectra as a GNUPlot file for publication quality output
  • Overlay labeled x-ray emission lines and x-ray absorption edges
  • Define and integrate regions-of-interest
  • View spectrum contextual information
  • Archive spectra to a searchable database
  • Sub-sampling of spectral data to simulate shorter acquisition times
  • Basic spectrum math functions
  • Background modeling or background stripping
  • Energy axis linearization
  • Spectrum smoothing
  • Peak removal (trimming)
  • Peak search / identification
• Spectrum Simulation
  • Analytical (φ(ρz)) simulations of energy dispersive x-ray spectra
    • Normal or oblique incidence angle
    • Variable beam energies, beam fluxes, materials
  • Monte carlo simulations of energy dispersive x-ray spectra
    • Spectra from bulk samples
    • Mounted or unmounted thin films
    • Cubical or spherical particles with or without a substrate
  • Simulated spectra may be manipulated as experimental spectra
  • Variety of detector options including Si(Li), SDD and microcalorimeter
• Standards-based Quantification
  • Standards-based quantification of EDS spectra
  • Filter-fit linear-least squares fitting of reference spectra
  • Quantification based on references or like-standards
  • φ(ρz) correction of the k-ratios
  • ζ-factor correction of thin-film samples
  • Results reported as HTML with estimates of uncertainty
• Reporting
  • Actions are recorded in a daily HTML activity report
  • Report may be opened in an alternative HTML viewer
• Platforms and Source Code
  • DTSA-II is based on the EPQ library – a full-featured library of electron probe quantification algorithms
  • DTSA-II only exposes a fraction of the power within the EPQ library. The remainder may be accessed via custom Java applications or via Jython scripting.
  • The EPQ library includes the full NISTMonte for Monte Carlo simulation of electron/x-ray transport
  • DTSA-II / EPQ library are available as source code
  • DTSA-II / EPQ library are written in Java SE 6 compatible source
  • DTSA-II / EPQ library can execute on any platform supporting Java SE 6 or later
  • DTSA-II / EPQ library is regularly tested on Windows XP, Ubuntu Linux & Apple OS X

Disclaimer

This software was developed at the National Institute of Standards and Technology by employees of the Federal Government in the course of their official duties. Pursuant to title 17 Section 105 of the United States Code this software is not subject to copyright protection and is in the public domain. DTSA and the EPQ library are experimental systems. NIST assumes no responsibility whatsoever for its use by other parties, and makes no guarantees, expressed or implied, about its quality, reliability, or any other characteristic. We would appreciate acknowledgement if the software is used. This software can be redistributed and/or modified freely. The author requests that any derivative works bear some notice that they are derived from it, and any modified versions bear some notice that they have been modified.

Any mention of commercial products is for information only; it does not imply recommendation or endorsement by NIST nor does it imply that the products mentioned are necessarily the best available for the purpose.

See: https://cstl.nist.gov/div837/837.02/epq/dtsa2/

2. HyperSpy

HyperSpy is an open source Python library which provides tools to facilitate the interactive data analysis of multi-dimensional datasets that can be described as multi-dimensional arrays of a given signal (e.g. a 2D array of spectra a.k.a spectrum image). HyperSpy aims at making it easy and natural to apply analytical procedures that operate on an individual signal to multi-dimensional arrays, as well as providing easy access to analytical tools that exploit the multi-dimensionality of the dataset. Its modular structure makes it easy to add features to analyze different kinds of signals.

Highlights

• Two families of named and scaled axes: signal and navigation.
• Visualization tools for multi-dimensional spectra and images.
• Easy access multi-dimensional curve fitting and blind source separation.
• Built on top of NumPy, SciPy, matplotlib and scikit-learn.
• Modular design for easy extensibility.

The development has been motivated by the data analysis needs of the electron microscopy community but it is proving useful in many other fields.

See: https://hyperspy.org/

3. AZtec

• AZtecFeature is an innovative particle analysis system specifically optimised for usability and high-speed throughput. It combines the raw speed and sensitivity of the Ultim Max Silicon Drift Detector with the superior analytical performance and ease of use of the AZtec® EDS analysis suite to create the most advanced automated particle analysis platform on the market. Gunshot Residue Analysis in the SEM with AZtecGSR is fast and accurate: it gives reproducible Gunshot Residue Analysis results to ASTM E1588 – 10e1.
• AZtecGSR combines ease of use through its guided workflow, with the ultimate accuracy using the latest Ultim Max detectors and Tru-Q® algorithms. LayerProbe is an exciting software tool for thin film analysis in the SEM. An option for the AZtec EDS microanalysis system, LayerProbe is faster, more cost-effective and higher resolution than dedicated thin film measurement tools.The most powerful EBSD software available, AZtecHKL combines speed and accuracy of results for routine analysis, with the flexibility and power required for applications that push the frontiers of EBSD.
• AZtec3D combines simultaneous EDS and EBSD data acquisition & analysis with the automated milling capabilities of a FIB-SEM.AZtecLiveOne software platform is the ideal solution for carrying out a complex task like EDS as quickly and as easily as possible. No need for substantial training or advanced knowledge of the EDS technique. Users can be trained in a matter of minutes and will have complete confidence in their results. AZtecTEM is an innovative EDS software specifically optimised for advanced TEM applications. AZtecSynergy provides a powerful solution for the simultaneous collection of EDS and EBSD data. All of the tools to collect excellent integrated data are included in one place with no complicated switching from one navigator to another.
• AZtecSteel is an automated steel inclusion analysis package developed specifically for the analysis and classification of steel inclusions using Energy Dispersive X-ray microanalysis (EDS) in a scanning electron microscope (SEM). It detects, measures and analyses the inclusions, processes the resulting data set to published standard methods, and includes functionality to plot complex ternary diagrams. AZtecLive is a revolutionary new approach to EDS analysis that enables a radical change in the way users perform sample investigation in the SEM. It combines a live electron image with live X-ray chemical imaging to give an intuitive new way of interacting with your samples. Collecting good quality data is only the beginning of any complete EBSD analysis. AZtecCrystal provides all the necessary tools to process and interrogate your EBSD data and to solve your materials problems. Seamlessly integrated with AZtecHKL or operated as a standalone program, AZtecCrystal sets the standard in EBSD data processing for experts and novices alike.
• AZtecAM is a powerful, automated, solution for the analysis of metal powders used in additive manufacturing. Based on AZtecFeature, AZtecAM optimises the particle analysis workflow to enable the rapid and accurate characterisation of metal powders. AZtecMineral is a powerful, automated, Mineral Liberation Analysis solution. It enables ore characterisation, provides vital data on metal recovery and enables process yield characterisation using multipurpose SEMs. It is also a valuable tool for the characterisation of rocks in research environments, enabling the automation of otherwise laborious optical analyses.

See: https://engineering.virginia.edu/oxford-instruments-offering-free-aztec-suite-software-electron-microscopy-analysis

4. ESPRIT Family

ESPRIT 2 unites four analytical methods under a single user interface. These include EDS for SEM and (S)TEM, WDS, Micro-XRF for SEM and EBSD. This makes it easy for the user to switch between methods with a single mouse click. Additionally, it facilitates combining different method results from the same sample area and to so gain much more information. To name only the most important, coupling of following methods is supported:

• EDS and EBSD
• EDS and WDS
• EDS and Micro-XRF for SEM

The software is designed to suit the needs of all levels of users – from beginner to expert. Novices will benefit from the assistants that help performing routine tasks without having to learn details of the measurement method. More experienced users will value the option to drill down deeper, when they need it, meaning both detailed setup of measurements as well as in-depth analysis of results and automation of tasks.

See: https://www.bruker.com/en/products-and-solutions/elemental-analyzers/eds-wds-ebsd-SEM-Micro-XRF/software-esprit-family.html

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In this course the general introduction to Raman spectroscopy and microscopy will be provided and practical tips as well as examples will be given. The capability of Raman spectroscopy for the analysis of real-life samples (paint components, clays, coating materials, etc.) taken from historical and archaeological objects will be discussed.

1. Principles of Raman spectroscopy

Raman spectroscopy is widely used in the investigation of cultural heritage materials due to its high spatial resolution (typically in the range of 1 to 10 µm), large amount of obtainable information, non-destructivity and ability to perform in-situ analysis.^1,2 With Raman spectroscopy it’s possible to analyse various materials: minerals, inorganic and organic pigments, binding media, varnishes, ceramics, plastics, textile fibres etc.²

The following video explains the principles and instrumentation of Raman spectroscopy.https://www.uttv.ee/embed?id=29055

Similarly to infrared spectroscopy, Raman spectroscopy is classified as vibrational spectroscopy.³ Raman spectroscopy is based on Raman scattering (or Raman effect) that reveals the vibrational, rotational and other low frequency modes of molecules⁴. In this technique, the sample is exposed to an intense beam of monochromatic light (typically a laser beam) in the frequency range of visible, near-infrared or near-ultraviolet region.⁵ The electromagnetic radiation, interacting with a substance, can be transmitted, absorbed, or scattered⁶. When the monochromatic radiation is scattered by molecules, the majority of the radiation undergoes the common Rayleigh scattering (radiation’s  frequency/wavelength is unchanged). However, a small fraction of the scattered radiation is observed to have a slightly different frequency from that of the incident radiation. This is known as the Raman effect⁷. The Raman lines show up pairwise. The dominant Stokes lines have a lower frequency (longer wavelength) than the initial radiation, whereas the weaker (often nondetectable) anti-Stokes lines have a higher frequency (shorter wavelength).^4,5 The frequency shifts are virtually independent of the excitation wavelength and are characteristic of the particular substance/molecule. Usually one only records the relatively strong Stokes lines, which therefore are attributed a positive frequency shift. Such spectral coordinate is called the Raman shift and measured in wavenumbers (in cm^-1).⁴ See scheme in Figure 1.

Figure 1. Scheme of Raman scattering.

In Raman spectroscopy, as it is a scattering technique, samples are simply placed in the laser beam and the scattered radiation is collected and analysed⁸. Raman spectrometer measures the wavelength-dependent intensity of the inelastically scattered light.

The obtained Raman spectra are essentially vibrational spectra. Hence, if presented in the Raman shift scale, they are directly comparable to corresponding infrared absorption spectra (see Figure 2). However, Raman spectrum arises in a different manner and the rules, which vibrations are Raman-active (and thus produce signals in the spectrum), are different. It turns out that a vibration is Raman-active (i.e. revealed as a spectral line in the Raman spectrum), if the polarizability of the molecule changes during the vibration.⁷ It often happens that vibrations that are active (or give high-intensity signals) in Raman scattering are inactive (or give low-intensity signals) in the infrared, and vice versa.⁷Therefore, Raman spectra often provide complementary information to IR spectra.

Figure 2. Raman (laser 514.5 nm) and IR spectra of benzene.

1.1. Instrumentation

There are two types of Raman spectrometers: dispersive spectrometers (based on the use of diffraction grating) and interferometer containing Fourier-transform Raman spectrometers (FT-Raman)⁹.

In general the main components of Raman spectrometers are presented on the following scheme:

In Raman spectroscopy, the choice of excitation wavelength and intensity is very important. Different wavelengths are suitable for the analysis of different types of material. The wavelength will affect the Raman intensity, spatial resolution, background fluorescence, and potential damage to the sample. Almost exclusively lasers are used as excitation sources, because they are highly monochromatic, give high-intensity radiation and can be efficiently focused due to their high coherence. Only continuous wave (CW) lasers are used, as pulsed lasers easily damage the sample. Some popular CW lasers are presented in Table 1. Traditionally, laser wavelengths up to 830 nm have been used in dispersive instruments while the 1064 nm laser line has been employed in FT-Raman setups. With the availability of sensitive InGaAs array detectors, it has become meaningful to use also the 1064 nm lasers with dispersive Raman instruments.

Table 1. Laser sources for Raman spectroscopy.

Raman scattering efficiency decreases with increasing excitation wavelength as λ⁻⁴. However, short-wavelength lasers more easily induce fluorescence, absorb in the sample or cause other undesirable effects due to their high photon energy. Hence, most common laser wavelengths in Raman spectroscopy are in the visible and NIR region (such as 633 or 785 nm) which offer low fluorescence whilst retaining relatively high Raman intensity. For samples which exhibit fluorescence even under red excitation (for example dyes), the 1064 nm laser may be needed. While near-infrared lasers have a smaller photon energy, compared to visible lasers, they are usually more powerful, in order to compensate for the reduced Raman scattering efficiency. Therefore, they may still damage the sample. It is especially important for strongly absorbing (black) samples, in which case the UV/visible lasers (operating at lower intensities) may yield a stronger Raman signal.

Dispersive Raman spectrometers

A dispersive spectrometer utilizes a diffraction grating to angularly disperse the light. As a result, at the detector plane, different wavelengths become spatially separated. Nevertheless, prior to entering the spectrometer, the incoming light should go through a special edge or notch filter to suppress the primary (Raman-scattered) light and thereby reduce the scattering inside the spectrometer. A matrix detector is used to record the dispersed spectrum. Typically, a silicon-based cooled CCD is used, which is very sensitive in the visible and NIR region (up to 1100 nm).

FT-Raman spectrometers

Commercial FT-Raman spectrometers were introduced in the late 1980s¹⁰. Their operating principle is similar to that of FTIR spectrometers and is based on an interferometer. As the Raman-scattered light enters the instrument, the interferometer selectively modulates the individual spectral components by systematically changing an optical path length difference. The resulting beam of light is recorded by a point detector. FT-Raman is superior to a dispersive instrument in the near-IR region beyond 1000 nm. Commonly, the 1064 nm laser excitation along with germanium or indium gallium arsenide (InGaAs) detector is used. They also offer excellent wavelength accuracy and can potentially combine IR absorption and Raman measurement capacity in single instrument. However, FT-Raman frequently needs to use high laser intensities due to the reduced Raman scattering efficiency at longer wavelengths, which may damage the sample.

Different types of Raman Spectroscopy

A variety of Raman instruments and special techniques are used for the analysis of cultural heritage materials. The choice of instrument determines the sensitivity, spectral range and resolution, spatial resolution, availability of different excitation sources, and convenience of operation. 

• Micro-Raman spectrometer (or Raman microscope) is the most common bench-top Raman instrument. A high-resolution spectrometer (either dispersive or FT) and one or several laser sources are coupled through an optical microscope. The excitation beam is focused and the secondary emission is collected simultaneously by the microscope objective in backscattering geometry. A high-numerical aperture (NA) objective yields both a high spatial resolution and a high collection efficiency.
• Surface-enhanced Raman spectroscopy (SERS) involves inelastic light scattering by molecules placed close to nanometal surfaces, which amplify the scattering by plasmonic resonance. One approach is to study molecules adsorbed onto corrugated metal surfaces such as silver or gold nanoparticles¹¹. Another approach is to stimulate the molecules by a sharp metal tip. Such tip-enhanced Raman spectroscopy is typically implemented by combining a confocal microscope and a scanning probe microscope. 
• In Resonance Raman spectroscopy (RRS) the incident photon energy is close in energy to an electronic transition of a compound or material under examination. 
• In a portable Raman spectrometer, a miniature dispersive spectrometer and a small laser source are integrated into a portable, hand-held device. Hence, the instrument can be used to perform in situ analysis in museums, archives, also outdoors on archaeological sites for the analysis of mural or cave paintings. Such portable devices frequently employ a fiber-optic probes. 

1.2. Problems with Raman spectroscopy

Compared to IR absorption, the primary disadvantage of Raman spectroscopy is the fluorescent background (see Figure 3). As Raman scattering is inherently weak, one has to use an intense laser beam for excitation, and for many materials, this results in a strong fluorescence – either due to the material itself of impurities. Sometimes even trace impurities – if they are strongly fluorescent – can lead to disturbing fluorescence background. Fortunately, Raman lines are spectrally close to the laser beam whereas fluorescence has typically a large Stokes shift. 

Figure 3. Example of the fluorescence in the Raman spectrum of red lead containing paint.

Relative to the Raman signal, the fluorescent background can be highly intense and even the tail of the fluorescence band may obscure the Raman spectrum. Although the problem can be partially resolved by careful sample preparation, time resolved spectroscopy or coherent anti-Stokes Raman spectroscopy (CARS), there will always be experiments that remain difficult to perform.⁷

In addition to fluorescence, intense focused laser irradiation can cause heating and degradation of the sample. The problems are typical for organic, soft, photosensitive or dark/coloured materials whereas transparent inorganic materials have usually quite high damage threshold.

2. Analysis with Raman spectroscopy

In the following video Senior Research Fellow Dr. Valter Kiisk demonstrates and explains how to perform measurements with a typical micro-Raman spectrometer.https://www.uttv.ee/embed?id=29396

Identification of the composition of the studied material is often based on the comparison of its Raman spectrum with a spectral library of reference materials.¹² Different papers and books have been published from where Raman spectra or information about excitation wavelengths and list of wavenumbers in the Raman spectra are available ^5,13,14. Also a very valuable on-line database is made available by the Infrared & Raman Users Group (IRUG)– http://irug.org/ – from where different Raman (and also IR) spectra of cultural heritage materials can be obtained free of charge.

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Interaction of an electron beam with a sample target produces a variety of emissions, including x-rays. An energy-dispersive (EDS) detector is used to separate the characteristic x-rays of different elements into an energy spectrum, and EDS system software is used to analyze the energy spectrum in order to determine the abundance of specific elements. EDS can be used to find the chemical composition of materials down to a spot size of a few microns, and to create element composition maps over a much broader raster area. Together, these capabilities provide fundamental compositional information for a wide variety of materials.

How it Works – EDS

EDS systems are typically integrated into either an SEM or EPMA instrument. EDS systems include a sensitive x-ray detector, a liquid nitrogen dewar for cooling, and software to collect and analyze energy spectra. The detector is mounted in the sample chamber of the main instrument at the end of a long arm, which is itself cooled by liquid nitrogen. The most common detectors are made of Si(Li) crystals that operate at low voltages to improve sensitivity, but recent advances in detector technology make availabale so-called “silicon drift detectors” that operate at higher count rates without liquid nitrogen cooling.

An EDS detector contains a crystal that absorbs the energy of incoming x-rays by ionization, yielding free electrons in the crystal that become conductive and produce an electrical charge bias. The x-ray absorption thus converts the energy of individual x-rays into electrical voltages of proportional size; the electrical pulses correspond to the characteristic x-rays of the element.

Strengths

• When used in “spot” mode, a user can acquire a full elemental spectrum in only a few seconds. Supporting software makes it possible to readily identify peaks, which makes EDS a great survey tool to quickly identify unknown phases prior to quantitative analysis.
• EDS can be used in semi-quantitative mode to determine chemical composition by peak-height ratio relative to a standard.

Limitations

• There are energy peak overlaps among different elements, particularly those corresponding to x-rays generated by emission from different energy-level shells (K, L and M) in different elements. For example, there are close overlaps of Mn-K_α and Cr-K_β, or Ti-K_α and various L lines in Ba. Particularly at higher energies, individual peaks may correspond to several different elements; in this case, the user can apply deconvolution methods to try peak separation, or simply consider which elements make “most sense” given the known context of the sample.
• Because the wavelength-dispersive (WDS) method is more precise and capable of detecting lower elemental abundances, EDS is less commonly used for actual chemical analysis although improvements in detector resolution make EDS a reliable and precise alternative.
• EDS cannot detect the lightest elements, typically below the atomic number of Na for detectors equipped with a Be window. Polymer-based thin windows allow for detection of light elements, depending on the instrument and operating conditions.

Results

A typical EDS spectrum is portrayed as a plot of x-ray counts vs. energy (in keV). Energy peaks correspond to the various elements in the sample. Generally they are narrow and readily resolved, but many elements yield multiple peaks. For example, iron commonly shows strong K_α and K_βpeaks. Elements in low abundance will generate x-ray peaks that may not be resolvable from the background radiation.

EDS spectrum of multi-element glass (NIST K309) containing O, Al, Si, Ca, Ba and Fe (Goldstein et al., 2003). 

EDS spectrum of biotite, containing detectable Mg, Al, Si, K, Ti and Fe (from Goodge, 2003). 

References

• Severin, Kenneth P., 2004, Energy Dispersive Spectrometry of Common Rock Forming Minerals. Kluwer Academic Publishers, 225 p.–Highly recommended reference book of representative EDS spectra of the rock-forming minerals, as well as practical tips for spectral acquisition and interpretation.
• Goldstein, J. (2003) Scanning electron microscopy and x-ray microanalysis. Kluwer Adacemic/Plenum Pulbishers, 689 p.
• Reimer, L. (1998) Scanning electron microscopy : physics of image formation and microanalysis. Springer, 527 p.
• Egerton, R. F. (2005) Physical principles of electron microscopy : an introduction to TEM, SEM, and AEM. Springer, 202.
• Clarke, A. R. (2002) Microscopy techniques for materials science. CRC Press (electronic resource)

Related Links

• Petroglyph–An atlas of images using electron microscope, backscattered electron images, element maps, energy dispersive x-ray spectra, and petrographic microscope– Eric Chrisensen, Brigham Young University
• SEM/EDX webpage from Indiana University – Purdue University Fort Wayne

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X-ray is a kind of electromagnetic wave, the same as light. The wavelength of visible light is 400 to 800nm, while the wavelength of x-ray is much shorter (higher energy), at 0.001nm to 10nm, and is known to have strong penetrating power.

Fig. 1 shows the interactions between a material and X-ray, and various analysis methods that make use of these interactions. These interactions provide important clues for learning the state of a material. As a familiar example, an X-ray image for medical application is a well-known use of transmission X-ray. Here we will introduce an elemental analysis method called fluorescent X-ray spectrometry.

Fig.1 Analytical methods and its application interaction of X-ray and matter

Fluorescent X-ray Spectrometry

When irradiating X-rays onto a material, fluorescent X-ray (characteristic X-ray), which has energy (wavelength) unique to the element that composes the material will be generated. When we measure the fluorescent X-ray energy, the contained element is identified (qualitative analysis), and we can calculate the concentration (quantitative analysis) from the intensity of the fluorescent X-ray of each element. Thus, the qualitative or quantitative analyses of a material by irradiating X-rays onto an unknown material and analyzing the fluorescent X-ray that is generated, is called fluorescent X-ray spectrometry.

There are two types of fluorescent X-ray spectrometry; the wavelength dispersive type (WDXRF) using analyzing crystals, and the energy dispersive type (EDXRF) using semiconductor detectors (EDS).

Comparison between Energy Dispersive Type and Wavelength Dispersive Type Spectrometers

The characteristics of a wavelength dispersive type spectrometer (WDXRF) are high sensitivity, high accuracy, high resolution, and high reproducibility. We can expect sensitivity and accuracy at levels one order of magnitude higher than those of the energy dispersive type spectrometer (EDXRF). These characteristics are provided by a high-power X-ray tube (3 to 4 kW) and its cooling device, a goniometer which makes complicated movements and an exchange mechanism for the analyzing crystal and detector and so on. Naturally, the instruments are larger, with a complicated structure and high price. The specimen surface is required to be flat and the available analysis area is from several mm to 30mm or so. This type of device is suitable for process management where specimens with the same form are analyzed one after another.

The characteristics of the energy dispersive type spectrometer (EDXRF) are simple structure and low price, its adaptability to a variety of specimens, and its user-friendliness. The X-ray bulb is compact (several tens W) and air-cooled, and since the EDS (semiconductor detector) itself performs the analysis, a complicated spectroscopy section is not necessary.

The roughness or shape of specimen does not matter, so analysis of large specimens or micro areas is possible. Each characteristic is shown in Fig. 2. The images are the large instrument for WDXRF, and the compact simple instrument for EDXRF.

Wavelength Dispersive Type (WDXRF) Advantages: High Sensitivity, High Resolution High Accuracy, High Reproducibility Disadvantages: Complicated and large-sized, high price Specimen is limited to flat platesEnergy Dispersive Type (EDXRF) Advantages: Simple Operation, compact, low price Flexibility in specimen shape Disadvantages: Low resolution (overlapped peaks) Cooling mechanism requiring liquid nitrogen or the like

Fig.2 Comparison between Wavelength Dispersive Type (WDXRF) and Energy Dispersive Type (EDXRF)

Sampling of Solid/Powder/Liquid Samples

One of the characteristics of EDXRF is the ease of use. Sampling of solid, powder, and liquid samples is explained below.

Sampling of Solid Sample

Analysis of a solid sample is possible by simply placing the sample at the X-ray illumination position.

In case of small sample, use of a dedicated cell will make it easier to set the sample. Fig. 3 shows a simplified illustration of the solid sample sampling method.

Fig.3 Sampling of Solid Sample

Sampling of Powder Sample (rock, soil, incinerated ash, etc)

Powder samples are typically analyzed by producing a pellet using a compression device. As a simplified method, analysis is possible on the powder placed into a specially-designed cell. Fig. 4 shows a simplified illustration of the powder sample sampling method.

Fig.4 Sampling of Powder Sample

Sampling of Liquid Sample

For liquid samples, a dedicated cell is used. Fill a dedicated cell with the liquid and analyze. In addition, there is another method where you can drop liquid onto a filter, dry it, and then analyze it. Fig. 5 shows a simplified illustration of liquid sample sampling methods.

Fig.5 Sampling of Liquid Sample

FP Quantitative Method / Film Thickness Analysis of Thin Film Sample

FP (fundamental parameter) quantitative method

The EDXRF instrument employs a theoretical calculation method called the FP quantitative method, allowing quantitative analysis of an unknown sample without the need for a standard sample.
The FP quantitative method assumes that the sample is uniform, sufficiently large and thick, and that all elements (100% in total) are quantified. Naturally, a sample must satisfy these assumptions, so attention is needed.The flow chart of FP quantitative method is shown in Fig. 6.

Fig.6 The flow chart of FP quantitative method

Flow Chart Explanation

1. First, measure the unknown sample and obtain the measurement intensity.
2. Assume the initial concentration of the sample and obtain a calculated intensity using the FP method.
3. Compare the measurement intensity and the calculated intensity.
4. Change the assumed concentration so that the measurement intensity and the calculated intensity match.
5. Obtain a new calculated intensity with the new assumed concentration using the FP method.
6. Repeat steps 3 to 5.
7. The assumed concentration that gives a calculated concentration that matches the measurement concentration is the analysis result.

Film Thickness Analysis of Thin Film Sample

In the case of a thin film sample, there is a correlation between the x-ray intensity of the elements composing the film and the film thickness. Therefore, by irradiating X-rays onto the surface of a thin film and measuring the X-ray intensity of the elements composing the film, the film thickness can be analyzed without destroying it.

A Single layer film can be analyzed using a calibration curve, but with the calibration curve method, a standard sample must be prepared for each kind of film. When the thin film FP quantitative method is used, it is not only possible to analyze single layer films, but also to analyze the thickness and composition of each layer in a multi-layer thin film, up to 5 layers , without a standard sample, which is very convenient. Fig. 7 shows a diagram of the thin film FP method, Fig. 8 shows a measurement example of Au/Ni/Cu film.

Thin Film FP (fundamental parameter) method

• Simultaneous non-destructive analysis of thickness and composition of thin film
• Up to 5 layers, and up to 20 elements for each layer
• Film thickness of about 10nm to 10μm (differs depending on element)
• Standard sample is not necessary (theoretical calculation)
• Information of layering order, elements, and density of the film is needed.

Fig.7 Schematic diagram of a thin film FP method

Fig.8 Measurement of the film Au / Ni / Cu thin film FP method

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Nuclear Magnetic Resonance (NMR) spectroscopy is an incredibly powerful tool for characterizing molecular structures. When submitting to the FDA or other regulatory agencies, full structural characterization by NMR provides crucial evidence of compound identity. A combination of 1-dimensional and 2-dimensional NMR experiments are necessary for complete confidence in chemical structure.

This post will walk you through the steps to fully characterize a molecule by 1- and 2-dimensional NMR, including on how to perform NMR interpretation.

Step 1: ¹H-NMR

The first step in structural characterization is 1-dimensional proton ¹H-NMR. The chemical shift, multiplicity, coupling constants, and integration are all factors to consider when assigning protons. In this example, only three protons can be assigned by the proton spectrum alone: protons 3, 4, and 6.

To begin, let’s start with proton 3. Proton 3 is the only methyl group in the structure, and therefore must integrate to 3 protons. The only peak with an integration of 3 is the doublet at 1.770 ppm. The high field chemical shift supports this assignment. The peak is split into a doublet with a coupling constant of 1.2 Hz, reflecting the long-range coupling between protons 3 and 4, which also supports this assignment.

Protons that are coupled to each other should exhibit the same coupling constant. The long-range coupling constant observed for proton 3 (J=1.2 Hz, split into a doublet by proton 4) is reflected in the coupling constant for proton 4 (J=1.2 Hz, split into a quartet by proton 3). Therefore, the peak at 7.690 ppm must represent proton 4! The integration and chemical shift support the assignment, as proton 4 is the only aromatic proton in the structure.

There is only one singlet in the ¹H-NMR spectrum. The only proton that should show up as a singlet is proton 6, as it has no neighboring protons that would split the peak (the nearest proton is 5 bonds away!). The chemical shift of 11.256 ppm supports this assignment, as imide protons often show up far downfield. The peak also integrates to 1 proton, supporting the assignment.

The remaining protons are doublets, triplets, and multiplets that can be assigned by 2-dimensional COSY.

Step 2: ¹H-¹H COSY

¹H-¹H Correlation Spectroscopy (COSY) shows the correlation between hydrogens which are coupled to each other in the ¹H NMR spectrum. The ¹H spectrum is plotted on both 2D axes. While 2-bond and 3-bond ¹H-¹H coupling is easily visible by COSY, long range coupling can also be observed with long acquisition times. The cross-peaks (not on the diagonal) that are symmetric to the diagonal show the COSY correlations. For example, protons 3 and 4 are coupled to each other, since they form a box pattern symmetric to the diagonal. This confirms assignments 3 and 4 made from the proton spectrum alone.

Two types of COSY coupling: 3-bond short range coupling between protons 7 and 8 (red) and 4-bond long range coupling between protons 3 and 4 (blue).

My favorite way to analyze a COSY spectrum with many unassigned protons is to make a table of correlations, like the one seen here. Look at the table for any clear differences in correlation and begin there! In this example, all unassigned protons show one or two COSY correlations-except the proton at 4.233 ppm, which correlates to threeother protons by COSY. The only proton expected to correlate with three nonequivalent protons is proton 9!

Now that proton 9 has been assigned, the fun really begins. Thymidine’s structure suggests that proton 9 should couple protons 8, 10, and 11. Based on the COSY, proton 9 couples protons at 2.068 ppm (2H), 3.754 ppm (1H), and 5.209 ppm (1H). From this list, we can easily assign proton 8 as the peak at 2.068 ppm based on its integration of 2 protons. To differentiate protons 10 and 11, take a look at our COSY table; 3.754 ppm shows two COSY correlations, while 5.209 ppm only shows one. Therefore, we can assign proton 10 as 5.209 ppm and proton 11 as 3.754 ppm.

Once proton 8 has been assigned, we can easily assign proton 7 based on the remaining COSY correlation for proton 8. Proton 7’s peak at 6.163 ppm is split into a triplet by the two 8 protons, confirming the assignment.

All that remains are protons 12 and 13. We can assign proton 12 (3.564 ppm) based on its integration of 2H and its COSY correlation to proton 11. The last remaining peak at 4.999 ppm must be proton 13; this is confirmed by COSY correlation with proton 12, triplet multiplicity based on splitting by proton 12, and integration of one proton.

Now we have a fully assigned ¹H-NMR spectrum! This spectrum will help us assign our carbons using HSQC and HMBC NMR spectroscopy.

Step 3: ¹³C-NMR

Carbon NMR is a necessary step in full structural characterization. However, ¹³C-NMR alone does not provide enough information to assign the carbons in the molecule. The NMR spectrum below does confirm the number of carbons in the molecule; however, HSQC and HMBC (we will get to these soon!) are necessary to assign the carbons with confidence. Note that one of the carbons is hidden beneath the solvent signal but is clearly visible after zooming into that region.

Step 4: DEPT-45, 90, and 135

Distortionless Enhancement of Polarization Transfer (DEPT) experiments help assign carbon peaks by determining the number of protons attached to each carbon. For very simple molecules, DEPT may be enough to partially or fully assign all carbons. In complex molecules, DEPT and HSQC together are useful for confirming both carbon and proton assignments. For example, the DEPT experiments below can only identify carbon 3-it is the only CH₃ peak. I always go back and use DEPT to confirm the carbons I assigned by HSQC.

• DEPT-45 shows CH, CH₂, and CH₃ carbons as positive peaks. Carbons with no protons are not visible.
• DEPT-90 shows only CH peaks as positive peaks. Carbons with no protons, CH₂, and CH₃ carbons are not visible.
• DEPT-135 shows CH and CH₃ carbons as positive peaks and CH₂ carbons as negative peaks. Carbons with no protons are not visible.

Step 5: ¹H-¹³C HSQC

¹H-¹³C Heteronuclear Single Quantum Coherence Spectroscopy (HSQC) shows which hydrogens are directly attached to which carbon atoms. The ¹H spectrum is shown on the horizontal axis and the ¹³C spectrum is shown on the vertical axis. The HSQC spectrum is most valuable when protons have already been assigned.

For example, HSQC shows a correlation between proton 4 and the carbon at 136.113 ppm; this carbon is now assigned as carbon 4. Carbons 3, 4, 7, 8, 9, 11, and 12 are assigned by HSQC. Only 1-bond correlations are observed, so HSQC assignments are relatively straightforward. The DEPT experiments also confirm these assignments. HSQC is also useful in confirming proton assignments of nitrogen or oxygen-bound protons; they show no signal by HSQC. This further supports the assignments of protons 6, 10, and 13.

An example correlation between proton and carbon 4 is observed by HSQC.

Step 6: ¹H-¹³C HMBC

¹H-¹³C Heteronuclear Multiple Bond Correlation Spectroscopy (HMBC) shows the correlations between protons and carbons that are separated by multiple bonds. The ¹H spectrum is shown on the horizontal axis and the ¹³C spectrum is shown on the vertical axis. Correlated atoms are shown in blue and the connecting atoms are shown in red. Note that direct hydrogen-carbon bonds (1-bond correlations) are generally not seen. For example, hydrogen 4 shows correlations with carbons 1, 2, 3, 5, and 7, but not carbon 4.

HMBC interactions between proton 4 and carbons 1, 2, 3, 5, and 7.

HMBC is incredibly useful for assigning carbons that have no protons attached. In this example, carbons 1, 2, and 5 have no protons attached. Carbon 1 is assigned by HMBC interactions with protons 3, 4, and 6; carbon 2 by interaction with protons 3, 4, 6, and 7; and carbon 5 by interactions with protons 4 and 7 only. The chemical environment of carbon 5 suggests it would appear more downfield than carbon 1, which confirms these assignments.

HMBC also confirms assignments that were based solely on the proton and COSY spectrum. For example, protons 10 and 13 are differentiated by HMBC; proton 10 is confirmed by interactions with carbons 8, 9, and 11, while proton 13 is confirmed by interactions with 11 and 12. HMBC supports all proton and all carbon assignments, unambiguously confirming both the structure and analysis of thymidine.

At Emery Pharma, we are experts in 1D and 2D NMR characterization and structure elucidation; in fact, 2D NMR projects are some of our favorites! We have supported numerous pharmaceutical companies in full NMR characterization for API submissions to regulatory agencies, as well as complete structure elucidation of impurities. We provide a fully annotated report with images similar to those seen here and support our results with high resolution mass spectrometry and elemental analysis. 

Some nuclei rotate around their axis like electrons. In the presence of an external magnetic field, a rotating nucleus has only a small number of stable orientations. Nuclear magnetic resonance (NMR) occurs when a spinning core is excited from a lower energy orientation to a higher energy orientation in the presence of a magnetic field by absorbing enough electromagnetic radiation. Nuclear magnetic resonance spectroscopy involves measuring the amount of energy required to change spin nuclei from a stable orientation to a more unstable orientation in a magnetic field. Because spin-core nuclei change direction in a magnetic field at different frequencies, different frequencies of absorbing radiation are needed to change the orientation of spin-core nuclei. The frequency at which the absorption takes place is used for analysis and spectroscopy [1].

Nuclear magnetic resonance was first discovered independently in 1946 by Felix Bloch of Stanford University and Edward Parcel of Harvard University. They were able to show the absorption of electromagnetic radiation as a result of the transfer of the energy level of the nucleus in a strong magnetic field. The two physicists won the Nobel Prize in 1952 for their work. In the first five years after the discovery of the nuclear magnetic resonance method, chemists discovered that the molecular environment of objects affects the absorption of radiation by nuclei in the presence of a magnetic field, and this effect could be related to the structure of the molecule. Since then, the growth of magnetic resonance spectroscopy has been explosive and this method has had a significant effect on the development of organic chemistry, inorganic chemistry and biochemistry [2]. In 1999, a team of Canadian physicists developed a new method using the Beta Nuclear Magnetic Resonance Method, which is capable of demonstrating the magnetic and electrical properties of very thin layers and surfaces. BetaNMR methods are used in nanoscience. Be [3].

The magnitude of the spin angle motion in the nuclei is determined by the quantum number of the nucleus spin. Quantum number The core spin of any number can be integer or semi-integer. In 16 O and 12C non-spin nuclei, the quantum spin number of the nucleus is zero. Cores that are not spin and therefore do not have the magnitude of the spin angle motion can not be detected by NMR spectroscopy. Spin-core cores with spherical charge distribution have a spin quantum number of 1/2. Examples of these nuclei include 13C, 19F, 3H, 15N, 31P and 1H, which have a quantum number of 1/2 and a magnetic moment. In order for a nucleus in a magnetic field to absorb a large amount of electromagnetic radiation, it must have a high frequency in the sample and also have a relatively large magnetic moment (µ). Cores that have both properties in question include 1H, 19F, 21P. Most NMR measurements are usually performed for 1 h. Measurements of other nuclei are often performed using signal amplification methods to observe the spectrum. Usually, among the nuclei with low relative frequency that show the magnetic resonance of the nucleus, 12 C, 15N, 16O are the most important for chemists. The magnetic resonance method of the hydrogen nucleus (1H), which is used more than other nuclei, has a magnetic torque of about 79.2 برای. It will be magnetic. For other cores used for nuclear magnetic resonance spectroscopy, the magnetic torque for 21P, 19F 12C is 6873.2, 1305.1 and 0.7022, respectively [4]. In most cases, the sensitivity of non-proton core magnetic resonance devices, such as 12C, etc., is lower than that of HNMR. Also, in most compounds, the natural abundance of non-proton magnetic nuclei is significantly lower than that of protons. This factor causes the NMR spectra of non-proton nuclei to have a relatively low noise signal. The peaks of these spectra are small, and often the spectrum cannot be determined if the same device used for proton nucleus (PMR) NMR is used. Due to the low signal-to-noise ratio in these cases, most devices designed to record the NMR spectra of non-proton nuclei use multiple traverses with signal averaging techniques. The most common devices for spectral peak extraction use the Fourier transform. Fourier transformers are also used to prepare PMR spectra of dilute solutions and complex molecules, such as proteins, in which the amount of a particular proton in the molecule is small. The difference between PMR spectra and other NMR spectra is in the range of chemical displacement. The chemical displacement range for PMR is 10PPM in most cases. While for the 12C core the chemical displacement is up to about 200PPM, for the 19F and 21P spectra it is 300 and 400PPM, respectively. In NMR methods, the units used are usually time (seconds), angle (degrees or radians), temperature (Kelvin), magnetic field strength (Tesla, T), energy (joules), vibration (rpm) and power ( Watts) is. [5] Components of the NMR Device The important components of an NMR spectrometer are shown schematically in Figure (1). A brief description of each component is given below.

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Over the past fifty years nuclear magnetic resonance spectroscopy, commonly referred to as nmr, has become the preeminent technique for determining the structure of organic compounds. Of all the spectroscopic methods, it is the only one for which a complete analysis and interpretation of the entire spectrum is normally expected. Although larger amounts of sample are needed than for mass spectroscopy, nmr is non-destructive, and with modern instruments good data may be obtained from samples weighing less than a milligram. To be successful in using nmr as an analytical tool, it is necessary to understand the physical principles on which the methods are based.

The nuclei of many elemental isotopes have a characteristic spin (I). Some nuclei have integral spins (e.g. I = 1, 2, 3 ….), some have fractional spins (e.g. I = 1/2, 3/2, 5/2 ….), and a few have no spin, I = 0 (e.g. ¹²C, ¹⁶O, ³²S, ….). Isotopes of particular interest and use to organic chemists are ¹H, ¹³C, ¹⁹F and ³¹P, all of which have I = 1/2. Since the analysis of this spin state is fairly straightforward, our discussion of nmr will be limited to these and other I = 1/2 nuclei.

The following features lead to the nmr phenomenon:

1. A spinning charge generates a magnetic field, as shown by the animation on the right. The resulting spin-magnet has a magnetic moment (μ) proportional to the spin.
2. In the presence of an external magnetic field (B0), two spin states exist, +1/2 and -1/2. The magnetic moment of the lower energy +1/2 state is aligned with the external field, but that of the higher energy -1/2 spin state is opposed to the external field. Note that the arrow representing the external field points North.
3. The difference in energy between the two spin states is dependent on the external magnetic field strength, and is always very small. The following diagram illustrates that the two spin states have the same energy when the external field is zero, but diverge as the field increases. At a field equal to Bx a formula for the energy difference is given (remember I = 1/2 and μ is the magnetic moment of the nucleus in the field).
Strong magnetic fields are necessary for nmr spectroscopy. The international unit for magnetic flux is the tesla (T). The earth’s magnetic field is not constant, but is approximately 10-4 T at ground level. Modern nmr spectrometers use powerful magnets having fields of 1 to 20 T. Even with these high fields, the energy difference between the two spin states is less than 0.1 cal/mole. To put this in perspective, recall that infrared transitions involve 1 to 10 kcal/mole and electronic transitions are nearly 100 time greater. For nmr purposes, this small energy difference (ΔE) is usually given as a frequency in units of MHz (106 Hz), ranging from 20 to 900 Mz, depending on the magnetic field strength and the specific nucleus being studied. Irradiation of a sample with radio frequency (rf) energy corresponding exactly to the spin state separation of a specific set of nuclei will cause excitation of those nuclei in the +1/2 state to the higher -1/2 spin state. Note that this electromagnetic radiation falls in the radio and television broadcast spectrum. Nmr spectroscopy is therefore the energetically mildest probe used to examine the structure of molecules.  The nucleus of a hydrogen atom (the proton) has a magnetic moment μ = 2.7927, and has been studied more than any other nucleus. The previous diagram may be changed to display energy differences for the proton spin states (as frequencies) by mouse clicking anywhere within it.
4. For spin 1/2 nuclei the energy difference between the two spin states at a given magnetic field strength will be proportional to their magnetic moments. For the four common nuclei noted above, the magnetic moments are: 1H μ = 2.7927, 19F μ = 2.6273, 31P μ = 1.1305 & 13C μ = 0.7022. These moments are in nuclear magnetons, which are 5.05078•10-27 JT-1. The following diagram gives the approximate frequencies that correspond to the spin state energy separations for each of these nuclei in an external magnetic field of 2.35 T. The formula in the colored box shows the direct correlation of frequency (energy difference) with magnetic moment (h = Planck’s constant = 6.626069•10-34 Js).

      2. Proton NMR Spectroscopy
This important and well-established application of nuclear magnetic resonance will serve to illustrate some of the novel aspects of this method. To begin with, the nmr spectrometer must be tuned to a specific nucleus, in this case the proton. The actual procedure for obtaining the spectrum varies, but the simplest is referred to as the continuous wave (CW) method. A typical CW-spectrometer is shown in the following diagram. A solution of the sample in a uniform 5 mm glass tube is oriented between the poles of a powerful magnet, and is spun to average any magnetic field variations, as well as tube imperfections. Radio frequency radiation of appropriate energy is broadcast into the sample from an antenna coil (colored red). A receiver coil surrounds the sample tube, and emission of absorbed rf energy is monitored by dedicated electronic devices and a computer. An nmr spectrum is acquired by varying or sweeping the magnetic field over a small range while observing the rf signal from the sample. An equally effective technique is to vary the frequency of the rf radiation while holding the external field constant.

As an example, consider a sample of water in a 2.3487 T external magnetic field, irradiated by 100 MHz radiation. If the magnetic field is smoothly increased to 2.3488 T, the hydrogen nuclei of the water molecules will at some point absorb rf energy and a resonance signal will appear. An animation showing this may be activated by clicking the Show Field Sweep button. The field sweep will be repeated three times, and the resulting resonance trace is colored red. For visibility, the water proton signal displayed in the animation is much broader than it would be in an actual experiment.

Since protons all have the same magnetic moment, we might expect all hydrogen atoms to give resonance signals at the same field / frequency values. Fortunately for chemistry applications, this is not true. By clicking the Show Different Protons button under the diagram, a number of representative proton signals will be displayed over the same magnetic field range. It is not possible, of course, to examine isolated protons in the spectrometer described above; but from independent measurement and calculation it has been determined that a naked proton would resonate at a lower field strength than the nuclei of covalently bonded hydrogens. With the exception of water, chloroform and sulfuric acid, which are examined as liquids, all the other compounds are measured as gases.

Why should the proton nuclei in different compounds behave differently in the nmr experiment ? 
The answer to this question lies with the electron(s) surrounding the proton in covalent compounds and ions. Since electrons are charged particles, they move in response to the external magnetic field (B_o) so as to generate a secondary field that opposes the much stronger applied field. This secondary field shields the nucleus from the applied field, so B_o must be increased in order to achieve resonance (absorption of rf energy). As illustrated in the drawing on the right, B_o must be increased to compensate for the induced shielding field. In the upper diagram, those compounds that give resonance signals at the higher field side of the diagram (CH₄, HCl, HBr and HI) have proton nuclei that are more shielded than those on the lower field (left) side of the diagram. 
The magnetic field range displayed in the above diagram is very small compared with the actual field strength (only about 0.0042%). It is customary to refer to small increments such as this in units of parts per million (ppm). The difference between 2.3487 T and 2.3488 T is therefore about 42 ppm. Instead of designating a range of nmr signals in terms of magnetic field differences (as above), it is more common to use a frequency scale, even though the spectrometer may operate by sweeping the magnetic field. Using this terminology, we would find that at 2.34 T the proton signals shown above extend over a 4,200 Hz range (for a 100 MHz rf frequency, 42 ppm is 4,200 Hz). Most organic compounds exhibit proton resonances that fall within a 12 ppm range (the shaded area), and it is therefore necessary to use very sensitive and precise spectrometers to resolve structurally distinct sets of hydrogen atoms within this narrow range. In this respect it might be noted that the detection of a part-per-million difference is equivalent to detecting a 1 millimeter difference in distances of 1 kilometer.

Chemical Shift

Unlike infrared and uv-visible spectroscopy, where absorption peaks are uniquely located by a frequency or wavelength, the location of different nmr resonance signals is dependent on both the external magnetic field strength and the rf frequency. Since no two magnets will have exactly the same field, resonance frequencies will vary accordingly and an alternative method for characterizing and specifying the location of nmr signals is needed. This problem is illustrated by the eleven different compounds shown in the following diagram. Although the eleven resonance signals are distinct and well separated, an unambiguous numerical locator cannot be directly assigned to each.

One method of solving this problem is to report the location of an nmr signal in a spectrum relative to a reference signal from a standard compound added to the sample. Such a reference standard should be chemically unreactive, and easily removed from the sample after the measurement. Also, it should give a single sharp nmr signal that does not interfere with the resonances normally observed for organic compounds. Tetramethylsilane, (CH₃)₄Si, usually referred to as TMS, meets all these characteristics, and has become the reference compound of choice for proton and carbon nmr.
Since the separation (or dispersion) of nmr signals is magnetic field dependent, one additional step must be taken in order to provide an unambiguous location unit. This is illustrated for the acetone, methylene chloride and benzene signals by clicking on the previous diagram. To correct these frequency differences for their field dependence, we divide them by the spectrometer frequency (100 or 500 MHz in the example), as shown in a new display by again clicking on the diagram. The resulting number would be very small, since we are dividing Hz by MHz, so it is multiplied by a million, as shown by the formula in the blue shaded box. Note that ν_ref is the resonant frequency of the reference signal and ν_samp is the frequency of the sample signal. This operation gives a locator number called the Chemical Shift, having units of parts-per-million (ppm), and designated by the symbol δ   Chemical shifts for all the compounds in the original display will be presented by a third click on the diagram.

The compounds referred to above share two common characteristics:

• The hydrogen atoms in a given molecule are all structurally equivalent, averaged for fast conformational equilibria. 
• The compounds are all liquids, save for neopentane which boils at 9 °C and is a liquid in an ice bath.

The first feature assures that each compound gives a single sharp resonance signal. The second allows the pure (neat) substance to be poured into a sample tube and examined in a nmr spectrometer. In order to take the nmr spectra of a solid, it is usually necessary to dissolve it in a suitable solvent. Early studies used carbon tetrachloride for this purpose, since it has no hydrogen that could introduce an interfering signal. Unfortunately, CCl₄ is a poor solvent for many polar compounds and is also toxic. Deuterium labeled compounds, such as deuterium oxide (D₂O), chloroform-d (DCCl₃), benzene-d₆(C₆D₆), acetone-d₆ (CD₃COCD₃) and DMSO-d₆ (CD₃SOCD₃) are now widely used as nmr solvents. Since the deuterium isotope of hydrogen has a different magnetic moment and spin, it is invisible in a spectrometer tuned to protons.

From the previous discussion and examples we may deduce that one factor contributing to chemical shift differences in proton resonance is the inductive effect. If the electron density about a proton nucleus is relatively high, the induced field due to electron motions will be stronger than if the electron density is relatively low. The shielding effect in such high electron density cases will therefore be larger, and a higher external field (B_o) will be needed for the rf energy to excite the nuclear spin. Since silicon is less electronegative than carbon, the electron density about the methyl hydrogens in tetramethylsilane is expected to be greater than the electron density about the methyl hydrogens in neopentane (2,2-dimethylpropane), and the characteristic resonance signal from the silane derivative does indeed lie at a higher magnetic field. Such nuclei are said to be shielded. Elements that are more electronegative than carbon should exert an opposite effect (reduce the electron density); and, as the data in the following tables show, methyl groups bonded to such elements display lower field signals (they are deshielded). The deshielding effect of electron withdrawing groups is roughly proportional to their electronegativity, as shown by the left table. Furthermore, if more than one such group is present, the deshielding is additive (table on the right), and proton resonance is shifted even further downfield.

The general distribution of proton chemical shifts associated with different functional groups is summarized in the following chart. Bear in mind that these ranges are approximate, and may not encompass all compounds of a given class. Note also that the ranges specified for OH and NH protons (colored orange) are wider than those for most CH protons. This is due to hydrogen bonding variations at different sample concentrations.

Proton Chemical Shift Ranges*
Low Field Region		High Field Region
	* For samples in CDCl3 solution. The δ scale is relative to TMS at δ = 0.

To make use of a calculator that predicts aliphatic proton chemical shifts Click Here. This application was developed at Colby College.

Signal Strength

The magnitude or intensity of nmr resonance signals is displayed along the vertical axis of a spectrum, and is proportional to the molar concentration of the sample. Thus, a small or dilute sample will give a weak signal, and doubling or tripling the sample concentration increases the signal strength proportionally. If we take the nmr spectrum of equal molar amounts of benzene and cyclohexane in carbon tetrachloride solution, the resonance signal from cyclohexane will be twice as intense as that from benzene because cyclohexane has twice as many hydrogens per molecule. This is an important relationship when samples incorporating two or more different sets of hydrogen atoms are examined, since it allows the ratio of hydrogen atoms in each distinct set to be determined. To this end it is necessary to measure the relative strength as well as the chemical shift of the resonance signals that comprise an nmr spectrum. Two common methods of displaying the integrated intensities associated with a spectrum are illustrated by the following examples. In the three spectra in the top row, a horizontal integrator trace (light green) rises as it crosses each signal by a distance proportional to the signal strength. Alternatively, an arbitrary number, selected by the instrument’s computer to reflect the signal strength, is printed below each resonance peak, as shown in the three spectra in the lower row. From the relative intensities shown here, together with the previously noted chemical shift correlations, the reader should be able to assign the signals in these spectra to the set of hydrogens that generates each. If you click on one of the spectrum signals (colored red) or on hydrogen atom(s) in the structural formulas the spectrum will be enlarged and the relationship will be colored blue.
Hint: When evaluating relative signal strengths, it is useful to set the smallest integration to unity and convert the other values proportionally.

Hydroxyl Proton Exchange and the Influence of Hydrogen Bonding

The last two compounds in the lower row are alcohols. The OH proton signal is seen at 2.37 δ in 2-methyl-3-butyne-2-ol, and at 3.87 δ in 4-hydroxy-4-methyl-2-pentanone, illustrating the wide range over which this chemical shift may be found. A six-membered ring intramolecular hydrogen bond in the latter compound is in part responsible for its low field shift, and will be shown by clicking on the hydroxyl proton. We can take advantage of rapid OH exchange with the deuterium of heavy water to assign hydroxyl proton resonance signals . As shown in the following equation, this removes the hydroxyl proton from the sample and its resonance signal in the nmr spectrum disappears. Experimentally, one simply adds a drop of heavy water to a chloroform-d solution of the compound and runs the spectrum again. The result of this exchange is displayed below.

R-O-H   +   D2O      R-O-D   +   D-O-H

Hydrogen bonding shifts the resonance signal of a proton to lower field ( higher frequency ). Numerous experimental observations support this statement, and a few of these will be described here.

i)   The chemical shift of the hydroxyl hydrogen of an alcohol varies with concentration. Very dilute solutions of 2-methyl-2-propanol, (CH3)3COH, in carbon tetrachloride solution display a hydroxyl resonance signal having a relatively high-field chemical shift (< 1.0 δ ). In concentrated solution this signal shifts to a lower field, usually near 2.5 δ.
ii)   The more acidic hydroxyl group of phenol generates a lower-field resonance signal, which shows a similar concentration dependence to that of alcohols. OH resonance signals for different percent concentrations of phenol in chloroform-d are shown in the following diagram (C-H signals are not shown).
iii)   Because of their favored hydrogen-bonded dimeric association, the hydroxyl proton of carboxylic acids displays a resonance signal significantly down-field of other functions. For a typical acid it appears from 10.0 to 13.0 δ and is often broader than other signals. The spectra shown below for chloroacetic acid (left) and 3,5-dimethylbenzoic acid (right) are examples.
iv)   Intramolecular hydrogen bonds, especially those defining a six-membered ring, generally display a very low-field proton resonance. The case of 4-hydroxypent-3-ene-2-one (the enol tautomer of 2,4-pentanedione) not only illustrates this characteristic, but also provides an instructive example of the sensitivity of the nmr experiment to dynamic change. In the nmr spectrum of the pure liquid, sharp signals from both the keto and enol tautomers are seen, their mole ratio being 4 : 21 (keto tautomer signals are colored purple). Chemical shift assignments for these signals are shown in the shaded box above the spectrum. The chemical shift of the hydrogen-bonded hydroxyl proton is δ 14.5, exceptionally downfield. We conclude, therefore, that the rate at which these tautomers interconvert is slow compared with the inherent time scale of nmr spectroscopy.
Two structurally equivalent structures may be drawn for the enol tautomer (in magenta brackets). If these enols were slow to interconvert, we would expect to see two methyl resonance signals associated with each, one from the allylic methyl and one from the methyl ketone. Since only one strong methyl signal is observed, we must conclude that the interconversion of the enols is very fast-so fast that the nmr experiment detects only a single time-averaged methyl group (50% α-keto and 50% allyl).

Although hydroxyl protons have been the focus of this discussion, it should be noted that corresponding N-H groups in amines and amides also exhibit hydrogen bonding nmr shifts, although to a lesser degree. Furthermore, OH and NH groups can undergo rapid proton exchange with each other; so if two or more such groups are present in a molecule, the nmr spectrum will show a single signal at an average chemical shift. For example, 2-hydroxy-2-methylpropanoic acid, (CH₃)₂C(OH)CO₂H, displays a strong methyl signal at δ 1.5 and a 1/3 weaker and broader OH signal at δ 7.3 ppm. Note that the average of the expected carboxylic acid signal (ca. 12 ) and the alcohol signal (ca. 2 ) is 7. Rapid exchange of these hydrogens with heavy water, as noted above, would cause the low field signal to disappear.

π-Electron Functions

An examination of the proton chemical shift chart (above) makes it clear that the inductive effect of substituents cannot account for all the differences in proton signals. In particular the low field resonance of hydrogens bonded to double bond or aromatic ring carbons is puzzling, as is the very low field signal from aldehyde hydrogens. The hydrogen atom of a terminal alkyne, in contrast, appears at a relatively higher field. All these anomalous cases seem to involve hydrogens bonded to pi-electron systems, and an explanation may be found in the way these pi-electrons interact with the applied magnetic field.
Pi-electrons are more polarizable than are sigma-bond electrons, as addition reactions of electrophilic reagents to alkenes testify. Therefore, we should not be surprised to find that field induced pi-electron movement produces strong secondary fields that perturb nearby nuclei. The pi-electrons associated with a benzene ring provide a striking example of this phenomenon, as shown below. The electron cloud above and below the plane of the ring circulates in reaction to the external field so as to generate an opposing field at the center of the ring and a supporting field at the edge of the ring. This kind of spatial variation is called anisotropy, and it is common to nonspherical distributions of electrons, as are found in all the functions mentioned above. Regions in which the induced field supports or adds to the external field are said to be deshielded, because a slightly weaker external field will bring about resonance for nuclei in such areas. However, regions in which the induced field opposes the external field are termed shielded because an increase in the applied field is needed for resonance. Shielded regions are designated by a plus sign, and deshielded regions by a negative sign. 
The anisotropy of some important unsaturated functions will be displayed by clicking on the benzene diagram below. Note that the anisotropy about the triple bond nicely accounts for the relatively high field chemical shift of ethynyl hydrogens. The shielding & deshielding regions about the carbonyl group have been described in two ways, which alternate in the display.

Sigma bonding electrons also have a less pronounced, but observable, anisotropic influence on nearby nuclei. This is seen in the small deshielding shift that occurs in the series CH₃–R, R–CH₂–R, R₃CH; as well as the deshielding of equatorial versus axial protons on a fixed cyclohexane ring.

Solvent Effects

Chloroform-d (CDCl₃) is the most common solvent for nmr measurements, thanks to its good solubilizing character and relative unreactive nature ( except for 1º and 2º-amines). As noted earlier, other deuterium labeled compounds, such as deuterium oxide (D₂O), benzene-d6 (C₆D₆), acetone-d6 (CD₃COCD₃) and DMSO-d6 (CD₃SOCD₃) are also available for use as nmr solvents. Because some of these solvents have π-electron functions and/or may serve as hydrogen bonding partners, the chemical shifts of different groups of protons may change depending on the solvent being used. The following table gives a few examples, obtained with dilute solutions at 300 MHz.

For most of the above resonance signals and solvents the changes are minor, being on the order of ±0.1 ppm. However, two cases result in more extreme changes and these have provided useful applications in structure determination. First, spectra taken in benzene-d₆ generally show small upfield shifts of most C–H signals, but in the case of acetone this shift is about five times larger than normal. Further study has shown that carbonyl groups form weak π–π collision complexes with benzene rings, that persist long enough to exert a significant shielding influence on nearby groups. In the case of substituted cyclohexanones, axial α-methyl groups are shifted upfield by 0.2 to 0.3 ppm; whereas equatorial methyls are slightly deshielded (shift downfield by about 0.05 ppm). These changes are all relative to the corresponding chloroform spectra.
The second noteworthy change is seen in the spectrum of tert-butanol in DMSO, where the hydroxyl proton is shifted 2.5 ppm down-field from where it is found in dilute chloroform solution. This is due to strong hydrogen bonding of the alcohol O–H to the sulfoxide oxygen, which not only de-shields the hydroxyl proton, but secures it from very rapid exchange reactions that prevent the display of spin-spin splitting. Similar but weaker hydrogen bonds are formed to the carbonyl oxygen of acetone and the nitrogen of acetonitrile. A useful application of this phenomenon is described elsewhere in this text.

Spin-Spin Interactions

The nmr spectrum of 1,1-dichloroethane (below right) is more complicated than we might have expected from the previous examples. Unlike its 1,2-dichloro-isomer (below left), which displays a single resonance signal from the four structurally equivalent hydrogens, the two signals from the different hydrogens are split into close groupings of two or more resonances. This is a common feature in the spectra of compounds having different sets of hydrogen atoms bonded to adjacent carbon atoms. The signal splitting in proton spectra is usually small, ranging from fractions of a Hz to as much as 18 Hz, and is designated as J (referred to as the coupling constant). In the 1,1-dichloroethane example all the coupling constants are 6.0 Hz, as illustrated by clicking on the spectrum.

1,2-dichloroethane		1,1-dichloroethane

The splitting patterns found in various spectra are easily recognized, provided the chemical shifts of the different sets of hydrogen that generate the signals differ by two or more ppm. The patterns are symmetrically distributed on both sides of the proton chemical shift, and the central lines are always stronger than the outer lines. The most commonly observed patterns have been given descriptive names, such as doublet (two equal intensity signals), triplet (three signals with an intensity ratio of 1:2:1) and quartet (a set of four signals with intensities of 1:3:3:1). Four such patterns are displayed in the following illustration. The line separation is always constant within a given multiplet, and is called the coupling constant (J). The magnitude of J, usually given in units of Hz, is magnetic field independent.

The splitting patterns shown above display the ideal or “First-Order” arrangement of lines. This is usually observed if the spin-coupled nuclei have very different chemical shifts (i.e. Δν is large compared to J). If the coupled nuclei have similar chemical shifts, the splitting patterns are distorted (second order behavior). In fact, signal splitting disappears if the chemical shifts are the same. Two examples that exhibit minor 2nd order distortion are shown below (both are taken at a frequency of 90 MHz). The ethyl acetate spectrum on the left displays the typical quartet and triplet of a substituted ethyl group. The spectrum of 1,3-dichloropropane on the right demonstrates that equivalent sets of hydrogens may combine their influence on a second, symmetrically located set. 
Even though the chemical shift difference between the A and B protons in the 1,3-dichloroethane spectrum is fairly large (140 Hz) compared with the coupling constant (6.2 Hz), some distortion of the splitting patterns is evident. The line intensities closest to the chemical shift of the coupled partner are enhanced. Thus the B set triplet lines closest to A are increased, and the A quintet lines nearest B are likewise stronger. A smaller distortion of this kind is visible for the A and C couplings in the ethyl acetate spectrum.

What causes this signal splitting, and what useful information can be obtained from it ? 
If an atom under examination is perturbed or influenced by a nearby nuclear spin (or set of spins), the observed nucleus responds to such influences, and its response is manifested in its resonance signal. This spin-coupling is transmitted through the connecting bonds, and it functions in both directions. Thus, when the perturbing nucleus becomes the observed nucleus, it also exhibits signal splitting with the same J. For spin-coupling to be observed, the sets of interacting nuclei must be bonded in relatively close proximity (e.g. vicinal and geminal locations), or be oriented in certain optimal and rigid configurations. Some spectroscopists place a number before the symbol J to designate the number of bonds linking the coupled nuclei (colored orange below). Using this terminology, a vicinal coupling constant is ³J and a geminal constant is ²J.

The following general rules summarize important requirements and characteristics for spin 1/2 nuclei :

1)   Nuclei having the same chemical shift (called isochronous) do not exhibit spin-splitting. They may actually be spin-coupled, but the splitting cannot be observed directly.
2)   Nuclei separated by three or fewer bonds (e.g. vicinal and geminal nuclei ) will usually be spin-coupled and will show mutual spin-splitting of the resonance signals (same J’s), provided they have different chemical shifts. Longer-range coupling may be observed in molecules having rigid configurations of atoms.
3)   The magnitude of the observed spin-splitting depends on many factors and is given by the coupling constant J (units of Hz). J is the same for both partners in a spin-splitting interaction and is independent of the external magnetic field strength.
4)   The splitting pattern of a given nucleus (or set of equivalent nuclei) can be predicted by the n+1 rule, where n is the number of neighboring spin-coupled nuclei with the same (or very similar) Js. If there are 2 neighboring, spin-coupled, nuclei the observed signal is a triplet ( 2+1=3 ); if there are three spin-coupled neighbors the signal is a quartet ( 3+1=4 ). In all cases the central line(s) of the splitting pattern are stronger than those on the periphery. The intensity ratio of these lines is given by the numbers in Pascal’s triangle. Thus a doublet has 1:1 or equal intensities, a triplet has an intensity ratio of 1:2:1, a quartet 1:3:3:1 etc. To see how the numbers in Pascal’s triangle are related to the Fibonacci series click on the diagram.

If a given nucleus is spin-coupled to two or more sets of neighboring nuclei by different J values, the n+1 rule does not predict the entire splitting pattern. Instead, the splitting due to one J set is added to that expected from the other J sets. Bear in mind that there may be fortuitous coincidence of some lines if a smaller J is a factor of a larger J.

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Spin 1/2 nuclei include ¹H, ¹³C, ¹⁹F & ³¹P. The spin-coupling interactions described above may occur between similar or dissimilar nuclei. If, for example, a ¹⁹F is spin-coupled to a ¹H, both nuclei will appear as doublets having the same J constant.  Spin coupling with nuclei having spin other than 1/2 is more complex and will not be discussed here.

To make use of a calculator that predicts first order splitting patterns Click Here. This application was developed at Colby College.

Some Examples

Test your ability to interpret ¹H nmr spectra by analyzing the seven examples presented below. The seven spectra may be examined in turn by clicking the “Toggle Spectra” button. Try to associate each spectrum with a plausible structural formula. 
Although the first four cases are relatively simple, keep in mind that the integration values provide ratios, not absolute numbers. In two cases additional information from infrared spectroscopy is provided. When you have made an assignment you may check your answer by clicking on the spectrum itself. In the sixth example, a similar constitutional isomer cannot be ruled out by the data given.

      3. Carbon NMR Spectroscopy
The power and usefulness of ¹H nmr spectroscopy as a tool for structural analysis should be evident from the past discussion. Unfortunately, when significant portions of a molecule lack C-H bonds, no information is forthcoming. Examples include polychlorinated compounds such as chlordane, polycarbonyl compounds such as croconic acid, and compounds incorporating triple bonds (structures below, orange colored carbons).

Even when numerous C-H groups are present, an unambiguous interpretation of a proton nmr spectrum may not be possible. The following diagram depicts three pairs of isomers (A & B) which display similar proton nmr spectra. Although a careful determination of chemical shifts should permit the first pair of compounds (blue box) to be distinguished, the second and third cases (red & green boxes) might be difficult to identify by proton nmr alone.

These difficulties would be largely resolved if the carbon atoms of a molecule could be probed by nmr in the same fashion as the hydrogen atoms. Since the major isotope of carbon (¹²C) has no spin, this option seems unrealistic. Fortunately, 1.1% of elemental carbon is the ¹³C isotope, which has a spin I = 1/2, so in principle it should be possible to conduct a carbon nmr experiment. It is worth noting here, that if much higher abundances of ¹³C were naturally present in all carbon compounds, proton nmr would become much more complicated due to large one-bond coupling of ¹³C and ¹H.

The most important operational technique that has led to successful and routine ¹³C nmr spectroscopy is the use of high-field pulse technology coupled with broad-band heteronuclear decoupling of all protons. The results of repeated pulse sequences are accumulated to provide improved signal strength. Also, for reasons that go beyond the present treatment, the decoupling irradiation enhances the sensitivity of carbon nuclei bonded to hydrogen. 
When acquired in this manner, the carbon nmr spectrum of a compound displays a single sharp signal for each structurally distinct carbon atom in a molecule (remember, the proton couplings have been removed). The spectrum of camphor, shown on the left below, is typical. Furthermore, a comparison with the ¹H nmr spectrum on the right illustrates some of the advantageous characteristics of carbon nmr. The dispersion of ¹³C chemical shifts is nearly twenty times greater than that for protons, and this together with the lack of signal splitting makes it more likely that every structurally distinct carbon atom will produce a separate signal. The only clearly identifiable signals in the proton spectrum are those from the methyl groups. The remaining protons have resonance signals between 1.0 and 2.8 ppm from TMS, and they overlap badly thanks to spin-spin splitting.

Unlike proton nmr spectroscopy, the relative strength of carbon nmr signals are not normally proportional to the number of atoms generating each one. Because of this, the number of discrete signals and their chemical shifts are the most important pieces of evidence delivered by a carbon spectrum. The general distribution of carbon chemical shifts associated with different functional groups is summarized in the following chart. Bear in mind that these ranges are approximate, and may not encompass all compounds of a given class. Note also that the over 200 ppm range of chemical shifts shown here is much greater than that observed for proton chemical shifts.

13C Chemical Shift Ranges*
Low Field Region		High Field Region
	* For samples in CDCl3 solution. The δ scale is relative to TMS at δ=0.

The isomeric pairs previously cited as giving very similar proton nmr spectra are now seen to be distinguished by carbon nmr. In the example on the left below (blue box), cyclohexane and 2,3-dimethyl-2-butene both give a single sharp resonance signal in the proton nmr spectrum (the former at δ 1.43 ppm and the latter at 1.64 ppm). However, in its carbon nmr spectrum cyclohexane displays a single signal at δ 27.1 ppm, generated by the equivalent ring carbon atoms (colored blue); whereas the isomeric alkene shows two signals, one at δ 20.4 ppm from the methyl carbons (colored brown), and the other at 123.5 ppm (typical of the green colored sp² hybrid carbon atoms).

The C₈H₁₀ isomers in the center (red) box have pairs of homotopic carbons and hydrogens, so symmetry should simplify their nmr spectra. The fulvene (isomer A) has five structurally different groups of carbon atoms (colored brown, magenta, orange, blue and green respectively) and should display five ¹³C nmr signals (one near 20 ppm and the other four greater than 100 ppm). Although ortho-xylene (isomer B) will have a proton nmr very similar to isomer A, it should only display four ¹³C nmr signals, originating from the four different groups of carbon atoms (colored brown, blue, orange and green). The methyl carbon signal will appear at high field (near 20 ppm), and the aromatic ring carbons will all give signals having δ > 100 ppm. Finally, the last isomeric pair, quinones A & B in the green box, are easily distinguished by carbon nmr. Isomer A displays only four carbon nmr signals (δ 15.4, 133.4, 145.8 & 187.9 ppm); whereas, isomer B displays five signals (δ 15.9, 133.3, 145.8, 187.5 & 188.1 ppm), the additional signal coming from the non-identity of the two carbonyl carbon atoms (one colored orange and the other magenta).

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Atomic force microscopy (AFM) is a technique with multiple applications in biology. This method is a member of the broad family of scanning probe microscopy and was initially developed in 1986 by Binnig et al to overcome the disadvantages of the scanning tunneling microscopy (STM) [1]. In the case of STM, only conductive materials can be studied as the resolution is obtained by using a tunneling current between a sharp probe and the sample surface[1]. In contrast, AFM uses small forces on the surface by a probe, thus do not damage samples and can provide information of surface topography of biological materials. AFM soon attracted the attention of the biophysical scientists in biomembrane as well as synthetic membrane research due to its capability of observing biological molecular system with resolution on nanometer scale and its possibility of three dimensional imaging [2].

Fundamental Elements of AFM

An atomic force microscope consists of a flexible cantilever containing a sharp probe, laser, photodiode detector, piezoelectric scanner and feedback electronics [3]. The microscope obtains the surface topography by scanning the tip in gentle touch with the sample. The tip motion is monitored by the piezoelectric scanner. As the tip scans the sample, the forces between the tip and the sample surface cause the cantilever to bend. A photodiode detector detects the deflection of a laser beam reflected off the back of the cantilever onto a two- segment photodiode. In most operating modes, a feedback circuit connected to the cantilever deflection sensor keeps the interaction between the tip and the sample at a fixed value and controls the tip-sample distance. The feedback signal is recorded by a computer to reconstruct a 3D image of the surface topography.

The force between the probe and the sample surface depends on the spring constant (stiffness of the cantilever) and the tip-sample distance). The amount of force is calculated based on Hooke’s law:F=−kx(6.1.1)(6.1.1)F=−kx

• FF: Force
• kk: spring constant
• xx: cantilever deflection.

Imaging modes

There are three primary imaging modes in AFM: contact, non-contact and intermittent (tapping) mode [4]. During contact mode, the probe is in contact with the sample and repulsive Van der Waals forces prevail, whilst attractive Van der Waals forces are dominant when the tip moves further away from the sample surface [5].

Contact Mode

In contact mode, the tip is constantly in touch with the sample surface. The applied force is kept constant while the tip scans the surface, creating the surface image [4]. This imaging mode is good for samples with rough and rigid surfaces as it provides fast scanning with high resolution. One disadvantage of this imaging mode is that soft samples like tissues can be deformed or damaged due to the applied force. This drawback can be solved by measuring the sample in aqueous environments to reduce the interaction force between the tip and the sample.

Tapping Mode

In tapping mode, the tip is not in constant contact with the sample surface. Instead, the cantilever is oscillated at its resonant frequency, which makes the tip lightly tap on the surface during scanning. A constant tip-sample interaction is maintained by monitoring the oscillation amplitude and an image is obtained [4]. Several parameters that affect the image contrast are the height, phase signals and amplitude [6]. Phase signals are influenced by material properties of the sample, for example viscoelasticity [6]. The force during scanning is greatly reduced, therefore this mode is useful for biological samples, where the samples are easily damageable or loosely bound to their surface. However, this imaging mode requires a slower scanning speed and is more challenging to measure in liquids.

Non-contact mode

There is no contact between the sample surface and the probe in non-contact mode. The probe oscillates above the sample surface, forming a weak attractive force between the tip apex atom and the sample surface atom. Feedback signals are obtained by measuring a frequency shift in the mechanical oscillation of the cantilever [6].

The force exerted on the surface sample is very low in this case. Moreover, as there is no contact between the probe and the surface, the probe lifetime can be extended. Another advantage of this operating mode is the possibility to observe an atomic defect if the very weak attractive force can be detected. The drawback of this mode is the reduction of resolution, and the oscillation of the cantilever is affected in case there are contaminants on the sample surface. Usually this operation mode requires a careful control of the environment (in UHV) to carry out [7].

Cantilever and Tips

The scanning probe is an important component of the AFM. The dimensions of the cantilever are in micrometer range, while its tip has a radius of a few nanometers [4]. Different cantilever lengths, shapes and materials lead to various spring constants and resonant frequencies. The most common materials of the probes are silicon nitride (Si₃N₄) or silicon (Si) [5]. Figure 6.1.46.1.4 shows a scanning electron microscope (SEM) image of a silicon nitride (4a, 4b) and silicon (4c, 4d) cantilever chip, where a tiny tip having a pyramid shape is integrated at the end. The silicon nitride probe is often used in static contact mode, where the stiffness of the cantilever should be as low as possible [4]. The silicon probe is usually used in dynamic operation mode, which requires higher values for the spring constant to reduce noise and instabilities [4].

Typically, spring constants of AFM cantilevers vary between 0.01 Nm^-1 and 100 Nm^-1, enabling a force sensitivity of 10-11N [4]. The force sensitivity is influenced by thermal, electrical and optical noise. [5] For biological samples, cantilevers in contact mode often have resonance frequencies between 5 and 50 kHz in vacuum [8]. Figure 6.1.56.1.5 reports an AFM tip made of carbon nanotubes (CNTs), which was a breakthrough in terms of resolution. CNTs tips have a high aspect ratio, small diameter, and a well-defined surface chemistry, therefore appearing to be the ideal probe for biological applications [4].

AFM on membranes

Native membranes studied by AFM

Biomembrane sample preparation

In order to study membranes using AFM, the membranes need to be fixed on a flat solid support [8]. Several solid supports such as mica, highly ordered pyrolitic graphite (HOPG), template stripped gold and molybdenum disulfide have proved to give high resolution images [6, 8]. While mica is an insulator and exposes a hydrophilic surface, HOPG is a good conductor and hydrophobic [8]. The similarity between these two substrates is an atomically flat surface [8]. Based on chemical adsorption mechanism, membranes are attached onto the solid support by adjusting pH and ionic strength. As the gap between membrane and the support is very small (0.5-2nm), this may cause impaired mobility for membrane proteins that are directly attached to the support [6]. Furthermore, the adsorption force may affect the conformation of the membrane proteins. To sum up, current sample preparation methods still need further consideration in order to study dynamics and structure of native membrane proteins.

AFM images of native membrane

AFM can obtain the images of native membranes at submolecular resolution, which is a great advantage comparing to other methods [6]. It is effective in providing information of the native organization of membrane proteins and their complexes. Figure 6.1.66.1.6 shows an example of the study of native membrane using AFM. Disk membranes were prepared from mouse retina and then attached on mica support [6]. The AFM image revealed tight rows of dimers packed in the structure arrangement of rhodopsin [6]. This provides a platform for interaction with arrestin and transducin.

Model lipid membranes studied by AFM

Preparation of supported lipid bilayers.

Supported lipid bilayers (SLBs) have been used as a biomimetic model for biomembranes in numerous studies [3, 9]. This system consists of two lipid leaflets spread on a solid support [3]. Although this model lacks some features of the real membranes, it still provides an insight of the structural organization and characteristics of cell membranes. The first method to prepare SLBs is the fusion of lipid vesicles on solid supports [9]. The vesicles are prepared via sonication or extrusion, then adsorbed on the surface of the solid support. The adsorbed vesicles either form larger vesicles by fusing together, or directly rupture and form SLBs.

Another method is to use a hydrophilic substrate on which two consecutive lipid monolayers are deposited by Langmuir-Blodgett transfer [3]. A Teflon-coated trough contains the aqueous solution, with two movable Teflon barriers used to control the area for lipid spread and form a monolayer at the air-water interface. There is also a balance to measure the surface pressure, controlling lipid packing. The solid support is then pulled vertically through the lipid monolayer, depositing the first lipid layer on the substrate. The transference of the second lipid layer can be completed by dipping the lipid support either horizontally or vertically. This technique can be applied to fabricate SLBs having two different lipid composition.

AFM studies of SLBs formation.

SLBs formation process by fusing lipid vesicles on solid supports can be studied in situ by AFM technique, as illustrated in Figure 6.1.76.1.7. The vesicles spread from the edge towards the center, then stacked on top of each other. The edges of the top and bottom bilayers are joined together to form bigger patches.

Different protocols to prepare multi-component and phase-separated SLBs can affect the asymmetry of the resulting SLBs. In Figure 6.1.86.1.8, the extruded small unilamellar vesicles (SUVs) composed of DLPC/DSPC are heated at 65⁰C, then fused on mica at 20⁰C. The resulting SLB are fully symmetric fluid/gel membranes. On the other hand, using sonicated SUVs heated at 20⁰C prior to fusion results in a completely asymmetric SLBs.

Summary

AFM is a powerful technique for scientists to have an insight in membrane biophysics. Advantages of this method including:

• The ability to image cell surfaces, molecular assemblies in their native aqueous environment at a very high resolution.
• No requirement of a conductive sample.
• Provide 3-D surface profiles.
• The ability to operate in liquid environment and ambient air.

Disadvantages of AFM are limited scanning area and the scanning speed.

Recently there have been some progress in improving AFM scanning speed and resolution, for example high speed AFM (HS-AFM) or high resolution AFM (HR-AFM) [10, 11]. HF-AFM consists of modified components in order to maximize scanning seed, for example soft small cantilevers having high resonance frequencies, high resonance frequency scanners and fast data acquisition devices [10]. AFM is also combined with several techniques such as fluorescence microscopy to acquire more efficient data [9]. The potential improvement of AFM will enhance the possibility to apply this technique in a wider range of biological fields.

References

1. Binnig, G., C. F. Quate, and C. Gerber, Atomic force microscope. Phys. Rev. Lett, 1986(56): p. 930–933.
2. D.J.Muller, Y.F.D., Atomic force microscopy as a multifunctional molecular toolbox in nanobiotechnology. Nat.Nanotechnol, 2008. 3: p. 261-269.
3. Morandat, S., et al., Atomic force microscopy of model lipid membranes. Anal Bioanal Chem, 2013. 405(5): p. 1445-61.
4. Alessandrini, A. and P. Facci, AFM: a versatile tool in biophysics. Measurement Science and Technology, 2005. 16(6): p. R65- R92.
5. Bullen, R.A.W.a.H.A., Lecture notes: Introduction to Scanning Probe Microscopy
6. Frederix, P.L., P.D. Bosshart, and A. Engel, Atomic force microscopy of biological membranes. Biophys J, 2009. 96(2): p. ​329- ​38.
7. S. Morita, R.W., E. Meyer, Noncontact Atomic Force Microscopy. Springer, 2002. 1.
8. Muller, D.J. and A. Engel, Atomic force microscopy and spectroscopy of native membrane proteins. Nat Protoc, 2007. 2(9): p. ​2191-7.
9. Goksu, E.I., et al., AFM for structure and dynamics of biomembranes. Biochim Biophys Acta, 2009. 1788(1): p. 254-66.
10. Ando, T., T. Uchihashi, and N. Kodera, High-speed AFM and applications to biomolecular systems. Annu Rev Biophys, 2013. ​42: p. 393-414.
11. Bippes, C.A. and D.J. Muller, High-resolution atomic force microscopy and spectroscopy of native membrane proteins. Reports on Progress in Physics, 2011. 74(8): p. 086601.

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Vibrating Sample Magnetometry (VSM) is a measurement technique which allows to
determine the magnetic moment of a sample with very high precision. The aim of this
lab course M106 is to enlarge upon the use of this widespread technique introduced in
the lab course B512, where different ferromagnetic samples were characterized
concerning magnetic hysteresis and demagnetization. Here, we will gain a deeper
understanding of the behavior of magnetic materials and its measurement.

In order to
lay the foundations, first the measurement principle and the properties of ferromagnetic
materials will be summarized (magnetic domains, magnetic hysteresis,
demagnetization) and then we will elaborate on the magnetic anisotropy of
ferromagnetic materials.

A vibrating sample magnetometer (VSM) systems are used to measure the magnetic properties of materials. The vibrating component causes a change in the magnetic field of the sample, which generates an electrical field in a coil based on Faraday’s Law of Induction.

If the sample is placed within a uniform magnetic field H, a magnetization M will be induced in the sample. In a VSM, the sample is placed within suitably placed sensing coils, also held at the desired angle.

And the vibrating sample component is made to undergo sinusoidal motion, i.e., mechanically vibrated.

The hysteresis loop shows the “history dependent” nature of magnetization of a ferromagnetic material. Once the material has been driven to saturation, the magnetizing field can then be dropped to zero and the material will retain most of its magnetization (it remembers its history).

Procedure
Before using the VSM, you must carry out a series of configuration steps.
• Insert the Ni standard into the VSM. The standard is ball-shaped, therefore
magnetically isotropic, and has a magnetic moment of 6.92 emu at 5000 Oe.
• Find the exact position of the standard in respect to the center of the pickup coils. The
vibrating rod can be adjusted by three screws on top of the VSM for x, y and z
direction. The pickup coils are connected in a way that, the sample being in the center
of the coils, there will be a signal minimum along x-, a maximum along y- and a
maximum again along z-direction.
• Run Calibrations → Moment gain to calibrate the instrument, i.e. to convert the
measured voltage signal into the correct value of the magnetic moment.
After calibration of the VSM, the following measurements aim to address two topics. The
first part covers basic magnetic characterization and the information that can be
deduced from magnetization curves. The second part cope with demagnetization.

1. Magnetocrystaline anisotropy energy:
   Fix the Fe single crystal to the sample holder. Set H0 to 3500 G and record the
   magnetic moment of the crystal during a 360° rotation of the sample.
   Find the angles corresponding to the different crystallographhic / magnetic axes and
   record the magnetization curves of the easy axis and the hard axis.
2. Stress induced magnetic anisotropy
   Mount a sheet sample clamped in a sample holder provided by the supervisor into the
   VSM. Record the magnetization curves of the sample with and without applied stress
   along and perpendicular to the stress direction.
   Determine the volume of each sample that you have measured