{"id":235,"date":"2018-12-04T10:24:41","date_gmt":"2018-12-04T10:24:41","guid":{"rendered":"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=235"},"modified":"2018-12-04T11:17:29","modified_gmt":"2018-12-04T11:17:29","slug":"elementray-excitations","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/chapter\/elementray-excitations\/","title":{"rendered":"Elementray Excitations"},"content":{"raw":"<div>\r\n<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/7F692YRrhCs\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\nLearning Outcomes\r\n\r\n&nbsp;\r\n\r\n<strong>After studying these modules, you shall be able to<\/strong>\r\n<ul>\r\n \t<li style=\"text-align: justify\">Learn about the combined effect of electrical and magnetic properties of materials and their importance in the technological applications.<\/li>\r\n \t<li style=\"text-align: justify\">Learn about the physics of M\u00d6ssbauer parameter and the basics theory involved<\/li>\r\n \t<li style=\"text-align: justify\">Know the a) types of interactions and b) how they are different from each other<\/li>\r\n \t<li style=\"text-align: justify\">Learn about the journey of resonant florescence from atomic to nuclear level<\/li>\r\n \t<li>Learn about the analogy of recoil free<span style=\"text-align: initial;font-size: 1em\"> event between daily life experience and atomic &amp; nuclear experiment<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n<div>\r\n\r\n<strong>\u00a0 \u00a0 1.Introduction<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">M\u00d6ssbauer Spectroscopy is Spectroscopic technique based upon recoilless resonant emission and absorption of gamma rays in solids. This resonant emission and absorption was first observed by Rudolf M\u00d6ssbauer during his graduate studies in 1957, called the Mossbauer Effect in his honor. Like NMR, M\u00d6ssbauer spectroscopy probes tiny changes in the energy levels of nucleus in response to its environment. Typically three types of nuclear interaction can be observed: an isomer shift; quadrupole splitting; and magnetic or hyperfine splitting also known as Zeeman Effect. Due to high energy and extremely narrow line widths of gammas rays , M\u00d6ssbauer spectroscopy is one of the most sensitive techniques in terms of energy resolution , capable of detecting change in just a few parts per 1011.<\/p>\r\n&nbsp;\r\n\r\n<strong>2.Basic principle<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Just as a gun recoils when a bullet is fired, conservation of momentum requires a free nucleus to recoil during emission or absorption of a gamma ray(photon). If a nucleus at rest emits a gamma ray, the energy of the gamma ray is slightly less than the natural energy of the transition, but in order for a nucleus at rest to absorb a gamma ray, the gamma ray's energy must be slightly greater than the natural energy, because in both cases energy is lost to recoil. This means that nuclear resonance (emission and absorption of the same gamma ray) is unobservable with free nuclei, because the shift in energy is too great and the emission and absorption spectra have no significant overlap<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">Nuclei in a solid crystal, however, are not free to recoil because they are bound in place in the crystal lattice. When a nucleus in a solid emits or absorbs a gamma ray, some energy can still be lost as recoil energy, but in this case it always occurs in discrete packets called phonons (quantized vibrations of the crystal lattice). Any whole number of phonons can be emitted,\u00a0<span style=\"text-align: initial;font-size: 1em\">including zero, which is known as a \"recoil-free\" event. In this case conservation of momentum is satisfied by the momentum of the crystal as a whole, so practically no energy is lost. This was the major breakthrough done by M\u00d6ssbauer so to observe first nuclear <\/span>floresence<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">As an analogy, imagine jumping from a boat to shore, and imagine that the distance from <\/span>boat<span style=\"text-align: initial;font-size: 1em\"> to shore is the longest you can possibly jump (on land). If the boat is floating in water, you will fall short because some of your energy goes into pushing the boat back. If the water is frozen solid, however, you will be able to make it.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">M\u00f6ssbauer found that a significant fraction of emission and absorption events will be recoil free, which is quantified using the <\/span>Lamb\u2013M\u00f6ssbauer factor. <span style=\"text-align: initial;font-size: 1em\">This fact is what makes M\u00f6ssbauer spectroscopy <\/span>possible,<span style=\"text-align: initial;font-size: 1em\"> because it means gamma rays emitted by one nucleus can be resonantly absorbed by a sample containing nuclei of the same isotope, and this absorption can be measured.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">3.Typical method<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In M\u00f6ssbauer absorption spectroscopy, a solid sample( in the form of powder or thin film) is exposed to a suitable beam of <\/span>gamma radiation <span style=\"text-align: initial;font-size: 1em\">(Mossbauer probe), and a detector measures the intensity of the beam transmitted through the sample. The atoms in the source emitting the gamma rays must be of the same isotope as the atoms in the sample absorbing them<\/span>.If<span style=\"text-align: initial;font-size: 1em\"> the emitting and absorbing nuclei are in identical chemical environments, the nuclear transition energies would be exactly equal and resonant absorption would be observed with both materials at rest. The difference in chemical environments, however, causes the nuclear energy levels to shift in a few different ways in terms of electric and magnetic hyperfine interactions. Although these energy shifts are tiny (often less than a micro-<\/span>electronvolt), <span style=\"text-align: initial;font-size: 1em\">the extremely narrow <\/span>spectral linewidths <span style=\"text-align: initial;font-size: 1em\">of gamma rays for some radionuclides make the small\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">energy shifts correspond to large changes in <\/span>absorbance. <span style=\"text-align: initial;font-size: 1em\">To bring the two nuclei back into resonance it is necessary to change the energy of the gamma ray slightly, and in <\/span>practice<span style=\"text-align: initial;font-size: 1em\"> this is always done using the <\/span>Doppler effect.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">During M\u00f6ssbauer absorption spectroscopy, the source is accelerated through a range of velocities using a <\/span>linear motor <span style=\"text-align: initial;font-size: 1em\">to produce a Doppler effect and scan the <\/span>gamma ray<span style=\"text-align: initial;font-size: 1em\"> energy through a given range. A typical range of velocities for <\/span>57Fe, <span style=\"text-align: initial;font-size: 1em\">for example, may be \u00b110.047 mm\/s (1 mm\/s = 48.075 <\/span>neV<span style=\"text-align: initial;font-size: 1em\">). In the resulting spectra, <\/span>gamma ray<span style=\"text-align: initial;font-size: 1em\"> intensity is plotted as a function of the source velocity. At velocities corresponding to the resonant energy levels of the sample, a fraction of the gamma rays <\/span>are<span style=\"text-align: initial;font-size: 1em\"> absorbed, resulting in a drop in the measured intensity and a corresponding dip in the spectrum. The number, positions, and intensities of the dips (also called peaks; dips in transmitted intensity are peaks in absorbance) provide information about the chemical environment of the absorbing nuclei and can be used to characterize the samples.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">4.Selecting a suitable source<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">M\u00f6ssbauer spectroscopy is limited by the availability of a suitable gamma-ray source. Usually, this consists of a radioactive parent that decays to the desired isotope. For example, the source for <\/span>57Fe <span style=\"text-align: initial;font-size: 1em\">consists of <\/span>57Co, <span style=\"text-align: initial;font-size: 1em\">which decays by <\/span>electron capture <span style=\"text-align: initial;font-size: 1em\">to an <\/span>excited state <span style=\"text-align: initial;font-size: 1em\">of 57Fe, then subsequently decays to a <\/span>ground state <span style=\"text-align: initial;font-size: 1em\">emitting the desired gamma-ray of energy 14.4KeV known as M\u00d6ssbauer Probe for all iron contain samples especially magnetic materials. <\/span>Similarly<span style=\"text-align: initial;font-size: 1em\"> for semiconductor type <\/span>samples<span style=\"text-align: initial;font-size: 1em\"> we use Tin as M\u00d6ssbauer probe so as to study semiconductor properties. In <\/span>superconductor<span style=\"text-align: initial;font-size: 1em\"> we use Europium as M\u00d6ssbauer probe. <\/span>Ideally<span style=\"text-align: initial;font-size: 1em\"> the <\/span>parent <span style=\"text-align: initial;font-size: 1em\">isotope will have a sufficiently long half-life to remain useful, but will also have a sufficient decay rate to supply the required intensity of radiation. Also, the gamma-ray\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">energy should be relatively low, otherwise the system will have a low recoil-free fraction resulting in a poor <\/span>signal-to-noise ratio <span style=\"text-align: initial;font-size: 1em\">and requiring long collection times.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">5.Analysis of M\u00f6ssbauer spectra<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">As described above, M\u00f6ssbauer spectroscopy has an extremely fine energy resolution and can detect even subtle changes in the nuclear environment of the relevant atoms. Typically, there are three types of <\/span>nuclear interactions <span style=\"text-align: initial;font-size: 1em\">that are observed, <\/span>isomer shift <span style=\"text-align: initial;font-size: 1em\">(or <\/span>chemical shift),quadrupole splitting <span style=\"text-align: initial;font-size: 1em\">and <\/span>hyperfine splitting <span style=\"text-align: initial;font-size: 1em\">(or <\/span>Zeeman splitting)<span style=\"text-align: initial;font-size: 1em\">. Isomer shift is linked with monopole interaction, quadrupole splitting arise due to change in shape of nuclei which is further linked with Electric Field Gradient (EFG),Hyper fine splitting tells us about strength<\/span><span style=\"text-align: initial;font-size: 1em\">of magnetic field locally so <\/span>as<span style=\"text-align: initial;font-size: 1em\"> understand the magnetic interactions (Ferromagnetic<\/span>,ferrimagnetic,antiferromagnetic<span style=\"text-align: initial;font-size: 1em\"> etc.)<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">6.Applications of M\u00f6ssbauer spectroscopy<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">M\u00f6ssbauer spectroscopy is unique in its sensitivity to subtle changes in the chemical environment of the nucleus including oxidation state changes, the effect of covalency on a particular atom, and the magnetic environment of the sample<\/span>..<span style=\"text-align: initial;font-size: 1em\">It has been especially useful in the field of geology for identifying the composition of iron-containing specimens including meteors and moon rocks. Because of high precision and <\/span>resolution ,<span style=\"text-align: initial;font-size: 1em\"> M\u00d6ssbauer spectroscopy is highly useful in Forensic Science for Finger Printing. <\/span><em style=\"text-align: initial;font-size: 1em\">In situ<\/em><span style=\"text-align: initial;font-size: 1em\"> data collection of M\u00f6ssbauer spectra has also been carried out on <\/span>iron rich<span style=\"text-align: initial;font-size: 1em\"> rocks on Mars.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Another significant application of M\u00f6ssbauer spectroscopy is the study of phase transformations that occur in iron catalysts during <\/span>Fischer\u2013Tropsch synthesis. <span style=\"text-align: initial;font-size: 1em\">While these catalysts initially consist of hematite (Fe2O3), during reaction they are transformed into a mixture of <\/span>magnetite <span style=\"text-align: initial;font-size: 1em\">(Fe3O4) and several <\/span>iron carbides. <span style=\"text-align: initial;font-size: 1em\">The formation of carbides appears to\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">improve catalytic activity, <\/span>however<span style=\"text-align: initial;font-size: 1em\"> it can also lead to the mechanical break-up and attrition of the catalyst particles. This can cause difficulties in the final separation of catalyst from reaction products. M\u00f6ssbauer spectroscopy has also been used to determine the relative concentration change in the oxidation state of antimony <\/span>(Sb) <span style=\"text-align: initial;font-size: 1em\">during the selective oxidation of <\/span>olefins. <span style=\"text-align: initial;font-size: 1em\">During <\/span>calcination <span style=\"text-align: initial;font-size: 1em\">all the Sb ions in an antimony-containing tin dioxide catalyst transform into the +5 oxidation state. Following the catalytic reaction, almost all Sb reverts from +5 to a +3 oxidation state. A significant change in the chemical environment surrounding the antimony nucleus occurs during the oxidation state change which can easily be monitored as an isomer shift in the M\u00f6ssbauer spectrum. In <\/span>synthesis<span style=\"text-align: initial;font-size: 1em\"> of <\/span>Ferritesome times<span style=\"text-align: initial;font-size: 1em\"> Fe3+ converts into Fe2+ during sintering process so as to deteriorate the magnetic character of ferrite<\/span>.Through<span style=\"text-align: initial;font-size: 1em\"> Mossbauer <\/span>analysis<span style=\"text-align: initial;font-size: 1em\"> we can know the ratio of Fe2+ and Fe3+ ions<\/span>.More<span style=\"text-align: initial;font-size: 1em\"> recently, M\u00f6ssbauer spectroscopy has been instrumental in developing an understanding of the structure and function of <\/span>iron containing<span style=\"text-align: initial;font-size: 1em\"> enzymes and the model complexes synthesized to mimic the functions of these enzymes.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">7.M\u00f6ssbauer spectrometer<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">A <\/span><strong style=\"text-align: initial;font-size: 1em\">M\u00f6ssbauer spectrometer<\/strong><span style=\"text-align: initial;font-size: 1em\"> is a device that performs M\u00f6ssbauer spectroscopy, or a device that uses the M\u00f6ssbauer effect to determine the chemical environment of M\u00f6ssbauer nuclei present in the sample. It is formed by three main parts; a source that moves back and forth to generate a <\/span>doppler effect, <span style=\"text-align: initial;font-size: 1em\">a <\/span>collimator <span style=\"text-align: initial;font-size: 1em\">that filters out non-parallel <\/span>gamma rays <span style=\"text-align: initial;font-size: 1em\">and select suitable energy of <\/span>gamma raysay<span style=\"text-align: initial;font-size: 1em\"> 14.4Kev for iron and a detector(Proportional counter)<\/span><span style=\"text-align: initial;font-size: 1em\">. Through Multichannel arrangement data can be collected and displayed on the screen. <\/span>Large<span style=\"text-align: initial;font-size: 1em\"> number of counts (in lakhs) justify the good quality of Spectra. After fitting with minimum <\/span>Chi square<span style=\"text-align: initial;font-size: 1em\"> values we can calculate Isomer Shift, Quadrupole moment<\/span>,magnetic<span style=\"text-align: initial;font-size: 1em\"> dipole moment by using recommended <\/span>soft ware<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/p>\r\n\r\n<\/div>\r\n<img class=\"aligncenter size-full wp-image-247\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-74.png\" alt=\"\" width=\"603\" height=\"416\" \/>\r\n\r\n&nbsp;\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Elementray Excitations<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/7F692YRrhCs\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n<p style=\"text-align: justify\">8 <strong>Summary <\/strong>: The interdisciplinary nature of Mossbauer effect and low cost technique are highly useful in emerging technological areas such as nano magnetic system, metallurgy, biology and forensic science. Information on the type of magnetism, the onset of magnetic ordering ,the magnetic structure and magnetization can be obtained. The Mossbauer spectra of such substances frequently show interesting features in the critical region near magnetic ordering transitions. The nature and properties of superconductor and semiconductor can be better understood by using M\u00d6ssbauer spectroscopy.But fact of the matter is this technique is not so used in India.<\/p>\r\n&nbsp;\r\n<div>\r\n\r\n<strong>\u00a0 \u00a0Value Addition:<\/strong>\r\n\r\n&nbsp;\r\n\r\n<strong>Do You Know?<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong>The Mossbauer effect or recoilless nuclear resonance florescence,is a physical phenomenon discovered by Rudolf Mossbauer in 1958 during his master programme .It involves the resonant and recil-free emission and absorption of gamma radiation by nuclei bound in a solid. Precise resolution is the key factor in this phenonmenon.The discovery was rewarded with the Noble prize in Physics in 1961.This spectroscopy can be use from low temperature to high temperature including room temperature.Mossbauer spectrum is characterized by the number,shape,position and relative intensity of the various absorption lines.These features result from the nature of the various hyperfine interactions and their time dependence,as well as on any motion of the Mossbauer nuclei.The total absorption intensity of the spectrum is a function of the concentration of Mossbauer nuclei in the absorber and the cross-sections of the processes involved.This absorption intensity ,together with the signal to noise ratio of the detection system and the total number of counts ,determine the quality and accuracy of Mossbauer spectrum.<\/strong><\/p>\r\n&nbsp;\r\n\r\n<strong>Suggested Reading<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong>Electronic spin relaxation and superparamagnetic relaxation play the crucial role for which Mossbauer spectroscopy help us to understand these phenomenon in depth. Time dependent effects, relaxation and dynamics need to be understand at advanced level so as to understand cryogenic in field experiments.<\/strong><\/p>\r\n&nbsp;\r\n\r\n<strong>For More Details ( on this topic and other topics discussed in Text Module) See<\/strong>\r\n<ol>\r\n \t<li>Wickman H. H. Mossbauer Effect Methodolgy Vol. 2, New York, Plenum Press 1966<\/li>\r\n \t<li style=\"text-align: justify\">Goldanskii V. I. and Makarov E.F. Chemical Applications of Mossbauer Spectroscopy, New York, Academic Press, 1986<\/li>\r\n<\/ol>\r\n<strong>\u00a0 \u00a0 For General Study on Mossbauer spectroscopy<\/strong>\r\n\r\n&nbsp;\r\n\r\n<strong>Wertheim G.K. : <em>M\u00f6ssbauer Effect<\/em> <em>\u2013<\/em> <em>Principles and Applications.<\/em> Academic Press, New York, 1964.<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong><em>Dominic P.E.Dickson,Frank J.Berry M\u00f6ssbauer Spectroscopy Cambridge University Press London ,New York 1986.<\/em><\/strong><\/p>\r\n&nbsp;\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">Glossary:<\/strong>\r\n\r\n&nbsp;\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">Isomer Shift or Chemical Shift <\/strong>:<span style=\"text-align: initial;font-size: 1em\"> difference of local, chemical environment between source and sample.<\/span>\r\n\r\n&nbsp;\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">Quadrupole splitting<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">If the nucleus is subjected to an electric field gradient, local symmetry of the nucleus changes which is nothing but Quadrupole splitting. If Q.S is zero then <\/span>nucleus<span style=\"text-align: initial;font-size: 1em\"> is spherical, if Q.S is non zero then nucleus is either oblate or prolate.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Magnetic Splitting<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In the presence of <\/span>magnetic<span style=\"text-align: initial;font-size: 1em\"> field the nuclear spin moment experience a dipolar interaction with the magnetic field that is <\/span><strong style=\"text-align: initial;font-size: 1em\">Zeeman<\/strong><span style=\"text-align: initial;font-size: 1em\"> splitting.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Super paramagnetic state<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">With the help of Mossbauer <\/span>analysis<span style=\"text-align: initial;font-size: 1em\"> we can distinguish <\/span>ferro,para and super paramagnetic<span style=\"text-align: initial;font-size: 1em\"> state<\/span>.For example<span style=\"text-align: initial;font-size: 1em\"> if spectra <\/span>consists<span style=\"text-align: initial;font-size: 1em\"> of six lines then it is <\/span>ferro<span style=\"text-align: initial;font-size: 1em\"> or <\/span>ferri<span style=\"text-align: initial;font-size: 1em\">, if it consists of doublet then it is para and if it consists of singlet then it is <\/span>superpara<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/p>\r\n\r\n<\/div>","rendered":"<div>\n<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/7F692YRrhCs\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Learning Outcomes<\/p>\n<p>&nbsp;<\/p>\n<p><strong>After studying these modules, you shall be able to<\/strong><\/p>\n<ul>\n<li style=\"text-align: justify\">Learn about the combined effect of electrical and magnetic properties of materials and their importance in the technological applications.<\/li>\n<li style=\"text-align: justify\">Learn about the physics of M\u00d6ssbauer parameter and the basics theory involved<\/li>\n<li style=\"text-align: justify\">Know the a) types of interactions and b) how they are different from each other<\/li>\n<li style=\"text-align: justify\">Learn about the journey of resonant florescence from atomic to nuclear level<\/li>\n<li>Learn about the analogy of recoil free<span style=\"text-align: initial;font-size: 1em\"> event between daily life experience and atomic &amp; nuclear experiment<\/span><\/li>\n<\/ul>\n<\/div>\n<div>\n<p><strong>\u00a0 \u00a0 1.Introduction<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">M\u00d6ssbauer Spectroscopy is Spectroscopic technique based upon recoilless resonant emission and absorption of gamma rays in solids. This resonant emission and absorption was first observed by Rudolf M\u00d6ssbauer during his graduate studies in 1957, called the Mossbauer Effect in his honor. Like NMR, M\u00d6ssbauer spectroscopy probes tiny changes in the energy levels of nucleus in response to its environment. Typically three types of nuclear interaction can be observed: an isomer shift; quadrupole splitting; and magnetic or hyperfine splitting also known as Zeeman Effect. Due to high energy and extremely narrow line widths of gammas rays , M\u00d6ssbauer spectroscopy is one of the most sensitive techniques in terms of energy resolution , capable of detecting change in just a few parts per 1011.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>2.Basic principle<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Just as a gun recoils when a bullet is fired, conservation of momentum requires a free nucleus to recoil during emission or absorption of a gamma ray(photon). If a nucleus at rest emits a gamma ray, the energy of the gamma ray is slightly less than the natural energy of the transition, but in order for a nucleus at rest to absorb a gamma ray, the gamma ray&#8217;s energy must be slightly greater than the natural energy, because in both cases energy is lost to recoil. This means that nuclear resonance (emission and absorption of the same gamma ray) is unobservable with free nuclei, because the shift in energy is too great and the emission and absorption spectra have no significant overlap<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Nuclei in a solid crystal, however, are not free to recoil because they are bound in place in the crystal lattice. When a nucleus in a solid emits or absorbs a gamma ray, some energy can still be lost as recoil energy, but in this case it always occurs in discrete packets called phonons (quantized vibrations of the crystal lattice). Any whole number of phonons can be emitted,\u00a0<span style=\"text-align: initial;font-size: 1em\">including zero, which is known as a &#8220;recoil-free&#8221; event. In this case conservation of momentum is satisfied by the momentum of the crystal as a whole, so practically no energy is lost. This was the major breakthrough done by M\u00d6ssbauer so to observe first nuclear <\/span>floresence<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">As an analogy, imagine jumping from a boat to shore, and imagine that the distance from <\/span>boat<span style=\"text-align: initial;font-size: 1em\"> to shore is the longest you can possibly jump (on land). If the boat is floating in water, you will fall short because some of your energy goes into pushing the boat back. If the water is frozen solid, however, you will be able to make it.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">M\u00f6ssbauer found that a significant fraction of emission and absorption events will be recoil free, which is quantified using the <\/span>Lamb\u2013M\u00f6ssbauer factor. <span style=\"text-align: initial;font-size: 1em\">This fact is what makes M\u00f6ssbauer spectroscopy <\/span>possible,<span style=\"text-align: initial;font-size: 1em\"> because it means gamma rays emitted by one nucleus can be resonantly absorbed by a sample containing nuclei of the same isotope, and this absorption can be measured.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">3.Typical method<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In M\u00f6ssbauer absorption spectroscopy, a solid sample( in the form of powder or thin film) is exposed to a suitable beam of <\/span>gamma radiation <span style=\"text-align: initial;font-size: 1em\">(Mossbauer probe), and a detector measures the intensity of the beam transmitted through the sample. The atoms in the source emitting the gamma rays must be of the same isotope as the atoms in the sample absorbing them<\/span>.If<span style=\"text-align: initial;font-size: 1em\"> the emitting and absorbing nuclei are in identical chemical environments, the nuclear transition energies would be exactly equal and resonant absorption would be observed with both materials at rest. The difference in chemical environments, however, causes the nuclear energy levels to shift in a few different ways in terms of electric and magnetic hyperfine interactions. Although these energy shifts are tiny (often less than a micro-<\/span>electronvolt), <span style=\"text-align: initial;font-size: 1em\">the extremely narrow <\/span>spectral linewidths <span style=\"text-align: initial;font-size: 1em\">of gamma rays for some radionuclides make the small\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">energy shifts correspond to large changes in <\/span>absorbance. <span style=\"text-align: initial;font-size: 1em\">To bring the two nuclei back into resonance it is necessary to change the energy of the gamma ray slightly, and in <\/span>practice<span style=\"text-align: initial;font-size: 1em\"> this is always done using the <\/span>Doppler effect.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">During M\u00f6ssbauer absorption spectroscopy, the source is accelerated through a range of velocities using a <\/span>linear motor <span style=\"text-align: initial;font-size: 1em\">to produce a Doppler effect and scan the <\/span>gamma ray<span style=\"text-align: initial;font-size: 1em\"> energy through a given range. A typical range of velocities for <\/span>57Fe, <span style=\"text-align: initial;font-size: 1em\">for example, may be \u00b110.047 mm\/s (1 mm\/s = 48.075 <\/span>neV<span style=\"text-align: initial;font-size: 1em\">). In the resulting spectra, <\/span>gamma ray<span style=\"text-align: initial;font-size: 1em\"> intensity is plotted as a function of the source velocity. At velocities corresponding to the resonant energy levels of the sample, a fraction of the gamma rays <\/span>are<span style=\"text-align: initial;font-size: 1em\"> absorbed, resulting in a drop in the measured intensity and a corresponding dip in the spectrum. The number, positions, and intensities of the dips (also called peaks; dips in transmitted intensity are peaks in absorbance) provide information about the chemical environment of the absorbing nuclei and can be used to characterize the samples.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">4.Selecting a suitable source<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">M\u00f6ssbauer spectroscopy is limited by the availability of a suitable gamma-ray source. Usually, this consists of a radioactive parent that decays to the desired isotope. For example, the source for <\/span>57Fe <span style=\"text-align: initial;font-size: 1em\">consists of <\/span>57Co, <span style=\"text-align: initial;font-size: 1em\">which decays by <\/span>electron capture <span style=\"text-align: initial;font-size: 1em\">to an <\/span>excited state <span style=\"text-align: initial;font-size: 1em\">of 57Fe, then subsequently decays to a <\/span>ground state <span style=\"text-align: initial;font-size: 1em\">emitting the desired gamma-ray of energy 14.4KeV known as M\u00d6ssbauer Probe for all iron contain samples especially magnetic materials. <\/span>Similarly<span style=\"text-align: initial;font-size: 1em\"> for semiconductor type <\/span>samples<span style=\"text-align: initial;font-size: 1em\"> we use Tin as M\u00d6ssbauer probe so as to study semiconductor properties. In <\/span>superconductor<span style=\"text-align: initial;font-size: 1em\"> we use Europium as M\u00d6ssbauer probe. <\/span>Ideally<span style=\"text-align: initial;font-size: 1em\"> the <\/span>parent <span style=\"text-align: initial;font-size: 1em\">isotope will have a sufficiently long half-life to remain useful, but will also have a sufficient decay rate to supply the required intensity of radiation. Also, the gamma-ray\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">energy should be relatively low, otherwise the system will have a low recoil-free fraction resulting in a poor <\/span>signal-to-noise ratio <span style=\"text-align: initial;font-size: 1em\">and requiring long collection times.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">5.Analysis of M\u00f6ssbauer spectra<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">As described above, M\u00f6ssbauer spectroscopy has an extremely fine energy resolution and can detect even subtle changes in the nuclear environment of the relevant atoms. Typically, there are three types of <\/span>nuclear interactions <span style=\"text-align: initial;font-size: 1em\">that are observed, <\/span>isomer shift <span style=\"text-align: initial;font-size: 1em\">(or <\/span>chemical shift),quadrupole splitting <span style=\"text-align: initial;font-size: 1em\">and <\/span>hyperfine splitting <span style=\"text-align: initial;font-size: 1em\">(or <\/span>Zeeman splitting)<span style=\"text-align: initial;font-size: 1em\">. Isomer shift is linked with monopole interaction, quadrupole splitting arise due to change in shape of nuclei which is further linked with Electric Field Gradient (EFG),Hyper fine splitting tells us about strength<\/span><span style=\"text-align: initial;font-size: 1em\">of magnetic field locally so <\/span>as<span style=\"text-align: initial;font-size: 1em\"> understand the magnetic interactions (Ferromagnetic<\/span>,ferrimagnetic,antiferromagnetic<span style=\"text-align: initial;font-size: 1em\"> etc.)<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">6.Applications of M\u00f6ssbauer spectroscopy<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">M\u00f6ssbauer spectroscopy is unique in its sensitivity to subtle changes in the chemical environment of the nucleus including oxidation state changes, the effect of covalency on a particular atom, and the magnetic environment of the sample<\/span>..<span style=\"text-align: initial;font-size: 1em\">It has been especially useful in the field of geology for identifying the composition of iron-containing specimens including meteors and moon rocks. Because of high precision and <\/span>resolution ,<span style=\"text-align: initial;font-size: 1em\"> M\u00d6ssbauer spectroscopy is highly useful in Forensic Science for Finger Printing. <\/span><em style=\"text-align: initial;font-size: 1em\">In situ<\/em><span style=\"text-align: initial;font-size: 1em\"> data collection of M\u00f6ssbauer spectra has also been carried out on <\/span>iron rich<span style=\"text-align: initial;font-size: 1em\"> rocks on Mars.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Another significant application of M\u00f6ssbauer spectroscopy is the study of phase transformations that occur in iron catalysts during <\/span>Fischer\u2013Tropsch synthesis. <span style=\"text-align: initial;font-size: 1em\">While these catalysts initially consist of hematite (Fe2O3), during reaction they are transformed into a mixture of <\/span>magnetite <span style=\"text-align: initial;font-size: 1em\">(Fe3O4) and several <\/span>iron carbides. <span style=\"text-align: initial;font-size: 1em\">The formation of carbides appears to\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">improve catalytic activity, <\/span>however<span style=\"text-align: initial;font-size: 1em\"> it can also lead to the mechanical break-up and attrition of the catalyst particles. This can cause difficulties in the final separation of catalyst from reaction products. M\u00f6ssbauer spectroscopy has also been used to determine the relative concentration change in the oxidation state of antimony <\/span>(Sb) <span style=\"text-align: initial;font-size: 1em\">during the selective oxidation of <\/span>olefins. <span style=\"text-align: initial;font-size: 1em\">During <\/span>calcination <span style=\"text-align: initial;font-size: 1em\">all the Sb ions in an antimony-containing tin dioxide catalyst transform into the +5 oxidation state. Following the catalytic reaction, almost all Sb reverts from +5 to a +3 oxidation state. A significant change in the chemical environment surrounding the antimony nucleus occurs during the oxidation state change which can easily be monitored as an isomer shift in the M\u00f6ssbauer spectrum. In <\/span>synthesis<span style=\"text-align: initial;font-size: 1em\"> of <\/span>Ferritesome times<span style=\"text-align: initial;font-size: 1em\"> Fe3+ converts into Fe2+ during sintering process so as to deteriorate the magnetic character of ferrite<\/span>.Through<span style=\"text-align: initial;font-size: 1em\"> Mossbauer <\/span>analysis<span style=\"text-align: initial;font-size: 1em\"> we can know the ratio of Fe2+ and Fe3+ ions<\/span>.More<span style=\"text-align: initial;font-size: 1em\"> recently, M\u00f6ssbauer spectroscopy has been instrumental in developing an understanding of the structure and function of <\/span>iron containing<span style=\"text-align: initial;font-size: 1em\"> enzymes and the model complexes synthesized to mimic the functions of these enzymes.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">7.M\u00f6ssbauer spectrometer<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">A <\/span><strong style=\"text-align: initial;font-size: 1em\">M\u00f6ssbauer spectrometer<\/strong><span style=\"text-align: initial;font-size: 1em\"> is a device that performs M\u00f6ssbauer spectroscopy, or a device that uses the M\u00f6ssbauer effect to determine the chemical environment of M\u00f6ssbauer nuclei present in the sample. It is formed by three main parts; a source that moves back and forth to generate a <\/span>doppler effect, <span style=\"text-align: initial;font-size: 1em\">a <\/span>collimator <span style=\"text-align: initial;font-size: 1em\">that filters out non-parallel <\/span>gamma rays <span style=\"text-align: initial;font-size: 1em\">and select suitable energy of <\/span>gamma raysay<span style=\"text-align: initial;font-size: 1em\"> 14.4Kev for iron and a detector(Proportional counter)<\/span><span style=\"text-align: initial;font-size: 1em\">. Through Multichannel arrangement data can be collected and displayed on the screen. <\/span>Large<span style=\"text-align: initial;font-size: 1em\"> number of counts (in lakhs) justify the good quality of Spectra. After fitting with minimum <\/span>Chi square<span style=\"text-align: initial;font-size: 1em\"> values we can calculate Isomer Shift, Quadrupole moment<\/span>,magnetic<span style=\"text-align: initial;font-size: 1em\"> dipole moment by using recommended <\/span>soft ware<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-247\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-74.png\" alt=\"\" width=\"603\" height=\"416\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-74.png 603w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-74-300x207.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-74-65x45.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-74-225x155.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-74-350x241.png 350w\" sizes=\"auto, (max-width: 603px) 100vw, 603px\" \/><\/p>\n<p>&nbsp;<\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Elementray Excitations<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/7F692YRrhCs\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">8 <strong>Summary <\/strong>: The interdisciplinary nature of Mossbauer effect and low cost technique are highly useful in emerging technological areas such as nano magnetic system, metallurgy, biology and forensic science. Information on the type of magnetism, the onset of magnetic ordering ,the magnetic structure and magnetization can be obtained. The Mossbauer spectra of such substances frequently show interesting features in the critical region near magnetic ordering transitions. The nature and properties of superconductor and semiconductor can be better understood by using M\u00d6ssbauer spectroscopy.But fact of the matter is this technique is not so used in India.<\/p>\n<p>&nbsp;<\/p>\n<div>\n<p><strong>\u00a0 \u00a0Value Addition:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Do You Know?<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong>The Mossbauer effect or recoilless nuclear resonance florescence,is a physical phenomenon discovered by Rudolf Mossbauer in 1958 during his master programme .It involves the resonant and recil-free emission and absorption of gamma radiation by nuclei bound in a solid. Precise resolution is the key factor in this phenonmenon.The discovery was rewarded with the Noble prize in Physics in 1961.This spectroscopy can be use from low temperature to high temperature including room temperature.Mossbauer spectrum is characterized by the number,shape,position and relative intensity of the various absorption lines.These features result from the nature of the various hyperfine interactions and their time dependence,as well as on any motion of the Mossbauer nuclei.The total absorption intensity of the spectrum is a function of the concentration of Mossbauer nuclei in the absorber and the cross-sections of the processes involved.This absorption intensity ,together with the signal to noise ratio of the detection system and the total number of counts ,determine the quality and accuracy of Mossbauer spectrum.<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Suggested Reading<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong>Electronic spin relaxation and superparamagnetic relaxation play the crucial role for which Mossbauer spectroscopy help us to understand these phenomenon in depth. Time dependent effects, relaxation and dynamics need to be understand at advanced level so as to understand cryogenic in field experiments.<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>For More Details ( on this topic and other topics discussed in Text Module) See<\/strong><\/p>\n<ol>\n<li>Wickman H. H. Mossbauer Effect Methodolgy Vol. 2, New York, Plenum Press 1966<\/li>\n<li style=\"text-align: justify\">Goldanskii V. I. and Makarov E.F. Chemical Applications of Mossbauer Spectroscopy, New York, Academic Press, 1986<\/li>\n<\/ol>\n<p><strong>\u00a0 \u00a0 For General Study on Mossbauer spectroscopy<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Wertheim G.K. : <em>M\u00f6ssbauer Effect<\/em> <em>\u2013<\/em> <em>Principles and Applications.<\/em> Academic Press, New York, 1964.<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong><em>Dominic P.E.Dickson,Frank J.Berry M\u00f6ssbauer Spectroscopy Cambridge University Press London ,New York 1986.<\/em><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">Glossary:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">Isomer Shift or Chemical Shift <\/strong>:<span style=\"text-align: initial;font-size: 1em\"> difference of local, chemical environment between source and sample.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">Quadrupole splitting<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">If the nucleus is subjected to an electric field gradient, local symmetry of the nucleus changes which is nothing but Quadrupole splitting. If Q.S is zero then <\/span>nucleus<span style=\"text-align: initial;font-size: 1em\"> is spherical, if Q.S is non zero then nucleus is either oblate or prolate.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Magnetic Splitting<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In the presence of <\/span>magnetic<span style=\"text-align: initial;font-size: 1em\"> field the nuclear spin moment experience a dipolar interaction with the magnetic field that is <\/span><strong style=\"text-align: initial;font-size: 1em\">Zeeman<\/strong><span style=\"text-align: initial;font-size: 1em\"> splitting.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Super paramagnetic state<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">With the help of Mossbauer <\/span>analysis<span style=\"text-align: initial;font-size: 1em\"> we can distinguish <\/span>ferro,para and super paramagnetic<span style=\"text-align: initial;font-size: 1em\"> state<\/span>.For example<span style=\"text-align: initial;font-size: 1em\"> if spectra <\/span>consists<span style=\"text-align: initial;font-size: 1em\"> of six lines then it is <\/span>ferro<span style=\"text-align: initial;font-size: 1em\"> or <\/span>ferri<span style=\"text-align: initial;font-size: 1em\">, if it consists of doublet then it is para and if it consists of singlet then it is <\/span>superpara<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/p>\n<\/div>\n","protected":false},"author":3,"menu_order":15,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["prof-mahavir-singh"],"pb_section_license":""},"chapter-type":[],"contributor":[59],"license":[],"class_list":["post-235","chapter","type-chapter","status-publish","hentry","contributor-prof-mahavir-singh"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters\/235","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":6,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters\/235\/revisions"}],"predecessor-version":[{"id":248,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters\/235\/revisions\/248"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters\/235\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/media?parent=235"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapter-type?post=235"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/contributor?post=235"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/license?post=235"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}