Colossal Magneto Resistance (CMR) manganites are capable of exhibiting the coexistence of metallic conductivity along with ferromagnetic behavior at low temperatures (below Tc) and insulating behavior along with paramagnetic behavior at high temperatures (above Tc). The double exchange mechanism was used by Zener  to explain correlation between metallic conductivity and ferromagnetism in these materials. Further Millis et al. , suggested that the double exchange mechanism alone cannot account for the magnitude of the resistivity drop below Tc and the electron-phonon coupling, originally due to Jahn Teller distortion, might also play an important role among CMR materials. Thus, this most interesting motivating and effective behavior exhibited by CMR materials fascinated research community in studying structural, magnetic and electrical transport properties and their potential applications in memory devices   . Among these CMR materials, the charge-ordered phase in half-doped manganites, with compositions, R0.5A0.5MnO3 (R = La, Pr, Sm, and Nd; A = Sr and Ca) exhibit interesting phenomena such as charge, orbital, and spin ordering, along with magnetic and electric field driven transitions  . Moreover, it was reported that doping with Cr in the place of Mn site is an effective way to modify the charge ordered (CO)/orbital ordered (OO) and anti-ferromagnetic insulating (AFMI) phases. As the Cr3+ ion is iso-electronic with Mn4+ ion, Mn site substitutions with Cr in manganites have attracted great interest. Magnetic impurities such as Cr and Ru at the Mn site can effectively induce both metallicity and ferromagnetism in the insulating antiferromagnetic R0.5A0.5MnO3 (A = Ca, Sr)  . It was reported that among the dopants, chromium is the most efficient one to induce a metal insulator transition in charge ordered undoped insulators, and lead to a much higher CMR effect   .
Finally, in the theory of solids, study of the elastic behavior has particular significance in understanding the nature of inter atomic and inter ionic forces in them . Further, the general idea of elastic moduli values that characterize mechanical strength, fracture toughness and thermal shock resistance will be useful in study the high strains that might develop when ceramic perovskites are subjected to a high magnetic field . Moreover, the ultrasonic velocity measuring technique is a non-destructive one and is a very sensitive tool not only for studying the defects of microscopic process in solids but also most conventional technique for determination of elastic constants . In view of this, the influence of Cr ion doping on structural and elastic behavior of Pr0.5Sr0.5Mn1−xCrxO3 (x = 0, 0.1, 0.2, 0.3 & 0.4) system is presented in this article.
2. Experimental Details
Polycrystalline Pr0.5Sr0.5Mn1−xCrxO3 (x = 0, 0.1, 0.2, 0.3 & 0.4) samples were synthesized by the sol-gel method  using pure metal nitrates as the initial materials (99.9% pure). The compositions of the samples are henceforth designated as PSMCO-0, PSMCO-1, PSMCO-2, PSMCO-3 and PSMCO-4 respectively. These powders were calcinated at 1100˚C for 8 h followed by sintering at 1300˚C for 4 h in air. The structural characterization was carried out by powder X-ray diffraction (XRD) using Phillips expert diffractometer at room temperature in the 2θ range of 20˚ - 80˚. The bulk densities of all the samples were calculated by means of immersion method. With the help of these bulk densities and X-ray densities, the porosity values were measured. Micro structural studies of the samples were carried out using a Scanning Electron Microscope. Fourier transform infrared spectroscopy (FTIR) was recorded on a Jasco FTIR spectrometer (Model: FT/IR-4200typeA) within a range of 400 - 4000 cm−1.
The longitudinal and shear wave velocity values were calculated by ultrasonic pulse transmission technique using a pulse generator RPR-4000 (RITEC INC., USA). The pulse oscillator generates RF pulses and a transmitting transducer converts them into acoustic pulses. The acoustic pulses propagating through the disc shaped testing sample of thickness ~2.5 mm and diameter ~10 mm, these pulses will convert into electrical signals at the receiving transducer. The amplified output signals are displayed on a storage oscilloscope. Quartz transducers with ability to generate ultrasonic signals of 1 MHz were used for the both the operations like generating and detecting signal. The longitudinal and shear wave signals can be generated by using X and Y-cut transducers respectively. The transmission time of the ultra sound was measured up to an accuracy of 1 μs using a 100 MHz digital storage oscilloscope (Tektronix model: TDS2012C). The overall correctness of these measurements in velocity is about 0.25% and elastic moduli are about 0.5%. The block diagram of ultrasonic pulse transmission technique is shown in Figure 1.
3. Results and Discussions
3.1. Structural Characterization
3.1.1. X-Ray Diffraction
X ray diffraction patterns of all the samples are shown in Figure 2(a). A systematic investigation of the XRD data clearly reveals that all the samples are having single phase without any noticeable impurity. Rietveld refinement technique  was used to analyze the XRD data by assuming orthorhombic structure (Pnma space group). The Rietveld refinement is fitted for the graph of PSMCO-0 sample and is shown in Figure 2(b). The tailored parameters of all the samples are given in Table 1. As per the earlier reports , in the case of lattice parameters, a systematic variation with Cr doping is not noticed and the same behavior is observed in the present study also. This may be attributed to the fact that there is a minor difference between the ionic radii of Cr3+ and Mn3+ .
Figure 1. Block diagram of pulse transmission technique.
Figure 2. (a) XRD patters of Cr doped Pr0.5Sr0.5 MnO3 system; (b) Reitveld reﬁned XRD pattern of PSMCO-0 sample. Circles indicate; (c) Experimental points while Red line indicates reﬁned data and the green line indicates difference between experimental and refined data.
Table 1. Crystallographic data of Cr doped Pr0.5Sr0.5MnO3 system.
3.1.2. Scanning Electron Microscopy
The micro structural investigation of all the samples was carried out using a Scanning Electron Microscope and the micrographs of the samples are shown in Figure 3. It is interesting to note that the grain sizes of parent compound PSMCO-0 are small and are in the range of 50 - 80 nm. It can also be seen from the micrographs that the shape of the grains of all the samples are not having any particular pattern. It is interesting to note that with increasing Chromium content, the grain size is also increased.
(a) (b) (c) (d) (e)
Figure 3. SEM images of Cr doped Pr0.5Sr0.5MnO3 system. (a) PSMCO-0; (b) PSMCO-1; (c) PSMCO-2; (d) PSMCO-3 and (e) PSMCO-4.
3.1.3. FTIR Spectra
The FTIR transmission spectra of Cr doped PSMO samples are presented in Figure 4, which represents the chemistry for the formation perovskite materials. The absorption peak at 600 cm–1 corresponds to stretching of the metal-oxygen bond in the perovskite, which involves the internal motion of a change in Mn-O-Mn bond length in MnO6 octahedral. Interestingly the position of this absorption band is shifted towards higher frequency side up to PSMCO-3 then decreased. The broad absorption peak at 3350 cm−1 is the characteristic of absorbed water or hydroxyl group in the alcohol. A band at 1100 cm−1 reveals the formation of CH3-CH3-, CH3-NH2-, CH3O-bands when the polymerization takes place with metal nitrate, citric acid, and ethylene glycol. The peak at 1115.39 cm−1 is attributed to the C-C-O structure from ethylene glycol in the polymerization process.
3.2. Ultrasonic Velocity Studies
The longitudinal and shear wave velocities (Vl & Vs) values of all the samples are presented in Table 2, and are found to increase continuously with doping concentration of Cr and the behavior is in consistence with earlier reports of some other CMR materials  and manganites . With the support of velocity values, Poisson’s ratios (σ) of all the samples were calculated by the well-known relation , and the calculated values are given in Table 2.
Further the Poisson’s ratio values are found to be in the range, 0.24 - 0.28 for different compositions. The elastic moduli values were also measured using the well-known methods  and the values are given in Table 3. The Young’s modulus and rigid moduli values of all the samples are found to increase with the increasing doping concentration of dopant ion and the same behavior was detected earlier in some other CMR materials  .
Figure 4. FTIR vibration spectrum of Cr doped Pr0.5Sr0.5 MnO3 system.
Table 2. Porosity percentage and ultrasonic velocities of Cr doped Pr0.5Sr0.5 MnO3 system.
Table 3. Elastic constants of Cr doped Pr0.5Sr0.5 MnO3 system before and after porosity corrections.
3.3. Porosity Correction
The elastic properties of any material depend on the density and the porosity percentage of the testing samples . As the samples of the present investigation are prepared by the well-known sol-gel method, they exhibit ceramic nature with porosity. It is important to measure the percentage of porosity in these materials. The porosity values were calculated from bulk density and XRD densities of the samples and the measured porosity values are presented in Table 2. The porosity percentage of all the samples is found to have in the range of 12% - 30%. As all the samples under the study are found to be porous, the measured elastic moduli will be less than those of non-porous ones and as such of these values do not have any significance unless they are corrected to zero porosity  . For this to resolve, Hasselman and Fulrath model has been used . This model proposed on the assumption that the samples prepared by solid state reaction method can mainly posses spherical type of pores. According to this model , Young's and shear wave moduli can be specified by,
where E0 and G0 are the Young’s and Rigidity moduli of non-porous matrix respectively, whereas E and G are the experimental measured values of Young’s and rigidity moduli respectively, and P is porosity of the material. By means of Equations (2) and (3), porosity corrections have been completed for the experimental elastic moduli and are the zero porous values are presented in Table 3. From Table 3, one may see that the values of Young’s modulus values are found to increase continuously with doping concentration which conforms with the similar behavior reported earlier in the case of some manganite based materials  .
3.4. Acoustic Debye Temperature (θD) Values
Acoustic Debye temperature (θD) which can be calculated from mean sound velocities affords useful information about the physical properties of solids. The Debye temperatures of all the samples of the current investigation have been measured using Anderson’s relation 
where, h and k are Planck’s and Boltzmann’s constants respectively, NA is the Avogadro’s number, VA is the mean atomic volume given by (M/ρ)/q and M is the molecular weight, q is the number of atoms in the formula unit and Vm is the average sound velocity calculated using the formula 
Mean sound velocity:
The calculated values of Acoustic Debye temperature (θD) are given in Table 3 and are found to increase with increasing doping concentration.
3.5. Elastic Behavior in Terms of Strength
Usually, the elastic behavior of any oxide materials can be explained in terms of binding forces between various ions . Depending upon the effect of dopant ion on the binding forces, the elastic moduli of a material system can increase or decrease continuously with increasing dopant concentration . As the elastic moduli along with Debye temperatures of all the samples are found to increase continuously with increasing Cr concentration, the binding forces between various ions of these materials might be increasing continuously.
1) CMR materials with compositional formula Pr0.5Sr0.5Mn1−xCrxO3 (x = 0, 0.1, 0.2, 0.3 & 0.4) were synthesized without any detectable impurity and there is no systematic variation in the lattice parameters with the Cr doping is observed.
2) The grain size of parent compound is found to vary between 50 - 80 nm and for the remaining samples; the grain size is increased with doping concentration up to doping percentage of 30%.
3) Ultrasonic longitudinal and shear velocities were found to increase with increasing Cr concentration.
4) The zero porous elastic moduli were found to increase continuously with increasing Cr concentration.
5) It is clearly observed that the mechanical strength of the samples was found to be increased with the Cr concentration.
The authors thank the Registrar, JNTU Hyderabad for financial support to carry out this work under the project JNTUH/TEQIP-III/CRS/2019/MECH/02. The authors also thank, Dr. P. Venugopal Reddy, Vidya Jyothi Institute of Technology, Hyderabad, for providing facilities to carry out experimental work.
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