 Thank you very much for nice introduction and thank you Dina for particularly for the invitation and all the work. It is a really great pleasure to present my work in this webinar. So today I like to show the structural complexity and local heterogeneity of nanocrystals observed by Coelantex ray diffraction imaging. I may want to use the laser pointer. Okay. Can you see the laser pointer? Yes, we can. Okay, good. Actually, before I go into the main topics of my talk, I like to take an opportunity to introduce the synchrotrons and on on except very in Korea briefly, since it is not well known to all the Europeans, particularly. So currently, we have a third generation synchrotron PRS to upgraded in 2011 to 3 GB machine and XFL, which is par XFL started the user operation in 2017. In par XFL, two hard X ray beam lines stations, which are X ray scattering and spectroscopy and nano crystallography and imaging and one soft X ray beam line or soft X ray scattering and spectroscopy. The detailed descriptions is shown here and the inside of the hard X ray stations are shown here. The experimental area at XSS station is also shown here for your information. And the third generation synchrotron PRS to has 36 of him lines and one particular beam line, 90 is dedicated to the Coelantex ray scattering. And we will have a new force generation synchrotron, which is located at OChang, which is in the middle of South Korea. And which is actually the plan construction is started officially last year. So now technical design is in progress. And we hope that we can do more work related to the coherence. And among the 10 first beam lines planned, two of them are dedicated to the current applications. So now I will start main subject. And let's do the cage. There are tremendous effort to make nanoparticles for various applications. So by techniques based on electrons, for example, mainly by scanning electron microscopy and transmission electron microscope microscopy is dedicated to characterize the structures. In this case, the shape of nanocrystals and with nano with atomic resolution of the structures were available to determine. However, it is still difficult to get the local heterogeneity in in an entire nanocrystals, which the size with the example 100 nanometers, even by TM. It is still difficult not convenient to measure in situ and or operand conditions. Therefore, in my talk, I like to show a few examples of local heterogeneity of the nano crystals observed by current tax rate deflection imaging technique. So, I guess that there are already introduced and discussed about the current tax rate deflection imaging technique. So I may not need to introduce in detail about the current tax rate deflection imaging technique in this webinar series. But just I like to briefly mentioning about how it works about the current tax rate deflection imaging at break geometry. So when the current tax rate are exposed at a crystal sample, one can observe break peak at the center and fringes along the crystal shape or crystal orientation. But with this pattern, we cannot get the imaging result because we measured the intensity. So which means we lost the phase information. However, starting with this phase retrieval algorithm, which is known well to us. So starting with a random phase and the proper set of iterations in phase retrieval process, we can get the image of the shape and wages, which can be converted to atomic displacement of the entire sample. So three dimensional image can be obtained by from the current tax rate deflection pattern with the rocking cobs can in the next slide. So here it shows which we can see the three dimensional deflection pattern by rotation of the samples and we can get the three dimensional image by reconstruction process. So by having done that, we can really get the shape of the crystals in three dimensional three dimensions. So now, using this break current tax rate deflection imaging is achievable at nano scale with the picometer sensitivity to the crystalline lattice distortions, which is shown here. So, which means actually spatial resolution of this technique is still a few tens of nanometers or best thing is like a 10 or five nanometers, but the sensitivity of the lattice changes can be less than atomic resolution, which means the picometer level distortions can be detected. Also, as you can see, the in situ measurement or measurement, depending on the synthetic conditions are easily available. So the experimental results shown in my talk are carried out at the following beam lines, 30 C, 30 IDC at advanced photo source and P10 at Petros 3 in the G and 9C at PLS 2 in Korea and XCS station in LLS in U.S. So, as an example of a local heterogeneity, I like to show what we found with the GSM-5 geolite microcrystals first. So in GSM-5 microcrystal is nano porous silicate, which synthesized with such organic base with material sources. So by employing REC-CDI technique, it was successfully obtained the shape of the crystal and internal distribution of the displacement and strain shown here. So the surprise comes from the measurement with the temperature dependence shown on the right side. So actually at 200 Celsius, the diffraction pattern shows distorted, which is unexpected because the synth crystal or orientation of the crystal or the shape of the crystal should not change at 200 Celsius. So the reason for this strain structure is mainly due to inner part with very minor organic residue having opposite thermal expansion behavior, which means basically the GSM-5 crystal shows the negative thermal expansion up to 200 Celsius. And above that actually positive thermal expansion behavior, but with the synthetic process inner part has a very minor magnitude of organic residue still there. And this with a small amount of organics, the inside of the crystal shows opposite thermal expansion behavior, which means the core part shows the positive thermal expansion behavior, but the outside shell part shows the negative thermal expansion, which cause really the unexpected distortion in the diffraction pattern as well as the result comes to the imaging result. This small, very minor magnitude of the organic residue was confirmed by confocal fluorescence microscopy, which means this is a heterogeneity of the nano crystal originated from the synthetic process of the zeolite crystals. The next one is another example of heterogeneity of the zeolite crystal, but in this case we measured kappa ion exchanged GSM-5 zeolite crystals during the oxygenation of nitrogen oxide with propene, which is a crucial catalytic process in vehicle exhaust. So in this case, same type of GSM-5, but we actually exchanged kappa ion and actually the actual location of the kappa is near aluminum side. So in this particular experiment, we used in-situ time resolved covalent X-ray diffraction imaging conducted at LCLS, XCS station at LCLS to observe structural response, responses with different reactants. Our study was conducted in two stages, one for propene adsorption here, and the second step was actually NO-XD oxygenation by inserting NO, NO, and oxygen in the presence of the adsorbed propene. So in this case, what we observed was during the propene adsorption are shown on the left and then the second step of the nitrogen oxide DOCG-Nation process are shown on the right hand side. So at a selected time, when distinct changes are observed are shown here. So as you can see, really with the increasing exposure time of the propene, the distorted diffraction pattern observed. And then when NO nitric oxide and oxygen entered, even severely distorted diffraction pattern observed and then end of the reaction process finishes, actually the diffraction pattern becomes to the initial stage almost. So in this case, after the propene adsorption finishes, we removed the leftover propene, which means actually NO and O2 with the adsorbed propene reaction finishes, the crystal becomes the normal. So the next law shows the imaging result. And again, we can observe the distorted or heterogeneity of the crystals observed. And interestingly, the lattice constant, actually in this case, the change of the lattice constant with respect to the lattice, which we defined as strain-rate coefficient changes opposite direction. So when the propene adsorbed, the lattice strain-rate coefficient shows negative direction, but during the nitric oxide DOCG-Nation process, the strain-rate coefficient actually becomes positive. So it is clear the interaction between the kappa ions and introduced gas molecules are reflected in the all-average variations in the lattice spacing. So to find the origin of the unusual strain development during the adsorption and catalytic processes related to the heterogeneity, we take an X-ray fluorescence microscopy at Harder X-ray NanoProbe Station at NSLS-2. So this is the image of the kappa exchanged GSM-5. The result shows actually inhomogeneous distribution of kappa forming ring-like regions. Actually, this inhomogeneous distribution of kappa is related to inhomogeneous aluminum distribution of the crystals. So with this inhomogeneous distribution, we can get the model with this propene adsorption and actually using the finite elemental analysis, we can model them and compare with the experimental result, which means actually our data shows our result shows the adsorption stage of the propene as a model, this model, and finite elemental analysis result and experimental data during the propene adsorption at different times are consistent with our experimental result. And even though the result at 250.5 seconds and 251 seconds, which is just 0.5 seconds difference, but still our experimental result shows consistent, I mean, very well, very good agreement with the simulation result, which means actually using the X-ray fluorescence short pulse, we can really see the changes with the 0.5 second time resolution. So this result mainly is related to the heterogeneity related to the inhomogeneous kappa distribution. To confirm that result, we calculated the origin of the effect of the reactants on the lattice using density functional theory. The most stable positions of the molecules are compared with the ones located at different poles and compared with those molecules located to the closed, close to the active sites in the sample here. So our result shows the actually that we confirmed the heterogeneity by modeling using the finite elemental analysis with stress tensors. So we conclude in that in addition to the inhomogeneous distribution of the kappa ion in GSN5, the coexistence of nitric oxide and oxygen molecules located near the propene and kappa active sites in the sample is critical to the generation of unusual strain distribution in this nitric oxide deoxygenation process. Another case, actually in this case, we investigated the internal deformation of the same kappa exchange geolite crystal during the adoption of four different hydrocarbons. Depending on alkyl chain lengths and existence of the double bond in the molecule or linear structure versus benzene ring structure, etc. with the temperature and duration of time. So here is just a brief summary of with the temperature. And as you can see, propene and propane are compared with the existence of double bond in three carbon molecular structure and N hexane and benzene are either linear or ring structures in the six carbon system. So their chemical properties and relative molecular size to the four channels allow different effects of the other options, the interactions on the kappa ion kappa two plus sites, which results in barrier strength of the internal strain distribution of the geolite crystal. So in this case heterogeneity of the GSN5 due to same inhomogeneous distribution of kappa ion in the geolite is found. Some more details about the result I'm showing here. So in each molecule system, temperature dependent strain field evolution is observed here. Okay. So the current x-ray diffraction patterns and retrieved images consistent with the FEA, I mean finite element analysis simulation result show how the internal structures including lattice deformation of the crystal can be buried with different molecules. So the comparison of the experimental results here and then calculation or simulation by finite element analysis during the propene shown in the left and during the propane other options are shown on the right. So, actually, the each panel includes the experimental data and retrieved geolitex ray diffraction pattern are compared and displacement field from the experiment and displacement from the simulation are compared. Actually, this simulation result is from the model on the right hand side. So, actually, this was a two dimensional result, so which we cannot get all three dimensional images. So we basically summed in depth direction, but interestingly, it is very consistent with our experimental result. The main message here is when kappa GSM-5 crystals were exposed in three carbon systems, even at room temperature, more fringes were observed in the CXD patterns here. And 100 celsius, for example, already the center of peak was changed and dramatic variations in the diffraction pattern were revealed at 150 celsius and higher. The deformation of the displacement obtained from the retrieval process was released of the 100 celsius, showing relatively weak chemical interactions of the GSM of the kappa 2 plus sites. And over 150 celsius, the strong deformation from the top side edges connected to the bottom was observed, meaning that the molecules observed at the kappa ions from the outer shell and to the center part of the crystal with increasing temperature. So this result showed very good agreement with the experimental, I mean, the FEA model. And in comparing two systems, propene showed a relatively more dramatic evolution in the lattice deformations than the propane absorption at lower temperature. So which means actually the heterogeneity comes from the inhomogeneous distribution of kappa, as well as the chain length and the double bond existence affecting to the strain development. Similarly, in the six carbon systems, both benzene and n-hexane, the CXD patterns shows variation of the center peak at 100 celsius here, so actually the center peak shape is actually changed. And the strong strains at the upper sides were evolved at the bottom with the increasing temperatures up to 150 celsius. So the strong deformation suggests that n-hexane and benzene adsorbed at the kappa side, kappa ions at both the outer shell and the center part at the same temperature reflected in the FEA model 2. So more active variation in the internal structure have occurred in the benzene adsorption, as you can see here. So overall, four-card hydrocarbons allowed noticeably different internal deformations in the kappa jsn5 crystal. However, we found that when the diffusion occurred in the center ring here, the shape of the central red peak in the coerontaxate diffraction patterns was changed to triangular, mainly due to the apogee sign of the summer expansion coefficient in the region compared to the pure jsn5 without hydrocarbons or the job, which is a similar result I showed in the first case of the jsn5 without kappa exchange the case. So our work provides internal structural variation of kappa exchange the jsn5 crystal due to inhomogeneous distribution of kappa ion with different size and diffusion rate of the hydrocarbons by the strain evolution during their adsorption processes. Actually, next topic I'd like to show is the active site localization observed during the methane oxidation process, which is important in vehicle catalytic converter. So our platinum nanoparticles were grown by deviating method and activation temperature was about several hundred k. So actually, the coerontaxate diffraction pattern and imaging result in 3D video in the previous slide is this platinum nano crystal actually. So, as you can see, to see the structural changes along the steps of the catalysis, we measured with the controlled gas environment. As you can see, we exposed 1% of hydrogen first to clean the surface of the platinum nanoparticles and then evacuated all the hydrogen gases and inserted 20% of oxygen. And we measured the EXD patterns for oxygen adsorption and then after the diffraction pattern doesn't change up to the diffraction pattern doesn't change. So, we removed all the excessive the excessive oxygens and we entered the 1% of methane in the sample chamber. So, which means we during the methane oxidation, we observed again the coerontaxate diffraction pattern. In order to see whole changes during the catalytic process with different gas environment and exposure time, we applied pure correlation function to the total three dimensional CXD patterns to understand how distortion evolved during the catalytic process. So, the gas environment together with the exposure time I indicated on the X and Y axis. So, experimental conditions are all so indicated in the map with black arrows shown here. So, immediate distortion appeared after the oxygen was introduced, as you can see here, and then the original diffraction was recovered after like 22 minutes of the, 22 minutes of the methane exposure, which means this reversion can be attributed to the available oxygen. This is the reason being consumed by catalytic oxidation. So, I mean during this measurement, same procedure measurement, we actually carried out the gas analysis to check the catalytic reaction and resultant products as well. So, briefly, the coerontaxate diffraction pattern, even clearer pattern are shown here. So, below activation temperature, we didn't see any changes independent of the gas composition. But at 700K, which is above the activation temperature, we observed like 20% of oxygen, really the diffraction pattern changes near the breakthrough, which means it looks like long range order changes appeared. And 1% of methane, even the severe changes of the distortion observed. And as I mentioned, in the end of the methane exposure, which means after finishing the reaction process, the diffraction pattern becomes to the original. So it appeared again, 1% of the hydrogen exposure. So, my coerontaxate diffraction imaging result is consistent with what I mentioned in the diffraction pattern itself. So, in hydrogen and 20% of oxygen, actually it becomes very blue and, sorry, this is 600K, so actually it becomes blue, but not really local changes, but just the entire thing becomes blue. And 1% of methane exposure, not much changed. And 1% of hydrogen, or 600K, changes relatively very small. But 700K, consistent with our observation in the diffraction pattern, with the 20% of oxygen exposure, one side becomes blue and the other side becomes yellow or red. So, as you can see, the displacement in red means with respect to the direction of measurement, actually with respect to this direction, the blue means the opposite direction, just changed the displacement in opposite direction. But in red means the same displacement with the same direction, which means actually blue in this direction, this side, and red in this side means actually overall the nanocrystals actually shrunk. And with 1% of methane, the amount of the displacement becomes larger. And again, after the process finishes, 1% of hydrogen becomes more or less, becomes to the original. So to elucidate the reaction mechanism of methane oxidation on platinum, large, again I like to show, this was really video is not working, so I like to show just as it is. So to elucidate reaction mechanism of methane oxidation of platinum, large scale reactive molecular dynamics simulations were performed. So snapshots of the atomic displacement of platinum nanocrystals in hydrogen and in oxygen gases and in the methane after the oxidation are also shown here. So in hydrogen gas, we observed limited interaction between the platinum and hydrogen consistent with the experimental observations. And in O2 gases, the effect of oxidation of the nanocrystals are shown at the edges and corner sites where platinum atoms are undercoordinated. So molecular oxygen are fizzy of the surface of the nanocrystals, but really the chemically adjoved oxygen atoms at oxygen molecules are appeared in the edge of the crystals or corner sites. So to simulate the methane oxidation in limited adjoved oxygen environment, we removed an unadjoved oxygen molecules while the adjoved molecules, oxygen molecules are bonded and bonded oxygen atoms were retained. And then we introduced the methane molecules and ran additional isothermal isobaric dynamics. So in this figure, we observed the bonding of methane molecules to the dissociated oxygen atom at the edge and corners, corner sites. So the strain evolution of the nanoplatium nanoparticles are summarized during the oxygen adjoption and methane oxidation on the left and the side here. And then experimental results are compared with the dissimulation result of the reactive molecular dynamics informed by the finite element analysis are shown on the right side. So as I mentioned, three dimensional image are colored by local displacement field of the surface at vertical cross sections are shown in the right hand side of each data. So as you can see, with respect to the major direction, actually experimental data shows exactly same as what I described here in the left hand, I mean the blue in this direction and red in other side, which means actually the crystal lattice shrunk in oxygen environment. And in with the methane exposure initially when the catalytic process starts and actually the part showing blue becomes even more blue and red becomes more red. So, and then after the reaction finishes, it becomes the original displacement, which is exactly consistent with our simulation result. And now, actually, we, during the same experimental process, we observed really the heterogeneity of sample related to the defect were observed. As you can see, same process by locking up with the different conditions of the gas exposure, the main peak during the locking curve actually decreases the intensity and another peak appears, as you can see, the cross section of the depraction pattern are shown at A and B correspondingly here. So, which means initially we didn't understand what is going on here. However, later on, this is the result because during the oxygen exposure when two peaks appeared, imaging was not available in the beginning without understanding what is going on. So now, later on, three-dimensional reconstruct image with network, defect networks, actually, we were able to obtain. So during the oxygen process, we observed like a defect near the surface with their volumes in purple. So the dislocations of the defect were identified from their displacement field or this is an indicated by purple arrow here. So the volume of the defect is expanded inside of the nano crystal with oxygen exposure and the size of the instantaneous defect reached the maximum with the methane exposure. So, in this case, is the apparent loss of the density arises from the high number of dislocation cores or stacking faults that interrupt the diffraction conditions in those regions of the crystals. So, in fact, these parts are not disappeared. So, in the imaging result, the missing part was related to the because of the defect. Electron density is not contributed to this black peak, but after the oxidation process finishes, it becomes back. So, which means really that part related to the defect was rotated. So it is not contributed to the black electron density. So, the strains represented in the cross section of the particle in the previous slide, the change of the compressive shown in blue and tensile in red strains are shown on the oxygen and methane flow here. So the initial tensile strain was enlarged with the oxygen gas exposure and considerable propagation with even W shape is shown here. So it is enlarged through the connection of the strongly strained parts. So as the oxygen exposure time increases, the one-on-one black density volume decreases, and the boys were absorbed inside of the crystal, as I mentioned in the previous slide. So the behavior continued when crystal was exposed to methane flow and the recovery of density loss after the reaction finishes, as you can see here. So remarkably, the parts enlarged with the tensile and compressive correspond to the origin of defect networks we observed here. So in addition, in the analysis of strain-filled distribution inside of the crystal, by calculating the normalized strain energy, strain-filled energy and amplitude volume at 700K here shown here. So below activation temperature, which is 600K, the independent of gas actually shows the same, but this normalized strain-filled energy and amplitude volume shows exactly what we expected. And then we compared with the elastic strain energy with dislocation cost, which means the particle having defects and without having defects. So we calculated the strain-filled energy depending on the gas environment and with the exposure time compared with dislocation cost we calculated, which is very consistent with our theoretical calculation and experimental result. So which means in this case the defects in the nanocrystals actually contribute the more strain-filled energy to exceed the dislocation cost. So that's how we can observe such behavior related to heterogeneity. As a last topic, actually I'd like to show very recent results observed in heterogeneity in chiral nanoparticles, which are particularly interested in their catalytic and optical and electronic properties. So in this case, it is important to determine the three-dimensional distribution of exposed surfaces in terms of the eject indexing of the crystallographic planes and determining the corresponding strain distribution. So in this case, our chiral nanoparticles are mainly induced by the ligands. So our nanoparticle was, actually I can show the next page, but here the helical surface of 432 helicoid-3 chiral nanoparticles. So in this case, as I mentioned, structural identification of hidden gaps in chiral nanoparticles are very important to determine and correlating crystallographic and elastic properties are important in understanding the gross mechanisms. So using the Quarantex-ray depraction scattering imaging, we actually can understand the full understanding of chiral optical properties of nanostructures, which means strain-tuned optical chirality, probably we can understand. So since time is close to the end, I like to just finish very briefly. So we measured the CDI pattern at 2-0-0 blackpink from this 432 helicoid-3 chiral nanoparticles, and owing to its very complicated and complex morphology and the direction of the surface of passage, this result shows complex interference fringes in the multiple directions. And these directions were mainly distributed in the high miller index region under stereographic projections and calculated stereographic whole figure projection of the CXD pattern shown here, and this is the immediate result. And by taking absolute value of complex electron density, the three-dimensional morphology of 432 helicoid-3 is shown here, and actually this figure shows the spatial distribution of miller indices, and this is visual being a complex geometry, and we determined all the crystallographic orientation of nanoparticles from the Q vector shown, determined here, and surface normal direction parallel to the lattice vector, which is determined from the fitting based on the Terras step-kink model, which maximized the Terras ratio, the surface. So the kink density also was calculated from the extracted miller index and mapped on the 432 helicoid-3 morphology. So it was confirmed that the chiral kink sites were mainly exposed on the surfaces of concave gaps. So from this analysis, we can obtain important evidence for the understanding of sin-setting mechanism during the growth, and we learned the chiral gap structure comprises symmetric bridge of the high miller index surfaces. And also, we convert the surface normal vectors into the stereographic projections, so the distribution of surface miller indexes are shown on the right, depending on the orientations. So the surface area of each miller index with color scale is shown for overall distribution of miller indices, mapped in two dimensions, and surface miller indices of the four gaps and three gaps, and one gap is observed in 100 and 111, 111, three gaps, and one gap is observed in 110 respectively. And we also analyzed strain field of the 432 helicoid-3 with regard to geometry and surface miller indices. And the strain field was calculated using Q component of the displacement gradient, and both tensile and compressive strain were observed here. And in the surface strain, distributed chiral gap facing one zero, actually this is one bar, perpendicular to Q, the area indicated here in this regime, actually the compressive strain was observed at the concave edge, whereas tensile strain was observed at the side passage. So for more detailed information, Kantor map of the miller index is shown here, and the miller index Kantor map of the gap with this region showed the deepest edge consisting of the 001 bar here. 001 bar and 100 and high miller indices connecting these two directions, whereas side passage consisted of the high miller indexes, or just 111 in this case. So this strain miller index relationship was confirmed by plotting the strain at each miller index on 1001 bar stereographic projections are shown here. And the strain fields of the 100 and 101 actually shown here with depth dependence. So you can really see inside the strain patterns, strains clearly can see and this is like a diagonalized with the tensile and compressive strains are like shown shown in upper side. Also, we measured the strain development during the course. So actually the emergence of the chiral retic and strain development was measured actually also generated by initial selective interaction of the chiral ligand and metal surface. So actually this result contributes the correction of the reflective index related to the optical chirality. So our strain information gives the correction of the reflective index in optical chirality. So basically our result shows the resultant sensitivity of the chiral molecular detection. We can improve the sensitivity of the chiral molecular detection of the nano photonics. So as a conclusion by black Coelantex retifraction imaging technique, I showed a few examples of the measuring local heterogeneity. So the first case, the heterogeneity originated from the organic residue during the synthetic process. And secondly, inhomogeneous distribution of the exchanged kappa ions in geolite during the NOx deoxygenation. And thirdly, same inhomogeneous distribution of exchanged ions in geolite during the hydrocarbon adjuvant process. We also observed active site localization and defect dynamics of platinum nanoparticles during the methane oxidation related to the selective site adjuption and catalytic process and defect related to heterogeneity. And we also obtained a map of internal strain distribution of chiral old nanoparticle, which gives corrections to optical reflective index or chiral molecular detection of the nano photonics. I think all the members in my group and department of the samples of geolite are mainly from the chemistry department of Seogang and all the measurements are actually in collaboration with the advanced photon source in Argonne National Laboratory and Petroslin-Degi and LCLC in US, I mean, FLAC and Brookhaven National Laboratory and PRS2. I also acknowledge the funding agency and all the current group members are shown here. And thank you very much for your attention. Thank you so much for this overview on the research. It's quite impressive number of results you show there. So now the session is open for questions. You can just write them in a chart or you can raise your hand and I will unmute yourself and ask questions immediately. I have I have one about the XPCS that you have shown you've gone quickly through those results. I understand that I mean there is a clear signature of sudden event. And it wasn't clear to me which time resolution you had there. So are you are you saying that during the various chemical processes there is either a full correlation so that the changes on structure are sudden or did I misinterpret or maybe the time. I'm not so sure which one but on the platinum. Okay, okay. One moment. Are you mean this one. Are you stop sharing so I don't know. Yeah. Yes, this one. Okay, this one. Yeah. The sudden changes actually. This is the reading. Here. Because to clarify the process, we actually use the one guess. At the time and with the hydrogen. And then, after a while, we exchange the gas after removing all the gases and then put entered a new one. So, here, for example, for example, here is zero starts. Zero means actually the time entering inserting the oxygen. But it is clear. Starting oxygen shows, I mean, like a certain change of the distortion, but with all the other jobs to the oxygen environment, when we put the machine. The methane molecules go to onto the oxygen. It did not show any. The abrupt to change is it shows more continuous changes, but the severe distortion appeared. Is it clear. Yes, I understand that.