 Good afternoon everyone welcome So this is our 10th lecture for the provost lecture series. So so it marks a great milestone and so I will let Evan to introduce the professor yabinchi, but before we do that. I just want to quickly Remind everyone so during the Q&A so we we placed a couple Speaker Speakerphones at the at the front of the row. So if you have any questions, please come forward and so since we we do not have enough and So let me just Quickly showcase the provost lecture series. What's the purpose? We started in November 2022 so about a year ago and So the lecture provides a great opportunity only for always faculty members to celebrate their milestones such as being promoted to associate or full professors with tenure and and also to celebrate those who receive awards and so you can see kind of a wide range of posters here and showing our faculty members and with very different disciplines and So today so so I'm very happy that so professor yabinchi will present his work to celebrate several Significant awards he received in the past couple years Also, I would like to thank All of you and many of you who are not here for the support including people from the office of the provost and also people from CPR and Also people from the core facilities, especially from the engineering section Patrick Kennedy and also we have a new recruit chat Chat sort from a core facility. So we just recently recruited him in the machine shop so Also for the next few months. We have secured three speakers professor Takahashi It's going to retire by the end of the fiscal year. So we will Celebrate his retirement on February 1st and also Professor Satoshi Mitara. I was promoted to full professor recently and his lecture is already decided on March 21st and Also probably professor cash of Danny at the end of March and we have several more professors who have been promoted So they will be kind of lined up starting the fiscal year 2020 for so that's all from me Thank you, Amy, so it's my my great honor to introduce professor yabinchi and his For his provost lecture so Yabin I think you all know pretty well that the unit is one of the real powerhouses here at OIST and has been one of the most You know successful units in the past decade here in terms of doing a lot of science and very high-impact science and making an impact it's also of course their their research is very important for the sustainability of Our planet and the materials that can help us achieve our sustainability goals. So from that perspective Yabin is going to be even more important to the future of OIST and and making sure that OIST is contributing on a global stage to solving humanity's great problem, so So just to introduce yabin a bit. He got his bachelor's from Nenjing University in 2000 Went on to get a master's at Hong Kong University After that and did a PhD at Berkeley where he graduated in 2008 He did a few years as a postdoc at Princeton before coming to OIST in 2011 and setting up the energy materials and surface science unit and Sen Sen has has done lots of different Projects and research which I'm sure we'll we'll hear about including one project on ants just letting you know that We actually did a small collaboration, but I'm recently he says as Amy says has has been raking in many honors including the fellow of the Royal Society of Chemistry in 2019 for the last several years has been Recognized as a highly cited researcher. So one of the top very top 1% of Sighted researchers in the world He won a award from the cow foundation in 2022 and then this past year in 2023 became a fellow of the materials research Society a very prestigious honor and also a fellow of the science and technology of materials interfaces and processing society also called AVS so AVS Fellowship And and many others as well. So his work has been Sighted over 20,000 times and is being cited You know on the scale of 4,000 times a year. So very impressive impact that the research that is going on here at OIST. So We're very proud to have him here on our faculty and looking forward to hearing today about his research So yeah, that's welcome. Yeah, Bing So Yeah, first of all, I want to thank Amy for giving me this opportunity to give this talk here. It's wonderful Thanks a very good number. Okay, and also would like to thank Evan for the nice introduction. Yeah, just a small correction. I got my master's degree from Hong Kong University of Science and Technology Yeah, it's a different University. Yeah, I just want to clarify and Yeah, today, I'm going to share with you our research findings About surface sciences and provost gas solar cells Which have been our main research focus of our unit Before I start my talk, I would like to give a few acknowledgments and First of all, I'd like to really give all the thanks to The members in my unit as well as our collaborators today. I see many of the unit members are actually sitting in the audience Thank you for your long time support. Okay, and Also, I'd like to thank the strong support from OISD in the past more than 10 years Including many I will say innovative funding program such as IND cluster research program as well as provokoncept program also last but not least I would like to thank some public funding from the Takenki and also JST a step research grounds Today my talk will consist of three parts First I will introduce the background and the purpose for this research Then I will provide several examples of our surface science studies on metal highlight provost guides Which have been a class of new materials with a strong potential for solar cell applications Towards the end, I would like to briefly discuss a few examples to illustrate how we can Utilize our surface science fundamental research findings into the solar cell applications Now let's start with the first part So a global warming as everyone know has become a grand challenge facing the human society It has led to many changes and consequences And some of which are just happening in our neighborhood To illustrate how global warming is impacting our local environment in Okinawa I would like to Mention the specific example of coral breaching so here is a Photo of our beautiful campus on top of the photo here We can see the ocean ocean or Okinawa is quite unique in a sense It is also the habitat for the largest coral reef community in this region When you go to the seaside, you will see these coral reefs Which consist of a variety of different corals with Very beautiful colors and very very interesting shapes And sponges and algae and many types of fish Which representing an incredible diversity of marine ecosystem in Okinawa But this has been drastically changing as a result of the global warming Global warming can lead to the rise of ocean water temperature When the water temperature rises above a certain level it causes these corals to turn completely white This phenomenon is called coral bleaching According to a survey conducted in 2017 more than half of coral reefs close to Okinawa Had died as a result of coral bleaching Which as you can imagine has a tremendous negative impact on the marine ecosystem around Okinawa So the essential question for everyone to answer is how can we Achieve sustainable development and environmental conservation at the same time and this is also the purpose of our research To mitigate the negative impact of the global warming while still keep the sustainable economic growth It is essential to develop the clean sustainable energy and to reduce the carbon footprint So the goal of our research is to develop so-called zero net energy building That is 100% self sustainability zero CO2 emission To achieve this goal we plan to develop novel low cost high efficiency solar cells batteries and lighting devices So the goal here is to develop novel low cost energy related devices Such energy device Application research is carried out in our energy device lab Which is equipped with a four line of the fabrication tools and characterization tools On the other hand Equally important there's another line of research which is at heart of our approach That is we also perform fundamental research in our surface science and advanced characterization lab To understand better the structure and property relationships of energy materials We then apply these findings from our fundamental research to guide our energy device applications Due to the Time constraint today. I will only focus on our solar cell studies In this slide. I would like to provide some information about the history of solar cell development This chart here shows the evolution of best research cell efficiency for various types of solar cells as a function of time Not all the solar cells can be mass produced at a low cost Here I would like to highlight a few important solar cells, which can be suitable for the large scale deployment Roughly speaking So far researchers have worked on three generations of the solar cells The first generation solar cell is the crystalline silicon cell Its efficiency increased at a relatively fast rate Between 70s and 90s last century then it experienced a stagnation period for almost the 30 years Interestingly enough The efficiency has started increasing again since 2015 and reached a record high efficiency of about 26 percent as of today These crystalline silicon cells has excellent efficiency and also superb Endurance, but it is relatively expensive to make especially in the early stage of its development So to reduce the fabrication cost Researchers have been developing the second generation of solar cell with Silicon synium cell as the representative Synium silicon cell can be made at a lower cost, but it also suffers from low Efficiency of about 14 percent Which is about half of the crystalline silicon cells So to achieve the high efficiency and also the lower fabrication cost The third generation of solar cells have been developed with the provosca solar cell as its most prominent Representative over the past decades provosca solar cell has been intensively studied With its record high efficiency now exceeding 26 percent So here I put all these three curves together for you to get a direct comparison It is very clear as we can see a provosca solar cell has the most rapid increase in its efficiency Making it a strong contender for the next generation solar cells For any solar cell technology, there are three important parameters Forming the so-called golden triangle Fabrication cost efficiency and lifetime combined together to determine the overall cost to utilize this solar cell technology Now let's examine provosca solar cell in the context of these three important parameters First of all over the past 14 years the efficiency of provosca solar cell has Increased from the initial 3.8 percent reported by professor Miyazaka in his 2009 Jack's paper to nowadays exceeding 26 percent Which is already on par with even the best crystalline silicon cell While a crystalline silicon cell requires expensive and also energy intensive Processing to fabricate provosca solar cell can take advantage of many local fabrication methods But provosca solar cell is still facing a key challenge That is these cells often suffers from fast degradation And relatively short lifetime and this is a key issue currently under intensive Investigation by many research groups including ourselves So here in this slide, I would like to briefly introduce the major instrument we use for our research works Here is a photo of the ultra high vacuum system in our lab It has a base pressure of 10 to the minus 10 tall Which provides a desirable clean environment for us to perform the atomic scale in situ studies The scanning tunneling micro v tool on the left hand side of the ultra high vacuum system Enables us to determine the atomic structures of the materials And the spectroscopy tools on the right hand side of our uhv system Can help us understanding better the material properties So here we can establish a one-to-one correspondence between atomic scale structures and their material properties Also, our uhv system is equipped with a multiple vacuum evaporators Which can be used for in situ deposition of a synpheum samples Here in this slide, I would like to introduce the operation principles for scanning tunneling microscopy And this slide actually was made by my former phd student aftien. I thank her for allowing me to use this slide so in stm experiments, we first prepare and Clean atomically flat conductive sample, and then we bring an Atomically sharp stm tip close to the proximity of the sample surface so that the tip and the sample Is in the electrical tunneling region when we apply a bias voltage across this junction so using the tunneling current as the feedback signal the stm tip raster scans the surface and generate stm images Because the stm tip is atomically sharp and the tunneling current has a very strong dependence on the tip sample distance These stm images usually show atomic resolution That's why we can use stm to observe atomic scale material properties Also, we can use a related technique so-called scanning tunneling spectroscopy to get More details about the local electron properties of the sample surface In the next I would like to give a few examples to illustrate our surface size studies on the metal halide provoskites The first example is our stm study to determine atomic structure of the metal halide provoskite single crystal samples And this study was mainly carried out by robin and louis and I see louis sitting over there And this collaboration Oh, this is also a collaboration work with strong support from professor nangu park from skku in south korea And professor lee's group in sudo university china provided dfd calculation support for this work for this study We realized that the most important Pre-liquidate to obtain atomic resolution stm images is to prepare a clean atomic left flat sample surface So our strategy was to grow provoskite single crystals using the reported solvent exchange method The size of these single crystals growing by this method can range from a few millimeters up to one centimeter We then mount one of such single crystal sample To the sample holder and transferred it to our ultra-high vacuum system And finally we used a knife to perform vacuum cleavage of these single crystal samples and successfully obtained Clean atomic left flat sample surface Then we performed stm studies on these single crystal samples the The model shown on the left is the typical crystal structures of the provoskite materials And in the case of ma pb br3 Each of the pb lead iron is surrounded by six bromine ions forming the so-called pb br6 octahydrate Then eight of such octahydrate form a cage At the center of which the ma cation is located By comparing the experimental stm image with the dft simulation results We were able to determine that these white protrusions on the stm image Obtained on the reconstructed surface of single crystals are all bromine ions Which form a capitalistic dimer structure On the other hand Because the ma cation has a much lower surface density of states than the bromine ions Under the typical stm operation condition. They cannot be observed When we scan much larger regions of the sample surface We find many regions with perfect Latis and almost a defect free So here in this example, we can see everywhere shows the Chiristic bromine dimer structure On the other hand when we scan some other regions of the sample surface We observed the defects For example in this image here the dark depressions Point defects as you can see from the Line profile on the bottom At the defect side the stm height is lower than the surrounding region by about point three astral Another observation of our stm study is that on average the density of point defects is below one percent With respect to the total number of the bromine surface ions In the next example, I would like to introduce to you the stm studies on the mixed halide provolse guides And this study was performed by manly by germy In collaboration with professor yam far yam from university of toledo And also received strong support from professor ito mongaza So first of all why we are interested in the mixed halide provolse guides This is because these mixed halide compositions can enable us to have multiple advantage Such as band gap tuning and beta stability But there were also several puzzles pending for these mixed halide provolse guides such as what is the Surface structure and what is the mechanism for stability improvements For this study we use two types of the sample operation method To prepare our samples the first method is the previously used vacuum cleavage of the provolse guide single crystal samples and the second method is the Shown here as you can see it's a dual source co evaporation method to evaporate two precursors These two precursors will arrive at the substrate and react with each other to form the provolse guide single field The film sickness can be precisely monitored by these micro balance sensors and we usually Grow provolse guide single films with a typical film sickness of a few nanometers The film sickness here is to ensure We minimize the subject effect while still ensuring the stable SDM operation By comparing very thoroughly on the SDM imaging results obtained on both type of samples either Vacuum cleaved single crystal sample or in situ grown single film sample. We find that The results were highly coherent. Therefore in the foreign discussion I will not differentiate between these two type of samples In this study the first sample I we scanned are the pure MABR3 provolse guide sample The top image is the experimental SDM image and the bottom is the simulated image according to the DFT calculations As you can see once again, we observed the characteristic repeating bromine dimer structure and the top experimental image agrees quite well with the simulation image Then by vacuum deposition of a small amount of pbi2 we substituted part of the bromine surface ions with the iodine ions because iodine ions have a larger ion radius They appear as the bright protrusions in the SDM image On the other hand By vacuum deposition of a small amount of the pbcl2 We substituted part of the bromine surface ion with a chlorine ion because chlorine ion have Smaller ion radius than the bromine ions. They appear as dark depressions in the SDM image Then we scanned larger regions of all these three samples try to Determine whether these additional deposited Halide ions they form any specific order structure So the top row shows here the large area scan SDM experimental images for all these three samples the bottom Row shows the corresponding fast Fourier transform the images As you can see For both type of the mixed halide provolse guide samples, there are no additional new sports This suggests that the newly deposited halide ions are randomly distributed. There are no face aggregation for these additional ions to further understand the impact of the The halide mixing our theory collaborators also calculated the decomposition energy, which is an indicator for material stability So in a case of the incorporating of the iodine ions into the ma pbbr3 surface We found that the surface stability decreases monotonically as the surface iodine ratio increases And this suggests that incorporation of iodine ions on the surface of ma pbbr3 decreases the surface stability on the other hand when we Try to substitute part of the Surface bromine ions with the chlorine ions. We find that the surface stability first increases until which is a maximum and at about 15 percent of the chlorine Concentration So this suggests that indeed a suitable amount of chlorine ion can improve the provolse guide film Surface stability our x-ray photo electron spectroscopy experiments also confirmed this finding in our follow-up study, which is Performed by afshan together with a collaboration from professor yin We also observed the similar results for another provolse guide material ma pbbr3 So as I mentioned in one of the previous slides One of the pending challenges for provolse guide solar cells They are relatively short lifetime So to get a better understanding about this issue. We started the effect of ion Iding waiver on the iodine containing provolse guide and observed accelerated degradation And this study was performed by sheng ha. So in the next couple of slides, I would like to use the Cartoon animation to illustrate such effects So here is a structure of provolse guide solar cell And it has multiple layers of functional materials at the center of the cell is the photo absorbing layer Which in this case is the ma pbi3 provolse guide Now let's zoom into this layer to realize the microscopic picture of the self degradation mechanism Which is a main conclusion derived from our study here So in the solar cell operation Light incident on the solar cell part of the light will be converted into the electricity By the solar cell but a larger portion of the remaining light will turn into the heat Which lead to the increase of the cell temperature and cause the initial degradation of the provolse guide layer in a local scale Also the provolse guide solar cell is operated in the ambient condition So the ambient gas molecules such as water and oxygen can interact with the provolse guide layer also causing the initial degradation of provolse guide and by product of the Initial degradation is adding to the iodine two is quite diffusive and can migrate to other regions of provolse guide layer Lead to the further degradation of the provolse guide as a result iodine two more iodine two is generated and so on and so forth Such degradation events will finally lead to the degradation of provolse guide layer at a much larger scale and eventually the performance of these provolse guide solar cell will deteriorate In this study we not only look at the MAPB i3 provolse guide, but also look at many other kinds of provolse guide materials what we find that is For all the provolse guide materials that contains iodine the iodine vapor exposure lead to the faster degradation But when we perform the similar studies on the MAPB BR3 that is replacing the Halide composition in provolse guide structure from the bromine from the iodine to the bromine We find that the MAPB BR3 shows much better stability against either the iodine two vapor exposure or bromine two vapor pressure So this provides us with additional insight that Halide composition can indeed have a very vital impact on the stability of provolse guide materials The other aspects that need to be addressed prior to the large area or large scale deployment of provolse guide solar cell is that how can we Make large area provolse guide solar cell while maintaining their high performance So in the previous slide, I showed the best research cell efficiency chart And provolse guide solar cell has already reached a very high efficiency exceeding 26 But please note that this high efficiency is only achieved on a small area research cell with a typical Size of about 0.1 centimeter square or even smaller For on the other hand for the practical applications a size of about one meter square is usually required So here we see a size gap of about five orders of magnitude That is why it is very important to upscale provolse guide solar cell application So in the past few years, we have made a very dedicated efforts towards this direction And fabricated 5 by 5 10 by 10 and 15 by 15 provolse guide solar modules in the next couple of slides. I would like to show you several examples of such efforts In the first example, we developed a so-called holistic approach to interface stabilization for fabricating large area provolse guide solar modules and this study was performed by Zhonghao and Longbin for each of the interfaces and surfaces in the provolse guide solar module structure, they applied a certain strategy to optimize And as a result, we could obtain the provolse guide solar module on an area of 22.4 centimeter square not only showing a high efficiency 16.6 percent, but also demonstrating stable operation for 2000 hours In a more recent study, which was performed by Tong Le Tong Le introduced the MACO as additive into the provolse guide precursor solution to modulate crystal growth of the provolse guide synpheoms And by combining this strategy with several surface and bulk preservation methods He was able to obtain high quality provolse guide synpheoms on a much larger scale using a doctor blade coating, which is a scalable fabrication method As a result, we were able to obtain a provolse guide solar sub module with an area exceeding 200 centimeter square with an efficiency of 15.3 percent To summarize in this talk here, I have shown you using surface sciences as a very strong tool We understand much better about the surface and also structure and property relationships of the metal highlight provolse guide material and furthermore we apply these surface science findings in our solar cell and obtain some very interesting applications With that I would like to close my talk and thank you very much for your attention Thank you very much. Um, so we have plenty of time for some questions Like if anyone would like to ask you know being some questions Thank you. Thanks. You're being it's always amazing to see your productivity and all all the beautiful results How easy is it to scale this up to the one meter scale that you mentioned? The first question and second question is the 3d structure. Would that be helpful? 3d 3d. So you talked about 2d structure here surface structure, but would 3d structure be also helpful? So essentially two questions the first question is about you know further upscaling and Yes, and no, you know our Motivation is always try to get the bigger and bigger probably try to bridge the You know the size gap eventually to one meter square But also there's a limitation I think Even you know when we see the solar modules made from the crystalline silicon cells actually The panel is not a single Module they actually contains multiple modules together. So my guess is that you know I'm not sure about the provost gas solar cell probably is a very similar strategy in the end Is for each of module probably is up to say for example 30 centimeter By 30 centimeter square, you know and then you put all these modules together and forming a large area one meter square solar panel and that could be the case and also I would like to highlight you know for this kind of Approach and also the efforts probably is not only I will say more efficiently done by collaboration Between the academia and also industry as well. It cannot be achieved solely by the Research groups in the universities The second one is about the three dimensional structures, right? And indeed if you look at all the aspects I have shown here, maybe more than 95 percent I'm talking about the surfaces, right? There are two reasons for that Okay, first is because surfaces are important. Well, I mean that goes without any doubt, right? And because if you even look at the very simple structure of the provost gas solar cell There are already five six interfaces. Okay, and plus if you think about these Uh provost guide layer there is not a single crystalline And intrinsically they have ground boundaries And ground boundary can also be regarded As a interface in some sense So, uh, the main reason or first reason I would say is because interfaces are important Secondly is uh, so far, you know, our technique You know, at least the ones I'm using the scanning tunneling microscopy and UPS XPS spectroscopy Is possible to scan or to probe up to say example a few nanometers Go into the bulk Okay, so there's also a little bit technical limitation for these tools But I'm not suggesting the bulk Properties are not important. Actually, they are probably also important probably equally important Together with surface properties, uh, but the problem will need to develop some innovative technology and also Tools for enhancing our capability, which is also some of the Our group members are trying to make efforts Um, so I have two questions. Yeah being so one is you mentioned this efficiency about 26 percent And that's considered to be high Uh, I'm just curious. So so what's the limitation? Let's say if you can overcome all the technical challenges Uh, what kind of percentage it will be? This might be the best. We go back to the research cell efficiency chart. Yeah, indeed you will see There are a few type of solar cells they can achieve Even much higher efficiency than for those guys solar cells and let me try to Calify, you know, what are these? Solar cells, you know, for instance, you know for the up there, you know, these solar cells Especially the top few these are called multi junction solar cells They are basically combined single junctions solar cells together each junction focusing a certain wavelength Try to get the best efficiency for that particular wavelength. So that's why it can reach much higher efficiency But as you can imagine the uh kind of fabrication Procedure is much more complicated and plus for these Solar cells to work. They also use some spatial materials and these materials is Generally much more expensive than the provost guy solar cell and also silicon cells as well. So here In the sense, you know of the how can you determine what is the right type of the solar cell? It really depends on application if you focus on the Example the large area deployment On the earth, right put on the roof then the lower cost we must take into account But on my hand for example outer space, right the spaceship, right? They really have limited small space for mounting a solar cell probably efficiency is more important and Yeah, so considering the ok now and like a local environment, you know with typhoon rainy Seasons and you know high salt concentration Have you tried to test your solar cells like in The real environment. How how does that perform excellent question? Yes In the past few years, you know, I was really engaged in the discussion of doing that And it turns out it's not that simple. Okay, okay now. I usually You know has a very good sunny days, but also very kind of running days running season which make the Maimment of these solar cells not that straightforward. We have to really Kind of Incapsulate the mirroring device probably Especially the electronic part in a case so that it will not be damaged during the running season But it is possible and there are so they can be easily damaged Yeah, the the cells. I think in the end has to be durable for the You know the field applications outside, right? But for doing these things, uh, you know electronics in our lab probably first have to really make that compatible. Yes Okay, thank you. Thank you very much and congratulations So if I remember correctly when you came to oist you are working on like a Organic solar cells and then how could you quickly shift to this pervoskite type of solar cells And the answer is yes. Yes. I worked on the organic solar cells at the beginning and well, it was I would say it was more like Take advantage of the The opportunity because at a time, you know, I kind of obtained quite in-depth understanding about organic solar cells and the new type of material pervoskite just came out And I kind of try to see, you know, whether in this new type of solar cell Can overcome the limitations of organic solar cell which at a time had a very serious stagnation in their efficiency It was kind of like kept as a constant for 14 13 percent for a very long time But once again, I mean nobody knows nowadays. I think things about maybe three four years back Researchers find a new class of the materials organic materials Now the efficiency is indeed much higher than the previously 13-14 percent So organic solar cells become also a strong candidate for the next generation solar cells So probably my best answer is Nobody can predict what will be the winning, you know technology in the end Probably the best strategy is we have to keep eye on all these parallel Developing technologies of the solar cell And probably your expertise in Fine measurement of the surface was a good advantage, I guess Yeah For the organic solar cells the surfaces are even more important Because compared to the provoskite solar cell the layers are typically hundreds of the nanometers Organic solar cells typically 50 nanometer Sometimes even 30 nanometer is even much thinner And talking about the surface to the bulk ratio is even much higher So I agree with you probably the importance of the surface in organic solar cell development Is even more important than provoskite solar cells And another question. So this uh, provoskite includes lead Can that cause environmental concern when they are disposed? It is a very open question for discussion actually. So nobody has reached the conclusion yet There are very serious calculations calculating, you know, how, you know, this will happen if, you know, provoskite solar module breaks when it's outside, right And even in our own group We actually developed a encapsulation technology in 2019 Just to simulate in the extreme weather condition if the provoskite solar cell breaks During several health right a big ice ball hitting on the solar panel make that a break, you know And the lead will come out as a leakage, right? And for that type of, you know, method we developed the so-called self healing In capsulant, which is a polymer material and If it's broken at room temperature Of course it might Cause the problem, but the nice part about that if the weather gets better, for example, the next day, you know It's a warm temperature, right? Like, you know, for the third for the degree can be reached. It will be self healed And then that very effectively Prevents the leakage of the lead Lead, you know, into the soil and water, etc. Yeah, but but this is a pending, I think discussion hasn't been Completely, I think agreed on In consensus, okay. Thank you very much If maybe I can ask one question to close out and then we can go on to the tea time But how long do you think until we have pescovite Panels covering a house like you showed at the end. I mean, what how far out are we from that? If you look at the development, I think the main challenge is lifetime If we can overcome the bottleneck of the lifetime, we can have that in a reasonable period of time I always say up to five years But if that cannot be overcome As many other technology comes and goes So I think the key really is how can we understand beta about the Degradation mechanism, how can we circumvent this as the biggest challenge for provost guy solar technology So this is also one of the main topic actually in our group. We are still making a big effort towards that direction Okay, thank you very much. So let's thank yabin again for the wonderful talk