Chemical Forums
Chemistry Forums for Students => Physical Chemistry Forum => Topic started by: pnacze199204 on May 17, 2018, 01:27:02 PM
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Wikipedia says that diamond converts to graphite at ~700 °C. But then, in the same article we can find an information: "But diamonds (sp3C) are unstable against high temperature (above about 400 °C (752 °F)) under atmospheric pressure. The structure gradually changes into sp2C above this temperature". I'm a little bit confused. Does that mean that the surface of diamond is more susceptible to high temperatures or what? What would be the temperature in which this mineral starts to change its structure? Thank you for helping me!
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You can check out the phase diagram of carbon to see what phases are most stable as a function of temperature and pressure. Note, this only reflects thermodynamics, not kinetics. So, for example, the diamond phase can exist indefinitely at low temperature and pressure, because of the large activation energy for transformation of diamond to graphite.
http://www.bris.ac.uk/Depts/Chemistry/MOTM/diamond/diamond1.htm
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Thank you for replying me! We all know that diamond is one enormous molecule of Carbon and in one of the Physics handbooks I found the information, that the oxidation and graphitization of diamond is practically impossible at standard conditions. I read also that the transformation of diamond into graphite starts at temperature of ≈700 ∘C. But today I've entered Wikipedia and I've found the two information, one of them in the section of "Surface Property" when it is said that diamond are unstable above 400 ∘C. I thought that it would be related with Hydrogen and Oxygen termination of the diamond surface. I'm asking because I would like to know at what temperature diamond film starts to graphitize and at what temperature the reaction would be impossible to happen.
P.S. Sorry for my English, it's not my native language and I'm still learning it :)
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If you view the phase diagram in the link I provided above, you can see that as temperature increases, graphite is more thermodynamically favored even at moderately high pressures. E.g., if you start at a pressure of 5 GPa and ambient temperature, diamond is the thermodynamically favorable form. But as you increase temperature, you will eventually come to a point (maybe around 1500 C) where graphite becomes the more thermodynamically favorable form. It is important to note that this doesn't necessarily mean that a diamond held at 5 GPa will suddenly change to graphite at 1500 C! It just means that eventually (be it 5 seconds or timescales longer than the age of the universe) under these conditions, the equilibrium state will favor graphite.
You can link the wikipedia article you are referring to if you want - it is hard to comment on text I haven't read.
The question, "When does such and such a process begin?" or "when is the process impossible" doesn't make a lot of physical sense. If you have a diamond ring right now, and graphite is the thermodynamically favored state at ambient conditions, then the conversion process has begun. The process begins as soon as the system is created. A nonequilibrium state is always spontaneously moving toward equilibrium. But, the conversion rate may be imperceptibly small due to the large kinetic barrier of the process.
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Here's the article: https://en.wikipedia.org/wiki/Diamond
If it has no sense to ask when does the process begin, then why so many papers indicate that the transformation STARTS above 700 C? I don't get it. I know that the process is happening all the time and that it is extremely slow, but I thought maybe there's a temperature at which the surface of diamond starts to graphitize immediatelly or something like that.
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Here is a good example of being careful with Wikipedia. If you actually go to the link, you will see the cited paper is about oxidation of diamond surfaces, not transformation to graphite. This is a chemical oxidation process and seems to have little relevance to the direct phase transition of diamond to graphite. As to why it "begins" at 700 degrees: the figure in the paper shows that indeed oxidation of the diamond surfaces, as determined by weight loss of diamond in TGA as a function of temperature, becomes significant around this temperature. Note even the Wikipedia article says "approximately" (or "~"). Certainly from the figure shown in the cited paper (pasted below), you can't pick a single absolute, nonarbitrary temperature where the process "begins". The rate of oxidative decomposition just seems to become significant around this temperature (and it's a nice round number - we love those!). This temperature, as argued in the paper, is related to the activation energy for the oxidation process in air. Once the temperature gets high enough, a high probability of reaction events have enough energy to surmount the transition state energy and result in product conversion. Note that statistical mechanics are a probabilistic process - an inspection of the data show that some reaction events occur below 700 degrees C, because there are always a statistical distribution of molecular/atomic energies at every temperature. The point at where the reaction "begins" could be approximated as that were (XXX%) of them have enough to proceed to products. You can define XXX% however you want - there's no right answer. Even at room temperature there is a finite chance of one oxygen molecule somewhere oxidizing a diamond carbon atom. So the process never really "begins" at a discrete temperature - and, in a closed system, the process doesn't "end", either.
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Thank you!
So do I understand well that the activation energy accelerate the process of oxidation and graphitization of diamond and it still can happen spontanouesly without input of energy, but at the long period of time? Somewhere I've read that at standard temperature (25°) they can persist more than millions of years. What if I heated up diamond to 100 °C? I suppose the reaction would be faster, but would it be significant difference? Or a significant difference would start at approximately 450 °C as said in the paper? I know my questions may seem stupid, but I have nothing to do in my live with Chemistry or Physics and I would like to understand it well. :)
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No background in chemistry or physics? No problem!
But that does help to orient me a little bit. I’ve been throwing out some words that probably don’t mean a whole lot in that case. So let’s back up.
A process of going from diamond to graphite is something like this. Let’s say you have a herd of goats and there is a great grassy pasture a few miles to the east. Your goats naturally want to graze there because it’s good eating. If all your goats start off this morning going in the direction of the food, and let’s assume they all move independently (their motion to the food source is not dependent on following other goats), how long will it take for all the goats to arrive at the food?
You can imagine two scenarios – one in which there is a small hill between the herd and the grassy field, and one in which there is a big mountain in the way. In both cases the goats want to end up in the grassy field, because it is a state of lower energy (grass tastes good). But it is easy to understand that if there is a big mountain in the way, the chances of any goat making it to the field becomes small, such that the amount of time it takes for the whole herd to make it there is long. The rate at which the herd moves is inversely related to the height of the mountain. On the other hand, the rate may also depend on how hungry the goats are – if they are more motivated, they might be speedier about climbing over that mountain to get to the food.
In this analogy, the goats are carbon atoms. Initially, hungry goats are carbon atoms in diamond and full goats (gorged on yummy grass) are carbon atoms in graphite. All things being equal, the goats will end up at the grassy field because that’s the state of lower energy. Diamond will change to graphite. But there’s a mountain in the way. A big mountain. So big that the goats are very unlikely to cross over the mountain and get to the field. The question is: can we make them sufficiently hungry so that they cross the mountain on a realistic timescale?
The mountain is the “activation energy”, which is a characteristic of most chemical reactions – and indeed, most of life’s tasks. Even if the reaction is favorable, sometimes you have to put some energy in to get payoff later on, and the more energy you have to put in, the slower the reaction is, even if the payoff is large. (A good example of this is combustion – despite the fact that burning a carbon fuel releases a lot of energy and is very thermodynamically favorable, the reaction is very slow. A temperature of a few thousand degrees is necessary to make this reaction happen on any relevant timescale!)
Reaction mechanisms are complicated, even more so in the solid state, where surface characteristics become a factor of concern, but a simple model is the Arrhenius model, which fits to a surprisingly large number of chemical reactions, and also has been applied to many non-chemical processes. (I learned, while looking around for information on diamond to graphite, that is has even been used to model the blooming of Japanese cherry trees – who knew?! See: https://en.wikipedia.org/wiki/Cherry_blossom_front).
This will be the only equation I present, but it’s important:
[tex]rate = Ae^{-\frac{E_a}{RT}}[/tex]
The Arrhenius expression basically says this: the probability that a molecule (or whatever) will go from one state to another is related exponentially to the relationship between how much energy you need to make that transition happen and how much energy on average the molecules have by virtue of the temperature. In the expression, the rate is a function of: an activation energy, Ea; the temperature, T; the gas constant R; and a pre-exponential factor, A.
Ea is the height of the mountain – I.e., how much energy you have to put into a reaction to get payoff.
RT is a kind of measure of the amount of average thermal energy. In our analogy, this is how hungry the goats are. Higher temperature means more hungry and more motivated.
A is a measure of a lot of things, like, the probability that two reacting molecules are colliding from the right direction, stuff like that.
Generally, Ea and A are assumed to not be dependent of temperature, which is a good approximation for small changes in temperature. Anyway, what the Arrhenius equation basically says is that if the activation is large, the rate goes down, and if the temperature is high, the rate goes up. And those trends are highly exponential – a small change in activation energy makes a big change in rate. Now, there is a lot of chemistry and physics involved in determining what Ea and A are, but unless you want to go there, let’s ignore it and just play with numbers.
Not surprisingly, the transition from diamond to graphite is complicated. But I found some numbers we can play around with just to give you a sense of scale.
From the reference: G. Davies and T. Evans. Graphitization of diamond at zero pressure and at a high pressure. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 328, No. 1574 (Jun. 13, 1972), pp. 413-427
These guys basically took real diamonds, heated them in a vacuum at around 2000 degrees C), and measured the mass loss due to graphitization as a function of time. By measuring the reaction rate at different temperatures, they calculated an activation energy of around 730 kJ/mol for a particular crystalline plane of diamond.
You may not have a good sense for these things, but let’s be clear: that is a HUGE activation energy. It may at first seem strange that the energy mountain would be so large – after all, you are just taking carbon atoms and shifting their positions a little bit. In fact, the carbon atom arrangement in diamond is quite different from that of graphite, and so going from one to the other requires breaking a lot of strong carbon-carbon bonds, then rearranging them in space to form new ones. This is why the activation energy is so large. At 2000 degrees, of course, there is quite a bit of energy around to break bonds, and so the process happens over the course of a few hours at 1850 C, down to a matter of minutes at over 2000 degrees C.
Ok. What about at room temperature? Millions of years is actually probably a huge underestimate. Here’s where it takes a little bit of fudging the numbers and some big assumptions – namely that the activation energy and pre-exponential factors are the same at room temperature as they are at 2000 degrees. Plus I had to fudge a pre-exponential factor because the authors don’t directly report it in the paper. But if we bear in mind this aspect of crudeness, you can use the Arrhenius equation and project that at room temperature, the rate of graphitization is on the order of 1 x 10-114 μg/s! Let’s put that in perspective. A 1 carat diamond weighs about 200 mg (200,000 μg). It would take on the order of 1 x 10118 s for the diamond to be completely graphitized. Or 1 x 10111 years. That’s really a number beyond comprehension, so many times longer than the age of the universe that it doesn’t even bear thinking about.
Now, that number is based on such a crude calculation that it's probably very inaccurate, maybe off by dozens of orders of magnitude even, but I think it does at least show the sense of scale here. Truly, diamonds are (practically) forever. Unless you heat them to 2000 degrees, in which case you will get pencil lead in less time than it takes to watch Sean Connery and Charles Gray duke it out over a diamond-powered death satellite (https://en.wikipedia.org/wiki/Diamonds_Are_Forever_(film)).
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After checking Wiki's article... https://en.wikipedia.org/wiki/Diamond#Surface_property
There are two different ideas.
Diamond's oxidized surface can be reduced (=de-oxidized) but this needs a high temperature.
And the temperature is limited, anywhere in diamond, because of the transformation to graphite.
Wiki didn't detail this logic, that's confusing. A priori, no special risk that the surface is more sensitive to heat.
In case someone wants to de-oxidise a diamond surface, a logical action would use a reducing compound that acts at a temperature lower than molecular hydrogen needs. Something like a hydrogen plasma, or a liquid alloy that does not dissolve carbon (is there any?), or a molecule easily giving hydrogen atoms...
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Very interesting, thank you! So, what would happen to diamond first if we left it at ambient temperature and pressure- it would turn into graphite or evaporate? Which of those two reactions occur more rapidly? :)
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Because if I understand well, there exists a possibility that the carbon atom on the surface of diamond would transform into CO2 even without input of energy, but it would require a lot of time, am I right? So at the ambient temperature and pressure, what would happen first? If we had eternity to check this, which of the two reaction would be faster? Diamond turning into graphite or diamond evaporating? :)
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On https://physics.stackexchange.com/questions/215950/diamonds-are-not-forever I found very interesting question;
"It is frequently stated that although graphite is the more stable allotrope of carbon at STP, the activation energy of the diamond-to-graphite transformation is so high that our diamonds will never spontaneously turn into black dust.
Some sources add (correctly) that nothing is ever never, and reactions merely slow down with lower temperature, they never stop entirely. (The Arrhenius equation comes here). But nobody ever quantifies the non-neverness of the death of a diamond. So my question is:
Under normal conditions at room temperature, which of the following will happen first; when, and how fast?
Diamond transforming to graphite.
Diamond evaporating. Marshall and Norton ,J. Am. Chem. Soc., 1950, 72 (5), pp 2166–2171, seem to say that latent heat of carbon is 170kcal/mole, but I haven't got access to the whole paper to see what they say about the rate of evaporation.
Diamond spontaneously combusting to CO2.
Carbon decaying to iron via tunnelling. Barrow and Tipler, in The Anthropic Cosmological Principle (Oxford, 1986), p.654, quote 10^1500 years for this."
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At room temperature, all those processes are so slow as to be effectively the same: no change observed. I mean, you're talking time frames longer than current lifetime of the universe, so it's splitting hairs. This makes it incredibly hard to compare experimental rate constants, which may variously depend on a lot of factors, including the different crystalline faces of diamond, oxygen concentration/atmospheric pressure, temperature changes, and so forth.
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In contrast, the oxidation of the surface happens immediately at the timescale of our sensing abilities.
This does not mean "carbon dioxide". The last atoms in a solid have "pending bonds" that are not satisfied by the rest of the crystal. These pending bonds are extremely reactive and catch about any other atom that passes by. In the air, it can typically be an oxygen atom. At a surface, you have badly defined and varying terminations, which can be -OH for instance.
These terminations are not CO2. Only one bond from C is with the surface species, the rest is with other C atoms in the depth. The surface C atom is correctly called "oxidized" in this state despite it forms neither monoxide nor dioxide.
Even over the layer that saturates the pending bonds, you have a few layers of adsorbed molecules. These make no chemical bond with the crystal but hang by intermolecular forces. They can be desorbed more easily, their composition resembles the one of the surroundings and varies more easily over time.
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Ok, so does that mean that the surface of diamond can change slowly its structure over time and just dissapear? I mean, you have those pending bonds and C atom is oxidized, so as you said it can react more easily. I suppose that atom can be kicked out and step by step the mineral can just dissapear over time or change completely. Am I right?
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In theory. But by analogy, a bucket of gasoline left at room temperature in air doesn't just explode, either, even though the oxidation of hydrocarbons is extremely exothermic. The reaction is SLOW.
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So slow that we are still thinking about a time greater than the age of the universe? In that case, what about the nano diamond (size less than 1 micrometer)? Would the age of the universe be enough time to get rid of it?
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Well thankfully the original research article in the Wikipedia page you linked to (https://www.sciencedirect.com/science/article/pii/S0925963501006732?via%3Dihub) provides experimental numbers you can use. They report a pre-exponential factor of ~ 2 x 107 nm s-1 Pa-1 and an activation energy of 222 kJ mol-1. The atmospheric pressure of oxygen at room temperature at sea level is ~21000 Pa. So, the pre-exponential factor is ~ 4.3 x 1011 nm s-1. If we assume temperature independence of these factors (not a great assumption, but for rough estimates it's OK), then at room temperature (298 K, say) and regulator atmosphere at sea leavel, I calculated an approximate rate of 5 x 10-28 nm s-1. Or, 1.5 x 10-20 nm of diamond oxidized per year. To oxidize 1 full nm thickness of diamond (100 face) at room temperature and atmospheric pressure, then, would take on average about 6 x 1019 years. The age of the universe is about 1.4 x 1010 years. So, trillions of times the age of the universe would be an approximate estimate of the time it would take to oxidize 1 nm of diamond at room temperature.
In the paper, the authors do the oxidation reaction in a furnace at, say, 1000 K and concentrated oxygen atmosphere (~80,000 Pa). We can see that raising the temperature and increasing concentration of oxygen so much really increases the rate. In pure oxygen atmosphere of 80,000 Pa, the rate of oxidation becomes 4 nm/s: under these conditions, a 5 mm diamond (with a single 100 face exposed, mind) could evaporate to carbon dioxide in about 2 weeks - but still, if you think about it, that's TWO WEEKS at 1000 K and pure oxygen to oxidize a relatively small diamond (or relatively big, depending on your salary ;)).
Even under regular air the oxidation rate is significant at high temperature (about 4x slower).
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Well, I found an article in which it's written that diamond can disappear in sunlight: https://www.nature.com/news/2011/110715/full/news.2011.421.html . 10 billions of years would be sufficient to make 1 microgram of diamond evaporate. And here is the paper: https://www.osapublishing.org/ome/fulltext.cfm?uri=ome-1-4-576&id=220251 . I find that very interesting, but once again, I have a question :D
It would require removing a few or a dozen atoms from the surface of the diamond per year. In that case, would a diamond have to be in the sun 24 hours a day to make it happen? It is obvious that on Earth we have night and day, so if we cut off the sunlight, would the process have to start from the beginning to excite the atom? I don't know if I have expressed myself well, but I hope you understand me. :D
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I'm not 100% sure what your asking. Quantum events are probabilistic, not deterministic, so turning off the light source does not cause you to "start over" for a single reaction event. Single reaction events are practically instantaneous (not really, but based on a human frame of reference they might as well be). It's the low probability of a single reaction event happening at any given instant that drives the slow macroscopic change from reactant to product. That said, only having the light on for 50% of the time does effectively double your overall conversion time.
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Well, I ask because the speed of the process is highly linear, and as I read, a typicall diamond would lose only a few atoms per year if we put it in strong sunlight. So I wanted to know if cutting off the UV light influences the process. I thought that the atom gets excited becuse of the long exposure to sunlight and finally it pop off, but when the light is off the process has to start over. By the way, to this process happen we need 2 UV photons. Sunlight seems unlikely to do much, am I right?
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Cutting of the light source does influencing the time it would take, but not in the way you are thinking. "Starting over" is not the way photon-driven (or any, really) reactions - which are just ensembles of quantum events - work.
You can think of it like any other gambling process. Let's say you are in Vegas and you are doing slot machines, where the probability of winning the jackpot is (say) 1/1,000,000 for every pull of the lever. You do this from 10 AM to 12:00 PM and a friend comes by and says, "Hey, do you want to get some lunch?" If you agree to go to lunch, this doesn't cause you to "start over" when you come back, because every pull of the lever has the same chance of being a winner. On the other hand, if you had the time (and money) to use the machine continuously as long as the casino is open, it would be appropriate to say that, on average, it will take you a longer absolute amount of time on average to become a winner if the casino closes 8 hours every night, because you lose 8 hours every 24 hour period of lever-pulling-time. But, if you were to calculate the average number of playing hours it takes to win, it makes no difference if there are casino-closings or not. I.e., it's the number of pulls of the lever per playing time that makes the difference. Needless to say, if you could increase the number of machines you could play at one time, or rig the system to make it more likely that any given pull results in a winner, you can reduce the amount of time it takes to become a millionaire. In the chemistry world, these two things are akin to increasing the energy (temperature, light intensity) or applying a catalyst.
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I understand, thank you!
The paper says that to diamond lose its atoms it is requiered the ultraviolet light and even the sunlight or mercury-vapour lamp would be able to damage a diamond structure. They paper says also that there's no threshold, so the process can proceed at very low intenses of light. It is pretty hard to belive that the walvelenght of 380 nm would influence the structure of the stone, even if it is so slow.
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By the way, I have read some articles on the Internet and I understood that we can have Two Photon Absorbtion only with very high intensity light (laser sourse). Would the sullight be enough to excite the state of atom? :) The paper that I linked says yes, but maybe I misunderstand something.
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By the way, I have read some articles on the Internet and I understood that we can have Two Photon Absorbtion only with very high intensity light (laser sourse). Would the sullight be enough to excite the state of atom? :) The paper that I linked says yes, but maybe I misunderstand something.
TPA is a nonlinear optical phenomenon, meaning the intensity is not linearly correlated to irradiation power. Simultaneous absorption of two photons is proportional to the square of the incident photon intensity (power or fluence, however you want to define it), and the proportionality constant is kind of like a two-photon extinction coefficient. It can be related to molecular electronic structure, but honestly I'd have to think about how it'd be related to the surface properties of a solid. Although it is not true that two photon absorption occurs only with high intensity light, it is true that it will become a more prominent mechanism for light absorption using, e.g., a laser rather than ambient light. Sunlight is a continuum source, meaning it emits light over a broad wavelength range, whereas a laser is (mostly) monochromatic. In sunlight then you would have both one and two photon absorption going on simultaneously. But as before, this is mostly a matter of kinetics rather than "happen/not happen". Two photon absorption will probably be slow - all other things equal - because the photon fluence is low. That doesn't mean it won't happen.
(NB - there are certain selection rules to be concerned with as well. Honestly I don't remember what they are for two photon absorption. So this would impact the likelihood of an absorption event.)
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Maybe I'm obsessed with the topic, but I would like to ask if there's any possibility to calculate the number of atoms lost from diamond surface in sunlight per year? Let's say we have 1 cm2 of the stone and we put it in strong continous sunlight. :)
From the article:
"A notable corollary of the two-photon desorption mechanism at sub-ablation fluences is
that etching persists for very low UV fluences, and that even under incoherent illumination
diamonds will steadily lose mass. However, the effect under ambient light conditions is rather
insignificant. For example, continuous wave Hg lamp illumination at 253 nm for typical
irradiances (0.1 W cm-2) would require approximately 10^10 years to desorb a significant mass
(e.g. 1 µg) from a surface a few millimetres square. Under sunlight conditions the etching rate
is even slower due to the reduced irradiance (10-4 W cm-2; 300-350 nm) and the reduced
probability for TPA at longer wavelengths. "
Professor Mildren acclaims that if we left a diamond of area 1cm2 in the sun continuously, it would be a few atoms per year. I would like to know what that "a few" means :D
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I calculated that one microgram of diamond has (6.02 × 10^23 × 0.000001) ÷ 12.01= 5.0124896e+16 atoms. That means 5012489.59201 atoms ejected per year under Hg lamp illumination at 253 nm for typical irradiances (0.1 W cm−2). So I'm quite suprised by what Professor Mildren said about loosing atoms under sunlight condition, because as I mentioned he said "a few". I think the number of atoms ejected from diamond's surface for irradiance 10−4 W cm−2; 300-350 nm would be smaller, but I'm not sure if they would be so small to tell that there would be "a few atoms" per year. I don't know if I understand everything well, if not, please correct me. Thank you.
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I'd have to see the article to determine how the estimation was done. But bear in mind that there are a lot of variables and so a 'few' probably is probably just an order-of-magnitude projection. First, sunlight is variable in intensity depending on climate, latitude/altitude, local pollution, and so forth. Also, the diamond characteristics matter - physical dimensions and purity.
If you think about the amount of atoms in a microgram of diamond, however "a few" is defined (whether it is 1 or 100) is practically inconsequential. It's like saying that a beach loses a few grains of sand a year. In that sense, the meaning of "a few" is taken to be "effectively zero but not zero". This is an important distinction, though. In chemistry and physics, "exactly zero" happens very infrequently because it implies that a process is absolutely forbidden. It's good to remind a reader when there is a nonzero probability of a process occurring. Which basically means, the rules of physics allows it, and therefore there is room to make the process more efficient and technologically feasible.
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The full article is available here: https://www.osapublishing.org/ome/fulltext.cfm?uri=ome-1-4-576&id=220251
There's said that the 2-photon absorption rate and etch speed is highly linear, which provides control over the etch rate. Besides I found the other article related with previous one, in which is said that light could be used to pick apart a substance atom by atom: https://phys.org/news/2014-03-super-resolution-laser-machining.html . I thought it would be possible to calculate the number more or less at, for example, irradiance 10-4 W cm-2; 300 nm. :)