I wrote a short explanation of how superconductors work a few months back. Then I came across this excellent write-up over on The Conversation that explains why high-temperature superconductors would be so revolutionary.
Physicists hunt for room-temperature superconductors that could revolutionize the world’s energy system
Waste heat is all around you. On a small scale, if your phone or laptop feels warm, that’s because some of the energy powering the device is being transformed into unwanted heat.
On a larger scale, electric grids, such as high power lines, lose over 5% of their energy in the process of transmission. In an electric power industry that generated more than US$400 billion in 2018, that’s a tremendous amount of wasted money.
Globally, the computer systems of Google, Microsoft, Facebook and others require enormous amounts of energy to power massive cloud servers and data centers. Even more energy, to power water and air cooling systems, is required to offset the heat generated by these computers.
Where does this wasted heat come from? Electrons. These elementary particles of an atom move around and interact with other electrons and atoms. Because they have an electric charge, as they move through a material – like metals, which can easily conduct electricity – they scatter off other atoms and generate heat.
Superconductors are materials that address this problem by allowing energy to flow efficiently through them without generating unwanted heat. They have great potential and many cost-effective applications. They operate magnetically levitated trains, generate magnetic fields for MRI machines and recently have been used to build quantum computers, though a fully operating one does not yet exist.
But superconductors have an essential problem when it comes to other practical applications: They operate at ultra-low temperatures. There are no room-temperature superconductors. That “room-temperature” part is what scientists have been working on for more than a century. Billions of dollars have funded research to solve this problem. Scientists around the world, including me, are trying to understand the physics of superconductors and how they can be enhanced.
Understanding the mechanism
A superconductor is a material, such as a pure metal like aluminum or lead, that when cooled to ultra-low temperatures allows electricity to move through it with absolutely zero resistance. How a material becomes a superconductor at the microscopic level is not a simple question. It took the scientific community 45 years to understand and formulate a successful theory of superconductivity in 1956.
While physicists researched an understanding of the mechanisms of superconductivity, chemists mixed different elements, such as the rare metal niobium and tin, and tried recipes guided by other experiments to discover new and stronger superconductors. There was progress, but mostly incremental.
Simply put, superconductivity occurs when two electrons bind together at low temperatures. They form the building block of superconductors, the Cooper pair. Elementary physics and chemistry tell us that electrons repel each other. This holds true even for a potential superconductor like lead when it is above a certain temperature.
When the temperature falls to a certain point, though, the electrons become more amenable to pairing up. Instead of one electron opposing the other, a kind of “glue” emerges to hold them together.
Keeping matter cool
Discovered in 1911, the first superconductor was mercury (Hg), the basic element of old-fashioned thermometers. In order for mercury to become a superconductor, it had to be cooled to ultra-low temperatures. Kamerlingh Onnes was the first scientist who figured out exactly how to do that – by compressing and liquefying helium gas. During the process, once helium gas becomes a liquid, the temperature drops to -452 degrees Fahrenheit.
When Onnes was experimenting with mercury, he discovered that when it was placed inside a liquid helium container and cooled to very low temperatures, its electric resistance, the opposition of the electric current in the material, suddenly dropped to zero ohms, a unit of measurement that describes resistance. Not close to zero, but zero exactly. No resistance, no heat waste.
This meant that an electric current, once generated, would flow continuously with nothing to stop it, at least in the lab. Many superconducting materials were soon discovered, but practical applications were another matter.
These superconductors shared one problem – they needed to be cooled down. The amount of energy needed to cool a material down to its superconducting state was too expensive for daily applications. By the early 1980s, the research on superconductors had nearly reached its conclusion.
A surprising discovery
In a dramatic turn of events, a new kind of superconductor material was discovered in 1987 at IBM in Zurich, Switzerland. Within months, superconductors operating at less extreme temperatures were being synthesized globally. The material was a kind of a ceramic.
These new ceramic superconductors were made of copper and oxygen mixed with other elements such as lanthanum, barium and bismuth. They contradicted everything physicists thought they knew about making superconductors. Researchers had been looking for very good conductors, yet these ceramics were nearly insulators, meaning that very little electrical current can flow through. Magnetism destroyed conventional superconductors, yet these were themselves magnets.
Scientists were seeking materials where electrons were free to move around, yet in these materials, the electrons were locked in and confined. The scientists at IBM, Alex Müller and Georg Bednorz, had actually discovered a new kind of superconductor. These were the high-temperature superconductors. And they played by their own rules.
Scientists now have a new challenge. Three decades after the high-temperature superconductors were discovered, we are still struggling to understand how they work at the microscopic level. Creative experiments are being conducted every day in universities and research labs around the world.
In my laboratory, we have built a microscope known as a scanning tunneling microscope that helps our research team “see” the electrons at the surface of the material. This allows us to understand how electrons bind and form superconductivity at an atomic scale.
We have come a long way in our research and now know that electrons also pair up in these high-temperature superconductors. There is great value and utility in answering how high-temperature superconductors work because that may be the route to room-temperature superconductivity. If we succeed in making a room-temperature superconductor, then we can address the billions of dollars that it costs in wasted heat to transmit energy from power plants to cities.
More remarkably, solar energy harvested in the vast empty deserts around the world could be stored and transmitted without any loss of energy, which could power cities and dramatically reduce greenhouse gas emissions. The potential is hard to imagine. Finding the glue for room-temperature superconductors is the next million-dollar question.
Rubber-forehead aliens are basically a meme at this point. They make perfect sense in terms of production costs and limitations imposed by special effects technology at the time. The good news is that writing for print gives us far more options than would be possible otherwise. I think that they make it easier to relate to characters on screen but making all of your aliens look like humans with a few extra bits glued on requires a lot of worldbuilding to explain away. If you try to explain it that is.
The point of this post is not so much to provide an explanation of how life on other worlds could work but rather why it’s so hard to envision what life on other worlds could be like. This is because a) I am not a biochemist and b) it’s somewhat difficult to pin down just what “life” is. Once you’ve wrapped your head around this second idea and thought about some of the strange chemistries that are possible on alien worlds you will feel much freer to imagine strange new forms of life.
At this point, you are probably getting ready to type an angry comment or tweet along the lines of “WHAT DOES HE MEAN? OF COURSE WE KNOW WHAT LIFE IS. I’M ALIVE AREN’T I?” It’s actually a lot more complicated than that. Here on Earth we still have trouble deciding whether viruses are alive. Sure they can infect hosts and they use the same DNA/RNA coding that we and the rest of life here on Earth do, but they lack the machinery needed to make copies of themselves so they have to hijack ours. NASA has a definition of life that they use in the search for extraterrestrials and it’s probably the best one available to us, but there are still likely to be some who disagree with the definition.
“Life is a self-sustaining chemical system capable of darwinian evolution” – NASA
I’d be interested to hear whether readers think that viruses are included in this definition or not.
The reason that the definition of life is so hard to pin down is that we only have our own world to serve as a reference. In our solar system of eight planets and who knows how many planetoids and moons only one body, Earth, is known to support life. Yet there are two other planets, Mars and Venus, that might have once supported life and several moons that could even harbor life this very moment (I’m looking at you Europa).
We can look around at our own planet and describe how life works here. We can explain how DNA works, how organisms obtain energy, and how one organism gradually evolves into another over time. We know all that but we still do not know how life began on this planet. Without knowing how life began it is hard to definitely say whether a planet could support life or not. We tend to get excited when we find planets around other stars that could support conditions similar to those here on Earth, but when we talk about whether a planet is in a star’s “Goldilocks Zone” what we are really saying is that the planet could support life that is like us, and that’s a little arrogant I think.
Fortunately, our knowledge of chemistry and physics allows us to envision other ways in which life might arise. We are, after all, just bags of chemical reactions that happened to develop egos.
Excuse Me, Is This Life Organic?
These days a lot of people think that if something is organic it was produced from “natural” materials or grown without the use of certain fertilizers or pesticides. What they don’t realize is that oil is both organic and naturally occurring, but you wouldn’t want to eat it. When scientists say something is organic all that means is that it is composed of primarily carbon and hydrogen along with a smaller proportion of other elements.1
We and all the living organisms that we know of here on Earth are built out of carbon. Our DNA, our proteins, our hormones, our cell walls. Every bit of biochemical machinery that makes us is built on a scaffolding of carbon. Organic compounds are so prevalent in living things that the distinction between organic vs inorganic chemicals was originally based on whether they had come from a living thing or not.
Carbon is useful in all these ways because each carbon atom can form up to four bonds with other atoms. Carbon can form long chains with other carbon atoms and can also form double and triple bonds not only with itself but with other elements important to Earth life including both oxygen and nitrogen. Silicon is often suggested as a possible substitute for carbon on alien worlds, but silicon is less versatile than carbon and many of its compounds are unstable. This combined with the prevalence of carbon among molecules found in space does not bode well for silicon’s chances. There is however the clay hypothesis that has to do with the beginning of life on Earth.
Another point in carbon’s favor is that by now many complex organic molecules have been detected in space in molecular clouds around stars and on the surfaces of comets. Many of them being the same molecules used by living things here on Earth. With ready-made materials out there in the cosmos, why not take advantage of them?2
Water? I Hardly Know Her
Water is a really great solvent for life on our planet. Besides being everywhere and thus the most logical choice for life solvents, its properties allow both acid and base chemistry to take place. When we begin to consider different temperatures, pressures, and chemical makeup, a number of other solvent options become clear.
All it takes is a solvent that allowed for acid-base chemistry to take place. Water allows this, but there are other solvents that could, under different conditions, or with different commonalities. Waters is ubiquitous on Earth, but it doesn’t have to be on other planets.
Take a look at different solvents. Or familiar gases that would be liquid at other temperatures. The possibilities might surprise you.
Eating Sunshine (And Other Things)
Here on Earth, most ecosystems arise from the energy provided by the Sun. Just about everything either harvests light through photosynthesis or eats something that does. But even on Earth, we know that this is not the only option. In the deepest parts of our oceans, we have found extremophiles that feed off the heat and chemicals released by volcanic vents.
That is just on Earth. There are many sources of energy in the universe including gravity and magnetic fields. Alien life forms could catalyze the synthesis of vital metabolites using alpha and beta particles released by radioactive minerals to catalyze reactions or construct molecular machines on their cell membranes that harvest hydroelectric power.
The Galactic Habitable Zone
It’s weird to think that there might possibly be a shortage of resources on a galactic scale but once you get an idea of how elements are made it begins to make sense.
Basically, there is a band with indeterminate boundaries somewhere between the center of the galaxy and the edge that makes up the galactic habitable zone, a region that is determined by metallicity, the age of the stars, and how often stars in the area go supernova.
The center of the galaxy with its high concentration of stars is considered unsuitable for life, as the frequent supernovae release bursts of radiation that would sterilize nearby worlds and make the development of life difficult, if not impossible. Meanwhile, the edge of the galaxy is full of younger stars that have not had time to transmute the heavier elements that life needs.
All this results in an uncertain band looping around the galaxy where planets are more likely to be habitable. The boundaries of this band are uncertain, but
Turning The Weirdness Dial Up to Eleven
A lot of us tend to base alien species on the species we are familiar with here on Earth. A quick look at some extinct species will show that there are many, many variations on how weird life can get just on a single planet. Just because it didn’t happen HERE doesn’t mean it can’t happen SOMEWHERE.
In all honesty, it just depends on how strictly you want to adhere to known science. You could have aliens with bones like ours with gelatinous flesh or stationary mollusks that spend their days exploring complex algorithms in their minds.
Hard science fiction is all about finding plausible explanations based on what we know now. That doesn’t mean it can’t be weird.
If anything should be clear by now it’s that nothing is. The Milky Way is a big place and we can envision so many possibilities that it is just about impossible to anticipate all the possible variations of life. In fact, I came across so much information while reading this post that I wasn’t able to include it all in this one post. So stay tuned for future posts on the origins of life, panspermia, and whatever else catches my eye in the process.
Unfortunately for myself and other inorganic chemists. Our field is literally defined as “not organic” which makes it more than a little hard for someone to guess what we do.
I’ve come across a wealth of information on this topic and it’s all incredibly facinating. Enough so that I’ll probably have future posts on both on possible origins of life and on the wonderful hydrocarbons that have been found out there in the universe.
Some of these resources may be behind a paywall. Consult your friendly neighborhood librarian for help. Or in the case of research papers, it never hurts to email the author, they may just send you a copy!
Astrobiology: The Study Of The Living Universe by Christopher F. Chyba and Kevin P. Hand. Annu. Rev. Astron. Astrophys. 2005
Astrochemistry: From Astronomy to Astrobiology by Andrew M. Shaw
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Writers want their smart characters to sound smart. Making a character sound smart sounds hard. But really it just requires a surface-level understanding of the topics and an understanding of keywords.
As a scientist (a chemist) and a writer, I understand this challenge well. So I thought I would help by explaining some basic concepts, keywords, and tools used by scientists. This will be the first in a series of posts highlighting interesting parts of science (mainly chemistry) for writers looking to beef up their technobabble.
My own experience and knowledge of chemistry has biased much of this. My fellow scientists who are reading this and feel their favorite topics have been ignored can resolve this grievance by submitting a guest post or leaving a comment.
The “Three” Branches of Science
There are three basic branches of science, but each of them has many subfields and specialties each with it’s own quirks, norms, and standards. Do not mistake these fields as exclusive. Each field may have it’s own focus but in truth the are better at denoting specialties than limits. The lines that separate these fields are becoming blurrier as time goes on and science becomes increasingly interdisciplinary.
Physics – the “most fundamental science” according to Wikipedia. Physics aims to study force, energy, and motion to understand the fundamental laws of the universe.
Chemistry – the “central science.” Chemistry fills a space between physics and biology. Sometimes it is hard to determine where one begins and the other ends. In general, chemistry is concerned with reactions between different chemicals, or analysis of chemicals and their behaviors.
Biology – this field is concerned with the study of living things. Many think of counting fruit flies and dissecting frogs when they think of biology. Much of modern biology shares techniques with biochemistry as scientists have tried to pull apart the secrets of smaller and smaller systems.
Accurate – often confused with precise. To say that something is accurate assumes that there is a “true” value.
Aliquot – a very specific portion taken from a larger sample of liquid sample.
Amino Acids – amino acids are the building blocks of proteins. There are twenty common amino acids and all share some common structural features.
Atoms – atoms consist of a nucleus containing protons and neutrons, and are surrounded by a collection of “orbitals” where the atom’s electrons are found. An atom is composed primarily of empty space.
Atomic Orbitals – regions of space around an atom where an electron is likely to be. Orbitals that farther away from the nucleus contain higher energy electrons.
Bacteria – ubiquitous and mostly harmless microorganisms. Normally we only care about bacteria when we are sick. Bacteria inside our bodies perform many vital functions that are not completely understood.
Deoxyribonucleic Acid – nature’s data storage. DNA tells cells how to build the proteins that keep them functioning.
Elements – an element is a pure substance that contains only one type of atom (not counting isotopes). Elements can now be created artificially. Many of these are unstable and decay quickly, but some researchers have speculated about a potential “island of stability” hiding among the undiscovered high-mass artificial elements.
Evolution – the theory of evolution is a theory, as far too many would like to say. You can read more about that later. But it’s worth remembered that evolution is a fact. If you can’t wait a few million years you can watch it happen in a petri dish. The Theory of Evolution is simply out best explanation of how it works. Another vital thing to remember is that evolution has no pre-determined direction. “Good enough” is enough for nature.
Functional Groups – a segment of a molecule that determines is properties in a reaction. Examples of functional groups include hydroxyl groups, carbonyls, and much more.
Hypothesis – a hypothesis is an educated guess. A scientist takes known information and uses this information to predict what will happen in their experiments.
Inorganic Molecules – defined simply as “not organic,” inorganic molecules can contain both metals and non-metals.
Ions – ions are atoms that have lost or gained electrons and have a positive or negative charge as a result. Paired positive and negative ions form ionic salts.
Isotopes – isotopes are rarer forms of elements that differ in the number of neutrons contained in their nucleus. Natural samples contain a mix of isotopes in different rations depending on purity. Isotopes will vary in atomic mass and stability. These properties make isotopes useful in many applications.
Law – a law describes a known truth about the universe. Theories explain how laws work, laws do not change when a new theory is devised.
Light – both a wave and a particle. Light is a form of electromagnetic radiation. Light interacts with matter in a myriad of interesting ways. Scientists often take advantage of these interactions to study properties of matter that are invisible to the naked eye.
Molecules – molecules are built from atoms. Most things we interact with are some kind of molecule. Bonds within molecules are the result of interactions between electrons and atomic orbitals.
Organic Molecules – the components of gasoline are organic. Organic molecules make up all living things on earth and many dead or inert things as well. Carbon and hydrogen are the primary elements that make up organic molecules.
Peer Review – When a scientists completes a project they write up the results and submit it to a relevant journal in their field. The editor at that journal decides whether the topic is relevant to their publication. If it is, they send the article to reviewers, who are normally other experts in the field. These reviewers look at the article, comment on its merit, and specify what in the article needs to be changed or corrected. An article might go through multiple rounds of corrections before the reviewers decide it is worthy of publication.
Precise – often confused with accurate. Precision is about consistency. Repeated measurements of similar value are said to be precise. We can’t always expect to be accurate, so we aim to be precise instead.
Precipitate – a precipitate is a solid that forms out of a solution.
Proteins – these are how living cells do things. Proteins serve as structural elements, transport molecules, catalysts, and many other things.
Polymers – large chains of molecules constructed from smaller subunits called monomers. Polymers have many useful properties. Kevlar, nylon, spider silk, cellulose, and all plastics are polymers.
Redox Reactions – redox reactions are a huge part of chemistry and biology. The word redox comes from the two related reactions, reduction and oxidation, that are part of every redox system. A useful mnemonic is LEO the lion says GER. Lose Electrons = Oxidation. Gain Electrons = Reduction.
Ribonucleic Acid – DNA’s less popular cousin. RNA carries out several functions inside of a cell. For example, mRNA carries instructions from the nucleus to the ribosome.
Solutions – solutions are everywhere. Solutions have two parts; the solute and the solvent. The solute is a solid that dissolves into a liquid, the solvent. A good rule of thumb when making solutions is that like dissolves like. Polar compounds dissolve in polar solvents, nonpolar compounds dissolve in nonpolar solvents.
Theory – these explain how a particular phenomenon works and why.
Viruses – bits of DNA or RNA bundled up in a shell of proteins and sometimes lipids. Viruses can only survive for a short time outside of a host and reproduce by hijacking the machinery inside of host cells to make more of themselves.
Qualitative – qualitative measurements are somewhat vague. They care about quantities like bigger, smaller, lesser, greater, and so on.
Quantitative – quantitative measurements are exact. They yield a specific number and should have all kinds of statistical analysis to go alongside them.
Quantum – science fiction writers frequently abuse this word. Which is understandable, many trained and experience scientists struggle to grapple with quantum physics because of how unintuitive it is. At this scale the classical physics described by Newton is no longer adequate to model what we observe. So we have a separate branch of physics called quantum physics to describe the behavior of particles on the subatomic scale. Quantum physics is based on probabilities and energy. We can’t nail down the precise location of an electron, but we can determine where it is most likely to be.
Common Laboratory Tools
Balances – many people will recognize these as scales. Many classrooms still used old fashioned balances not unlike the scales found in a doctor’s office. Modern laboratory balances are electronic and can measure mass with a high degree of accuracy.
Dewar – a vacuum insulated container that can be filled with liquid nitrogen, dry ice, or ice water. A dewar is useful for a keeping a sample cold for extended periods.
Gloves – there are two reasons to wear gloves. To protect the scientist from the sample, or to protect the sample from the scientist. The same properties that make many chemicals useful also make them dangerous to human life. Just like many bacteria and viruses that are of interest to scientists are also dangerous. In other cases it is the scientist who could damage the sample. Humans are full of DNA, proteins, and all sorts of other things that could contaminate biological and forensic samples. Gloves are an important part of this. Another important thing to remember about gloves is that the material matters. Nitrile gloves are probably the most common but not all chemicals are compatible with nitrile. Some chemicals may breakdown nitrile or soak right through. Gloves made of other materials are available for those instances.
Glove Boxes – for samples that must be rigorously protected from oxygen, or for samples that may be dangerous to the user, glove boxes are the best option. Glove boxes are exactly what the sound like. A large box, with a glass window and a pair of large rubber gloves. The inside of a glove box is filled with an inert gas like argon or nitrogen.
Heating Mantle – chemists use heating mantles to drive chemical reactions by converting electricity into heat. Heating mantles are controlled by a variac that regulates the supplied voltage. Some heating mantles have a built-in variac, but in most cases the variac is a separate component. Heating mantles are often placed on top of magnetic stir plates.
Hot Plates/Stir Plates – hot plates are another option for heating solutions and materials in lab. Many have a built-in magnetic stirring function that can make a magnetic stir bar inside the reaction vessel spin.
Mortar and Pestle – a frequent component of imagined alchemy labs. Mortar’s and pestles remain useful tools in chemistry and biology labs.
Pipettes – pipettes transfer small volumes of liquids. Some pipettes are carefully calibrated, others are little more than fancy eye droppers.
Spatulas – spatulas are used to move solid chemicals from one place to the other. For example, from the bottle to a balance or from a weigh boat to a reaction flask. Metal spatulas will be common to most undergraduate, but some labs use disposable plastic spatulas.
Syringes – syringes are incredible useful. Biologists may find many uses for syringes in drawing blood or injecting drugs. Syringes are used to work on air free reactions. Syringes are fantastic for piercing septums and adding or subtracting aliquots with minimal interference from surrounding oxygen.
Common Laboratory Instruments and Techniques
Some instruments are available from commercial sources for thousands or millions of dollars. Others are so specific that they need to be custom built by the user.
Centrifugation – centrifuges separate sample components by density. The centrifugal force causes high density sample components to move outward and form layers.
Chromatography – chromatography separates sample components. All chromatography involves a mobile phase and a stationary phase. The mobile phase carries the sample through the stationary phase. As the sample interacts with the solid phase it becomes separated into its components. Many techniques pair chromatography with another analytical technique such a spectroscopy or mass spectrometry.
Electrophoresis – electrophoresis describes the movement of charged particles in an electric field. Multiple separation techniques use electrophoresis to separate sample components such as gel electrophoresis or capillary electrophoresis.
Fluorescence Spectroscopy – some molecules absorb light at one wavelength and emit light at another. Fluorescence is useful in many instances and especially in biology and biochemistry. The strong signal given by fluorescence makes it easy to distinguish from background noise. This is its main advantage over absorbance spectroscopy.
Infrared Spectroscopy (IR) -heat is transmitted through infrared waves. When those waves hit a molecule, parts of that molecule vibrate in characteristic ways. These vibrations are like finger prints for different functional groups.
Nuclear Magnetic Resonance Spectroscopy(NMR) – probably one of the most useful instruments in modern chemistry. Nuclear Magnetic Resonance takes advantage of the “spin” that is an inherent property of subatomic molecules like protons and electrons. Basically they behave like tiny magnets. An individual spin has a value of either +1 or -1 and when opposite spins are paired these spins cancel each other. Certain isotopes of common elements have an odd number of subatomic particles in their nucleus resulting in a non-zero spin. NMR works by placing a sample inside of a magnetic field. The unpaired spins then align with the field and the instrument hits the sample with radio waves of a specific frequency. The unpaired spins then flip as they absorb the energy from the radio waves and release energy as they return to their original orientation. The environment surrounding each unpaired spin affects the signal they emit, allowing us to determine the structure of molecules. Proton and Carbon 13 NMR are most common, but isotopes of Oxygen, Fluorine, Phosphorus, and more can also be targeted. Special, expensive solvents have to be used for liquid samples to avoid interferance. The same technology is also used in MRI except in this case the density of spins is used rather than the individual behavior of those spins.
Mass Spectrometry(MS) – another incredibly useful instrument in modern science. Mass spectrometry begins by injecting a sample, ionizing it, and shooting it at a charged plate. This results in peaks that show us the mass-to-charge ratio. Mass spectrometry can do a lot. So much that mass spectrometry research almost constitutes its own subfield, but it is useful to all other niches of chemistry.
Ultraviolent/Visible Spectroscopy(UV/Vis) – UV/Vis instruments are used to study a sample’s interactions with light in the visible and ultraviolet range. There are two basic types of readings we can get from this: absorbance and transmission. Absorbance is how much light the sample absorbs, transmission is how much light passes through the sample. Accurate readings depend on knowing the emission profile of the light source. Basic instruments assume that this profile is constant, more sophisticated instruments take constant readings of the light source. Interference in these experiments may come from fluorescence in the sample or form surrounding light sources.
X-Ray Spectroscopy – of all the electromagnetic waves X-Rays contain the most energy and are the most destructive. These high energy rays frequently ignore anything outside the nucleus. Various forms of X-Ray spectroscopy are used to determine the structures of solid crystals and identifying the elements and isotopes in a sample.