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My first thought is Obsidian. There are problems with this; it's a volcanic glass, and you're in a desert, but conceptually, the idea is reasonably sound.

I'm going to assume for the purposes of my answer that by 'desert', you mean a hot, dry sandy desert like the Sahara or Gobi, not the strict definition of a place with no rainfall that could also include Antarctica. I'm inferring from your question you're only looking at places with lots of sand and hot days.

In many countries, we use double glazing as an insulative material. There are even now triple glazing products, which effectively put 2 air pockets, or vacuums, between you and the elements. It's suprisingly effective, although obviously not as effective as walls with thick insulation bats. That said, if your inhabitants can shape a heavily tinted glass like obsidian or even manufacture it from the sand around them, then they can build homes with shelter from the sun via double or triple glazing using glass like obsidian which is (more or less) opaque.

Glass houses in the desert are a bad idea because of the greenhouse effect - the sunlight getting in gets trapped and heats up the internal areas of the glass house even further. Great if you're growing tropical plants in Scotland, terrible as a desert housing solution. What obsidian would offer is the ability to block the sun from getting in in the first place. You get shade which in the desert is important. What you don't get is a shelter medium that can breathe, and release the trapped heat. Glass can act as a thermal mass though, which could actually work in your favour on this point.

Deserts are known for being hot through the day, but they're also very cold at night. Why? because they have no water around them, meaning a very low thermal mass. Your obsidian would spend the day baking in the sun, retaining heat. because you've double glazed, you won't feel that heat until early evening, but through the night it starts to release it, meaning that it actually serve to keep you warm through the night, when the desert is bitterly cold.

So, if you do it right, all you've really got to do is introduce impurities into your glass that turn it black or some other colour, then build your homes with air gaps between panels, and you have a good chance of building homes that can regulate temperature reasonably well. You're still going to be hot during the day, cold at night, but not as much as you'd otherwise be.

You Need a Windcatcher House

Sheets of glass for the most part is not a great building material. Glass in the form of bricks can be structural, which will allow you to build up. You could build a glass house and yes, it would get hot in the desert. But proper desert homes don't get hot. Instead of building a house with four walls and a pitched roof, you just need to incorporate a few features to make your desert home comfortable.

You Need a Windcatcher

A windcatcher, also known as a malqaf, is a tower higher than the rest of the structure which has a shaft that leads from the tower to the living facility. The open face faces the prevailing wind, which catches it and pulls it down the tower, which cools your glass structure. The windcatcher does not necessarily cool the air itself, but rather relies on the rate of airflow to provide a cooling effect. They have been used in desert climates for thousands of years.

How about Making Ice?

You might find that this structure cools your home, but you want an extra blast of cooling for water storage, food storage or making ice, using only the wind. What you need to do is add another tower which faces the opposite direction of the prevailing wind. With this tower, the wind is drawn upward using the Coandă effect.

It's more effective with a basement and if your settlement is feeling industrious, an underground water channel with holes spaced along the length of the channel to the basement of each home. The ancient Persians called this channel a qanat.

• https://en.wikipedia.org/wiki/Coand%C4%83_effect


• https://en.wikipedia.org/wiki/Windcatcher


• https://en.wikipedia.org/wiki/Yakhch%C4%81l


• https://en.wikipedia.org/wiki/Qanat

This combination of design elements will keep your desert homes much more manageable and energy efficient because you're not spending resources on active cooling. It's passive and it works.

Good luck staying warm.

Problems

Reflection: Just as swimming will burn you faster than sunbathing (light reflecting off the water), light reflecting off the glass simply means that much more light to burn you.

• Solution: buff the glass to reduce reflection.

Refraction: There could easily be spots in the city, despite all efforts, that act as magnifying glasses (ants... magnifying glass... mine was a sordid childhood). Corners are your biggest problem, but any angle can create magnifying refraction. It doesn't actually need a curve (curves create precision for, e.g., distortionless vision, but any type of "bulge" will cause magnifying refraction).

• Solution: cut insets that break or redirect (like a prism) the "flow" of light through the glass.




• Solution: Color the glass to increase its opacity.

Benefits

Visibility: You can see your enemy coming! You can see where they are outside the wall! They can also see you taking a shower... so it might not be that much of a benefit.

• If this is desirable, then the previous solutions must be used carefully or the visibility is lost.

What is it about a glass city that intrigues you? The fact that it's glass? The transparency? The shiny reflection as the sun rises?

This is a very important question, because it will dictate how you solve your problem. BUT! There's one solution that might give you everything you want.

Thin silvering

Silvering glass is what makes mirrors. Thin silvering (silvering you can see through) is that makes one-way mirrors. So, anywhere in the city that wants privacy, you apply thin silvering inside that place or room. Thus, people can't see in, but they can see out. Light can't burn through into the room — but it would cause a horrible headache for anyone approaching from the wrong angle.

And if you really want to take advantage of that, use prisms as building roofs such that the light of the morning is redirected and cast behind the city, and vice-versa for the evening. Thus, between the prisms and the silvering, there isn't an approach to the city that isn't blinding.

Please note that I've made a few assumptions as to why you asked your question. If my assumptions are wrong, let me know and I'll adjust my answer.

Oh... and your buildings are going to want a LOT of ventilation. Preferably from holes dug deep in the sand. Really deep. But that's just an issue of construction.

Look at how termites in Africa build their colonies. To prevent from being cooked inside their homes, they build tall chimney like structures. The sun heats the chimneys, causing air circulation throughout the colony.

If your cities utilize a similar design, the city could remain fairly comfortable at the base levels. You use these convection currents throughout your city for other functions as it suits you.

https://www.sciencemag.org/news/2015/08/how-termite-mounds-breathe
here is a little article that may help.

Okay so other answers have touched on windcatchers, and yes, great idea to include this; mainly because it gives you the opportunity to make 100 meter tall glass spires.

But if you want, there might be another couple of cool little worldbuilding devices you can use.

What if they used slag glass to make most of their buildings? This stuff is the result of impurities such as iron oxide or copper. It's fairly opaque, and very beautiful.

However since the city resides on a desert of near perfect purity, they have a huge import of metalwork byproducts. This way the city can be referenced in political and economic dialogues with references to 'slag export'.

This will also allow the glass city to be extremely colorful as slag glass comes in all colors, depending solely on the type of impurity.

Tim has a very good answer about the pros (thermal mass) and cons (greenhouse effect, insulation) of glass and if you are dedicated to the idea of using glass I don't have much to add. However, I don't believe the root of your question was a city of transparent skyscrapers and comes more from the idea of building structures from the most readily available material: sand. If that is the case I'd like to draw your attention to the alternative of Rammed Earth.

Rammed earth is a construction concepts that basically boils down to creating man-made sandstone with sand and aggregates being primary ingredients. It has many of the same thermal properties as Tim discussed with Obsidian with the bonus of being considerably more structural, naturally insulated, and opaque. Most of the Great Wall of China was constructed using rammed earth and it's historically been a popular building method in the Australian outback. The only thing you'd need to figure out/explain away is a binding agent (typically clay or cement) which are less available in desert environments.

Glass is not out of the question here (everybody loves windows) just providing options.

It'll be fine, because your glass will be opaque, because of sandstorms.

To cite one reference:

Objects made of glass (such as automobile windshields) gradually lose
their transparency, first becoming pitted, then frosted, when exposed
to sand-blasting winds.

How about sand sandwiched between layers of glasses?

It will take care of the heating issues. Also desert doesn't have a solid foundation to build upon, how about using huge chunks of glasses as a foundation for your city? It will give you interesting options of having caverns made of glass.

You can build your structures out of dichroic glass.

The external structure can reflect IR coming in, while the inner structure can pass it outbound as necessary. It's the equivalent of the thermal film you can get for windows in this world, where they reflect heat but allow visible light to pass.

Since most of the heat from sunlight is in the form of IR, make the glass either absorb or reflect it. Also use a dome with shades that move as the sun moves across the sky blocking some of the visible light. Give the building a double wall with an air gap in middle, allowing the air to enter at the bottom and exit out the top and up a chimney to extract the extra heat. Use plants inside to help cool the temperature and provide some of the food for the residents. Last build some or most of the buildings underground leaving only a portion of it exposed to the sun.

I like the idea and while you have listed out several problems, I don't think these are factors that would stop such a city from existing.

One thing I would like to point out is that glass can be colored in many ways which can reduce the amount of solar radiation that comes into any building. Additionally if there are layers of platforms of glass that reduce the amount of light while providing a mechanism for harvesting energy. The space between the layers can allow for convection cooling and actually if the city is designed as a single unit or multiple smaller units, this could help to provide a cooling breeze as heat tries to escape upwards. This could also be used to provide heated water or cooking as well as more modern forms of energy harvesting like thermal electric or steam to drive turbines or small Stirling engines.

If light could be trapped into a highly precisely shaped diamond type structure or something with mirrors it is feasible that some optical energy could be stored until later

Another point is that while the main building block may be glass, no city on earth is a single material. Even when building were mostly wooden there was some clay, leaves etc that were also used. It would not be unlikely for imported, or rarer materials to be included. For example, modern houses tend to use tar shingles or tin. Maybe sandstone slabs/shingles might be used. It could be reflected away for energy harvesting as well. Imagine maybe having mirrors that reflect the light into a smaller tube like optical pipe to carry high amounts of solar energy to a point to be harvested as thermal or electrical energy.

One thing that might be a problem is cool nights. Infrared light may leak out through the glass depending on the optical and thermal properties.

I would like to give you one suggestion. When you think of sand giving you glass i recommend you to just think little further of making solar panels from silica instead of glass and lots of it to create the outer surface of what ever you want and also get electricity as a resource for further improvement.

You're asking:

Is there any way I can have a city of glass in the desert without cooking its denizens?

When in fact, what you need to ask is this:

Is there any way I can have a city of glass in the desert?

And the answer to that, unfortunately, is no.

The reason is your misconception that:

sand can become glass

While true in theory silica glass does exist, it is different to what most people would call "glass".

Sand is one component of glass, not the only component of glass.

The other components, are sodium, calcium, and aluminium (when fused together, form soda-lime aluminosilicate glass. This is going to be a problem in a sandy desert when all you have is sand (=silica quartz). You will need to obtain the other component either by mining (possibly granite mountains) or by trade.

My guess would be not to melt the sand completely, but rather mix it with some resin of sort to make engineered stone, or artificial stone. If your desert conditions allow it, you may add some sort of resin to the sand, though sand would still make the bulk of the material. Plus, it is opaque, and much lighter in color. This would allow it to absorb less heat that would bake the residents alive.

There is an attempt to use bacteria to 'grow' desert sand into hard structures.

TED talk: https://www.ted.com/talks/magnus_larsson_turning_dunes_into_architecture?language=en

https://blogs.scientificamerican.com/news-blog/stopping-desertification-with-bacte-2009-07-24/

Your question doesn't specify that the city is above-ground either so I would suggest looking into Frank Herbert's book Dune for examples of living in the desert.

However, the concern has come up that it would bake the citizens
alive.

Only if it is sufficiently hot or with enough radiant energy falling into it.

If it is a cold desert, or a desert on/near the far side of a tidally-lock world, I suppose getting backed through the glass wouldn't be an issue.

Additionally, the city could be made of convex panels that diffuse incoming light, and the panels could be arranged in multiple lattices separated in vacuum for insulation.

Furthermore, if the plot permits it, the glass would not need to be transparent. It could be opaque. Heck, it could be mirrors reflecting light outwards.