**Short answer**

 - Fan: Aluminum, titanium, or stainless steel

 - Compressor: Nickel-, cobalt-, or iron-based alloys. Additive are aluminum and/or titanium, chromium, as well as rare earth elements like yttrium.

 - Combustion chamber: Superalloys with refractory metals such as tungsten, molybdenum, niobium, tantalum. Ceramics and ceramic-metal mixes.

 - Turbine: Nickel-based superalloy, outside air is circulated through channels inside of the turbine blades. For lower pressure turbine blades iron-based superalloy or even stainless steel. The metals used for turbine blades are often grown as a single crystal.

 - Exhaust nozzle: Nickel Inconel and stainless steel alloys.

 - Casing: Aluminum or polymer matrix materials.


[![enter image description here][3]][3]

The high-pressure turbine is, with the combustion chamber, very hot (more than the exhaust nozzle). You may read this [Wikipedia article][1] which has a short list of materials used for turbine blades (with [alloys names][2] and cooling techniques).

----

The fan pushes about one ton of cold air in the engine every second in high power turbofans. This is why temperatures and pressures can be so large after compression and after combustion.

All quotes are from [Nasa Guide To Engines][4], 2007.

> In 1903, the Wright brothers built an aluminum
> block engine because of its light weight compared to cast iron. Its
> melting point of 660 °C was well above the engine’s operating
> temperature, so for them it was a good choice. However, aluminum could
> not be used in the hotter parts of a turbine engine where temperatures
> reach of 1800 °C or more because it would melt.

**Fan**

> This typically does
> not get very hot (<150 °C) so aluminum, titanium, or stainless steel
> are all suitable for the fan blades. Most engines use titanium because
> it has a high strength-to-weight ratio, is corrosion and fatigue
> resistant, and would be able to withstand the impact of a bird strike.

[Fan example][5] (with a fan blade missing after the engine blew apart).

**Compressor section**

> The pressure of the air can be raised up to 30 times and the
> temperature, depending on the number of stages in the compressor, can
> rise to 1000 °C. Here the materials must have high strength at high
> temperatures; must resist fatigue, cracking, and oxidation; and also
> must resist “creep.” Creep is the tendency of a material to slowly
> change shape when stressed at high temperature. Since no single metal
> would have all the desired properties, an alloy (a mixture of metals)
> is used. Very high- temperature alloys are called superalloys and are
> generally nickel-, cobalt-, or iron-based alloys. Aluminum and/or
> titanium are added for strength, and chromium, as well as rare earth
> elements like yttrium, are added to improve corrosion resistance.

[Compressor example][6] (high pressure rotors)

**Combustion chamber**

> Temperatures can exceed 1800 °C and again superalloys are used, but
> without the titanium or aluminum for strength because there are no
> moving parts. Instead, refractory metals are often added to a
> superalloy. These are metals of unusually high resistance to heat,
> corrosion, and wear such as tungsten, molybdenum, niobium, tantalum,
> and rhenium. They are used in alloys and not as pure metals because
> they are among the densest of all the elements, a negative property
> when it comes to aircraft that need to keep weight to a minimum.
> Ceramics and ceramic-metal mixes are also used here because of their
> high heat resistance. We are familiar with pottery, tile, crucibles,
> and fire bricks as types of ceramics. They have very high melting
> points and don’t require the cooling systems like those needed to keep
> metals from melting so they make for lighter, less complicated engine
> parts. The down side is that they tend to fracture under stress, so
> engineers seek to create new ceramics composites that incorporate
> other materials to improve properties.

[Combustion chamber example][7]

**Turbine**

[![enter image description here][8]][8]  

<sup>High-pressure turbine blade (source: [Wikipedia][9])</sup>

> The first set of turbine blades are in the highest pressure, hottest
> part of the gas flow and are generally made of nickel-based superalloy
> or ceramic blades. Unheated outside air is circulated through channels
> inside of the turbine blades to keep them from melting in this extreme
> environment. Further down the engine lower pressure turbine blades
> often sit. Since the gases have somewhat cooled by this point, the
> blades can be made of iron-based superalloy or even stainless steel.
> It is interesting to note that for strength, the metals used for
> turbine blades are often grown as a single crystal. A close look at
> most metals and alloys show that they are composed of crystals (also
> called “grains”), and the places where the crystals meet are called
> grain boundaries. A material is weaker at the grain boundaries than
> within the grains—especially at high temperatures— so turbine blades
> fashioned from metal formed as a single grain (no boundaries) are
> stronger.

See [single crystal material][10] (known as *monocrystalline* material in electronics) .

[Turbine example][11] (high pressure stator)

**Exhaust**

[![enter image description here][12]][12]  

<sup>Exhaust from Boeing 787 engine (GEnx, one of the world's largest jet engine - [Source][13])</sup>

From [FAA Aviation Maintenance Technician Handbook - FAA-8083-30][14]:

> Inconel and stainless steel alloys. The Inconel [nickel-chromium-iron]
> alloys are frequently used in turbine engines because of their ability
> to maintain their strength and corrosion resistance under extremely
> high temperature conditions.

See [Inconel details][15].

**Casing**

> Although it need not withstand high temperatures like the core of the
> turbine, the materials here need to be strong enough that if a blade
> were to break off it would be contained within the casing and not
> enter the wing or cabin of the aircraft and cause further damage.
> Aluminum or some polymer matrix materials are used as engine casings.


  [1]: https://en.wikipedia.org/wiki/Turbine_blade
  [2]: https://en.wikipedia.org/wiki/Turbine_blade#List_of_turbine_blade_materials
  [3]: https://i.sstatic.net/YTCpLax7.png
  [4]: http://er.jsc.nasa.gov/seh/ANASAGUIDETOENGINES%5B1%5D.pdf
  [5]: https://i.dailymail.co.uk/1/2018/04/20/02/2739414-5632767-The_FAA_has_ordered_ultrasonic_inspections_of_fan_blades_on_some-a-5_1524187433507.jpg
  [6]: https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/CFM56_High_Pressure_Compressor_Rotor.JPG/800px-CFM56_High_Pressure_Compressor_Rotor.JPG
  [7]: https://leehamnews.com/wp-content/uploads/2016/12/TAPS-combustor-larger.png
  [8]: https://i.sstatic.net/YKcxt.jpg
  [9]: https://en.wikipedia.org/wiki/Components_of_jet_engines
  [10]: http://www.appropedia.org/Single_Crystal_Turbine_Blades
  [11]: https://upload.wikimedia.org/wikipedia/commons/thumb/b/b7/CFM56_High_Pressure_Turbine_Vane.JPG/800px-CFM56_High_Pressure_Turbine_Vane.JPG
  [12]: https://i.sstatic.net/bZnn0.jpg
  [13]: https://blogs.mentor.com/jvandomelen/blog/2010/07/30/ultra-fast-power-switching-coming-soon-to-a-plane-near-you/
  [14]: https://www.faa.gov/regulations_policies/handbooks_manuals/aircraft/amt_handbook/media/FAA-8083-30_Ch05.pdf
  [15]: http://www.altempalloys.com/inconel-alloys.html