https://steelwatch.org/wp-content/uploads/2025/04/2504_MetCoal-1.pdf
Sunday, 12 April 2026
Metallurgical Coal: Price, Coking Coal, Uses, Production, vs Thermal Coal, India & Global Market
Metallurgical coal or coking coal is a grade of coal that can be used to produce good-quality coke.
Coke is an essential fuel and reactant in the blast furnace process for primary steelmaking. The demand for metallurgical coal is highly coupled to the demand for steel. Primary steelmaking companies often have a division that produces coal for coking, to ensure a stable and low-cost supply.
Metallurgical coal comes mainly from Canada, the United States, and Australia, with Australia exporting 58% of seaborne trade, mostly going to China. In the United States, the electric power sector used "93% of total U.S. coal consumption between 2007 and 2018"; only 7% of the total was metallurgical coal and coal for other uses such as heating.
Characteristics
Metallurgical coal is low in ash, moisture, sulfur and phosphorus content, and its rank is usually bituminous. Some grades of anthracite coal are used for sintering, pulverized coal injection, direct blast furnace charge, pelletizing, and in production of ferro-alloys, silicon-manganese, calcium-carbide and silicon-carbide. Metallurgical coal produces strong, low-density coke when it is heated in a low-oxygen environment. On heating, the coal softens, and volatile components evaporate and escape through pores in the mass. During coking, the material swells and increases in volume.
The coking ability of coal is related to its physical properties such as its rank, but laboratory testing is required to completely evaluate the coking ability of a coal. The strength and density of coke are particularly important when it is used in a blast furnace, as the coke supports part of the ore and flux burden inside the furnace. Metallurgical coal contrasts with thermal coal, which does not produce coke when heated. Because of their different end-uses, prices for the two types of coal are usually quite different.
The suitability of coal for conversion to coke is also referred to as the caking ability.
Types
There are several types of metallurgical coal:
- Hard coking coals (HCC)
- Medium coking coal (MCC)
- Semi-soft coking coal (SSCC)
- Pulverized coal for injection (PCI) coal
Metallurgical coal – often shortened to ‘met coal’ – is coal that is used in making iron and steel. Making iron in blast furnaces, using met coal, accounts for the majority of steel sector emissions.
Beyond the circle of industry specialists, met coal has little public visibility. Definitions of what exactly constitutes met coal are varied and confusing.
Despite being a significant contributor to climate change, met coal barely features in discussions at climate meetings, or in setting targets to phase out fossil fuel. Phasing out of coal has focused on reducing the use of ‘thermal coal’ – coal used in power plants.
This SteelWatch Explainer sets out: How met coal is defined; Where met coal is produced and used; Why it is a major problem for climate; Why it is coming under greater scrutiny; How lobbying attempts to defend continued use of met coal, camouflaging it with terminology.
What is met coal?
Met coal is coal used to make metals. It is principally used for reducing iron ore to iron in blast furnaces, before iron is made into steel. Over one billion tonnes per year of met coal are produced each year, and it accounts for around 14% of total global coal consumption.
Met coal and thermal coal
The core distinction between ‘met coal’ and ‘thermal coal’ is the purpose for which they are used. Met coal is used for making iron, and thermal coal is used for generating power. These different usages relate to differences in physical properties, such as met coal having higher carbon content and lower moisture content. This higher quality coal is more expensive, and it generally makes commercial sense to use it as met coal rather than burning it for power generation. But these physical differences are not rigid categories: they lie on a spectrum, with some overlaps. In particular, the lower quality met coal can be re-routed to be used as thermal coal instead.
Met coal and coking coal
The International Energy Agency (IEA) defines metallurgical coal as a group of coal products comprising “coking coal, semi-soft coal, and pulverised coal injection coal.” Confusingly, though erroneously, the terms ‘met coal’ and ‘coking coal’ are sometimes used interchangeably.
Recent data shows that coking coal accounts for around two thirds of met coal. Coking coal is converted to coke (or ‘met coke’) in coke ovens, before it is fed into the blast furnace, where it is indispensable.
Non-coking coal, accounting for the other third of met coal, includes pulverised coal injection (PCI) coal products and semi-soft coal. PCI coal is used in the blast furnace for operational and economic benefits, while semi-soft coal is used in the coke ovens along with coking coal to produce coke and also blended with PCI coal in the blast furnace. These coals are less distinct in their properties from thermal coal, and are the constituents of met coal that are most likely to be used instead as thermal coal. When non coking coal is used for thermal purposes, it no longer counts as met coal.
Why coal became central to iron and steel making
The history and geography of steel since the Industrial Revolution is intertwined with the mass exploitation of coal.
Blast furnaces, since their first appearance in the 12th century and for hundreds of years, relied on charcoal made from wood. Up to the 1700s, iron and steelmakers used charcoal both in their furnaces and to ‘carburise’ iron.
In 1709, Abraham Darby perfected the use of coke in a blast furnace to produce pig iron for pots and kettles. This new technique helped boost production, leading to further demand for coal and coke. As the industrial revolution took hold, iron and steelmaking developed in close proximity to coal mines. Then as global steel production spread in the 20th century, countries like the USA, China and India expanded their met coal mining while countries such as Japan and South Korea that depleted or lacked their own coal had to develop supply chains to import coal.
Today, 70% of steel produced globally is made in around 400 integrated steel mills that rely on met coal. This most widely spread steel production process is known as BF-BOF, where coking coal is heated to produce coke that is then fed into blast furnaces to produce iron, the prime ingredient of steel. Molten iron is fed from the blast furnace into a basic oxygen furnace (BOF) to make steel. Today’s large-scale blast furnaces, typically exceeding 1 Mtpa capacity – the largest can have over 5 Mtpa capacity – cannot operate without coal.
Met coal’s heavy climate impact
The use of met coal in iron and steelmaking is itself a significant contributor to climate change. The blast furnace produces more CO2 than iron, by weight. Transforming coal into coke (by heating it at high temperatures); burning it in the blast furnace; and processing the resulting iron into steel, means that for every tonne of steel produced, 2.3 tonnes of CO2 is emitted.
This alone means met coal has a massive carbon footprint, making it a major driver of the climate crisis.
But this is compounded by the vast quantities of methane released during its mining. Met coal is generally mined from deep underground where there is higher density of methane. Methane leaks are a frequent byproduct and are rarely well measured or reported. Methane emissions from met coal mining are estimated to be three times higher than for thermal coal. There is also a greater safety risk from explosions.
A 2022 report by the IEA estimated that methane leakage from met coal mining amounts to around 1 gigatonne of CO2e (carbon dioxide equivalent) per annum. Due to paucity of data on this phenomenon, most emissions statistics on coal-based iron and steelmaking ignore these methane emissions. If they were factored in, we estimate that steel production via the BF-BOF route emits 4.2 gigatonnes of CO2e per year. That would result in a very high emissions intensity of over 3 tonnes of CO2e per tonne of steel produced via the BF-BOF route.
In addition to its climate impact, met coal mining also impacts on biodiversity, air quality, human rights, and workers’ lives. For instance, in August 2023 a fire in a met coal mine in Kazakhstan owned by steelmaker ArcelorMittal killed five workers, and later in October a methane explosion killed 46 workers in the same mine.
Where is met coal mined, exported and imported?
According to the IEA, global met coal production in 2023 amounted to 1107 million tonnes, accounting for 12.3% of global coal production.
China is by far the largest producer, supplying its own steel industry and importing additional quantities to meet its needs. Internationally traded volumes represent a minority (32%) of total production. Australia dominates this category, accounting for around about 50% of global exports. The main importers are China, India, Europe and Japan.
At the company level, met coal is largely produced by global mining and trading giants such as BHP-Mitsubishi Alliance and Glencore. However, steelmakers such as Nippon Steel (Japan), POSCO (South Korea), MMK (Russia), SAIL (India), JSW Steel (India) and RINL (India) also have stakes in met coal mines. The investments by Nippon Steel and POSCO reflect the fact that these steelmakers rely heavily on met coal, but cannot count on domestic coal supplies.
For example, in 2023, Nippon Steel acquired 20% of Teck Resources Ltd, which describes itself as the “second largest producer of high-quality steelmaking (coking) coal in the world” (the remainder of Teck is owned by Glencore (77%) and POSCO (3%). Teck mines produce around 27 million tonnes/year. Nippon Steel argued that the acquisition would stabilise its profits by “ensuring resilience to externalities” affecting costs and supply in the global coal market.
Met coal mining is still expanding
Back in 2021, the IEA stated that if the world is to hit its target of net zero emissions by 2050, there must be no new coal mines, or coal mine lifetime extensions.
However, met coal mines are currently still expanding, driven by companies like Glencore, Mitsubishi Corporation, Teck Resources, BHP group and Whitehaven Coal. The expansion is well-financed by banks and investors. In the seven years from 2016 to 2023, finance for met coal expansion totalled USD557 billion (excluding finance received by Chinese companies). As of June 2023, investors that owned USD163 billion worth of the 50 largest met coal developers (excluding Chinese companies), included BlackRock (holding 11%), Vanguard (10%), and Japan’s Government Pension Investment Fund (5%).
Met coal-related methane emissions could increase by 7% by 2030 if all proposed projects that have announced a 2030 start date are developed, and up to 20%, if proposed projects without starting dates also go into development.
Met coal has been missing from the climate debate
Staying within the limits enshrined in the Paris Agreement will require a phase-out of all types of coal. While strides have been made in circumscribing the use of thermal coal, met coal has largely been sheltered from these efforts. In part, this is because of strategic lobbying by the steel and mining industries suggesting that there is no alternative to coal-based iron and steelmaking, unlike thermal coal, which is increasingly being replaced as an energy source by renewables.
Studies by Reclaim Finance’s Coal Policy Tool showed that, while 46% of the 300 major financial institutions surveyed have adopted a climate policy to restrict financing of thermal coal, only 14 such policies specifically cover the financing of met coal, and only one (Zurich Insurance) has a robust exclusion policies on the expansion of met coal.
But pressure is mounting. German campaign group Urgewald’s Met Coal Exit List (MCEL) spotlights 252 met coal mining projects run by 160 companies in 18 different countries, putting pressure on lenders to stop funding them. Now Zurich Insurance has become the first global player to stop insuring the expansion of met coal.
An industry on the defensive
Some industry actors are trying to polish the image of met coal, and maintain it as a safe haven for coal investment and expansion at a time when thermal coal is starting to be phased out.
Some companies suggest met coal is fundamentally different from other coal, calling it ‘good’ coal, or even trying to rebrand it by using new terms. Glencore, for example, uses the term “coal and carbon steel materials”. Don Lindsay, ex-CEO of Teck, claimed that investors were undervaluing the company because “they don’t distinguish between the good coal and the bad coal. Steelmaking coal is absolutely vital for decarbonisation, but they don’t care.” These terms such as “Steelmaking coal” and “carbon steel materials” are industry terms that seek to make met coal more acceptable and thus less susceptible for pressure for fossil-fuel phase out.
Met coal is defended on the grounds it is indispensable for steelmaking. FutureCoal, an industry lobby group, says it is “a crucial component in steel production and industrial growth.” As recently as August 2024, the Japanese steelmaker Nippon Steel claimed in its quarterly earnings release that even “carbon neutral production processes will require a certain amount of coking coal”. Coal industries of Australia, New Zealand and most recently of the USA have been pushing to declare met coal a critical raw material.
This is disingenuous: all coal is coal, with serious climate impacts. And while steelmaking is indeed a vital part of a greener future, it does not need to depend on coal.
Variations on this narrative emphasise that steel by definition is an alloy of iron and carbon, and that because finished steel contains carbon, coal will always be needed to produce it. This argument doesn’t hold water: the amount of carbon in steel can range from 0.25% – 2%, depending on quality and hardness of the steel. Such small amounts can be sourced from coal, gas or even biological sources and can be added at ironmaking or steelmaking stage. This requirement does not justify using 770kg of coal per 1000kg of steel.
A future for steel beyond met coal
Deep decarbonisation of iron and steelmaking is absolutely essential if we are to meet internationally agreed climate targets.
Achieving this means retiring blast furnaces and the use of coal completely from the steelmaking process. In practice, this means both increasing the share of steel produced with scrap in an electric arc furnace (EAF), and adopting different techniques for making iron.
Specifically, the latter involves rapidly expanding the use of new production methods which can do without the use of coal-based blast furnaces. Today, this means making virgin iron using the direct reduction of iron ore (DRI) process. Already, a small but growing quantity of iron is made via DRI process, so far mainly with fossil gas as the input, resulting in a substantial cut in emissions. But a much greater prize comes from substituting the fossil gas with green hydrogen produced with renewable energy, at which point near-zero emissions steel production becomes possible. The first successful production of steel using this method was in 2021.
The green hydrogen-based DRI method (green H2-DRI) is now being installed in the first large-scale steel plants that are scheduled to enter production in 2026.
Met coal: changing the narrative
It is time to recognise that met coal is a key part of steel’s climate problem, and is not indispensable.
Policymakers, investors and the industry need to pay attention to met coal and how it is phased out of steelmaking:
Coal mining, ironmaking and steelmaking companies need to adopt more transparent monitoring and measuring of met coal emissions, invest in immediate actions to cut emissions, and finalise plans to transition out of coal.
Regulators and policy makers need to be aware of the climate impacts of met coal, and not be misled into giving it special status by industry claims that it is essential or ‘better’ coal;
Financiers need to strengthen financial exclusions on met coal to match those on thermal coal. Until then, they should be aware that the term ‘met coal’ can be used to bypass their exclusions, by ‘camouflaging’ coal that may end up as thermal coal in power plants, cement plants or petrochemical factories.
The renewable energy, iron mining and steelmaking industries, alongside policymakers, need to invest in the transformation of ironmaking to a fully renewable-powered coal-free process as part of our emerging zero emissions economy.
Met coal is coal, pure and simple, with climate impacts that match or exceed thermal coal. Meeting climate targets means phasing it out, completely.
See also
Coal § Coke
Metallurgy
Coal analysis
Lignite
References
Paula Baker (2013-06-10). "The Coal Facts: thermal coal vs. metallurgical coal". Global News. Archived from the original on 2013-06-13.
"Coking-Steel Production Alternatives".
"How Steel Is Produced". 14 December 2020.
"Coke Production for Blast Furnace Ironmaking". Archived from the original on 2017-02-08. Retrieved 2017-03-05.
Reed Moyer, Competition in the Midwestern Coal Industry, Harvard University Press, 1964 ISBN 0674154002, page 56, pages 85-86
Uren, David (14 September 2021). "China's Ban on Australian Coal Reshapes Key Dry Bulk Market". The Maritime Executive.
"U.S. coal consumption in 2018 expected to be the lowest in 39 years - Today in Energy - U.S. Energy Information Administration (EIA)". www.eia.gov. Retrieved 2019-01-25.
"What is Metallurgical Coal".
Bell, Terence (2017-05-05). "How Is Metallurgical Coal—Coking Coal—Used?". The Balance.
Satyendra Kumar Sarna (2018-09-25). "Metallurgical Coal". IspatGuru. Retrieved 2019-10-05.
"Different types of Coal". underground COAL. Retrieved 2019-10-05.
Saturday, 28 March 2026
MSE 639 Interfaces and Materials Properties, mid sem, question paper and solution
MSE 639 Interfaces and Materials Properties, mid sem, question paper and solutions
MSE 639 Interfaces and Materials Properties, mid sem, question paper and solution
MSE 639 Interfaces and Materials Properties, previous year question paper, quiz, mid sem, end sem paper, assignments
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| MSE 639 Interfaces and Materials Properties, previous year question paper, quiz, mid sem, end sem paper, assignments |
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| MSE 639 Interfaces and Materials Properties, previous year question paper, quiz, mid sem, end sem paper, assignments |
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| MSE 639 Interfaces and Materials Properties, previous year question paper, quiz, mid sem, end sem paper, assignments |
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| MSE 639 Interfaces and Materials Properties, previous year question paper, quiz, mid sem, end sem paper, assignments |
MSE 639 Interfaces and Materials Properties, previous year question paper, quiz, mid sem, end sem paper, assignments
MSE 639 Interfaces and Materials Properties, previous year question paper, quiz, mid sem, end sem paper, assignments
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| MSE 639 Interfaces and Materials Properties, previous year question paper, quiz, mid sem, end sem paper, assignments |
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| MSE 639 Interfaces and Materials Properties, previous year question paper, quiz, mid sem, end sem paper, assignments |
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| MSE 639 Interfaces and Materials Properties, previous year question paper, quiz, mid sem, end sem paper, assignments |
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| MSE 639 Interfaces and Materials Properties, previous year question paper, quiz, mid sem, end sem paper, assignments |
Thermodynamics of Materials : MSE 616 PP set 05 | Department of Materials Science and Engineering Indian Institute of Technology Kanpur
Thermodynamics of Materials : MSE 616 PP set 05 | Department of Materials Science and Engineering Indian Institute of Technology Kanpur
Q1. Calculate the pressure required for distillation of mercury at 100°C. The vapor
pressure of liquid mercury is given as: lnP = −7611
T − 0.795lnT +17.168.
Q2. At normal boiling temperature of iron, 3330K, the rate of change of the vapor
pressure of liquid iron with temperature is 3.72x10-3 atm/K. Calculate the molar latent
heat of boiling of iron at 3330K.
Q3. The molar volumes of solid and liquid lead at the normal melting temperature of
lead (600K) are 18.92 and 19.47 cm3 respectively. Calculate the pressure that must be
applied to lead in order to increase its melting temperature by 20°C. The molar latent
heat of melting of lead at 600K is 4810 J/mol.
Q4. a. Find the triple points for the phase equilibria CaF2(α)-CaF2(β)- CaF2(v) and
CaF2(β)-CaF2(l)- CaF2(v)
b. Find the normal boiling temperature of CaF2.
Q5. (a) At 1 atm pressure and room temperature, iron exists in BCC structure
(named α-iron). Upon heating, it transforms to FCC structure (named γ iron) at
910°C. On further heating, the iron transforms back to BCC structure (named δ-iron)
at 1394°C and melts at 1538°C. Draw schematic G vs T curves, representing the
phase equilibria of iron at 1 atm.
(b) If pressure is increased to 2 atm, would the transformation temperature of
α to γ increase or decrease? Why?
Phase vapor pressure (p in atm)
CaF2(α) lnP = −54350
T − 4.525lnT + 56.57
CaF2(β) lnP = −53780
T − 4.525lnT + 56.08
CaF2(l) lnP = −50200
T − 4.525lnT + 53.96
MSE 201A
PP Set 4
Q6. Following figure shows the phase diagram for zirconia (ZrO2).
a) Indicate all stable triple points and corresponding phase equilibria
b) Draw G vs T curves for ZrO2 at P = 1atm
c) Draw G vs P curve at 2000°C. Also indicate metastable equilibria on this curve.
d) Draw G vs T curve at pressure corresponding to point a
Q7. The equation of state for hydrogen gas is given by PV = RT 1+ 6.4×10−4
( P).
Calculate the following
a. The fugacity of hydrogen at 500 atm and 298K
b. The pressure at which the fugacity is twice the pressure
c. The change in the Gibbs free energy caused by a compression of 1mole of
hydrogen at 298K from 1 to 500 atm
d. Magnitude of the contribution to the Gibbs free enrgy change in (c) from nonideality of hydrogen
α β γ L
V
Friday, 6 March 2026
MSE615: Structure and Characterization of Materials Quiz 5 Solutions PDF
MSE615: Structure and Characterization of Materials | IITK | Quiz 5 Solutions PDF
MSE615: Structure and Characterization of Materials | IITK | Quiz 5 Solutions PDF
MSE 615: Quiz-V
Date: November 12, 2025
Time: 50 minutes
Total Score: 60 Points
Question 1
Mention which of the following statements is/are correct.
(i) Which of the following is/are generally true regarding X-ray diffraction?
(a) Some of the diffractions predicted by Bragg equation do not occur in non-primitive unit cells.
(b) All the diffractions predicted by Bragg equation occur in primitive unit cells.
(c) Only for certain values of q, the reflections from all planes will add up in phase to give a strong reflected beam.
(d) All of the above.
(ii) Which of the following statements is/are true?
(a) Reciprocal lattice of BCC is FCC.
(b) Reciprocal lattice of FCC is BCC.
(c) For the square lattice, the shape of the lattice and the reciprocal lattice is the same and the rotation angle between them is 0 degrees.
(d) For the hexagonal lattice, the shape of the lattice and the reciprocal lattice is the same and the rotation angle between them is 0 degrees.
(iii) Which of the following statements is/are true?
(a) In order to satisfy Bragg’s condition, reciprocal lattice vector G must be located at the zone boundary of the first Brillouin zone.
(b) Whenever a reciprocal lattice point lies exactly on the Ewald sphere, Bragg’s equation is satisfied.
(c) Radius of the Ewald sphere changes with change in wavelength of X-rays.
(d) Only lattice points lying within the limiting sphere can diffract.
(e) All of the above.
(iv) Which of the following statements is/are true regarding XRD pattern analysis?
(a) Peak positions tell about the size and shape of the unit cell.
(b) Peak intensities provide information about location of atoms inside the unit cell.
(c) Peak widths and shapes give information on crystallite size.
(d) Peak intensity gives information on crystallite size.
(v) Which of the following statements is true?
(a) For positively charged impurity center, the defects are either anion vacancies or cation interstitials.
(b) For positively charged impurity center, the defects are either cation vacancies or anion interstitials.
(c) For negatively charged impurity centers, defects are either anion vacancies or cation interstitials.
(d) For negatively charged impurity centers, defects are either cation vacancies or anion interstitials.
Question 2
Short Questions. Answer in less than 200 words.
(a) When you receive a chest X-ray at a hospital, the X-rays pass through a series of parallel ribs in your chest. Do the ribs act as a diffraction grating for X-rays? Can you obtain an XRD pattern of your ribs similar to metals in laboratory experiments?
(b) In XRD the peak intensities drop off at higher diffraction angles. Do you expect the same behaviour in neutron diffraction? Explain.
(c) In the XRD pattern of simple cubic crystals, the (100) peak is observed, but for BCC and FCC structures no peak corresponding to (100) is detected. Explain why.
(d) Holding your hand at arm’s length, you can easily block sunlight from your eyes. Why can you not block sound from reaching your ears in the same way?
Question 3
A sample of BCC metal with lattice parameter a = 0.33 nm is placed in an X-ray diffractometer using incoming X-rays with wavelength λ = 0.1541 nm.
Using Bragg’s law (assume first order diffraction, n = 1), predict the positions of diffraction peaks (in 2θ) corresponding to the following planes:
{110}, {210}, {230}, {321}, and {431}.
Question 4
Calculate the Kroger-Vink diagram for WO3 if the oxide has Frenkel defects with oxygen interstitials dominating the intermediate PO2 levels.
Consider the Kroger-Vink diagram at low, intermediate, and high PO2 for both electronic and ionic defects.
Question 5
Consider the 2D lattice defined by primitive vectors:
a1 = (2, 0)a
a2 = (1, 1/2)a
(a) What kind of unit cell is this?
(b) What is the cell volume?
(c) Sketch the Wigner-Seitz primitive cell.
(d) What are the reciprocal lattice vectors?
(e) Sketch the reciprocal lattice and show the first Brillouin zone.
(f) What angles would the first X-ray diffraction ring occur at if λ = a/4?
MSE615: Structure and Characterization of Materials Quiz 4 Solutions PDF
MSE615: Structure and Characterization of Materials | IITK | Quiz 4 Solutions PDF
MSE 615: Quiz-IV
Date: September 11, 2025
Time: 50 minutes
Total Score: 60 Points
Question 1
Which of the following statements are TRUE and FALSE.
(i) Point defects are zero-dimensional defects.
(ii) Intrinsic point defects are always present in a crystalline material above absolute zero temperature.
(iii) All cation interstitials are Frenkel defects.
(iv) Non-equilibrium concentrations of point defects introduced by heat treatment can be classified as extrinsic defects.
(v) Point defects created by ion bombardment in a material can be classified as intrinsic defect.
Question 2
Using Kroger-Vink notation, considering only ionic defects in solids, write the defect reactions for the following compounds.
Please write two defect reactions for scenarios when cation and anion sublattice ideally filled.
(a) Li2O doped in TiO2
(b) Fe2O3 doped in Nb2O5
(c) Cr2O3 doped in Na2O
(d) AlF3 doped in Al2O3
Question 3
(a) Write the defect reaction for Schottky defect present in Nb2O5.
(b) Derive the expression for law of mass action, charge neutrality relationship and oxygen vacancy concentration arising from Schottky defect.
Question 4
Consider MgO having Rock-salt structure.
(a) Write the defect reaction corresponding to cation Frenkel disorder.
(b) Applying the law of mass action and charge neutrality condition derive the expression for various ionic defect concentrations possibly occurred due to this Frenkel disorder in MgO.
Question 5
Tungsten Oxide (WO3) has density of 7.16 g/cm3. Theoretical calculations indicate that the formation energy of a Schottky defect in WO3 is 2.6 eV.
(a) Derive the Schottky defect reaction corresponding to WO3.
(b) Calculate the number of Schottky defects per cm3 in WO3 at 1000 K ignoring the pre-exponential factor.
Given:
Atomic weight of Tungsten (W) = 184 g/mol
Atomic weight of Oxygen (O) = 16 g/mol
Boltzmann constant = 8.62 × 10⁻⁵ eV/atom-K
Avogadro’s number = 6.02 × 10²³ atoms/mol
MSE615: Structure and Characterization of Materials | IITK | Quiz 1 Solutions PDF
MSE615: Structure and Characterization of Materials Quiz 2 Solutions PDF
MSE615: Structure and Characterization of Materials | IITK | Quiz 2 Solutions PDF
MSE 615: Quiz-II
Date: August 29, 2025
Time: 50 minutes
Total Score: 70 Points
Question 1: Fill in the blanks
(a) Lattice is a 3D translationally periodic arrangement of __________.
(b) Among the different types of 2D space lattices, the only non-primitive lattice type is __________ lattice.
(c) __________ is a combined symmetry element found in 3D point groups, but absent in 2D point groups.
(d) ‘n’ glide is a glide along the half of a __________ diagonal.
(e) ‘d’ glide is associated with translation of __________ the unit cell.
(f) The corresponding point group of P2₁/c space group is __________.
(g) 2̅ is equivalent to __________ symmetry.
(h) In P4₃/m space group, the screw axis is associated with __________ translation along __________ direction.
(i) The number of 2D point groups is __________ and the number of 2D plane groups is __________.
Question 2
The definition of point group says it needs to be "Self-consistent." What do you mean by it?
Question 3
Prove mathematically that the possible crystallographic rotational symmetries are 1, 2, 3, 4, and 6-fold.
Question 4
Consider the following 2D crystals.
Label lattice points and identify the motif.
Write the symmetry of the lattice.
Write the symmetry of the motif.
Identify the symmetry of the crystal using the standard symmetry notation.
Determine which crystal class (2D lattice type) the crystals belong to.
Question 5
From each of the space groups listed below:
(i) F4₁32
(ii) P6₂22
(iii) F4̅3n
(iv) I2₁/a 3̅
(a) Identify the corresponding point group.
(b) For each point group, mention the axis or plane on which each symmetry element operates.
(c) Draw the stereographic projections for each point group showing the symmetry equivalent points and the location of the crystal physics axes Z₁, Z₂, and Z₃.
(d) If any screw axis or glide plane is present in the space groups, mention the translation amount along the axis or direction.
MSE615: Structure and Characterization of Materials | IITK | Quiz 1 Solutions PDF
Thursday, 5 March 2026
MSE615: Structure and Characterization of Materials Quiz 1 Solutions
MSE615: Structure and Characterization of Materials | IITK | Quiz 1 Solutions
MSE615: Structure and Characterization of Materials | IITK | Quiz 1 Solutions
MSE615: Structure and Characterization of Materials | IITK | Quiz 1 Solutions
MSE615: Structure and Characterization of Materials | IITK | Quiz 1 Solutions
MSE615: Structure and Characterization of Materials | IITK | Quiz 1 Solutions
MSE 615: Quiz-I
Date: August 21, 2025
Time: 20 minutes
Total Score: 45 Points
Question 1
Consider two point groups 23 and 32. Both the point groups have 3-fold rotational symmetry element.
(a) Is there any difference between the 3-fold symmetry existing in these two point groups?
(b) Which crystal systems do these two point groups belong to? Give the reasoning.
Question 2
The point group 6/m belongs to the hexagonal crystal system and it has 6-fold rotational symmetry and reflection symmetry.
Why can’t we write the point group as 6m instead of 6/m?
In other words, what special message is conveyed by expressing the point group as 6/m?
Question 3
In each of the following 1-D lattices, identify the motif and label the lattice points.
Also identify the symmetry elements present in the lattices.
(a) Identify motif, lattice points and symmetry elements for the given lattice.
(b) Identify motif, lattice points and symmetry elements for the given lattice.
Question 4
From each of the space groups listed below answer the following questions.
(a) Identify the Bravais lattice and the corresponding point group.
(b) For each point group, mention the axis or plane on which each symmetry element operates.
(c) Draw the stereographic projections for each point group showing the symmetry equivalent points and the location of the crystal physics axes Z1, Z2 and Z3.
(d) Specify if there is any redundant symmetry element for each point group.
(e) If there are any screw axis or glide plane present in these space groups, mention them along with the translation amount along the axis or direction.
The space groups are:
(i) R3̅c
(ii) P6̅
(iii) C2322
(iv) P43212
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