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Clay is the stuff of pots and fields, so it can seem an odd thing for a physicist to study. But clay is made of tiny crystals stacked in layers, and X-rays can measure the gaps between those layers. In the early 1950s, Purnima Sinha used that idea to classify clays from across India, working in a lab where students built their own instruments. This post sets out what is on record about her work, with one calculation you can do yourself.
Who was Purnima Sinha?
The fullest account of her research is a 2019 article in Science and Culture by Rajinder Singh and Suprakash C. Roy, Purnima Sinha and her Doctoral Work Under Professor S.N. Bose, based on a copy of her thesis. They record that Purnima Sinha, née Sen-Gupta, was the first woman to receive a D.Phil. in physics from the University of Calcutta, and one of the few students who did a doctorate under Satyendra Nath Bose, of Bose-Einstein statistics. Her thesis, "X-ray & differential thermal analysis of Indian clays", was submitted in 1955 and the degree was awarded in 1956. For more on her supervisor, read our post on Satyendra Nath Bose.
The same article says she later worked as a Research Associate in the Biophysics Laboratory of Stanford University and as a scientist at the Central Glass and Ceramic Research Institute in Kolkata.
How did she build her own X-ray equipment?
In her own account, quoted by Singh and Roy, she began her PhD with Bose around the middle of 1951 at the Khaira Laboratory in Kolkata. Bose suggested she study the structure of clays from various parts of India, using thermal and chemical analysis alongside X-ray scattering, and that she build her own X-ray tube of the Coolidge kind so its parts could be taken apart and put together at will. She described the lab's unwritten rule: "Each of us used to fabricate his or her own instrument according to individual need."
The high-voltage transformer was made in the university's applied physics department, and she recalled that the team put together its X-ray equipment from World War II surplus gathered in a lane in the city. According to her thesis, as summarised in the article, the tube had a copper target supplied with a peak voltage of 75 kilovolts and a water-cooled target, and she preferred adjustable plate cameras to the usual circular cameras because they let her bring samples closer to the film.
What did she discover about Indian clays?
She studied 50 samples of clays, soils and shales from different parts of India, Singh and Roy report, and classified them into four groups: montmorillonite; vermiculite, chlorite and micas; illite; and kaolinite. X-rays alone were not enough, because clays are not neat single crystals. So she combined X-ray diffraction with differential thermal analysis, which heats a sample beside a standard and records where heat is taken in or given out, plus base-exchange measurements and chemical analysis.
Part of the work appeared in Nature in 1954, in a paper with A.K. Bose of the Department of Physical Chemistry: X-Ray and Differential Thermal Studies of some Indian Montmorillonites. The samples included montmorillonites from Kashmir, Nimlinadi and Barme and black cotton soils from Satara and Indore. The glycerol-treated clay gave a basal spacing of 17.7 Å, matching standard montmorillonite, and one sample showed extra lines that the authors attributed to kaolinite. Their thermal data suggested some of these clays formed a subgroup between montmorillonite and a related iron-rich mineral, nontronite.
She also heated several bentonites to 550°C for four hours and found that the basal spacing contracted to about 9.8 Å: the layers had moved closer together. In 1962 she published a single-author note in Nature on the exothermic peak in thermal curves of vermiculites.
How does X-ray diffraction measure a layer spacing?
The key equation is Bragg's law, which Singh and Roy set out in their article: 2d sin θ = nλ. Here d is the spacing between layers, θ is the angle at which the X-rays meet the layers, n is a whole number (the order) and λ is the X-ray wavelength. When the equation is satisfied, waves bouncing off neighbouring layers reinforce each other and you see a bright line.
Worked example. Take X-rays of wavelength λ = 1.54 Å (a value given for this exercise) and first order, n = 1.
Glycerol-treated clay, d = 17.7 Å: sin θ = λ / 2d = 1.54 / 35.4 = 0.0435, so θ ≈ 2.49°.
Heated clay, d = 9.8 Å: sin θ = 1.54 / 19.6 = 0.0786, so θ ≈ 4.51°.
Smaller spacing, larger angle. When heating pulled the layers closer, the diffraction line moved to a larger angle on the film. That shift is how she could see the change.
Two common mistakes: forgetting the 2 in 2d, which doubles your sin θ, and mixing units. Keep λ and d both in ångström (1 Å = 10⁻¹⁰ m) so they cancel.
What did she do beyond physics?
The 2021 Science and Culture review of a book about her, Clay, Craft, Music and Science: Purnima Sinha's Life, shows by its title how wide her interests were. Singh and Roy end their account by placing her work in the Calcutta tradition, set by J.C. Bose, C.V. Raman and S.N. Bose, of scientists designing their own instruments. For another crystallographer's story, read about Dorothy Hodgkin.
What can a student take from how she worked?
Use more than one method. X-rays gave her the spacings, heat curves gave her the water and the chemistry. When one method leaves a question open, add another.
Know your instrument. She built hers. You can at least know where each number in a lab reading comes from.
Study what is around you. Very little work had been done on Indian clays, she wrote. Local questions can be real research questions.
If you get stuck setting up a diffraction or wave problem, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
Try it now: repeat the worked example for a spacing of 14 Å and check that the angle falls between the two answers above.
