In a nuclear reactor, criticality is achieved when the rate of neutron production is equal to the rate of neutron losses, including both neutron absorption and neutron leakage.
When a uranium-235 atom undergoes fission, it releases an average of 2.4 neutrons.
In the simplest case of an unreflected, homogeneous, spherical reactor, the critical radius was calculated to be approximately:
,
where M is the average distance that a neutron travels before it is absorbed, and k is the average neutron multiplication factor.
The neutrons in succeeding reactions will be amplified by a factor k, the second generation of fission events will produce k², the third k³ and so on.
In order for a self-sustaining nuclear chain reaction to occur, k must be at least 3 or 4 percent greater than 1.
In other words, k must be greater than 1 without crossing the prompt critical threshold that would result in a rapid, exponential increase in the number of fission events.


Fermi christened his apparatus a "pile".
Emilio Segrè later recalled that:
I thought for a while that this term was used to refer to a source of nuclear energy in analogy with Volta's use of the Italian term pila to denote his own great invention of a source of electrical energy.
I was disillusioned by Fermi himself, who told me that he simply used the common English word pile as synonymous with heap.
To my surprise, Fermi never seemed to have thought of the relationship between his pile and Volta's.


Another grant, this time of $40,000, was obtained from the S-1 Uranium Committee to purchase more materials, and in August 1941 Fermi began to plan the building of a sub-critical assembly to test with a smaller structure whether a larger one would work.
The so-called exponential pile he proposed to build was 8 feet (2.4 m) long, 8 feet (2.4 m) wide and 11 feet (3.4 m) high.
This was too large to fit in the Pupin Physics Laboratories.
Fermi recalled that: 
We went to Dean Pegram, who was then the man who could carry out magic around the University, and we explained to him that we needed a big room.
He scouted around the campus and we went with him to dark corridors and under various heating pipes and so on, to visit possible sites for this experiment and eventually a big room was discovered in Schermerhorn Hall.

The pile was built in September 1941 from 4-by-4-by-12-inch (10 by 10 by 30 cm) graphite blocks and tinplate iron cans of uranium oxide.
The cans were 8-by-8-by-8-inch (20 by 20 by 20 cm) cubes.
When filled with uranium oxide, each weighed about 60 pounds (27 kg).
There were 288 cans in all, and each was surrounded by graphite blocks so the whole would form a cubic lattice structure.
A radium-beryllium neutron source was positioned near the bottom.
The uranium oxide was heated to remove moisture, and packed into the cans while still hot on a shaking table.
The cans were then soldered shut.
For a workforce, Pegram secured the services of Columbia's football team.
It was the custom at the time for football players to perform odd jobs around the university.
They were able to manipulate the heavy cans with ease.
The final result was a disappointing k of 0.87.

Compton felt that having teams at Columbia University, Princeton University, the University of Chicago and the University of California was creating too much duplication and not enough collaboration, and he resolved to concentrate the work in one location.
Nobody wanted to move, and everybody argued in favor of their own location.
In January 1942, soon after the United States entered World War II, Compton decided on his own location, the University of Chicago, where he knew he had the unstinting support of university administration.
Chicago also had a central location, and scientists, technicians and facilities were more readily available in the Midwest, where war work had not yet taken them away.
In contrast, Columbia University was engaged in uranium enrichment efforts under Harold Urey and John Dunning, and was hesitant to add a third secret project.

Before leaving for Chicago, Fermi's team made one last attempt to build
In a nuclear reactor, criticality is achieved when the rate of neutron production is equal to the rate of neutron losses, including both neutron absorption and neutron leakage. When a uranium-235 atom undergoes fission, it releases an average of 2.4 neutrons. In the simplest case of an unreflected, homogeneous, spherical reactor, the critical radius was calculated to be approximately:
,
where M is the average distance that a neutron travels before it is absorbed, and k is the average neutron multiplication factor. The neutrons in succeeding reactions will be amplified by a factor k, the second generation of fission events will produce k², the third k³ and so on. In order for a self-sustaining nuclear chain reaction to occur, k must be at least 3 or 4 percent greater than 1. In other words, k must be greater than 1 without crossing the prompt critical threshold that would result in a rapid, exponential increase in the number of fission events.

Fermi christened his apparatus a "pile". Emilio Segrè later recalled that:
I thought for a while that this term was used to refer to a source of nuclear energy in analogy with Volta's use of the Italian term pila to denote his own great invention of a source of electrical energy. I was disillusioned by Fermi himself, who told me that he simply used the common English word pile as synonymous with heap. To my surprise, Fermi never seemed to have thought of the relationship between his pile and Volta's. 

Another grant, this time of $40,000, was obtained from the S-1 Uranium Committee to purchase more materials, and in August 1941 Fermi began to plan the building of a sub-critical assembly to test with a smaller structure whether a larger one would work. The so-called exponential pile he proposed to build was 8 feet (2.4 m) long, 8 feet (2.4 m) wide and 11 feet (3.4 m) high. This was too large to fit in the Pupin Physics Laboratories. Fermi recalled that: 
We went to Dean Pegram, who was then the man who could carry out magic around the University, and we explained to him that we needed a big room. He scouted around the campus and we went with him to dark corridors and under various heating pipes and so on, to visit possible sites for this experiment and eventually a big room was discovered in Schermerhorn Hall. 
The pile was built in September 1941 from 4-by-4-by-12-inch (10 by 10 by 30 cm) graphite blocks and tinplate iron cans of uranium oxide. The cans were 8-by-8-by-8-inch (20 by 20 by 20 cm) cubes. When filled with uranium oxide, each weighed about 60 pounds (27 kg). There were 288 cans in all, and each was surrounded by graphite blocks so the whole would form a cubic lattice structure. A radium-beryllium neutron source was positioned near the bottom. The uranium oxide was heated to remove moisture, and packed into the cans while still hot on a shaking table. The cans were then soldered shut. For a workforce, Pegram secured the services of Columbia's football team. It was the custom at the time for football players to perform odd jobs around the university. They were able to manipulate the heavy cans with ease. The final result was a disappointing k of 0.87.
Compton felt that having teams at Columbia University, Princeton University, the University of Chicago and the University of California was creating too much duplication and not enough collaboration, and he resolved to concentrate the work in one location. Nobody wanted to move, and everybody argued in favor of their own location. In January 1942, soon after the United States entered World War II, Compton decided on his own location, the University of Chicago, where he knew he had the unstinting support of university administration. Chicago also had a central location, and scientists, technicians and facilities were more readily available in the Midwest, where war work had not yet taken them away. In contrast, Columbia University was engaged in uranium enrichment efforts under Harold Urey and John Dunning, and was hesitant to add a third secret project.
Before leaving for Chicago, Fermi's team made one last attempt to build 
Chicago Pile-1