Lesson 1 of 3

Representing Materials Data

Combine lists, dictionaries and functions to store a small materials database, calculate derived properties, and select materials that meet design requirements.

About 30 minutes

In this lesson you will

Represent a set of materials as a list of dictionaries
Write functions that calculate derived properties from a record
Filter and rank materials against design criteria
Sort records by a property using sorted() with key=

Bringing the pieces together

This module applies everything from the course to realistic materials problems. A common first step in any computational project is deciding how to represent the data. For a collection of materials, each with several named properties, a natural choice is a list of dictionaries: each dictionary is one material's record, and the list holds the whole dataset.

example.py

materials = [    {"name": "Aluminium 6061", "density": 2.70, "youngs_modulus": 69,  "yield_strength": 276, "cost": 2.5},    {"name": "Titanium Ti-6Al-4V", "density": 4.43, "youngs_modulus": 114, "yield_strength": 880, "cost": 25.0},    {"name": "Steel AISI 4140", "density": 7.85, "youngs_modulus": 205, "yield_strength": 655, "cost": 1.2},    {"name": "Magnesium AZ31", "density": 1.77, "youngs_modulus": 45,  "yield_strength": 200, "cost": 4.0},    {"name": "Copper C11000", "density": 8.96, "youngs_modulus": 117, "yield_strength": 70,  "cost": 8.0},]# Units: density g/cm³, modulus GPa, yield strength MPa, cost $/kgprint(len(materials), "materials")print(materials[1]["name"], "yields at", materials[1]["yield_strength"], "MPa")

Output

5 materials Titanium Ti-6Al-4V yields at 880 MPa

Record your units

Unit mistakes are among the most common errors in scientific code. Write the units in a comment next to the data, include them in key names (such as density_g_cm3), or both.

Derived properties

Engineers often care less about a raw property than about a combination. For a lightweight part, what matters is strength or stiffness per unit mass: the specific strength (yield strength ÷ density) and specific stiffness (Young's modulus ÷ density). Small functions that take a record and return a derived value keep these formulas in one tested place.

example.py

def specific_strength(material):    """Yield strength divided by density, in MPa per (g/cm³)."""    return material["yield_strength"] / material["density"]def specific_stiffness(material):    """Young's modulus divided by density, in GPa per (g/cm³)."""    return material["youngs_modulus"] / material["density"]materials = [    {"name": "Aluminium 6061", "density": 2.70, "youngs_modulus": 69, "yield_strength": 276},    {"name": "Steel AISI 4140", "density": 7.85, "youngs_modulus": 205, "yield_strength": 655},    {"name": "Titanium Ti-6Al-4V", "density": 4.43, "youngs_modulus": 114, "yield_strength": 880},]print(f"{'Material':<20}{'Spec. strength':>16}{'Spec. stiffness':>17}")for material in materials:    print(f"{material['name']:<20}{specific_strength(material):>16.1f}{specific_stiffness(material):>17.1f}")

Output

Material Spec. strength Spec. stiffness Aluminium 6061 102.2 25.6 Steel AISI 4140 83.4 26.1 Titanium Ti-6Al-4V 198.6 25.7

Steel is the strongest and stiffest of the three in absolute terms, but per unit mass titanium is far stronger, and the three have almost identical specific stiffness. This is why aircraft use aluminium and titanium alloys.

Adding computed values to the records

Because dictionaries are mutable, you can store a derived value back in each record with a loop. Later code can then use it like any other property.

example.py

materials = [    {"name": "Aluminium 6061", "density": 2.70, "yield_strength": 276},    {"name": "Magnesium AZ31", "density": 1.77, "yield_strength": 200},]for material in materials:    material["specific_strength"] = round(material["yield_strength"] / material["density"], 1)print(materials[1])

Output

{'name': 'Magnesium AZ31', 'density': 1.77, 'yield_strength': 200, 'specific_strength': 113.0}

Selecting materials

Materials selection usually starts by removing candidates that fail a hard requirement, then ranking the rest. A loop with an if, or a function that returns True or False, expresses the requirements clearly.

example.py

materials = [    {"name": "Aluminium 6061", "density": 2.70, "yield_strength": 276, "cost": 2.5},    {"name": "Titanium Ti-6Al-4V", "density": 4.43, "yield_strength": 880, "cost": 25.0},    {"name": "Steel AISI 4140", "density": 7.85, "yield_strength": 655, "cost": 1.2},    {"name": "Magnesium AZ31", "density": 1.77, "yield_strength": 200, "cost": 4.0},    {"name": "Copper C11000", "density": 8.96, "yield_strength": 70, "cost": 8.0},]def meets_requirements(material, max_density=5.0, min_strength=250):    return material["density"] <= max_density and material["yield_strength"] >= min_strengthcandidates = []for material in materials:    if meets_requirements(material):        candidates.append(material)for material in candidates:    print(material["name"])

Output

Aluminium 6061 Titanium Ti-6Al-4V

Sorting records by a property

sorted() can't sort dictionaries on its own, because it doesn't know which property to compare. Its key= argument takes a function that is applied to each item to get the value to sort by. Notice that you pass the function's name without brackets: you are handing over the function itself for sorted() to call, not calling it yourself.

example.py

materials = [    {"name": "Aluminium 6061", "density": 2.70, "yield_strength": 276, "cost": 2.5},    {"name": "Titanium Ti-6Al-4V", "density": 4.43, "yield_strength": 880, "cost": 25.0},    {"name": "Steel AISI 4140", "density": 7.85, "yield_strength": 655, "cost": 1.2},    {"name": "Magnesium AZ31", "density": 1.77, "yield_strength": 200, "cost": 4.0},]def get_cost(material):    return material["cost"]def strength_per_dollar(material):    # MPa per (g/cm³) per ($/kg): higher is better value for a light, strong part    return material["yield_strength"] / material["density"] / material["cost"]print("Cheapest first:")for material in sorted(materials, key=get_cost):    print(f"  {material['name']}: ${material['cost']}/kg")best = max(materials, key=strength_per_dollar)print("Best strength per dollar:", best["name"])

Output

Cheapest first: Steel AISI 4140: $1.2/kg Aluminium 6061: $2.5/kg Magnesium AZ31: $4.0/kg Titanium Ti-6Al-4V: $25.0/kg Best strength per dollar: Steel AISI 4140

max() and min() accept key= too. Titanium is the best performer, but on strength per dollar the cheap steel wins: ranking depends on which criterion you choose.

Beyond lists of dictionaries

For larger datasets, scientists usually move to a table library such as pandas, or to specialised materials libraries such as pymatgen, which represent structures and properties with their own objects. The ideas are the same: records, derived properties, filters and rankings.

Knowledge check

Choose an answer and press Check answer. You can retry as often as you like.

How would you get the density of the third material in materials, a list of dictionaries?

materials["density"][2]materials[2]["density"]materials.density[3]

What does sorted(materials, key=get_cost) do?

Sorts the materials by the value get_cost returns for each oneRemoves materials that have no costCalls get_cost() once and sorts by its result

What is specific strength?

Yield strength multiplied by densityYield strength divided by density: strength per unit massThe strength of one specific sample