Homogeneous materials and direction dependence of properties

A homogeneous material is a material which has a uniform composition throughout.

What do we mean when we say "uniform composition"?

I have learnt about pure substances in Thermodynamics which have a uniform chemical composition throughout. Air can be assumed as a pure substance because no matter where I take a unit volume, the chemical composition - the percentages of its constituents (nitrogen, oxygen, CO2 etc) will remain same everywhere.

• Does calling a material homogenous the same as calling it a pure substance?

Furthermore, homogenous materials at every point have same properties in a direction. Modulus of elasticity doesn't have a direction, how this makes sense?

• What is meant by "same properties in a direction"?
• Modulus of elasticity does have a direction! For example the modulus of wood is very different along the grain and perpendicular to the grain. A single crystal of a substance is both a pure substance and homogeneous, but most crystalline materials are not isotropic. For a general anisotropic material there are 21 different independent elastic moduli, not just two (i.e. Young's modulus and Poisson's ratio), Sep 28 at 13:48
• "Does being homogeneous, the same as being a pure substance" What? Have you left some words out? Sep 28 at 13:55
• @SolarMike I edited Sep 28 at 14:02
• @alephzero Oh. So is it like, if we have a prismatic bar made of wood, and if we apply load along longitudinal direction, the ratio of stress and strain in this direction (which is E) will be different than the ratio of stress and strain, if we were to load it perpendicular to the longitudinal axis (in simple tension). Sep 28 at 14:04
• @HarshitRajput wood is quite difficult to tell with regard to the elastic modulus because its basically made from cellulose. The big difference in the wood example is in strength. However elasticity is also significantly affected but its better evidenced when different material of different moduli are the constituents of the composite material. Sep 28 at 14:25

This might change depending of what discipline you are investigating but:

• homogeneous: refers to a material that you cannot distinguish different phases in it. Usually it refers to the density properties, and it's an indicator that the density is uniform when you look at it at various scales (from m to sub mm).

(some etymology: the word comes from the greek "ομογενής", which means "the one who comes from the same breed/genealogy/group").

• isotropic usually refers to the mechanical properties.

(again some etymology: the word comes from the greek "ισο-τροπος". ισο means equal, and τροπος: is the behaviour, so its something that behaves the same way in all directions).

Homogeneity does not necessarily imply isotropy. For example sheets of metal after being cold rolled have different properties in the direction along the length of the cold rolling, compared to the through thickness. They come from the same material and they have the same density (homogeneous), but the have different properties in the different directions.

Figure : cold rolled sheets of metal (source: manufactruing guide )

Also regarding:

Modulus of elasticity doesn't have a direction

Modulus of elasticity can have a direction. The prime example is unidirectional fibrous composite materials.

Figure : Different types of fiber orientation in composites: a) unidirectional; b) random; c) bidirectional; and d) multi-directional for different planes (source: Hasan Ali Alhashmy)

For example the composite material (a) will have significantly different properties in the direction of the fibres compared to the other two directions.

• Consider having a structural member made of mild steel and its homogeneous. I take a 1mm3 volume at some location 1 in the member, and this 1mm3 was made by x% iron and y% carbon. Then, if I were to take this 1mm3 at any other location will the 1mm3 volume be still made of x% iron and y% carbon? is that what we mean when say homogeneous? Sep 28 at 14:42
• Its not only that the percentages are the same, but - at least to my interpretation - even the allotropes of the iron (or at least their percentages) should be the same in that $mm^3$. (However, that begs the question at which scale - if there is any - do you start to consider the different crystal structure? for example at some point you see atoms of iron and atoms of Carbon. I am afraid that is something I never bothered to find out). Sep 28 at 14:48
• Thanks @NMech you clear my doubts to a great extent, always. Sep 28 at 15:02

The following presumes a system at uniform temperature and pressure throughout.

What do we mean when we say "uniform composition"?

We mean that the composition averaged over a certain spatial volume of the substance remains the same moving through any location in the substance. The spatial volume may be the size of atom or molecule in a pure substance. It may be the size of a sufficient volume to contain a representative sampling of all chemical constituents in the substance as a mixture.

Air can be assumed as a pure substance because no matter where I take a unit volume, the chemical composition - the percentages of its constituents (nitrogen, oxygen, CO2 etc) will remain same everywhere.

Does calling a material homogenous the same as calling it a pure substance?

No. Air can be assumed to be uniform in composition over a spatial volume that is about the size on the order of magnitude of the mean free paths of the molecules in motion in the gas. A substance that is uniform in composition is not always a pure substance (e.g. air), but a pure substance is by default always uniform in composition (e.g. water).

What is meant by "same properties in a direction"?

First off, a materials' property is a moderating factor between an external stimulus and the response of the substance. By comparison, an inherent property of the substance is one that exists simply because the substance exists. Density is an inherent property. Transparency is a materials' property because we have to shine light on the substance to obtain its value.

We do not associate inherent properties with the need to measure in a specific direction in the substance. Instead, we say that in a homogeneous substance, inherent properties are always the same in all locations.

The additional statement applies to materials' properties. When we want a materials property, we have to apply an external stimulus. We often neglect that we do so in a certain direction relative to some fundamental arrangement of the chemical constituents in the material. When we shine light into a single crystal of quartz, the transmission will depend on which crystallographic direction we shine the light. Why? Because the atomic arrangements in quartz are different in different crystallographic directions. This anisotropic behavior of transmission is less apparent in a polymer. Why? Because the random arrangement of polymer molecules has no preferred direction when viewed externally. So the transmission of light is isotropic, meaning it is the same regardless of the incident direction of the light beam onto the material.