Empirical Rant

In metallurgy we often term very simple models to be `empirical models’ in contrast to `physical models’. I really wish there was a better name for the `empirical models` – since physical models are more empirical, and `empirical models’ are actually less empirical. Use of such equations can be very useful because they do provide a summary of observations with-in some range of observed behaviour. Even when a physical model exists these simple models are often still preferred because of the ease with which they can be used.

The source of my confusion is the now contradictory uses of the word empirical…

Physical models incorporate more physical understanding, are based on a theoretical understanding. Any theory can only be based on, and validated against, observations. (Edit: i.e. empirical observations)

A better description for our `empirical models’ would be Ad-hoc, make-do, summary or arbitrary.

Comparison of empirical and physical models
This is best described by an example. The martensite start temperature (MS) is often described by an equation of the form; MS = A*XC + B*XMn + C*XCr…

MS(C) = 521 – 353.C – 225.Si – 24.3.Mn – 27.4.Ni 0 17.7.Cr – 25.8.Mo

Another example is the use of various ‘carbon equivilant’s.
Carbon Equivilant = CE = C + Mn/5 + Mo / 5 + Cr/10 + Ni/50

Thomas Sourmail and Carlos Garcia-Mateo have written a paper on prediciton of M_S by various methods,
(Critical assessment of models for predicting the Ms temperature of steels, T. Sourmail and C. Garcia-Mateo Comp. Mater. Sci., 2005:34, p323-334) it is available on Thomas’s webpage;Predicting the martensite start temperature (Ms) of steels.

Ms/ K, all compositions in wt%
[8] 772-316.7C-33.3Mn-11.1Si-27.8Cr-16.7Ni-11.1Mo-11.1W
[9] 811-361C-38.9Mn-38.9Cr-19.4Ni-27.8Mo
[10] 772-300C-33.3Mn-11.1Si-22.2Cr-16.7Ni-11.1Mo
[11] 834.2-473.9C-33Mn-16.7Cr-16.7Ni-21.2Mo
[12] 812-423C-30.4Mn-12.1Cr-17.7Ni-7.5Mo
[12] 785-453C-16.9Ni-15Cr-9.5Mo+217(C)2-71.5(C)(Mn)-67.6(C)(Cr)

Potency of Elements on MS temperature (Change per weight percent).

N C Ni Co Cu Mn W Si Mo Cr V Al
-450 -450 -20 +10 -35 -30 -36 -50 -45 -20 -46 -53 P-1976
  • P-1976 F.B. pickering, `Physical metallurgy of stainless steel developments’, Int. Met. Rev., 21, pp 227-268, 1976.
  • 8 P. Payson and C. H. Savage. Trans. ASM, 33:261-281, 1944.
  • 9 R. A. Grange and H. M. Stewart. Trans. AIME, 167:467-494, 1945.
  • 10 A. E. Nehrenberg. Trans. AIME, 167:494-501, 1945.
  • 11 W. Steven and A. G. Haynes. JISI, 183:349-359, 1956.
  • 12 K. W. Andrews. JISI, 203:721-727, 1965.
  • 13 C. Y. Kung and J. J. Rayment. Metall. Trans. A, 13:328-331, 1982.

Neural network models have been developed to predict both martensite start and bainite start temperatures. It is also possible to calculate these using ‘physically’ based models based on thermodynamics.

They’re all just maths! 🙂


4 Responses

  1. I really wish there was a better name for the `empirical models`

    How about “phenomenological?”

    since physical models are more empirical, and `empirical models’ are actually less empirical.

    Empirical/phenomenological is usually contrasted by “ab initio” or “first principles.” I think this terminology makes sense & don’t really understand your objections to the term “empirical.”

    A better description for our `empirical models’ would be Ad-hoc, make-do, summary or arbitrary.

    No model should be “arbitrary,” and I think the other terms, while they can be accurately applied to empiricism, aren’t as precise..

  2. Thanks for the comment, maybe wikipedia explains my confusion better than I can….

    From Wikipedia, the free encyclopedia


    A central concept in science and the scientific method is that all evidence must be empirical, or empirically based, that is, dependent on evidence or consequences that are observable by the senses. It is usually differentiated from the philosophic usage of empiricism by the use of the adjective “empirical” or the adverb “empirically.” “Empirical” as an adjective or adverb is used in conjunction with both the natural and social sciences, and refers to the use of working hypotheses that are testable using observation or experiment. In this sense of the word, scientific statements are subject to and derived from our experiences or observations.

    In a second sense “empirical” in science may be synonymous with “experimental.” In this sense, an empirical result is an experimental observation. In this context, the term semi-empirical is used for qualifying theoretical methods which use in part basic axioms or postulated scientific laws and experimental results. Such methods are opposed to theoretical ab initio methods which are purely deductive and based on first principles.

    I like “phenomenological”… maybe “experimental” would convey the meaning better, since they mainly are used to express sets of experimental results, rather than expecting them to explain the results as I would expect a phenomenological model to do (for some reason I expect a phenomenological model to be more sophisticated – but I guess there is really no reason for that).

    Do you really believe that Ab-inito models are purely deductive? I don’t believe that, they are based on observations, all science is based on observation otherwise it has no value of its own, and we can use mysticism instead (maths you are a special case).

  3. Oh dear! Why are you blogging the poor thing? I mean the bainite…

  4. Well, I think phenomenological models usually try to give an insight as to why particular phenomenon occurs under given conditions. It is possible also that there would be a quantification element in such a model, for example the determination of the rate of occurrence of such a phenomenon.

    On the other hand, an empirical model may or may not address the occurrence of a phenomenon, rather, the focus would be on rough – or one may call it good enough – estimate of specific observation(s).

    What I am trying to say here is that the parameter(s) controlling a physical event are more clear in phenomenological models compared with the empirical ones. In that sense I would imagine that a phenomenological model can be empirical but not all empirical models are phenomenological 🙂

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